Multistage Production Decision Model Under the Deregulated Electricity Market (For CCGT)

Transcription

1 In The Name of God UNIVERSIDAD PONTIFICIA COMILLAS ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI) MÁSTER OFICIAL EN EL SECTOR ELÉCTRICO MASTER THESIS Multistage Production Decision Model Under the Deregulated Electricity Market (For CCGT) AUTOR: Samira Fazlollahi MADRID, July

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3 Preface This thesis has been written as part of the Master Thesis Project, the final course from the master Economic and Management of Industrial Networks (EMIN) as Erasmus Mundus student, at TU Delft University (Netherlands) and Comillas Pontifical University (Spain). I originally started with this study because of my broad interest, but because I found the energy domain particularly interesting, I chose system modeling as the specialization subject for my master. From October 2008 to June 2009, I have conducted the research described in this thesis at Gas Natural in Spain. The subjects of multistage production decision model under a deregulated electricity market (For CCGT), originated from Gas Natural the Spanish company, in which both the Comillas Pontifical University takes part. Because of my interest in these subjects, the six months have passed quickly, and have led to a satisfactory result. Due to the complexity and scope of the research, the thesis has become quite long. Readers who are interested in the electricity market should read Chapter 2. The proposed model explained in chapter 3. The results of the model testing and valuating can be found in chapter 4. Finally, I would like to thank my graduation committee: Prof. Julián Barquín Gil (first supervisor) for directing and commenting on my research, Emilio J. Cortés Moral (tutor) and Martin Martin, Ricardo for their daily comments and support at Gas Natural, and Prof. Vazquez Martinez (section professor) and Prof. Tomás Gómez (thesis director) for their supervision. Also, I want to thank Prof. Mariano Ventosa and Prof. Javier Garcia Gonzalez for their supervision and suggestions. Samira Fazlollahi July 4th, 2009 II

4 Summary In the electricity market, electricity price and the quantity of production are two main issues for utilities. In the regulated electricity market, Utilities are price taker which means they could not determined the electricity price with open competition and the price determined by central decision. In this case just quantity of production is the key issue for utilities and it is calculated by using the (centralized) Unit Commitment Method in the short term based on the cost minimization. Under deregulation, the electricity price set by open competition so both electricity price and quantities of production are key issues for producer. In this deregulated market the unit commitment method (UCP) for an electric power producer will require a new formulation that includes the electricity market properties. As mentioned before the main difficulty here is that the spot price of electricity is no longer predetermined but set by open competition. Thus far, the hourly spot prices of electricity have shown evidence of being highly volatile. The unit commitment decisions are now harder and the modelling of spot prices becomes very important in this new operating environment. The problem is more complicated for companies with multi business line in gas and electricity, because these companies could switch between these two markets in order to maximize their benefits. In this project new proposed model, which we call it multi stage production decision model for companies with multi business line in gas and Electricity generation in a deregulated market, and the tools for implementing and using the mode are explained. Based on the short introduction in the previous paragraph, the lack of efficient model for companies with multi business lines in deregulated electricity market is clear. Based on that the motivation of this project could be summarised in following points: To propose the suitable Model in deregulated electricity Market for the company with two business line in Gas and Electricity in order to consider: The deregulated Market properties The flexibility of these companies to switch from one market to another in regulatory framework The model in different time horizontal for a short and midterm planning. The flexible model which could run very fast with user friendly interface III

5 These are the main motivation of this project which is explained more in chapter three. The model consists of three stages: 1. The electricity price forecasting 2. The calculation of the marginal value of the gas 3. The optimal schedule of electricity production In the first stage the hourly electricity price in the market for short term, midterm and long term is estimated by using stochastic model. For this purpose, first we need to estimate the average electricity price and then forecast hourly electricity price by considering average electricity price estimation. There are different methods in the literature for average electricity price forecasting. We used MARAPE model for this purpose. This model, which is referred to as the probabilistic production costing model, incorporates the stochastic features of load and generator availabilities (VÁZQ, 05). The objective of this model is to allow the electricity company to evaluate the future evolution of the prices in the market in the middle term, i.e., ranging from one month to four or five years, both quantitatively and qualitatively. In the proposed model the average electricity price is not useful and we need hourly electricity price estimation. We suggest using financial price approach to estimate hourly electricity price by using historical data and average electricity price estimation as an input data. Finally the output of this step is hourly electricity price estimation (part 3.3). The second step of the proposed model is the gas model to calculate the gas marginal value and its optimum allocation for producing the electricity in the electricity market. We proposed the optimization mathematical model to calculate this gas marginal value. The objective of Gas model, therefore, is to obtain optimal allocation of gas for producing the electricity in thermal power plants so as to meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. The main idea is calculating the shadow price of Fuel balance equation, which is the marginal value of gas for producing the electricity or in the other words how much the benefit will change by adding one extra unit of gas for producing the electricity. In this way the company could compare the gas price in the gas market with this marginal value and if this marginal value is higher than the gas price in the gas market then it is better to allocate more gas for producing electricity instead of selling the original gas (part 3.4). The third step of the proposed model is the calculation of the optimal electricity production schedule. In this stage we propose the optimization mathematical model. The objective of this model, therefore, is to obtain an hourly schedule for each thermal power plant so as to IV

6 meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. The optimization method with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue is proposed to calculate the hourly schedule of electricity production for each plant, taking in to account the technical characteristic of thermal plants and limited gas fuel (part3.5). In order to implement the mathematical model we need to design a tool. GAMS is a good software for simulating and running the optimization model but it doesn t have a good interface. It is possible to make a connection between GAMS and excel so excel could be a good interface. The main Idea is to use excel as an interface. The user can import all data in excel sheets and then transfer them from excel sheet into INC file format.gams could easily import and read data from INC file format and also it could export the result into INC file format. After that we can import the result in to excel sheet from INC file format. In this way we designed the tool to implement and use the mathematical model. The company with multi business lines in gas and electricity could use this model in order to: Calculate the optimal allocation of the Gas quantity for gas and electricity market by calculating its marginal value Calculate the optimal production schedule of electricity for each plan CCGT Considering computationally efficient procedures to solve the model and design a user friendly tool for it. The model is run very fast by using the designed tools. In this report the model will be explained in details. V

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8 Table of contents 1. RESEARCH PROBLEM Projects Motivation Project Objective Methodology General description Literature review Market for electricity Industry Electricity price forecasting Game theory models Simulation models Time series Approaches to electricity market modelling Firm optimization model Exogenous price Deterministic models Stochastic models Price as a function of the firm s decisions Deterministic models Stochastic models Equilibrium models Cournot equilibrium Supply function equilibrium Market power analysis Electricity pricing Linear supply function equilibrium models Dynamic Hypothesis Conclusion Taxonomy of electricity system Principles of regulation Regulated (Centralized) electricity system Fundamentals of monopoly regulation Regulatory tools: traditional and incentive based regulation Traditional or cost of service regulation Advantages and drawbacks to traditional regulation Incentive based regulation Advantages and drawbacks to incentive based regulation Liberalized (Deregulated) electricity market Introduction An Over view of the generation business Why Liberalize Generation?...35 i

9 The technical constraints of electricity generation Financial aspects of electricity generation (pricing) Pricing on a competitive market Competitive markets and maximizing social welfare Time horizons Stranded costs Wholesale market design Organized wholesale market Over the counter market International experience Market power Modeling market power Estimating and monitoring market power Competitive Spanish electricity markets European Union deregulation The case of Spain Conclusion Model specification Multi stage production decision model Electricity generation using natural gas combined cycles Step one: Electricity price forecasting An overview of electricity price modeling methodologies The first step objective Average price Estimation price for each hour Conclusion Step two: Calculation of the marginal value of gas Objective Model approach Representing time Model assumptions Model structure Input data and criteria Technical characteristic of thermal units Thermal generation cost State Variables, objective function, Model formula Objective function Model Constraints Model Outputs Design of the Tool Modification of input data...79 ii

10 Running the Model Getting and analyzing the result Size of the model Step three: Optimal schedule of electricity production Objective Model approach Representing time Model assumptions Model structure Input data and criteria Technical characteristic of thermal units Thermal generation cost Decision and state Variables, objective function, Model formula Objective function Model Constraints Model Outputs Design of the Tool Modification of input data Running the Model Getting and analyzing the result Size of the model Conclusion Model testing Step two: Gas Model Reference behaviour of the model Verification Code check Dimension analysis Numerical error analysis Validation Extreme analysis Sensitivity analysis Conclusion Step three: optimum schedule of electricity production Reference behavior of the model Verification Code check Dimension analysis Numerical error analysis Validation Extreme analysis iii

11 Sensitivity analysis Conclusion Future Research Bibliography Appendix A: Appendix B: Figure Figure 1: some trends in electricity market modelling (Source: VENT, 05)... 8 Figure 2: static and dynamic incentives in regulation Figure 3: multi stage production decision model Figure 4: Operating diagram of a combined cycle plant Figure 5: chronological representation of time Figure 6: start up function Figure 7: excel sheet INPUT_DATA Figure 8: the excel sheet of running the model Figure 9: Import data excel sheet as an interface Figure 10: chronological representation of time Figure 11: start up function...89 Figure 12: Import data excel sheet as an interface Figure 13: the excel sheet of running the model Figure 14: excel sheet INPUT_DATA Figure 15: reference behaviour for Gas Margin Figure 16: Extreme condition in the case of non available thermal plants Figure 17: reference behaviour of hourly production Figure 18: reference behaviour of hourly production in Figure 19: reference behaviour of hourly production Figure 20: reference behaviour of hourly production in Figure 21: reference behaviour of hourly production in Figure 22: reference behaviour of hourly production in Figure 23: reference behaviour of hourly production in Figure 24: reference behaviour of hourly production in Figure 25: reference behaviour of hourly production in iv

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13 1. RESEARCH PROBLEM In the electricity market, electricity price and the quantity of production are two main issues for utilities. In the regulated electricity market, Utilities are price taker which means they could not determined the electricity price with open competition and the price determined by central decision. In this case just quantity of production is a key issue for utilities and it is calculated by using the (centralized) Unit Commitment Method in the short term based on the cost minimization. Under deregulation, the electricity price set by open competition so both electricity price and quantities of production are key issues for producer. In this deregulated market the unit commitment method (UCP) for an electric power producer will require a new formulation that includes the electricity market properties. As mentioned before the main difficulty here is that the spot price of electricity is no longer predetermined but set by open competition. Thus far, the hourly spot prices of electricity have shown evidence of being highly volatile. The unit commitment decisions are now harder and the modelling of spot prices becomes very important in this new operating environment. Different approaches can be found in the literature in this regard which are explained in part 1.5. The problem is more complicated for companies with multi business line in gas and electricity, because these companies could switch between these two markets in order to maximize their benefits. In this project the multi stage production decision model under deregulated electricity market for the company with two business line in gas and electricity is proposed. This chapter is organized as follows. Section 1.1 explains the project motivation. Section 1.2 describes the project objective, where as Section 1.3 focuses on methodology which is used to solve the problem. Section 1.4 presents the Literature review. Section 1.5 details dynamic Hypothesis which are considered in the project and, finally, Section 1.7 provides some conclusions Projects Motivation Based on the short introduction in the previous part, the lack of efficient model for companies with multi business lines in deregulated electricity market is clear. Based on that the motivation of this project could be summarised in following points: To propose the suitable Model in deregulated electricity Market for the company with two business line in Gas and Electricity in order to consider: 1

14 The deregulated Market properties The flexibility of these companies to switch from one market to another in regulatory framework The model in different time horizontal for a short and midterm planning. The flexible model which could run very fast with user friendly interface These are the main motivation of this project which is explained more in chapter three. In the next part the project objective based on these motivations is explained Project Objective By considering the project Motivation in part 1.2, the question here is, what is the optimal action of the company with multi business lines in Gas and electricity in the deregulated market and how they could manage these two markets?! Based on this question the objective of this project could be summarised as follow: Propose a production decision model for companies with multi business lines, in a deregulated market in order to: Calculate the optimal allocation of the Gas quantity for gas and electricity market by calculating its marginal value Calculate the optimal production schedule of electricity for each plan CCGT Considering computationally efficient procedures to solve the model and design a user friendly tool for it. These are the research question and objectives of this project which are explained more in details in chapter three. In the next part the Methodology which is used for this project to answer the research question is explained Methodology We use optimisation method based on mixed integer linear programming (MILP) to solve the problem. In the following chapter we will explained in details that why we used this method and in this part we will explain what system optimisation method is. In mathematics, optimization or mathematical programming refers to choosing the best element from some set of available alternatives. It refers to where there are multiple options but optimization is all about choosing the best one, it is the search for optimum strategies. 2

15 In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This (a scalar real valued objective function) is actually a small subset of this field which comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. The feasibility problem, which is just to find any feasible solution at all without regard to objective value, can be regarded as the special case of mathematical optimization where the objective value is the same for every solution. If the unknown variables are all required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which can be solved efficiently in the worst case, integer programming problems are in many practical situations (those with bounded variables) NP hard. 0 1 integer programming or binary integer programming (BIP) is the special case of integer programming where variables are required to be 0 or 1 (rather than arbitrary integers). This problem is also classified as NP hard, and in fact the decision version was one of Karp's 21 NP complete problems. In other words, integer programming is a general term that refers to any mathematical optimization or feasibility program in which some or all of the variables are restricted to be integral. In many settings the term integer program is used as short hand for integer linear programming If only some of the unknown variables are required to be integers, then the problem is called a mixed integer programming (MIP) problem. These are generally also NP hard. There are however some important subclasses of IP and MIP problems that are efficiently solvable, most notably problems where the constraint matrix is totally unimodular and the right hand sides of the constraints are integers. Advanced algorithms for solving integer linear programs include: cutting plane method branch and bound branch and cut branch and price Branch and bound (BB) is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization. It consists of a 3

16 systematic enumeration of all candidate solutions, where large subsets of fruitless candidates are discarded en masse, by using upper and lower estimated bounds of the quantity being optimized. The method was first proposed by A. H. Land and A. G. Doig in 1960 for linear programming General description For definiteness, we assume that the goal is to find the minimum value of a function f(x) (e.g., the cost of manufacturing a certain product), where x ranges over some set S of admissible or candidate solutions (the search space or feasible region). Note that one can find the maximum value of f(x) by finding the minimum of g(x) = f(x). A branch and bound procedure requires two tools. The first one is a splitting procedure that, given a set S of candidates, returns two or more smaller sets whose union covers S. Note that the minimum of f(x) over S is, where each vi is the minimum of f(x) within S i. This step is called branching, since its recursive application defines a tree structure (the search tree) whose nodes are the subsets of S. Another tool is a procedure that computes upper and lower bounds for the minimum value of f(x) within a given subset S. This step is called bounding. The key idea of the BB algorithm is: if the lower bound for some tree node (set of candidates) A is greater than the upper bound for some other node B, then A may be safely discarded from the search. This step is called pruning, and is usually implemented by maintaining a global variable m (shared among all nodes of the tree) that records the minimum upper bound seen among all sub regions examined so far. Any node whose lower bound is greater than m can be discarded. The recursion stops when the current candidate set S is reduced to a single element; or also when the upper bound for set S matches the lower bound. Either way, any element of S will be a minimum of the function within S. It was the short explanation about the methodology which is used for solving the problem Literature review The trend towards competition in the electricity sector has led to efforts by the research community to develop decision and analysis support models adapted to the new market context. This part focuses on literature review of electricity generation market modelling. Its aim is to help to identify, classify and characterize the somewhat confusing diversity of 4

17 approaches that can be found in the technical literature on the subject. The chapter is organized as follows. Section summarizes the Market for electricity Industry. Section describes different electricity price forecasting methods, where as Section focuses on those approaches to electricity market modelling Market for electricity Industry An electricity market is a system for effecting the purchase and sale of electricity, using supply and demand to set the price. Wholesale transactions in electricity are typically cleared and settled by the grid operator or a special purpose independent entity charged exclusively with that function. Markets for certain related commodities required by (and paid for by) various grid operators to ensure reliability, such as spinning reserve, operating reserves, and installed capacity, are also typically managed by the grid operator. In addition, for most major grids there are markets for electricity derivatives, such as electricity futures and options, which are actively traded. These markets developed as a result of the deregulation of electric power systems around the world. This process has often gone on in parallel with the deregulation of natural gas markets. In other words, in the last decade, the electricity industry has experienced significant changes towards deregulation and competition with the aim of improving economic efficiency. Under this restriction, different participants namely generation companies and consumers of electricity need to meet in a marketplace to decide on the electricity price (SCHW,88). In many places, these changes have culminated in the appearance of a wholesale electricity market. In this new context, the actual operation of the generating units no longer depends on state or utility based centralized procedures, but rather on decentralized decisions of generation firms whose goals are to maximize their own profits. All firms compete to provide generation services at a price set by the market, as a result of the interaction of all of them and the demand (VENT,05). Numerous publications give evidence of extensive effort by the research community to develop electricity market models adapted to the new competitive context Electricity price forecasting Under restructuring of electric power industry, different participants namely generation companies and consumers of electricity need to meet in a marketplace to decide on the electricity price (SCHW,88). In the current deregulated scenario, the forecasting of electricity demand and price has emerged as one of the major research fields in electrical engineering (BUNN,00). Application of energy price forecasting models fall into different time horizons: short term, medium term and long term price forecasting. Electricity price series are inherently uncertain over time due to the uncertainty in weather, equipment outages, fuel price and other price drivers. A lot of researchers and academicians are engaged in the activity of developing tools and algorithms for load and price forecasting. Amjady et al 5

18 (AMJA,06) reported the importance of the price forecasting problem, key issues and some techniques developed. Li.G et al (LIG_,05) presented various price forecasting techniques from input and output variables perspective and compared results of five different techniques and Time series forecasting procedures have been discussed by Contreras et al.,(cont,06). As mentioned above, numerous methods have been developed for electricity price forecasting and most of these algorithms are same as used for load forecasting and especially short term load forecasting (STLF). Previous review articles (GONZ,05) classified the price forecasting models in three sets: Game theory models, Simulation models and Time series models Game theory models The first group of models is based on game theory. This group studies the price evaluation and stressing the analysis of strategic behaviour of market participant. Since participants in oligopolistic electricity markets shift their bidding curves from their actual marginal costs in order to maximize their profits, these models involve the mathematical solution of these games, and price evolution can be considered as the outcome of a power transaction game (KUMA, 09). There are several equilibrium models available like Nash equilibrium, Cournot model, Bertrand model, and supply function equilibrium model. A detailed discussion on game theory models can be found in Bajpai et al (BAJP, 04) Simulation models The second group of models is simulation model. A simulation model is used to mimic the detailed operation of the power system with examining the underlying physical process in detail. These models are also called structural or fundamental models, and try to consider not only production costs but also the agents strategic behaviour impact on power market. MAPS and UPLAN are two kinds of simulation models. MAPS is market assessment and portfolio strategies algorithm developed by GE Power Systems Energy Consulting (BAST,99) and UPLAN is software developed by LCG Consulting (DEB_,00). MAPS is used to capture hour by hour market. Inputs to MAPS are detailed load, transmission and generation units data. UPLAN, a structural multi commodity, multi area optimal power flow (MMOPF) type model, performs Monte Carlo simulation to take into account all major price drivers. UPLAN is used to forecast electricity prices and to simulate the participants behaviour in the energy and other electricity markets like ancillary service market, emission allowance market. Both UPLAN and MAPS may be used for long as well as short range planning Time series Time series analysis is a method of forecasting which focuses on the past behaviour of the dependent variable (JENK,04). Previous review articles (KUMA,09) classified it in three sets: 6

19 Parsimonious stochastic models, regression or casual models and Artificial intelligence model. In stochastic models there are several univariat discrete type models like autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), and generalized autoregressive conditional heteroskedastic (GARCH). These are discrete time counterparts corresponding to the continuous time stochastic models. A detail discussion on these models can be seen in Bunn DW et al (BUNN, 03). Regression type forecasting model is based on the theorized relationship between a dependent variable like electricity price and a number of independent variables that are known or can be estimated (MOGH, 89). Kian et al. (KIAN, 01) presented a regression based model for electricity price. It was based on the assumption that power consumption and market prices are stochastic processes. Vucetic et al (VUCE, 01) have assumed a piece wise stationary price time series having multiple regimes with stable price load relationship in each regime. The idea of variable segmentation, i.e., framing the model as 24 separate hourly series, has been applied by Cuaresma et al. (CUAR, 04) and Weron et al.(wero, 05). They observed that an hour by hour modelling strategy for electricity spot prices improves significantly the forecasting abilities of linear univariate time series models. A detail discussion on Regression type forecasting model can be seen in Kumar Aggarwal et al., (KUMA, 09). Artificial intelligence (AI) models may be considered as nonparametric models that map the input output relationship without exploring the underlying process and can be further divided into two categories: (i) artificial neural network (ANN) based models and (ii) datamining models. A detail discussion on these models can be seen in Kumar Aggarwal et al., (KUMA, 09) Approaches to electricity market modelling A large number of papers have been devoted to modelling the operation of deregulated power systems. In this section, we draw upon some earlier reviews to compare and contrast the main approaches based upon model attributes. Such attributes can help us to understand the advantages and limitations of each modelling approach. From a structural viewpoint, the approaches to electricity market modelling reported in the technical literature (VENT, 05) can be classified according to the scheme shown in Figure 1.1. They fall into three main classes: optimisation, equilibrium, and simulation models. Optimisation models focus on the profit maximisation problem for a single firm competing in the market, while equilibrium models represent the overall market behaviour taking into consideration competition among all participants. Simulation models are regarded increasingly as an alternative to equilibrium models when the problem under consideration 7

20 is too complex (for example, too nonlinear or dynamic) to be addressed within a traditional equilibrium framework. Figure 1: some trends in electricity market modelling (Source: VENT, 05) Various assumptions are often made on the objectives, strategies, beliefs and capabilities of market participants. In game theory models, for example, participants are assumed to be rational in the sense that they can obtain and explore all the relevant information in order to deduce the best outcome. As we shall see shortly, some of these rigid assumptions can be relaxed with the help of agent based simulation, since participants may employ different strategies and be subject to different sets of rules to guide their behaviour. They may have access to different information and possess different computational capabilities. The challenge then is how to assign a particular agent the appropriate set of behavioural rules and computational capabilities. In the following parts the optimisation, equilibrium, and simulation models will explain Firm optimization model In this part, approaches based on the profit maximization problem of one firm are explained. These models take into account relevant technical and operational constraints of the generation system owned by the firm as well as the price clearing process. Previous review articles ( VENT, 05) devoted publications, in these models concentrate, into two types: price modelled as an exogenous variable with deterministic and stochastic price representation and price modelled as a function of the demand supplied by the firm of study, again with deterministic and stochastic price representation Exogenous price The lowest level of market modelling represents the price clearing process as exogenous to the firm s optimization program, i.e., the system marginal price is an input parameter for 8

21 the optimization program. Consequently, as the price is fixed, the market revenue becomes a linear function of the firm s production, which is the main decision variable in this approach. In view of that, traditional Mixed Integer Linear Programming (MILP) techniques can be employed to obtain the solution of the model. Unfortunately, this type of optimization model can only properly represent markets under quasi perfect competition conditions because it neglects the influence of the firm s decisions on the market clearing price. These models can again be classified into two subgroups, depending on whether they use a deterministic or probabilistic price representation (VENT, 05) Deterministic models Participants in a competitive electricity market develop bidding strategies in order to maximize their own profits. On the other hand, it is necessary for regulators to investigate strategic bidding behaviour in order to identify possible market power abuse and to limit such abuse by introducing appropriate market management rules (DAVI, 00). In this category a good example is the model proposed in Gross and Finlay (GROS, 96).The model provides a general framework for competitive electricity markets under Pool concept with perfect competition for supply side bidders. In this model an optimal bidding strategy is proved to be a unit s true cost under the assumption that the bid of each unit does not affect the market clearing price. In this model the price is considered to be exogenous and it is shown that the firm s optimization problem can be decomposed into a set of sub problems for each generator. The Author proposed the Lagrange Relaxation approach for solving the optimisation problem. As expected in a case of perfect competition, deterministic price and convex costs, the simple comparison between each generator s marginal cost and the market price decides the production of each generator; therefore, the best offer of each generation unit consists of bidding its marginal cost (VENT, 05). For future work, the authors attempts to investigate the relaxation of perfect competition that also considers demand side bidders, the study of market power, the impacts of transmission, and the incorporation of financial contracts into the strategies of bidders (DAVI, 00) Stochastic models Stochastic models provide energy optimization models that explicitly deal with uncertainty. The uncertainty usually stems from unpredictability of demand and/or prices of energy, or from resource availability and prices. Since most energy investments or operations involve irreversible decisions, a stochastic programming approach is meaningful. Many of the models deal with electricity investments and operations, but some oil and gas applications 9

22 are also presented. The oldest research precedes the development of linear programming, and most models within the market paradigm have not yet found their final form (STEI,03). The Deterministic approach, can be improved if price uncertainty is explicitly considered. For instance, Rajamaran et al. (RAJA, 01) describe and solve the self commitment problem of a generation firm in the presence of exogenous price uncertainty. This paper describes and solves the problem of finding the optimal self commitment policy in the presence of exogenous price uncertainty, inter product substitution options (energy versus reserves sales), and different markets (real time versus day ahead), while taking into consideration inter temporal effects. The generator models consider minimum and maximum output levels for energy and different kinds of reserves, ramping rate limits, minimum up and down times, incremental energy costs and start up and shut down costs. Finding the optimal market responsive generator commitment and dispatch policy in response to exogenous uncertain prices for energy and reserves is analogous to exercising a sequence of financial options. The method can be used to develop bids for energy and reserve services in competitive power markets. The method can also be used to determine the optimal policy of physically allocating generating and reserve output among different markets (e.g., hour ahead versus day ahead). In the model the authors correctly interpret that the scheduling problem for each generating unit can be treated independently, which significantly simplifies the process of obtaining a solution, thus permitting a detailed representation of each unit. The model uses backward dynamic programming. The algorithm used by the model can be thought of as a generalized tree that values and exercises a sequence of complicated options. This algorithm can be used to obtain optimal power market bids for energy and reserve services in markets that integrate both these needs. The method can also be used to profitably allocate output in different physical forward markets, e.g., hour ahead versus day ahead. A number of recent models represent the price of electricity as an uncertain exogenous variable in the context of deciding the operation of the generating units and at the same time adopting risk hedging measures. Fleten et al. (1997, 2002) address the medium term risk management problem of electricity producers that participate in the Nord Pool. Electricity producers in the Nordic wholesales market face significant uncertainty in inflow to reservoirs and prices in the spot and contract market. In the paper Fleten proposed the stochastic programming model for the coordination of physical generation resources with hedging throw forward and option market. They model risk aversion by means of penalizing risk through a piecewise linear target shortfall cost function. More recently, Unger (UNGE, 02) improves the Fleten approach by explicitly measuring the risk as conditional value at risk (CVaR). He studied risk management in the electricity market 10

23 in general and the interaction between physical production and electricity contracts in particular. From a risk management point of view, a power portfolio differs substantially from a traditional financial portfolio. To be able to compare production and contracts on a unified basis, he identified the set of contracts that corresponds to each power plant. The electricity market is heavily incomplete, why perfect hedges are not achievable for a number of contracts. Hence he introduced the concept of best hedge. The best hedge is found through an optimization, where risk, measured as CVaR, is minimized subject to a constraint on the expected profit. It turns out that this problem can be solved with linear programming, allowing handling problems of substantial size. However, this problem needs to be tailored for the electricity market because of the special characteristics of power portfolios. An optimal portfolio implies also an optimal dispatch of the production assets. He also developed a dynamic dispatch strategy. The optimization of a portfolio consisting of a hydro storage plant and electricity contracts hence needs to derive the optimal portfolio of contracts and the optimal dispatch strategy, or with financial terms the optimal exercise conditions for the corresponding options. He solved the problem with linear programming by maximizing the expected profit over a specified time horizon under the constraint that CVaR of the portfolio may not exceed some threshold, typically determined by the risk preferences of the firm. It turns out that a simultaneous optimization of the dispatch and the contracts is needed, since the dispatch depends on the volume risk in the entered contracts. A main result is the high value related to the operational flexibility of the hydro storage plant. By studying the dual of the linear portfolio optimization problem, he could actually quantify this value. In a performed case study it is shown that this value of flexibility can be substantial. Any valuation that does not take this operational flexibility into account may hence underestimate flexible power plants. Similar to the models proposed by Fleten and Unger, another stochastic approach, which focuses on the solution method, is presented in Pereira (1999). The resulting large scale optimization program is solved using the Benders decomposition technique, in which the entire firm s maximization problem is decomposed into a financial master problem and an operation sub problem. While the financial master problem produces financial decisions related to the purchase of financial assets (forwards, options, futures and so forth), the operation sub problems decide both the dispatch of the physical generation system and the exercise of financial assets providing feedback to the financial problem. The master problem and sub problems are solved using LP (VENT, 05) Price as a function of the firm s decisions In contrast to the former approaches in which the price clearing process is assumed to be independent of the firm s decisions, there exists another family of models that explicitly considers the influence of a firm s production on price. In the context of microeconomic theory, the behaviour of one firm that pursues its maximum profit taking as given the 11

24 demand curve and the supply curve of the rest of competitors is described by the so called leader in price model (VARI, 92). In such a model the amount of electricity that the firm of interest is able to sell at each price is given by its residual demand function. From the point of view of one firm, its residual demand function is obtained by subtracting the aggregation of all competitors selling offers from the demand side s buy bids. The term residual demand function is also known as effective demand function. Electricity market models of this type can also be classified in two sub groups depending on whether a probabilistic representation of the residual demand function is used (VENT, 05) Deterministic models As deregulation of the power industry is becoming a reality, there has been an intense interest in the strategic bidding for suppliers to optimize their benefits. The benefit gained by a supplier is related not only to its energy price bid curve but also to its submitted operational parameters such as minimum output, etc. This is especially so when market size is limited because of a limited number of competitors in the market itself or due to the transmission capacity constraints. Several papers address the study of strategic bidding for minimum output in a deregulated environment. The first publication on electricity markets based on the leader in price model is Garcia et al. (GARC,99). They address the unit commitment Problem, deals with the shortterm schedule of thermal units in order to supply the electricity demand in an efficient manner, of a specific firm facing a linear residual demand function. Given that the market revenue is a quadratic function of the firm s total output, in order to allow for the use of powerful MILP solvers, a piecewise linearization procedure of the market revenue is proposed. Shrestha, G.B et al. (SHRE, 01) presented the paper about Strategic bidding for minimum power output in the competitive power market. In this paper he analysed the impact of minimum output bids on the market result. A criterion with regard to minimum output bid to assess the outcome of competition among suppliers is derived. He proposed the method to optimize the benefit from a supplier's point of view by adjusting the bids for the minimum output and price. It is shown that an individual supplier can optimize its own benefit by fine tuning its minimum output and price when there are only a few suppliers dominating the market. A fairly thorough theoretical analysis of the bidding for minimum output is illustrated with a numerical example. Likewise, Baillo et al. (BAIL, 01) develop a MILP based model focusing on the problem of one firm with significant hydro resources. In this model the new short term problems that are faced by a generation company in a deregulated electricity market are addressed and a complete decision procedure is proposed. Additionally, a strategic unit commitment model, 12

25 which deals with the weekly operation of the firm s generating facilities is presented. The traditional cost evaluation techniques and the technical constraints that grant a feasible schedule have been combined with new market modelling equations. Strategic constraints, that allow the accomplishment of the firm s medium term objectives, are suggested. The model is formulated as a MIP optimization problem and is solved by means of a commercial algorithm instead of using the traditional Lagrange Relaxation approach. Results of the application of the method to a numerical example are presented. The procedure is as simplified version of one of the several tools currently used by a leading Spanish generation company, Iberdrola, for the weekly operation of its generation assets in the Spanish wholesale electricity market. The Baillo model is more advanced in that it allows nonconcave market revenue functions by means of additional binary variables Stochastic models Unlike previous approaches, Anderson and Philpott (PHIL, 02) do not formulate the problem of optimal production but rather the problem of constructing the optimal offer curve of a generation firm. They represent uncertainty in the residual demand function by a probability distribution. This approach constitutes an interesting starting point for the development of new models that convert the offer curve into a profitable risk hedging mechanism against short term uncertainties in the marketplace. The thesis of Baillo (BAIL, 02) advances the Anderson and Philpott approach by incorporating a detailed modelling of the generating system which implies that offer curves of different hours are not independent ( VENT, 05) Equilibrium models Approaches which explicitly consider market equilibrium within a traditional mathematical programming framework are grouped together into the equilibrium models category. Previous review articles (KAHN, 98; DAY_, 02; VENT, 05) have focused mostly on the equilibrium models found in game theory. Kahn s survey was limited to 2 types of equilibrium resulting from firms in oligopolistic competition: Cournot equilibrium, where firms compete on a quantity basis; and Supply Function Equilibrium (SFE), where they compete on both quantity and price. Although both models are based on the Nash equilibrium concept, the Cournot approach is usually regarded as being more flexible and tractable Cournot equilibrium Although the theoretical support of applying Cournot equilibrium model to electricity markets is controversial, the economic research community tends to agree that, in the case of imperfect competition, this is a suitable market model.( VENT, 05) Larger generators usually use quantity offers rather than price offers to improve their market positions, especially in peak periods. In other words, they seem to act like players in 13

26 Cournot competition. The assumptions underlying a Cournot solution correspond to the Nash equilibrium in game theory. At the solution point, the outputs (quantities dispatched) fall into an intermediate zone between fully competitive and collusive solutions. In effect, a second firm becomes a monopolist over the demand not satisfied by the first firm, a third over the demand not satisfied by the second, and so on. Inside the most regulatory frameworks, generators are forbidden from changing bid prices in the rebidding process, by shifting quantity commitments up or down between different price bands they can achieve a similar effect to changing prices directly. In reality, therefore, both quantity (directly) and price (indirectly) serve as decision variables. Thus the Cournot assumption may not be appropriate in these regulatory frameworks. Furthermore, by expressing generators offers in terms of quantities only (instead of offer curves), equilibrium prices are determined by the demand function. This shortcoming tends to reinforce the idea that Supply Function Equilibrium (SFE) approaches may be a better alternative to represent competition in these regulatory frameworks. (Rudkevich et al Supply function equilibrium in power markets: learning all the way). In an electricity market context, a Cournot solution posits rather short sighted behaviour on the part of generating agents. It implies that each of them modifies its bids in response to the bids and dispatches of others, without allowing for the fact that others may react in a similar manner. Previous review articles (VENT, 05) devoted publications, in these models concentrate, on four areas: market power analysis, hydrothermal coordination, electric power network and risk assessment. Market power measurement was the earliest application to electricity markets of a Cournotbased model. Borenstein et al. (BORE, 95) employed this theoretical market model to analyze Californian electricity market power instead of using the more traditional Hirschman Herfindahl Index (HHI) and Lerner Index. Later, Borenstein and Bushnell (BORE, 99) have extended this approach by developing an empirical simulation model that calculates the Cournot equilibrium iteratively. Finally, a collection of models most of them based on Cournot competition for measuring market power in electricity can be found in Bushnell et al. (BUSH, 99). This paper summarizes in tabular format these models, which have been applied to the analysis of some of the most relevant deregulated power markets: California, New England, England and Wales, Norway, Ontario, and New Zealand( VENT, 05). Apart from market power analysis, Cournot competition has also been considered in hydrothermal models. The first publication on this subject is by Scott and Read (SCOT, 96), in the context of New Zealand s electricity market. Bushnell (BUSH, 98) proposes a similar model for studying the California market. Its most significant contribution is its discussion 14

27 about the meaning of the firm s marginal water value in a deregulated framework. Similar to the Bushnell approach, Rivier et al. (RIVI, 01) state the market equilibrium using the equations that express the optimal behaviour of generation companies,i.e., by means of the firms optimality conditions. Kelman et al. (KELM, 01) combine the Cournot concept with the Stochastic Dynamic Programming technique in order to cope with hydraulic in flow uncertainty problems. Barquin et al. (BARQ, 03) introduce an original approach to compute market equilibrium, by solving an equivalent minimization problem (VENT, 05). Congestion pricing in transmission networks is another area in which Cournot based models have also played a significant role. Both Hogan (BOTH, 97) and Oren (OREN, 97) formulate a spatial electricity model wherein firms compete in a Cournot manner. More recently, Hobbs (HOBB, 01) models imperfect competition among electricity producers in bilateral and POOLCO based power markets as a Linear Complementarily Problem (LCP). In these models, it is assumed that the generation units of each firm are located at only one node of the network which is, obviously, a particular case. Unfortunately, since in the general case in which each firm is allowed to own generation units in more than one node, apure strategy equilibrium does not exist, as it is pointed out by Neuhoff (NEUH, 03). Finally Batlle et al. (BARL, 00) present a procedure capable of taking into account some risk factors, such as hydraulic inflows, demand growth and fuel costs. Cournot market behaviour is considered using the simulation model described in Otero Novas et al. (OTER, 00), which computes market prices under a wide range of scenarios. The Batlle model provides risk measures such as value at risk (VaR) or profit at risk (PaR) Supply function equilibrium In the absence of uncertainty and knowing competitors strategic variables, Klemperer and Meyer (MEYE, 89) showed that each firm has no preference between expressing its decisions in terms of a quantity or a price, because it faces a unique residual demand. When a firm faces a range of possible residual demand curves, however, in general it expects a greater profit in return for exposing its decision tool in the form of a supply function (or offer curve) indicating those prices at which it is willing to offer various quantities to the market. This Supply function equilibrium (SFE) approach, originally developed by Klemperer and Meyer (MEYE, 89), has proven to be an attractive line of research for the analysis of equilibrium in wholesale electricity markets. To calculate an SFE requires solving a set of differential equations, instead of the typical set of algebraic equations that arises in traditional equilibrium models. Thus SFE models have considerable limitations concerning their numerical tractability. 15

28 Previous review articles (VENT, 05) devoted publications, in these models concentrate, on four areas: market power analysis, electricity pricing, linear supply function equilibrium models and electric power network Market power analysis The SFE approach was extensively used to predict the performance of the pioneering England & Wales (E&W) Pool, whose revolutionary design did not seem to fit into more conventional oligopoly models. The relatively unimportant role played by the transmission network in this particular power system increased the relevance of these studies. (VENT, 05) Green and Newbery (NEWB, 92) analyze the behaviour of the duopoly that characterized the E&W electricity market during its first years of operation under the SFE approach. In that time most of the British electricity supply industry has been privatized. Two dominant generators supply bulked electricity to an unregulated pool. They submitted a supply schedule of prices for generation and received the market clearing price, which varied with demand. Despite claimed that this should be highly competitive, Green and Newbery showed that the Nash equilibrium in supply schedules implies a high mark up on marginal cost and substantial deadweight losses. In other words, it is shown that the large firm finds price increases more portable and therefore has a greater incentive to submit a steeper supply function. The small firm then faces a less elastic residual demand curve and also tends to deviate from its marginal costs Electricity pricing The possibility of obtaining reasonable medium term price estimations with the SFE approach is considerably attractive, particularly when conventional equilibrium models based on the Cournot conjecture have proven to be unreliable in this aspect mainly due to their strong dependence on the elasticity assumed for the demand curve (VENT, 05). Rudkevichet al. (RUBK, 98) in his paper presents an analysis that estimates the price of electricity dispatched and sold through a pool co on the basis of bids made by rational, profit maximizing generating firms. His results were calculated from a closed form mathematical formula that provides the instantaneous market clearing price of electricity when generating firms adopt bidding strategies constructed from the Nash Equilibrium. This formula is derived from the analytical concept of the supply function equilibrium (SFE). In his analysis, he compares the market clearing prices resulting from Nash Equilibrium based bidding to a benchmark given by the perfectly competitive price of electricity in a pool co. His results show that, as one would expect, the market clearing price of electricity decreases as the number of generating firms bidding into the pool co increases. 16

29 Linear supply function equilibrium models In 1996 Green published a paper about The Electricity Contract Market in England and Wales where wholesale electricity is sold in a spot market partly covered by long term contracts which hedge the spot price. Two dominant conventional generators can raise spot prices well above marginal costs, and this is profitable in the absence of contracts. If fully hedged, however, the generators lose their incentive to raise prices above marginal costs. Competition in the contract market could lead the generators to sell contracts for much of their output. Since privatization the generators have indeed covered most of their sales in the contract market. Green in his model considers the case of an asymmetric n firms oligopoly with linear marginal costs facing a linear demand curve whose slope remains invariable over time. An SFE expressed in terms of affine supply functions is obtained. Baldick et al. (BALD, 00) extend the privies model and considered supply function equilibrium (SFE) model and assumed a linear demand function. They also considered a competitive fringe and several strategic players all having capacity limits and affine marginal costs. They assumed that bid rules allow affine or piecewise affine non decreasing supply functions. The found that a piecewise affine SFE can be found easily for the case where there are non negativity limits on generation. Upper capacity limits, however, pose problems and they proposed an ad hoc approach. They applied the analysis to the England and Wales electricity market, considering the 1996 and 1999 divestitures. The piecewise affine SFE solutions generally provide better matches to the empirical data than previous analysis. Baldick and Hogan (BALD, 01) perform a comprehensive review of the SFE approach. In their paper they consider a supply function model of an electricity market where strategic firms have capacity constraints. We show that if firms have heterogeneous cost functions and capacity constraints then the differential equation approach to finding the equilibrium supply function may not be effective by itself because it produces supply functions that fail to be non decreasing. They analyzed the non decreasing constraints and characterize piecewise continuously differentiable equilibrium. To find stable equilibrium, they numerically solved for the equilibrium by iterating in the function space of allowable supply functions. Using a numerical example based on supply in the England and Wales market in 1999, they investigate the potential for multiple equilibriums and the interaction of capacity constraints, price caps, and the length of the time horizon over which bids must remain unchanged. They empirically confirm that the range of stable supply function equilibrium can be very small when there are binding price caps. Even when price caps are not binding, the range of stable equilibrium is relatively small. They also find that requiring supply functions to remain fixed over an extended time horizon having a large variation in demand reduces the incentive to mark up prices compared to the Cournot outcome. 17

30 1.5. Dynamic Hypothesis The following assumptions are considered in the model: We just consider one firm in optimization model The transmission grid is not included in the model We Just consider the combined-cycle plants in the model That is called the single node approach The chronological evolution of the system hour by hour must be modeled. The time wise representation of hourly period is used A thermal set is not allowed to start up shut off at any time of day An uncertainty is not considered, a deterministic approach is used Increasing in the gas consumption in each step of running the model is small The Constance start up duration for startup ramp The efficiency curve (input output curve) for each thermal plant is considered as linear function 1.6. Conclusion In this chapter we explained about the problem, project motivation and objective. We are using optimisation programming to design the model in order to determine the optimal action of the company with multi business lines in Gas and electricity in the deregulated market. 18

31 2. Taxonomy of electricity system In economic terms, electricity is a commodity capable of being bought and sold. An electricity market is a system for effecting the purchase and sale of electricity, using supply and demand to set the price. Wholesale transactions in electricity are typically cleared and settled by the grid operator or a special purpose independent entity charged exclusively with that function. Markets for certain related commodities required by (and paid for by) various grid operators to ensure reliability, such as spinning reserve, operating reserves, and installed capacity, are also typically managed by the grid operator. In addition, for most major grids there are markets for electricity derivatives, such as electricity futures and options, which are actively traded. These markets developed as a result of the deregulation of electric power systems around the world. This process has often gone on in parallel with the deregulation of natural gas Market. Electricity supply is essential for every society to function properly. Its price is a crucial factor in the competitiveness of a substantial part of the economy. The combination of technical and economic characteristics of electricity (part 2.1.1) imposes the need for the electricity sector to be regulated. The basic purpose of electricity regulation is to regulate the electricity sector with the traditional, three fold goal of guaranteeing the supply of electric power, its quality and the provision of such supply at the lowest possible cost. In order to increase the efficiency of electricity system, the regulated system moved to deregulated or liberalized system. The deregulated electricity markets have been in operation in a number of countries since the 1990s. During the deregulation process, vertically integrated power utilities have been reformed into competitive markets, with initial goals to improve the market efficiency, minimize the production cost and reduce the electricity price. Given the benefits that have been achieved by the deregulation, several new challenges are also observed in the market. In this chapter these two electricity system, regulated and deregulated system, will be explained. This part is organized as follows: In section 2.2 Principles of regulation and regulated electricity market explained. In Section 2.3, liberalized (decentralized) electricity market discussed. The Competitive Spanish electricity markets have been outlined in Section 2.4 and finally part 2.5 is a short conclusion. 19

32 2.1. Principles of regulation Regulation is understood to mean a system (of rules and institutions) that allows a government to formalise and institutionalise its commitments to protect consumers and investors [Tenenbaum, 1995]. Regulation seeks to protect consumers from the power of monopolies and oligopolies that can potentially misuse their market power to set unjustifiably high prices or reduce the quality of their services. Regulation establishes a limit to the prices that companies can set, along with obligations they must meet in terms of quality and service continuity; it also defines rules on service coverage and participates in investment planning. Such participation may adopt several forms. The State may plan investments directly, for instance, or make company plans contingent upon governmental authorisation. Regulation also seeks to protect investors from possible opportunistic action on the part of the State, such as the establishment of tariffs and supply requirements that would prevent them from recovering their investment. In regulated industries, where investors must make enormous investments in specific assets that can only be used where they are installed, there is very little investors can do once the investment is made to protect themselves from opportunistic action. The State, in turn, may have a vested interest in such action to benefit consumers, for instance, or reduce inflation. Regulation precludes such behavior by setting rules whereby prices must reflect costs and, often, transferring the power to establish prices to independent regulatory bodies. Electricity industry regulation world wide has traditionally been based on a standard system involving State planning and intervention. Under this traditional system prices are fixed to exactly cover the costs incurred by electric utilities and investment either requires regulator authorisation or is State planned. In this approach there is no electricity market per se and transactions take place in accordance with the rules laid down by the regulator. Consequently, the vertical and horizontal structure of the industry is of scant importance and this often leads to the existence of a single utility, a vertically integrated monopoly. Today, electricity industry regulation is changing in many countries. The main component in this change is the creation of electricity markets which establish prices and provide the infrastructure for trading. The first step in creating such markets is to abolish the limitations to competition with which the industry is fraught. While calling for broad knowledge and technical analysis, this is a relatively simple task because all it involves is drafting and approving suitable legislation for the industry Regulated (Centralized) electricity system Electricity supply is essential for every society to function properly. Its price is a crucial factor in the competitiveness of a substantial part of the economy. The technological 20

33 development of the electricity industry and the way it is structured as regards its requirements for raw material supplies are determining factors in the evolution of other industrial sectors. Moreover, electricity transmission and distribution constitute a natural monopoly as capital intensive activities requiring direct links to consumers whose demand for electric power a non storable product fluctuates over relatively short periods of time. Furthermore, the fact that electricity cannot be stored means that supply must necessarily match demand at all times and requires electricity generation to be well coordinated as well as the coordination of decisions involving investment in the generation and transmission of electric power. This combination of technical and economic characteristics imposes the need for the electricity sector to be regulated. Consequently, the basic purpose of electricity regulation is to regulate the electricity sector with the traditional, three fold goal of guaranteeing the supply of electric power, its quality and the provision of such supply at the lowest possible cost. Environmental protection is yet another element to be taken into account in the equation and one of considerable importance given the characteristics of this particular sector of the economy. The legislation hinges on an explicit guarantee of supply to all those consumers nationwide who demand the service. The unified operation of the national electric power system ceases to be a public service belonging to and run by the State through a company with a majority state shareholding. Its functions are now to be performed by two private sector business entities whose respective responsibilities are the economic management and the technical management of the system. As far as economic management is concerned, the possibility of achieving some kind of theoretical optimization of the system is no longer its basis and, instead, the decisions of the economic players become paramount within the framework of an organized wholesale electric power market. Lastly, state planning is restricted to transmission facilities in an effort to link it up with town planning and territorial regulation. The idea of planning as determining the investment decisions of electricity companies is discarded and replaced by planning that offers guideline parameters for the way the electricity industry is expected to develop in the near future, thus facilitating the investment decisions to be made by the different economic agents. The liberalizing intention goes further than just restricting more tightly the State s activities within the electric power sector. Far reaching changes are made to the way it is regulated through the expedient vertical segmentation of the different activities required for electricity supply. In electric power generation, the right to freely set up in business is acknowledged and this activity is run under the principle of free competition with economic remuneration based on the organization of a wholesale market. The principle of remuneration through investment costs fixed by the Administration through a process of 21

34 standardization of the different electricity generation technologies is no longer contemplated. Transmission and distribution are liberalized by allowing third parties widespread access to the networks. Ownership of networks does not guarantee their exclusive use. The economic efficiency arising out of the existence of a single network which forms the basis of the socalled natural monopoly is now put at the disposal of the different players involved in the electric power system and of consumers. Remuneration for transmission and distribution shall continue to be set by the Administration, thus avoiding any possible abuse of dominant positions that may stem from the existence of a single network. Likewise, to guarantee the transparency of said remuneration, regulated and non regulated activities of electric power companies are to be legally unbundled in terms of economic remuneration. Electricity retailing (supply sales) is officially introduced in the most regulatory framework. It is not just a possibility to be submitted to the Government for its consideration but rather a reality that takes on a tangible shape under the principles of free trading and free choice of suppliers as set out in this piece of legislation. A transitional period is established so that the liberalization of electricity retailing is phased in gradually, ensuring that full freedom of choice becomes a reality for all consumers within 10 years. An electric power system is thus set up to operate on the basis of the principles of objectiveness, transparency and effective competition, where free, private enterprise will be able to take on its rightful leading role. All of the above will take place without prejudice to the necessary regulation of the industry s actual characteristics themselves, especially the need for it to function on the basis of economic and technical coordination. In Spain there is a ACT on THE ELECTRIC POWER SECTOR. This Act incorporates into Spanish legislation the provisions contained in the European Parliament and Council Directive 96/92/EC, dated December 19th (LCEur 1997\191), on common rules for the internal electricity market. This particular directive allows for different ways of organizing electric power systems to exist at one and the same time with the introduction of a number of requirements that are essential to guarantee gradual convergence towards a European electricity market. This Act also converts the principles of the Protocol signed by the Ministry of Industry and Energy and the leading electricity companies on December 11th, 1996, into legislation. The aforementioned Protocol was not enforceable in the same way as any general law but what it did do was put on paper a complex, overall design for the transition from a statecontrolled, red tape dominated system to a system for the sector that operated with greater freedom. It also represented an agreement reached with the main economic players 22

35 in the industry on a far reaching modification of the remunerative system that had been in force until then and on a phasing in of full market liberalization. Essentially, the Protocol was devised as a document whose full scope would be used to trigger a thorough process of change. The technical complexity of some of the characteristics of the electric power industry makes it necessary to ensure that it is run in a deregulated framework without any abuse of dominant positions and with strict respect for the practices of free competition. Consequently, this Act confers wide ranging powers on the National Electric Regulatory Commission with regard to requesting information and solving disputes and they way in which it is to collaborate with the Administration departments responsible for fair trading and restrictive practices is set out. At the same time, the hierarchy of areas of activity corresponding to the State Administration and the National Electric Regulatory Commission is clarified in more detail, the coordination mechanisms between them are enhanced and the work performed by the Commission is granted greater continuity by establishing a system of partial renewal of its members. Lastly, this Act makes an energy policy based on the progressive liberalization of the market compatible with the achievement of other aims that also inspire it, such as improved energy efficiency, reduced consumption and environmental protection. The special arrangements for electricity generation known as the special regime, the demand side management programmes and, above all, the promotion of renewable energies add to its position within the Spanish legal system (SPAN, 05) Fundamentals of monopoly regulation A monopoly exists when; a given company becomes the sole supplier of a product or service. Any such company would be in a position to charge consumers a price much higher than its production costs, with the concomitant loss of economic efficiency. Consequently, some form of regulation is required to ensure efficiency under these circumstances. The electricity industry has been traditionally dominated by national or regional monopolies subject to price control regulation, with the regulator setting new tariffs from time to time. After industry deregulation and liberalization, the generation and sale of electric power to end consumers are viewed as activities that can be undertaken on a competitive market, whereas network activities, i.e., electricity transmission and distribution, are considered to be natural monopolies and still in need of regulation (TOMA, 03 1). According to economic regulation theory, the monopolistic supplier of products or services regarded to be in the public interest should be prevented from exploiting its market power through due regulation or some other form of control, such as State or local institution ownership. And yet the same ideal of economic efficiency that underlies the operation of 23

36 perfect markets, namely that company owners are motivated to innovate, invest in new projects and reduce costs by the potential profit to be earned, and driven to reduce prices by competitive pressure, should also be the inspiration that drives the design of efficient monopoly regulation. Regulators may choose from a number of regulatory variables as tools to reach efficiency objectives. Arguably, the most important of these approaches is the regulation of the revenues from electricity sales that the company is allowed. Such revenues must be sufficient to enable the utility to cover its operating costs and make any necessary investments, while earning a suitable return on the capital invested. In other words, revenues should ensure the company s medium and long term economic and financial viability, without driving it to bankruptcy. Moreover, in the case of an essential service such as electricity, unjustifiably high prices also have an adverse impact on the competitiveness of a country s industry (TOMA, 03 1). The service quality standards that the company is required to meet is another variable that regulators may draw on to enhance efficiency. In the electricity industry such quality is related to: 1) reliability of supply, i.e., the number and severity of the power supply interruptions to consumers, 2) voltage quality, defined by the existence or otherwise of disturbances that may affect the proper operation of apparatus and equipment connected to the mains and 3) consumer satisfaction with the customer service standards maintained by the company. All these quality indicators are directly related to operating and maintenance costs, but also to company investment and the quality of the infrastructure installed. Regulation that encourages cost cutting or lower investment may lead, as noted above, to a gradual deterioration of the quality of the supply delivered to consumers. For all these reasons, the regulator should explicitly establish performance standards and link them to the revenues the company is allowed. Yet another variable sometimes explicitly controlled by regulators is investment for new infrastructure proposed by the company in its transmission grid or distribution network. The regulator s primary long term objective is to ensure that sufficient installed capacity is built to meet the expected demand at suitable levels of quality. This, as noted, is directly related to the rate of return on investment and any deviation, upward or downward, has undesirable consequences. The regulator may attempt to solve this difficult problem by establishing criteria to assess the suitability and necessity of the investments proposed by the company. One example of this can be found in network planning models. The increase in regulatory costs that the additional control and information gathering this entails must also be weighed, however (TOMA,03 1). Finally, the last variable that regulators can control is the entry into or exit from the business by companies other than the incumbent monopolist. This variable is very important where market regulation is concerned. In the case of monopolies, regulation 24

37 implies an agreement that grants the supplier rights, for instance, to distribute electric power exclusively in exchange for submission to regulator control. Furthermore, the company is obliged to supply power to all users, regardless of the associated cost, since electricity is an essential service. Companies may attempt to refrain from servicing high cost consumers or areas and focus on areas where unit costs are lower. Regulators must persuade or require operators to also provide service of sufficient quality in higher cost remote or rural regions. If despite such efforts service proves to be deficient or quality poor, regulators may establish incentives for other potential suppliers to enter the market: granting territorial franchises to small local co operatives, for instance. From the practical standpoint, the problem is to find the best regulatory design to achieve the objectives of economic efficiency sought by regulation. The following sections review the most common types of regulation: the traditional method used in the electricity industry for many years, known as cost of service or rate of return regulation, and a new mechanism that is becoming more and more popular in many countries since unbundling, known as incentive based regulation (TOMA, 03 1) Regulatory tools: traditional and incentive based regulation The electricity industry is not only enormously complex, both economically and technically speaking, but is a key factor in the economic and social development of any society. From its inception in the early twentieth century and throughout the history of the industry to its present maturity, enormous effort went into improving and optimizing decision making and operating processes to develop what is known today as traditional regulation. Although a wide variety of schemes was in place within the traditional framework, one of the characteristics of the organization of most electricity systems was their vertical integration and highly centralized decision making arrangements. While the industry could and can still be said to be organized in accordance with technical criteria on the one hand and economic criteria on the other, nearly all technical decisions still have underlying economic motivations and vice versa. Technical organization would include decision making in connection with system expansion and operation. These two aspects, which are actually two sides of the same problem viewed in the context of different time horizons, cover areas such as centralized generation and transmission planning, hydrothermal co ordination, fuel management, maintenance programming, hourly scheduling or economic dispatching and so on. Economic organization, in turn, focuses on the analysis of different industry cost items, processes for determining electric utility remuneration, the establishment of end user rates and so on( JUNE, 03). The introduction to the regulatory models begins with a discussion of the different tools used in regulation and the reasons for reforming them. This is followed by an introduction to the basic strategy for reform and an analysis of the activities comprising the electricity 25

38 industry, such as generation, transmission, distribution and supply, including both technical and financial aspects and posing the question, for each activity, of whether it can be conducted on a competitive marketplace. In the following part two main traditional approaches for regulatory framework will explain Traditional or cost of service regulation Traditional or cost of service regulation is the basic regulatory tool. In this system the cost of service estimated in advance is defined as follows: Ca(t) = CV(t) + A(t) + B(t) (1) Where : CV(t) : variable costs or expected operating costs in period t A(t) : period depreciation of assets (in t) B(t) : return on invested capital outstanding repayment, computed as B(t) = r(t) x K(t) where K(t) is the capital outstanding repayment and r(t) the return on investment allowed (per unit pound, dollar, euro, yen, yuan, peso, rupiah invested) The return on investment allowed r(t) is defined as the cost of the capital invested, adjusted for investment risk. This profitability rate provides for a normal return for investors, in other words, a rate similar to what they would obtain investing in other assets involving a similar level of risk. In economic lingo, r(t) is the opportunity cost of the funds invested and, therefore, there is zero economic or super normal profit on investment. Formally speaking, the different cost components appear as data in the problem, but sight should not be lost of the fact that the values in question are based on appraisals approved or computed by the regulator. Depending on the worth of these inputs, then, and how closely they reflect the actual situation, the resulting prices may be more or less suitable. In some countries, such as the USA and the United Kingdom, extremely detailed procedures have been developed for these calculations and appraisals. In others, the same principles are applied but much more laxly. In the simplest case, when cost and demand forecasts concur with actual costs and demand, the earnings allowed in period t are equal to the cost of service: R(t) = Ca(t) (2) P(t), the mean price of electricity (amount per kwh) or mean revenue is: Where D(t) is the expected demand in period t. P(t) = R(t) / D(t) (3), 26

39 The capital outstanding repayment is updated from one period to the next from the following formula: K(t+1) = K(t) A(t) + I(t+1) (4) Where I(t+1) is the investment made in period t+1 Finally, deviations frequently appear between the expected and the actual values. Differences may arise between the expected Ca(t) and the real cost of the service Cr(t) or between the revenue allowed, R(t), and the actual revenue during the period, Rr(t). Errors in demand forecasts, unexpected variations in fuel prices and unforeseen changes in interest rates, for instance, may all give rise to deviations. Cost of service type regulation corrects for these deviations by offsetting them in the following period. Deviation in period t is: D(t) = Cr(t) Rr(t) (5) Where revenues equal cost of service, deviation is zero. Therefore, when a deviation appears, it is added to (or, if negative, subtracted from) the allowable revenue in the following period, so that: Where r is the interest rate R(t+1)= Ca(t+1) + (1+r) D(t) (6) Formula (6) replaces the definition of allowable revenues given in (2). As may be readily deduced from the formula, the updated value of actual revenues obtained is equal to the updated real cost of service Advantages and drawbacks to traditional regulation The chief advantage to traditional regulation is that it ensures fair prices at any given time. Since revenues are equal to historic costs, this means that consumers do not overpay and investors are not under compensated. This is, certainly, an important advantage. From a dynamic perspective, however, traditional regulation is problematic because the historic cost may be inflated, i.e., not the lowest possible cost. There are three factors which, in combination, may lead to cost inflation under traditional regulation: Information asymmetries: the cost and demand data used by cost of service regulation are known much more precisely by utilities than by the regulator. Therefore, information may be manipulated by regulated operators to bring in higher revenues that cannot subsequently be recorded as earnings, but can be earmarked for certain cost items (such as higher salaries or a larger headcount). 27

40 Incentives for efficient management: keeping costs as low as possible (for a given amount and quality of service) calls for some effort from company managers. The traditional system of regulation makes no provision for incentives for managers to make this effort since, if costs grow, revenues are automatically adjusted to absorb the difference (see the exercise on the Averch Johnson effect below). Regulatory capture: utilities usually have a wealth of resources that they can deploy to influence regulator decisions and bias them in their favour. State resources are usually more limited. This undue influence on regulatory decisions, called regulatory capture, may be exerted in a variety of ways, including all forms of lobbying, Communication campaigns, regulator hire by the regulated utilities and vice versa (so called revolving doors ) Incentive based regulation The problems cited above gave rise in some countries to a revision of the regulatory mechanisms in place with a view to establishing explicit monetary incentives for the regulated companies to minimize costs. The idea, essentially, is to allow utilities to make a profit when they are able to lower costs. This means that prices do not necessarily mirror costs at any given time but, in exchange, companies have an incentive to cut costs. If this incentive is effective, costs should foresee ably be lower and efficiency greater and, in the long term, prices may also fall (JUNE, 03) Incentive based regulation Under the traditional approach, the basic outline of incentive based regulation can be summarized in a single idea: to refrain from correcting or to only partially correct deviations. Therefore, if a utility lowers its costs to less than the forecast, the difference between revenues and costs, or part of it, is not returned to consumers, but goes to raise the company s earnings. The expectation of such earnings is the incentive for companies to lower costs. Let s see how this idea works. The point of departure for incentive based regulation is a cost target for period t, which we ll call Co(t); for example, the cost target may be simply the expected cost defined in (1), in which case Co(t) = Ca(t). Another possibility is to define the cost target as the costs recorded in the previous period, updated to adjust for inflation, in which case Co(t)= e x Co(t 1), where inflation e is defined as e = (CPI(t) / CPI(t 1)); CPI(t) is the consumer price index in period t. The revenues allowed in year t are defined as: 28

41 R(t) = Cr(t) + s x (Co(t) Cr(t)) 0=< s =< 1 (8) What this formula is saying is that the company will be allowed to retain as earnings, a certain portion, s, of each currency unit by which it lowers its costs below the target figure. To see what this would mean, note that the earnings are: B(t) = R(t) Cr(t) = s x (Co(t) Cr(t)) (9) The value of s measures the strength of the incentive for companies to lower costs. When s is equal to 1, the incentive is at its highest and when it is equal to 0, there is no incentive, i.e., regulation is the same as in the traditional approach. The form of incentive based regulation most commonly used is known as CPI X (or RPI X ) regulation. In this system incentive strength is maximum (s=1) and the cost target is fixed on the grounds of the previous year s target, updated to adjust for inflation e less a certain efficiency or productivity factor, X. In so called revenue cap CPI X regulation: R(t) = Co(t) (10) Co(t) = (1+e X) x Co(t 1) (11) Factor X, which is fixed by the regulator, defines the cost reduction target (as a value between 0 and 1) for period t. If the utility reaches this target exactly, its earnings will be exactly the same, in real terms, as in the preceding year (in other words, they will rise in the same proportion as inflation). If the utility overshoots that target, its real earnings will grow. Although the value of X can be fixed arbitrarily, in practice it is associated with the regulator s estimate of the amount by which the company can reduce its costs. Thus, if productivity grows in a given activity by 3% yearly, a possible value for X would be These formulas are applied for a pre established length of time, such as four or five years, after which the values for factor X and the initial cost target are re set. Revenues in the first period that the formula is applied may be fixed arbitrarily, although a reasonable initial value would be the expected cost for that period. Alternatively, CPI X can be applied to prices ( price cap ), in which case: P(t)= (1+ e X) P(t 1) (12) And the allowable revenues in period t where demand is D(t) are defined as: R(t) = P(t) x D(t) (13) 29

42 The price in the first period that the formula is applied can be arbitrarily fixed, although a reasonable starting point would be the expected cost for the period divided by demand for the period Advantages and drawbacks to incentive based regulation The alleged advantages of incentive based regulation are lower prices and costs that can be obtained in the long term, even if prices are higher in the short term. This situation is illustrated in the graph below, which also reveals an important drawback to incentive based regulation: prices are not necessarily equal to costs in any given period. In other words, utilities are allowed to make a super normal profit. Figure 2: static and dynamic incentives in regulation The question is whether incentives work and the prices resulting from incentive based regulation decline (as shown on the chart) or whether, on the contrary, the two price lines never intersect. A number of arguments suggest that this question should be viewed with some scepticism. First, it is sustained that company managers foresee that the cost reductions achieved will eventually give rise to lower cost and price targets. Therefore, the argument goes, the incentive consisting of earning a short term profit is weakened by the knowledge that in the medium term allowed earnings will drop. The net result of these two opposite forces, called the ratchet effect, is uncertain. Second, criticism has also been leveled at incentive based regulation from the standpoint of its credibility. When the result of regulation is high earnings for utilities, consumers and other actors bring pressure to bear to change the incentive formula. If the opposite occurs and utilities lose money, pressure is likewise exerted to change the formula to prevent the quality of service from deteriorating or to parry the threat of company failure. Anticipated change in the formula cancels the beneficial effects of incentives. 30

43 Finally, this regulatory formula has been criticized because in practice it has been overly generous with some companies, suggesting that the values for X and the cost targets have been inadequate, although empirical evidence in this regard is still inconclusive (TOMA, 03 1) Liberalized (Deregulated) electricity market Electricity market restructuring (deregulation) emphasizes the potential for competition in generation and retail services, with operation of transmission and distribution wires as a monopoly. Network interactions complicate the design of the institutions and pricing arrangements for open access to the wires. The design of the institutions for the wholesale market can accommodate access for both wholesale and retail competition while recognizing the special requirements of reliability in the transmission grid. In economic terms, electricity is a commodity capable of being bought and sold. An electricity market is a system for effecting the purchase and sale of electricity, using supply and demand to set the price. Wholesale transactions in electricity are typically cleared and settled by the grid operator or a special purpose independent entity charged exclusively with that function. Markets for certain related commodities required by (and paid for by) various grid operators to ensure reliability, such as spinning reserve, operating reserves, and installed capacity, are also typically managed by the grid operator. In addition, for most major grids there are markets for electricity derivatives, such as electricity futures and options, which are actively traded. These markets developed as a result of the deregulation of electric power systems around the world. This process has often gone on in parallel with the deregulation of natural gas Market. This part is organized as follows: Section is a short introduction on Deregulated (decentralized) electricity market. In Section 2.2.2, an over view of generation business discussed. The Generation Liberalization is described in section Technical aspects of electricity generation have been outlined in Section and financial aspects of electricity generation are discussed in Section Wholesale market design explained in part Market power is discussed in part and finally European Union deregulation explained in part Introduction The liberalization and deregulation processes underway around the world, while differing substantially from one another, do have a number of traits in common, i.e.: 31

44 The separation of the areas of the electricity business that can be conducted on a competitive marketplace (generation and supply) from those that, constituting natural monopolies (transmission and distribution), must be regulated. The establishment of a wholesale market where generators compete. Third party access to the transmission network and the respective tariffs. Freedom of choice of supplier for qualified or eligible customers. One might ask why the market is so instrumental to these processes. Adam Smith provided the answer in his book, the wealth of nations, noting that individuals interact on the marketplace guided by an invisible hand that leads them to seek socially optimum results. Market price is the invisible hand that drives economic activity and ensures the efficient allocation of resources. Therefore, the study of the wholesale market is essential to understanding the workings of the electricity industry in this new environment. But the State can improve results when the market is unable to ensure an optimum allocation of resources, a fact that must also be taken into account in electricity market design. Under such circumstances, normally termed market failures, regulatory intervention is required to correct market results. As the reader may suspect, such intervention does not always attain the intended goals. The intervention mechanisms available must therefore be carefully analysed prior to designing a wholesale market to ensure that market operation is distorted as little as possible by regulation and the desired objectives are reached. The additional complexity of wholesale electricity market operation and design created by the specific characteristics of this industry will also be addressed in this unit. Market design is naturally conditioned, in turn, by higher ranking decisions relating to market structure and institutions and the possible transactions between different market agents. Both aspects determine the rules of the game governing the wholesale market. For instance, competition on the various electricity markets can be enhanced by increasing the interconnect ability with neighboring systems, which facilitates the sale and purchase of power by players outside the system. The decision to build the physical infrastructure that this requires is usually at least partially incumbent upon a Regulator. Furthermore, the sale and purchase of energy must also be made legally possible, particularly where the outside actors are foreign. Consequently, the regulations and institutions needed for this type of transactions, such as power exchanges where inter system power transmission rights are traded, have to be adapted to the laws governing the export of goods and services in both States involved: that is to say, the (existing or desired) physical, financial and legal structure in place in the system conditions the type of transactions possible and regulation required (TRAN, 03). 32

45 An Over view of the generation business The beginnings of today s modern electricity industry are associated with the light bulb. The earliest electric companies focused on public and private lighting. They needed authorisation from municipal authorities and other public bodies to deliver light to both sectors, if for no other reason than to erect the poles and dig the ditches needed to wire their networks. In the first century or so after the inception of the industry these ties between government and the electricity business grew more intense, and have only recently begun to loosen. Traditionally, the rationale invoked to defend extensive governmental regulation was that the delivery of electricity entails the existence of a natural monopoly. As discussed in preceding units, the existence of such a monopoly has been increasingly challenged over the last two decades or so, when a distinction has been drawn between activities that call for strict regulation and those that can be conducted under competitive conditions. The most prominent of the latter from the standpoint of the flows of funds involved is production or the generation business. Consequently, deregulation of the electricity industry has largely focused on deregulating the generation of electric power. The objective is for the various players to make their decisions based on the benefits accruing to them individually, in keeping with the law of supply of demand, as is the case for most of the rest of the economy in countries with free market systems. The decisions that companies must make cover both short term operating decisions as well as investment decisions involving longer term horizons. Both are impacted by the way that agents charge for their services, in other words, the how they are remunerated. A fundamental concept bequeathed to us by nineteenth century economists is marginal cost or the cost of producing the final unit of output. They proved that in an economy where perfect competition prevails, marginal cost should be equal to price. But perhaps more important, from the viewpoint of regulation, is the so called first theorem of welfare economics: that economies where prices equal marginal cost provide the greatest social benefit, at least from one vantage. The most liberal regulatory schemes instituted in recent years therefore attempt to ensure such equality between marginal cost and price. The danger, as always, is in the detail: despite the apparent clarity of the definition, there are several kinds of marginal cost, and it is not totally clear whether the assumptions underlying the first theorem of welfare are valid in the context of the electricity system (that they are not strictly applicable is obvious; the relevant question is whether that particular fact is significant). In any event, knowledge of the conceptual tools behind these assertions is indispensable (TRAN, 03). 33

46 Nor is the transition from a regulated to a liberalised system problem free. Investments made during the regulated period assume a certain, likewise regulated, future scenario. When that framework changes, the former plans can hardly be optimal (particularly if account is taken of the fact that it was dissatisfaction with the former model that prompted change). This problem is aggravated where the regulated system is totally or partially in private hands, since the owners of these companies will demand compensation of costs incurred under the former regulations that cannot be recovered under the new circumstances. Such stranded costs sometimes amount to very large sums of money, making some manner of material solution imperative. The market also has to be designed. A number of forms may be considered. One might be a market where demand and generation deal directly with one another, as in most other markets (over the counter market); but they may also trade on a sort of exchange (organised market). Moreover, there are several ways to organise both of these types of markets and several different products may be traded (power supply the next day at 1:00 p.m., or a whole package of power to be consumed between June and August in two years time, for instance). The organisation of electricity markets, including the possibility of not organising them, continues to be a controversial issue. This means that no solution is perfect. Indeed, all electricity markets are subject to a greater or lesser extent to the following problems (TRAN, 03): 1. The extremely precise co ordination required. Specifically, demand and generation must be constantly in balance: the system cannot tolerate significant differences over periods greater than one second long. The resources needed to achieve such equality, account taken of the inevitable real time disturbance that arises, are known as ancillary services. Other facilities needed to guarantee voltage levels and other technical constraints also fall under this category. 2. The very large investment required and the long lead times, on the order of years. Demand trends cannot be known in advance, so installed capacity may prove to be much higher or lower than necessary. Since the latter possibility is the one that has traditionally caused greater concern, this type of problems is generally analysed under the heading security of supply. 3. Another consequence of the large investments called for is that most electricity systems are serviced by only a small number of generating companies, some of which some may be able to significantly modify the conditions of supply, and more 34

47 specifically the price of electricity. This is what is known as market power, which is usually very difficult for regulators to control. 4. Electric power generation entails inevitable risks due to both physical (contingencies affecting generating units or lines, temperature changes that increase demand, and so on) and financial (changes in fuel prices, interest rates and so on) circumstances. In the traditional regulatory framework, such risks are ultimately borne by consumers or taxpayers. In a competitive system the generators themselves must bear and therefore learn to manage these risks. Risk analysis therefore acquires substantial importance Why Liberalize Generation? The liberalization of electricity markets is a world wide development. Yet the reasons driving change differ from one country to another, and never appear singly in any country. On the contrary, the present situation is the outcome of a long series of circumstances. Be it said, firstly, that deregulation has primarily meant deregulation of the generation business. Transmission and distribution are essentially natural monopolies and continue to be strictly regulated the world over. The supply of electric power to end consumers is also a competitive business, but has lagged significantly behind generation nearly everywhere in developing liberalized markets. Moreover, in most former systems, electricity was generated by vertically integrated utilities. Therefore, at the very least, deregulation has called for the transparent unbundling of the generation and distribution businesses within any given company. In some countries this process has been carried to the extreme of creating different companies for each business. In any event, the explanation for the onset of liberalization may be sought in a number of circumstances: Deregulation has been possible because the economies of scale in electric power generation are no longer as large as they once were. Today, gas fired combined cycle plants, which deploy what appears to be the least expensive technology to date, reach maximum efficiency at sizes on the order of 400 MW (50 Hz grid is 400 MW, 60 Hz is 250 MW). This is much smaller than the 1000 MW required for maximum efficiency in nuclear power plants, for instance, and in theory paves the way for greater industry fragmentation and therefore greater competition in the generation business. 35

48 It was also widely believed that the change from public to purely private management would enhance efficiency. This factor was, naturally, closely related to the dissatisfaction with the previous regulatory structure. Such dissatisfaction was particularly keen in the USA, where the significant differences in electricity prices in neighbouring states were difficult to justify. In other countries centralised planning had led to poorly sized systems. In some cases, overcapacity was a consequence of the fear of electricity shortages prompted by an oil crisis. The desire to attract private, and especially foreign, capital, to the industry. This was an important reason in Chile and in the rest of Latin America, where governments had limited resources that it was argued should be devoted to other needs (social security, education, infrastructure...). Political reasons, enhanced by the swing toward conservative positions in the nineteen eighties (Thatcher and Reagan administrations). This fact was particularly relevant in England, where liberalisation of the electricity industry was closely associated with coal mining related problems. An important factor in the European Union was the creation of a single market, which enabled electric companies in the various Member States to compete with one another. In fact, however, the tendency of Member States to protect their own national industries has limited the scope of the liberalisation proposed. Although at this writing liberalisation has still not been universally accepted (the industry continues to be governed under different variations on the traditional regulatory system in many countries), it is a reality that will endure for the foreseeable future in the systems where it has been implemented. In such countries it must be judged on the grounds of the efficiency of the electricity industry, regardless of the reasons initially put forward for undertaking deregulation. In other aspect, electric power generation includes essentially two types of activities: the financially efficient use of the existing facilities (operation); and investment to build new or upgrade existing facilities as demand grows or older installations become obsolete (TRAN, 03). These two activities are linked by the remuneration mechanisms open to the owners of generation assets, primarily electric companies. In a liberalized environment such remuneration mechanisms are, of course, market mechanisms. In other words, revenues (through trading on a pool, other types of organized markets or as over the counter contracts) from power sales and (to a lesser extent) ancillary services must cover the investment and operating costs incurred, as well as plant owners profits. From the regulatory standpoint, on a completely liberalized market investment is governed by the free entry principle: any investor should be able to create new capacity, subject only to certain legal obligations in connection with land use or environmental impact, for 36

49 example. That is to say, all that should be required is a license or authorization that the authorities must grant indiscriminately to ensure competition among the various players. Operation is likewise mediated by market signals. The amount of power generated by each plant in the system is determined by the amount sold on the various organized or over thecounter, spot or forward markets. Since the revenues earned must cover all (investment and operating) costs, price prediction in the various markets is a task of cardinal importance. Most liberalized systems are organized around the short term market. The design of these markets is complex and usually calls for considerable regulatory supervision. Ancillary service markets are more technical and subject to even stricter regulation. In all cases, regulation aims to attain prices, the signals used by generators as the basis for operating their plants and planning their investments, which lead to socially optimal system performance. Some type of regulatory objective (what is to be optimized?) is, of course, requisite to achieving this aim. The target or objective is usually assumed to be the so called net social benefit : the sum of generation surplus and demand. This objective is nonetheless often modified by another series of aims, such as greater generation capacity than the market alone would provide, protection of an autochthonous natural resource, diversification to other sources of generation or the development of technologies with a lower environmental impact. Theoretically, the desirability of such aims could be quantified in a function which, added to net social benefit, would yield a new target function to be optimized. An alternative approach would be to consider them as a constraint to be observed (TRAN, 03). As discussed above, the first theorem of welfare economics guarantees that o ptimal social benefit is reached when prices equal marginal costs, a goal attained in perfectly competitive economies. A corollary to this theorem sustains that to comply with the constraints described above, the price of the items involved (additional capacity or the reduction of one tone of carbon dioxide) must be defined by the dual variables or shadow prices associated with the problem of optimizing social benefit. This has a number of virtuous consequences: 1. The computer software needed to conduct these studies is the same as used in a traditional centralized framework. 2. The output from these programs includes not only the numerical values of shadow prices, but an analysis that provides insight into how they should be applied. Indeed, regulators cannot usually directly order compliance with these objectives, but only establish the mechanisms that encourage agents to meet them. The above procedures only furnish appropriate signals if the market is perfect. They serve as a point of departure in markets with significant imperfections. In any case there are models able to simulate imperfect markets. The meaning of the output variables and multipliers in 37

50 such models is often similar to the meanings used in centralized optimization (or perfect market) models and can be applied in a like manner (TRAN, 03) The technical constraints of electricity generation As discussed above, at any given time, the electric power delivered to and flowing out of the system must be equal. Furthermore, there are no economically viable procedures for storing large amounts of electric power. Batteries, for instance, are much too expensive for this purpose. Electric power can be indirectly stored in pumped storage plants, where water is pumped from a reservoir at a lower elevation to one at a higher elevation and fed to a turbine at some later time. The problem with this method, aside from the limits to the amounts that can be handled (there simply aren t many reservoirs with such a configuration), is that performance is around 70%. In other words, the amount of water that it takes one MWh of power to pump only yields 700 kwh of electricity. The fact that electric power consumption and generation must be the same at all times largely determines generation structure in electric power systems. Roughly, power plant operation involves a fixed cost deriving from investment (essentially to build the plant) plus a variable cost proportional to the power generated (essentially, the cost of fuel: coal, gas, uranium ). We should keep in mind that, certain types of generation simply cannot be controlled. These are essentially wind generation and hydroelectric generation in the absence of reservoirs, known as run of the river plants (a turbine installed in a riverbed, for instance). The power generated in cheaper plants can be profitably used in off peak times to pump water to storage reservoirs and later dump it onto turbines during peak times, instead of using plants with high variable costs for this purpose. Just how profitable this is depends, among others, on the efficiency of the pumping cycle, which is around 70% (the output in electric power for each MWh used to pump water is 0.7 MWh) (TRAN, 03) Financial aspects of electricity generation (pricing) Marginal production cost is a figure that plays a fundamental role in the analysis of competitive markets and its cost efficiency. Specifically, theory has it that on a perfectly competitive market, prices should equal marginal production costs. Given that on competitive markets prices are determined from the bids submitted by the various players, market design should be based on a coherent theory of marginal cost. Furthermore, market imperfections (including the exercise of market power) appear as the difference between prices and marginal costs (TRAN, 03). Marginal cost can be defined as the cost of supplying one more unit of output. In the case of an electric power plant, for instance, it is the cost of supplying one further kwh of electricity. 38

51 Pricing on a competitive market The various actors on a competitive market proceed to trade, buying and selling until a point is perhaps reached where none wishes to change its position. Such a situation, in which all negotiations have been brought to an end, is what is known as market equilibrium. This is a theoretical concept: in practice this situation is hardly attainable on any market. Nonetheless, real markets should not stray very far from this point, since if they did, the economic agents would be strongly inclined to change their positions and the deals concluded as a result would be expected to alter the market situation significantly. In theory, under equilibrium conditions the price on a competitive market may be expected to be equal to each company s marginal cost. If the situation is analyzed plant by plant, each one would produce either its maximum or minimum (which may be zero) output, or an amount somewhere in between. In the first case, the plant s marginal cost should be lower than the market price, since otherwise, it would profit from reducing production. In the second case the marginal cost must be higher than the market price, since otherwise it would begin to produce. In the third case, its marginal cost must be equal to the market price. The reason is that if a company owned a plant with a marginal cost lower than the market price, it would have an incentive to offer to generate extra output at a price somewhere between its marginal cost and the market price, and still make a profit (the difference between the price bid and its marginal cost). And it would surely find a buyer for power offered at a rate below the going market price. But this would entail negotiations between the players, from which it may be inferred that market equilibrium had not in fact been reached in the situation described. Similar reasoning can be applied to cases in which the market price is lower than the marginal cost (TRAN, 03). It may be deduced from the foregoing that a company s marginal cost is the marginal cost of the plant producing at a rate between its minimum and maximum output: this is known as the marginal plant. This is, however, subject to certain imperatives. Firstly, the various agents must be able to communicate readily (plant owners must be able to convey to possible buyers their willingness to produce at a price lower than the going market price), must not be able to affect the market price, and so on. Markets meeting these conditions are said to be perfectly competitive. This is likewise a theoretical concept, which never materializes in the real world. Nonetheless, given the beneficial effects of perfect markets on social welfare, one of the objectives of regulation should be to come as close as possible to creating one. In many markets, generators submit bids specifying the amount of power they are willing to produce at each price. In a perfectly competitive market, the bid submitted by each company mimics its marginal cost curve. Assume, for instance, that a plant bids a price 39

52 below its marginal cost. If the market price is higher than the marginal cost, it will produce at a rate equal to its maximum output, which is exactly what it would have done if its bid price had been equal to its marginal cost. If the market price is lower than the bid price, it will generate no power at all, which is exactly what it would have done had its bid price been the same as its marginal cost. But if the market price is between the company s bid price and its marginal cost, it will regret not having submitted a different bid, since the cost of the last MWh generated will be the same as its marginal cost, but it will sell at the market price, which is lower. A similar argument can be advanced to prove that it is not in a company s interest to bid at a price over its marginal cost. Therefore, all generators will offer to produce power on the market at their marginal cost (TRAN, 03). However, price is determined not only by generation supply, but by demand as well. The latter is indirectly related to price. That is to say, the demand curve can be plotted on the same graph used above to plot the marginal cost (which is also the generation supply) curve. The point where the generation supply and demand curves intersect defines the price, as well as the point of market equilibrium Competitive markets and maximizing social welfare From the regulatory standpoint, one important feature of competitive markets is that they are economically efficient, i.e., they afford the greatest possible social benefit, economically speaking. The problem of maximizing net social benefit leads to the same solution as the behavior of agents on a perfect market. Among other things, this fact makes it possible to simulate behavior on a competitive market: an exercise that may be useful for diagnosing possible market failures or evaluating the foreseeable effect of possible regulatory measures, by comparing the simulation to actual behavior. There are, in fact, any numbers of computer models, most developed when operation was still centralized, that can be used to solve the problem of maximizing net social benefit (TRAN, 03). In any event, the enormous complexity of the final models rules out the possibility of solving the problem of maximizing net social benefits, for reasons of computer capacity. A variety of models are used instead: generally very detailed models covering short periods of time are deployed in conjunction with more simplified models to analyze long term decisions, such as investments. One important question is whether the equivalence between the solution to the problem of maximising net social benefit and the ultimate result of market behaviour (in which each agent seeks to maximise its own profit) is maintained when the added complexities of the real world or at least, their meticulous modelling are factored in. 40

53 In fact, mathematically speaking more than differentiable, cost and utility functions must be convex. In economics, this mathematical concept translates into the requirement for rising production marginal costs and declining demand curves. Strictly speaking, generation cost functions are not convex. For this reason, there are differences between the result of maximizing net social benefit and the results obtained on a perfectly competitive market. The equivalence between the maximization of net social benefit and the result of the action of competitive markets is a specific case of a more general property of the optimization of convex cost functions: the possibility of coordinating the action of the different actors involved through suitably designed payments (TRAN, 03). Specifically, it doesn t suffice for total generation to equal total demand: rather, a certain reserve or margin is normally required as well (availability over and above actual generation). Other limitations may affect the entire system, such as a limit on carbon dioxide emissions. Such requirements affect all system agents (the system reserve is the sum of each agent s reserve, the carbon dioxide emitted is the sum of each agent s emissions). Each agent is further subject to its own individual constraints (such as a generation plant s technical limitations). As these internal constraints call for no overall coordination, however, they will not be addressed in this discussion. Each new restriction appears as an additional equation in the mathematical approach to maximising net social benefit. The most significant restriction is the need to maintain a balance between demand and the total hourly power generated by all companies. Mathematically speaking, these multipliers are the increment in the objective function for a one unit alteration or increment in the constraint. In the case of the generation demand balance constraint, for instance, the multiplier (of which there is one per hour, since there is one constraint per hour) is the increase in net social benefit if demand changes by 1 kwh. And this sum just happens to be the market price. In other words, the multiplier constitutes the capacity price that induces the different actors to co ordinate their investments so that the total capacity is the capacity desired, in much the same way that the price of electric power is the signal that induces players to coordinate their outputs so as to exactly meet the existing demands (TRAN, 03) Time horizons The use of a variety of models with different horizons is requisite to any accurate analysis of electric systems, inasmuch as it is impossible to conduct a simultaneous analysis of all the issues. This time wise segregation is associated with the different types of decisions to be made, as follows: 41

54 1. Very long term (3 10 years): decisions to install new plants. 2. Long tem (1 3 years): decisions to transform and overhaul plants, long term fuel purchase and power sale contracts, plant maintenance programming, multi annual reservoir management and nuclear fuel cycle management. 3. Medium term (6 12 months): fuel, annual reservoir and pumping management; futures contracts for fuel and power. 4. Short term (1 week): decisions to connect steam generating units, weekend shutdown management, weekly pumping management, prediction of pool or electricity spot market behavior. 5. Very short term (1 day): decisions to connect steam or hydroelectric generating units, overnight shut down management, formulation and submission of bids to the pool or energy spot markets and ancillary services. 6. Real time: economic dispatching, frequency and power regulation, submission of bids to ancillary service markets. The underlying assumption for the models developed or analyses conducted for each of these horizons is that the longer term decisions are already in place. Consequently, when weekly decisions are made to connect steam plants based on anticipated market behavior, the information on generating capacity or long term contracts is a given and not subject to change. This means that initially there are several ways to calculate optimal output for a given market price. It can be computed by equating the very short term marginal cost or the short or medium term cost, and soon to the price. The only difference in all these approaches is which parameters are regarded to be constant. In the very short term, the generating units connected, power sale and purchase contracts in other words, nearly everything are assumed to be constant. In the six to twelve month medium term, the known variables are assumed to be plants, long term fuel and power purchase or sale contracts, and multi annual reservoir and nuclear fuel management. That is to say, the decisions assumed to be known in a particular horizon are the ones made in longer term horizons. Obviously, then, the optimum outputs calculated for the various horizons can only be consistent if all the marginal costs are equal to one another and to the market price. This is what should happen in a system in equilibrium. More than that, in this case the average cost is also equal to the marginal cost (TRAN, 03). Such an ideal situation is highly unlikely to ever materialize, since the implication is that only optimum decisions are made in all horizons. Another practical consideration is that the assumptions involved in computing the marginal costs for the different horizons must be consistent. If they are calculated with different computer programs, however, this will 42

55 probably not be the case, since the scenarios considered by different tools tend to differ. Consequently, under these circumstances, marginal costs can hardly be expected to concur, even where optimum decisions are made all across the board. Nonetheless, if there are genuine differences between marginal costs in different horizons, they will tend to converge under marketplace pressure. Assume, for instance, that there are only two horizons: a short term horizon in which operating decisions (for example, which plants to connect and which bid to submit) are made and a long term horizon in which investment decisions are made. If there is a power pool, the daily price established will be the same as the short term marginal cost, since bids are made in the short term for the existing generating facilities. A short term marginal cost that is higher than the long term cost means that it is more cost effective to meet needs to increase output through additional investment (long term marginal cost) than through system operation manoeuvres (short term). Consequently, there is an incentive to invest until the two marginal costs converge. Where the short term marginal cost is lower than the long term cost, it is more cost effective to reduce output through divestment than by operational means. As mention before costs must naturally include the cost of capital (for example, interest not earned on bank deposits). This is particularly relevant in the long term. It should in any event be stressed that the equilibrium situation described is the ideal case, virtually impossible to find in the real world where the long term horizon covers several years, precisely the amount of time required to reach equilibrium. Nonetheless, this is also the point towards which perfectly competitive systems should tend (TRAN, 03) Stranded costs The transition from a regulated system to a market where the various agents compete freely may create considerable financial difficulties for the companies involved. In a regulated framework, utility remuneration is based on average generating costs. In a competitive framework remuneration is in keeping with marginal costs. If system regulation is geared to maximizing net social benefit, these two costs should be equal and the transition to a competitive market should not generate significant problems. This is seldom the case, however, if only because deregulation is undertaken with the intention of correcting a situation regarded to be improvable. Electric companies may, therefore, have incurred costs in a regulated context that cannot be recovered under competitive circumstances. These costs are a specific case of what the specialized literature terms sunk or stranded costs. 43

56 More generally, a sunk cost is one that cannot be avoided or recovered once incurred. Stranded costs, widespread in the electricity industry, are one of the major difficulties encountered in its regulation (TRAN, 03). Be that as it may, in a regulated framework the Regulator acquires a commitment to generating companies to allow them to charge the costs acknowledged to them by the legislation in effect at the time, even where the recovery of such costs is deferred to a future date when a competitive system is in place. The costs acknowledged to the industry (in the form of a competition transition charge) can be grouped under three main headings: 1. Investments in generating facilities whose total generating cost are in excess of the prices prevailing on competitive markets. 2. Third party power purchase contracts that companies have been obligated to establish on the grounds of cost and price forecasts that are higher than competitive market prices. 3. Assets generated by regulation, including taxes, pension funds, nuclear decommissioning and other costs deferred for reasons relating to rate policies, which companies may likewise be unable to cover if they need to compete with other generators not subject to similar commitments. Quantifying these costs calls for a comparison between company revenues on a competitive market and under contractual, hypothetical circumstances: the remuneration obtained for the business conducted if the regulated system had remained in effect. The sums found are substantial, generally speaking, although subject to discrepancies that can be justified in part by the different assumptions about the returns companies might earn on a prudent investment in a regulated framework (TRAN, 03). If deregulation is applied to a state owned monopoly, there is in fact no such problem: when the assets are sold to private investors, the respective bids will be based on their value in a competitive environment. The stranded costs are assumed by the State, which accepted to pay them in the first place, when the rate policy was established. The problem arises when some of the operators in a regulated framework are private agents. In this case the State has a commitment to such operator or operators that must be honored, and this entails quantification. In practice, since the magnitude of these costs is such that they may distort the results of the competitive market, careful attention must be paid to the specific mechanism for remuneration chosen Wholesale market design Act 54/1997 of 27 November on the Electricity Industry laid the grounds for the new regulatory scheme for the Spanish system that aims to enhance efficiency by introducing 44

57 market mechanisms in the businesses that can be conducted under competitive conditions. The result has been to forgo any attempt at theoretical optimisation and base the system on the decisions made by the economic agents in the framework of a wholesale electric power market. The electric power production market comprises the commercial transactions involving the purchase and sale of power and other related ancillary services that are indispensable to security of supply and product quality. But, why is organised electric power markets needed? Primarily for two reasons: To hedge risks by balancing long and short positions (long when an agent is entitled to sell the asset and short when there is a desire or a need to purchase it). From the agent s standpoint, the ideal situation is vertical integration, i.e., permanent equilibrium, inasmuch as the entire output is consumed by the agent itself. But there is no such thing as perfect integration. This means that forward markets are necessary, with contract durations geared to the needs of the supply (at least one year) and generation (as long as possible) businesses. As a tool for short term portfolio optimisation. Generating companies must make decisions on generation plant dispatch, determining which plants can be most effectively used at each hour of the following day, and whether it is preferable to produce or buy power; whilst suppliers must adjust to the needs of their customer portfolios. This calls for spot markets. The two alternative wholesale market models are briefly discussed below, together with a description of the advantages and drawbacks to each (TRAN, 03) Organized wholesale market When the model implemented is based on an organised wholesale market or pool, a designated institution centralises the offers to buy and sell power. Only financial transactions with no effect on dispatching are allowed outside this market. This institution, a market operator or manager, establishes and publishes the market price, which is the same for all the operations concluded within a given period. Default risk is centralised by the market operator, to whom all traders must submit collateral, performance bonds or other security. Organised markets may in turn be divided into two categories. On the one hand, a pool is a market linked to units of output and demand. It is a ( day before ) market where the players (generators, suppliers, large consumers) are called upon to submit their offers to buy or sell certain amounts of electric power for each hour of the following day, at a given price, all within a pre established time frame. At closing, the purchase and sale offers are matched, the quantities to be produced are awarded and the single price at which transactions are settled are announced. Pools may be strictly mandatory, such as in the 45

58 system formerly in place in the United Kingdom, or quasi mandatory such as in Spain, although there is every indication that this model is nearing extinction. Organised spot markets or power exchanges, in turn, are also typically day before markets, although participation is voluntary. They are primarily markets where the players (the same as in pools, but also including brokers) trade portfolio offers unrelated to production/demand units to adjust their portfolios and trade surpluses. Both models are marginalism organised markets: the market equilibrium price is the price of the most expensive quantity of power for sale accepted, i.e., the marginal price (TRAN, 03). There are a number of advantages to this alternative: it comes closest to what would be an explicit minimisation of operating costs. The model is transparent (the reference price is public and accessible) and fair (all traders receive the same treatment). Moreover, there are barely any entry barriers, since there is no need to access consumers directly. It does, however, have weak points. While in theory it is the model that conforms best to the operating cost minimisation approach, it poses a problem insofar as it is based not on costs but on prices (bids). Therefore, any (supply side) price manipulation affects the market as a whole. It calls, therefore, for a high degree of transparency, as well, naturally, as Market Operator neutrality. Moreover, the dispatching rules and algorithm design may be arbitrary or opaque in some instances. Finally, a brief comment is in order on the difference between physical and financial organised markets. On physical markets, transactions are concluded when the power is delivered, generally at a hub (such as the French or RWE Netz transmission networks). All physical operations must be approved by the System Operator responsible for maintaining network equilibrium and security, for which purpose it implements mechanisms to accommodate constraints and compensate for deviations (TRAN, 03). On financial markets, on the contrary, transactions are concluded by settling the difference between the contracted price and an index price (typically the pool or spot market price). The buyer pays the contract price and the seller pays the index price. Since buyers receive the index price, they can turn to the spot market to buy the power specified in the contract. It follows from the latter that the index price must be credible, reflecting the price at which power may actually be bought and sold on the market (which should be liquid ) at any given time Over the counter market In the over the counter (OTC) market model, each pair of counterparties reaches agreement and concludes their trades independently, generators and suppliers negotiate their contract 46

59 terms and electric power is physically transmitted: these contracts affect actual dispatching, without dealing on an organised market. Brokers, organisations that bring buyers and sellers together (centralising purchase and sale offers), also operate on these markets, but do not centralise default risk,. Clearing houses arise for precisely this purpose. There is no single price but organisations such as Dow Jones, Platt s, and so on attempt to compile information on the closing prices in OTC transactions and publish indices that players can use to establish the price of their operations (TRAN, 03). The advantage of this model over the preceding scheme is that it eliminates any possible adverse effect of arbitrary elements on centralised match making. It is a more flexible mechanism, ordinarily used by most markets where other kinds of goods are traded. Both buyers and sellers can plan their business strategies because they are allowed to execute futures contracts. The purpose of the spot market is increasingly believed to be to correct unexpected imbalances and programming failures, incidents that involve a small but the most expensive proportion of total system energy. In this vein, more than a few voices sustain that the pool price is not the most valid and efficient reference for electric power trading. The model has its critics, however, who argue that as the size of the residual market shrinks, there is a growing risk that it can be manipulated (which ultimately doesn t seem to be a major problem, since the only effect is to provide an incentive for long term contracting). At the same time, it is less transparent, a factor that may be relevant for electric power markets, which may tend to revert to vertical integration. In conclusion, a vast majority of goods and services are traded bilaterally or over the counter. In the case of electric power, the formula most commonly employed is physical OTC spot or forward trading. (Non mandatory) organised electricity markets normally have rather small trading volumes; of the two types, spot markets are more commonly used, primarily for adjustments and to optimise portfolios. To date, organised forward electric power markets are exclusively financial markets, but there are not very many: indeed, the only one presently operating with any success is Norpool (TRAN, 03) International experience The first electric power markets established in practice (England and Wales, Argentina) adopted a scheme that can be generally summarised as completely liberalised investment and substantially centralised operation, albeit each with its own peculiarities. On such markets, bids are matched with a classic optimisation (usually a unit commitment) model that covers all the equations and constraints defining system behaviour and whose input 47

60 data include the various agents technical and financial characteristics. These are tools that have been used in engineering for decades, with a proven capacity for system modelling. Nonetheless, their use as models to match supply and demand on a competitive market is presently being questioned due to their lack of transparency and the volatility of their results in terms of the consequences for individual players. The second generation of competitive electricity markets (Norway, California, Spain) represents a step forward in the liberalisation process and may be synthesised as "completely liberalised investment and significantly liberalised operation. Here generation dispatch and market prices are not computed by a complex and scantly transparent optimisation algorithm, whose results are normally difficult to analyse and explain, but rather, like in many other financial markets (such as securities exchanges or wholesale commodities markets), are determined by the unfettered interaction between supply and demand. The most popular recent scheme appears to be the model adopted for the United Kingdom after implementation of the NETA (New Electricity Trading Agreements), where OTC markets co exist with the organised spot markets that smooth over short term imbalances. Institution of the NETA involved eliminating the pool, accused of favouring the exercise of market power and containing design errors (which could have been remedied without eliminating the exchange altogether). The pool has, in fact, been replaced by a regulation market, to correct the deviations between the amounts of power physically delivered and the amounts freely contracted in advance Market power The existence of market power is a recurrent issue in the analysis of electricity markets. Market power may be defined to be the capacity of a given agent to maintain prices at other than the competitive level (marginal cost) and make a super normal profit. Any one player able to modify prices must be relatively large: a very small actor's actions should have no impact on the market. In the case of electric power markets the large players are nearly always generating firms, since demand is much more fragmented. Market power, therefore, is analysed here in terms of oligopolistic markets, which by definition are dominated by a few large players able to control a significant portion of supply. For this reason also, what some of the measures of market power, such as the Hirschman Herfindahl index introduced in unit 2.B, actually denote is industrial concentration. Another consequence is that market power in electricity systems usually leads to prices higher than the competitive price, inasmuch as producers benefit from high prices. 48

61 As a rule, market power is wielded by submitting bids higher than the marginal cost, which is the rate that would be submitted under the pressure of perfect competition. In the most frequent case in which market power is exercised by generators, the price quoted for each amount of energy offered is higher than the competitive price, since it is in generators' interest to raise the market price. It is often argued that market power is wielded with the marginal plant, or at least that the exercise of such power can be studied by analysing that plant's bids. Such assertions are normally made in light of the fact that market power implies the ability to alter prices, which are set by the marginal plant. In any event, although this analysis is correct as far as the first of the above two options is concerned (since the marginal plant's bids would be significantly higher than the competitive price), it is of little use if the second strategy is employed, for in that case the price is altered by a plant whose bid is missing Modeling market power Modelling market power or its equivalent, the behaviour of a mono or oligopolistic electricity market, is a difficult task. Initially, monopolistic markets can be modelled with the optimisation methods developed for centrally operated or perfectly competitive systems, using, instead of net social benefit, the monopolist's objective function as the objective function. Although such a function might be the monopolist's profit, this is rarely the case in practice, since such monopolies are seldom unregulated. Modelling oligopolistic systems is much more difficult and continues to be an active line of research. Its study requires the use of techniques deriving from game theory, which are anything but trivial. Strictly speaking, these are not problems of optimisation, although in some cases they may be studied with optimisation techniques. In both cases (mono and oligopolies) the elasticity of demand plays an essential role. In the case of unregulated monopolies, it limits the maximum price: if demand were wholly inelastic the monopolist could fix any price, no matter how high, in the assurance that it would be able to sell its output to all consumers. Qualitatively equivalent effects may arise in oligopolistic markets Estimating and monitoring market power In most systems, it is not having but exercising market power that is an offence. The possession of market power can be studied with models, from extremely simple ones such as the Herfindahl Hirschel index to very sophisticated models such as some Cournot game simulation models. In this regard, the output from these models is of less value for predicting real system behaviour than for predicting potential behaviour due to the existence of market power (what would happen if the players were to make full use of their 49

62 power?). They are particularly useful for purposes of comparison: in which of two possible situations market power is greater, for instance. Monitoring market power, which is quite something else, calls for the use of real data on market and system operation. The general principle is to seek situations where, assuming no change in price, the player suspected of wrongdoing would have produced more than it actually did. In other words, it benefited by withdrawing the amount of power offered. The problem is that as rule large amounts of information on costs and a long historic series on the exercise of market power are needed to obtain statistically significant conclusions. Naturally, if market power is exceptionally profitable it is easier to prove than if it is exercised more discreetly, which appears to be the case in a fair number of systems Competitive Spanish electricity markets The Spanish power sector may be a good example of a process of restructuring and liberalization. This part describes the regulatory situation in the wholesale and retail Spanish electricity markets. Despite the fact that there is more than a decade of experience in restructuring and liberalizing the electric power sector in some countries around the world, there is a growing feeling that this is still an ongoing and long process, with many unexpected obstacles and where the final success is not guaranteed. Instances of both major successes and failures have occurred; see [IEA, 2005] for instance. On one side there is a lack of consensus on how to approach some relevant issues: for instance, how to secure an adequate level of investment in generation and transmission, the correct assignment of risks among the market players, the active participation of the demand or the existence of windfall profits when the marginal prices increase because of environmental constraints or other regulatory interventions. On the other side, although the main guidelines to do the restructuring right are becoming quite clear by now, in many cases the policymakers do not seem to have the will to do whatever is necessary to implement the reforms effectively. The common objective appears to be to take advantage of the benefits of competition whenever this is possible generation and supply, and to use the best available schemes of price control for those activities that have the characteristics of natural monopolies in transmission, distribution and system operation. However, the regulators are finding that achieving real competition in electricity markets is harder than it initially appeared to be. And most politicians do not seem to understand the intricacies of markets and often do not want to embark in the additional and frequently also politically difficult measures that are typically needed to fix markets that have been functioning for several years and whose shortcomings have become apparent. 50

63 The creation of a wholesaler market of electricity generation is settled as the central element of the new liberalized electricity systems. Such market functions, in the majority of the countries, by means of a mechanism of competitive auctions with the consequent seeking of efficiency. However, the international experience has shown that generators can develop a conduct based on strategic behaviour as a consequence of the basic characteristics of the electricity industry. In this sense, the formation of two possible strategies by generator enterprises, whether hiding output whether increasing the selling price of marginal output, were observed in some territories, such as California, United Kingdom or PJM market. The objective of this part is to describe the most salient features in the regulation of the Spanish electricity market European Union deregulation The European Union is accelerating the process of liberalising the electricity and gas markets by adopting new electricity and gas directives (new numbers 2003/54/EC and 2003/55/EC respectively), which replace the existing ones and push the market liberalisation further. All non household customers will be able to freely choose their electricity and gas supplier by 1 July This possibility is extended to all customers no later than 1 July In reality however, full liberalisation is occurring at a faster pace, with markets already fully open to all customer categories in several EU Member States. The competition policy pursued by the European Commission has a direct impact on the daily life of the citizens of the European Union. The reduction of telephone charges, wider access to air transport and the possibility of buying a car in the EU country in which prices are lowest are tangible results. Other, less visible, areas of Community competition policy also produce positive effects for the public. For example, merger control ensures a diversity of mass market consumer goods and low prices for the final consumer. Likewise, by contributing to economic and social cohesion, the monitoring of State aid helps to promote viable and durable jobs throughout the Union. Whether they are consumers, savers, users of public services, employees or taxpayers, the Union s citizens enjoy the fruits of the competition policy in the various aspects of their everyday life. The competition policy implemented by the Commission and by the Member States authorities and law courts aims to preserve and develop a state of effective competition in the common market by impacting on the structure of markets and the conduct of market players. Requiring firms to compete with each other fosters innovation, reduces production costs, increases economic efficiency and, consequently, enhances the competitiveness of the European economy, particularly vis à vis its main trading partners. Firms stimulated by competition thus offer products and services which are competitive in terms of price and quality (EURO, 00). 51

64 These competitive products and services are of benefit initially to downstream firms, which gain in terms of efficiency and are able to pass the improved productivity on through their own production processes. The liberalisation of network industries, for example, has in the first place improved the competitiveness of European industry, which has benefited from more efficient and less expensive transport, telecommunications and energy services. The propagation of the competitive process thus helps to consolidate the industrial fabric of the internal market and, in so doing, provides clear back up to employment policies. Secondly, greater competition allows the consumer to choose from a wider range of products and services at lower prices. Thus, the same policy of liberalisation has had concrete effects for users in terms of lower prices and access to new services. A recent study has shown that some telephone charges have fallen by 35 %. The European Commission has exclusive power to monitor the State aid granted by the Member States public authorities. Aid is in principle prohibited by the Treaty if, by favouring certain firms, it is liable to cause damage to their competitors in other Member States, which in some cases might go as far as to jeopardise their very survival and, consequently, the jobs of their employees. Only if aid is justified by the existence of a Community interest will the Commission grant exemption from this general principle of prohibition. In some cases, State aid merely leads to activities which no longer meet the requirements of economic efficiency being maintained artificially or to competition with efficient firms in the same sector being distorted. Public aid sometimes has a purely placebo effect on firms in difficulty. For example, 30 % of assisted firms in the former German Democratic Republic had closed down within two years of receiving aid. Community policy prefers to give priority to measures which restore a firm s competitiveness, such as restructuring plans; only measures of this kind can return the firm to viability and provide durable jobs. Aid that serves merely to maintain the firm in existence also seriously disturbs markets and is detrimental to competing firms which make the necessary effort to remain competitive. The Commission s endeavours in favour of such firms protect them against unjustified economic discrimination. Effective competition improves the European public s quality of life and purchasing power, and the public is entitled to expect the Commission and national competition authorities and law courts to tackle obstacles to competition and thereby defend its interests. The Commission s competition policy meets this requirement in full. It enhances the quality and variety of goods placed on the market, fosters technological innovation and economic performance and, finally, promotes fair prices for users. However, the Commission s competition policy is not limited to protecting consumers from the dangers that face them. It also seeks to preserve and stimulate their ability to operate 52

65 on the market in such a way as to contribute to the competitive process. Ensuring that consumers are able to make choices which affect the conduct of firms is also a means of guaranteeing that markets function on a competitive basis. The Treaty on European Union states in its principles that the Community s Member States are to adopt an economic policy conducted in accordance with the principle of an open market economy with free competition. The Community s competition policy pursues a precise goal, which is to defend and develop effective competition in the common market. Competition is a basic mechanism of the market economy involving supply (producers, traders) and demand (intermediate customers, consumers). Suppliers offer goods or services on the market in an endeavour to meet demand. Demand seeks the best ratio between quality and price for the products it requires. The most efficient response emerges as a result of a contest between suppliers. Thus, competition leads everybody individually to seek out the means of striking this balance between quality and price in order to meet demand to the best possible extent. Competition is therefore a simple and efficient means of guaranteeing consumers a level of excellence in terms of the quality and price of products and services. It also forces firms to strive for competitiveness and economic efficiency. This consolidates the Community s industrial and commercial fabric so that it is able to confront the competitiveness of our main partners and to put Community firms in a position to succeed in markets around the world. In order to be effective, competition assumes that the market is made up of suppliers who are independent of each other, each subject to the competitive pressure exerted by the others. In order to preserve the ability of suppliers to exert such pressure on the market, competition law sets out to prohibit agreements or practices which might reduce it (EURO, 00) In addition to speeding up the market opening, or the so called quantitative measures, the newly adopted revision of the Electricity Market Directive also establishes qualitative measures to ensure full liberalisation such as legal unbundling of network businesses, regulated third party access, sector specific regulatory functions and reinforced public service obligations, including provisions on fuel mix disclosure by the supplier to its customers. Regulatory models in use in the soon to be enlarged EU are of paramount importance for a functioning internal market. The new directive harmonises some of the general issues in the regulatory framework in the EU: 1. The obligation to set up a regulator: this was already the case in most of the EU and Acceding Countries, with the most prominent exception being Germany. With the 53

66 new directive, it is obligatory to charge one or more competent bodies with the responsibility for carrying out the required regulatory functions. 2. A minimum set of common competencies: the regulators will have the competence to approve tariffs or at least the methodologies to calculate tariffs prior to their entry into force. Even if the new directive brings a certain level of harmonisation to the regulatory functions in the EU Member States, a lot of scope for variation still remains. The final outcome can, and will, still be a patchwork of diverging regulatory models (EURE, 04). In conclusion, the Commission and its departments responsible for competition encourage the active participation of consumers and their organizations. Given their knowledge of the day today functioning of markets, in particular those in mass market consumer goods, consumer organizations are able to provide the Commission with information of interest to the Community by raising complaints or through informal contact. Such information may enable the Commission to initiate investigation proceedings concerning practices which distort competition. Consumer organizations are also able to establish links of this kind with the national competition authorities where signs of restrictive practices emerge more at national than at Community level. This brochure has the dual objective of informing the public of the real benefits it can expect from European competition policy and arousing its interest and canvassing its help in implementing that policy The case of Spain The 1997 Electricity Act (Ley del Sector Eléctrico 54/97) reformed the Spanish power sector radically, by restructuring the incumbent vertically integrated companies and introducing wholesale and retail competition. The 1997 Electricity Act replaced an ambiguous 1994 Electricity Act that unsuccessfully tried to liberalize only a fraction of the wholesale and retail markets and that was never applied. With the first European Electricity Directive of 1996 already published, the Spanish Government decided to move ahead with a comprehensive reform opening the power sector to competition forces. More than twelve years before, in 1985, in a farsighted and somewhat lucky move, the Spanish Government had created Red Eléctrica de España (REE, the National Grid Company), a new company with the role that today is described as a System Operator, who also owned about 50% of the Spanish transmission grid. REE is still now the System Operator, with responsibilities in operating the power system, managing ancillary services and proposing the plans of network investment to the regulatory authorities. Besides, today REE practically owns the totality of the Spanish transmission network. The existence and ample experience of REE as System Operator was decisive in the quick and uneventful implementation of the wholesale Spanish market in a record time during the last few months of 1997 so that it could start by the scheduled date of January without any fear that the functioning of the competitive wholesale market could impair the security of the electric power system. 54

67 The remuneration of electricity generation under the 1997 Electricity Act and after January 1998 was based on market prices, and the companies requested and were granted a compensation for their stranded costs of generation. The 1997 Electricity Act was preceded by a formal agreement between the Government and the incumbent electric utilities the Electricity Protocol of December This Protocol specified the main lines of the regulatory reform including the future treatment of the stranded costs of generation, which in Spain were denominated competition transition charges or CTC. During most of 1997, several working groups, mostly under the guidance of the Electricity Regulatory Commission, designed and prepared the draft of the 1997 Electricity Act, as well as the most urgently needed secondary regulation to start a wholesale market by January , where only the largest consumers could participate directly. It was agreed in the Protocol that the new regulatory scheme would be evaluated and adjusted, if necessary, three years after its implementation. This never happened. Since 1997 many minor adjustments to the market rules have taken place and, most importantly, also some changes in the structure and ownership of the companies. Endesa sold Viesgo (about 3% of production and demand) to ENEL, EDP from Portugal presently controls Hidrocantábrico, and there are several new entrants (among which the most relevant one is Gas Natural, the dominant gas supply company in Spain, with a 6% of electricity generation share that is quickly growing), most of them belonging to some of the strongest electric utilities worldwide. Since 2003 all consumers are free to choose supplier, although all of them (at least for the time being) may stay under a regulated tariff. The Government has set this tariff every year, with a consistent bias towards estimating too low energy prices to be reflected in the tariff. The sharp increase in the energy market prices during the last few years has resulted in a tariff deficit and in the mechanism of recovery of CTC by differences (to be discussed later) yielding negative amounts of stranded costs. Ad hoc rules had to be fabricated to cope with this and other unforeseen situations. This problem was compounded when in 2003 a decree established a path of evolution of the regulated until 2010, almost with total independence of the market prices. The important deviations in the actual market behaviour, because, for instance, of the strong demand growth or the increase in the fuel prices, resulted in significant differences between the true operation margins of the companies and the ones that were officially computed for CTC recovery. During the more than 80 detailed interviews that the team of the White Paper in Spain held during about four months with all kinds of stakeholders in the reform process, it became clear that there was a general feeling that the market was not working and that the mechanisms of recovery of CTC and the unorthodox design of the tariffs were creating serious distortions. The high level of concentration was a major hurdle for a straightforward and transparent market design. Moreover, the declining trend of the electricity tariffs (32% in real terms, i.e. excluding inflation, during the period ), mostly due to the 55

68 decline in interest rates and the low costs of fuel) had come to an end, therefore rendering the sale of regulatory reforms more difficult for the Government. The 1997 Electricity Act establishes the creation of a wholesale electricity market whose energy price must be paid by the consumers, who have the option of purchasing the electricity from the organized short term market directly, or via bilateral contracts with suppliers or retailers or, indirectly, via an integral default tariff. Since January 2003 all consumers have this choice. All energy destined to the consumers that have decided to stay with the default tariffs has to be purchased from the organized short term market that is run by the Spanish Power Exchange OMEL. Obviously, there is nothing wrong with this. The problem stems from the fact that the secondary regulation (Royal Decree 1432/2002) has determined that, almost independently from the energy market price, the value of the regulated default tariff which every consumer has the right to use has to follow a prescribed path (actually it is a narrow band) from 2003 to Therefore, at the end of any year N the Government sets the collection of default tariffs that will be applicable to every type of consumer during year N+1. The values of these tariffs are not updated in any form once the actual market prices are known. Moreover, the calculation of the default tariffs during most of the last years has seriously underestimated the market prices, therefore resulting in the so called tariff deficit at the time of the economic settlement of the different business activities. Evidently this has led to conflicts between the utilities and the Government. It is true that only in a few occasions the regulatory authorities have found motives to start an in depth investigation on possible abuse of market power by the generation companies since the wholesale market started in January In any case, the dominant generation companies could have easily increased the prices well above the values that have actually happened. But, besides self restraint and fear of regulatory actions, there are two major reasons for this behaviour, whether alone or combined: the mechanism of recovery of CTC and the peculiar design of the default tariffs. the critical issue is that the expected level of future market concentration will impede that the price of energy that the market provides could be considered as the key economic signal in the new regulatory framework. But, if the energy market price is not reliable, the entire orthodox regulatory approach collapses, since the Government will not accept that the market price is passed through to the default tariffs. Then, the default tariffs will offer a lower cost refuge for any consumer that might have decided to purchase electricity directly from the market or from a retailer. And the retailers will not be able to compete with the regulated tariff and their business will disappear. The tariff deficit will persist, since the revenues from the tariffs will be insufficient to pay the market price to the generators. It is unlikely that any long term contract markets will flourish, if the underlying market price is not reliable. And the Spanish market will not have the credibility to attract new investments. 56

69 The situation regarding market concentration has improved since the market started in January It is also true that the technology mix that will determine the marginal price of energy in the Spanish (or Iberian) market during the next few years will be dominated by the combined cycle gas turbine (CCGT) plants and this will significantly reduce the possibilities of abuse of market power. However, as the market simulation results in section clearly show, the remaining concentration will be still excessive for the ensuing market price to be considered reliable in the years to come, if no mitigation measures are applied. When proposing regulatory reforms in Spain, one should not forget that several Governments, from different sides of the political spectrum, have always favoured a policy of national champions, despite the liberalization efforts that were made in parallel. Therefore, however questionable this policy may be, it does not seem realistic for the White Paper to try to fix the concentration problem by just requiring the two dominant companies to divest their assets. The Spanish electricity market has not achieved yet its basic purpose: a competitive market that functions correctly. The choice of a regulatory model for the Spanish energy sector and the serious energy problems that the Spanish society will have to face in the coming decades require setting up clear guidelines and a persistent commitment that go beyond the typical term of a legislature. In the white paper 2005, strategic reforms for Spanish electricity market was proposed. This first set of reforms is meant to allow a correct competitive functioning of the electricity market. Then, the first problem to be faced is that the price of energy does not have in the Spanish market the central character that it has in other successful electricity markets around the world. The energy market price either resulting from a bilateral or organized market, either short term or long term must be the reference economic signal for all economic transactions among the market agents. This market price must be used to pay generators and to charge consumers and also, if this is the case, to calculate any default integral tariffs for those consumers that decide to use them. The credibility of the market price will be a critical factor in facilitating the entry of new investors and this, in turn, will help in maintaining a healthy margin of the installed and available generation capacity over demand at all times. If this is the case, the situations where the margin is so tight that the price can be easily manipulated will be very rare, which is also helpful. Once the confidence in the market price has been re established, this price in fact, some suitable combination of the prices in different short and long term markets can be passed through as any other component of the default integral tariff. This default tariff must fulfil a function possibly only transitory of protection of the consumers who do not want to look for a better price in the free market. But it should never be a refuge tariff, systematically offering a clearly superior alternative to the market. 57

70 It is also inevitable to find a final solution to the treatment of the CTC in order to configure a permanent regulatory regime, meant to be stable, where the space left to ambiguous interpretations is as reduced as possible, and where the current market distortions are eliminated (IGNA, 06) Conclusion In this chapter the electricity market frameworks, regulated and de regulated are explained. As mentioned before electricity supply is essential for every society to function properly. Its price is a crucial factor in the competitiveness of a substantial part of the economy. The combination of technical and economic characteristics of electricity (part 2.1.1) imposes the need for the electricity sector to be regulated. The basic purpose of electricity regulation is to regulate the electricity sector with the traditional, three fold goal of guaranteeing the supply of electric power, its quality and the provision of such supply at the lowest possible cost. In order to increase the efficiency of electricity system, the regulated system moved to deregulated or liberalized system. The deregulated electricity markets have been in operation in a number of countries since the 1990s. During the deregulation process, vertically integrated power utilities have been reformed into competitive markets, with initial goals to improve the market efficiency, minimize the production cost and reduce the electricity price. Given the benefits that have been achieved by the deregulation, several new challenges are also observed in the market. 58

71 3 Model specification The purpose of this part is to explain about a new multi stage production decision model for companies with multi business line gas and Electricity generation in a deregulated market and consider computationally efficient procedures and tools to solve it. This part is organized as follows: In Section 3.1, a main Idea of proposed model explained. In Section 3.2, the first step of proposed model discussed in detail and a short introduction to price forecasting methodologies is given. The second steps in proposed multi stage production decision model have been outlined in Section 3.3 and the third step of proposed model is discussed in Section Multi stage production decision model In the electricity market, electricity price and the quantity of production are two main issues for utilities. In the regulated electricity market, Utilities are price taker which means they could not determined the electricity price with open competition and the price determined by central decision. In this case just quantity of production is a key issue for utilities and it is calculated by using the (centralized) Unit Commitment Method in the short term based on the cost minimization. Under deregulation, the electricity price set by open competition so both electricity price and quantities of production are key issues for producer. In this deregulated market the unit commitment method (UCP) for an electric power producer will require a new formulation that includes the electricity market properties. As mentioned before the main difficulty here is that the spot price of electricity is no longer predetermined but set by open competition. Thus far, the hourly spot prices of electricity have shown evidence of being highly volatile. The unit commitment decisions are now harder and the modeling of spot prices becomes very important in this new operating environment. Besides that, the problem is more complicated for companies with multi business line in gas and electricity, because these companies could switch between these two markets in order to maximize their benefits, so they need flexible model to help them for making a decision in these markets. For this purpose,i propose the multi stage production decision model for against with multi business line in gas and electricity generation.as mentioned before, these companies with two business lines have more flexibility from switching between selling the gas in gas markets or using it for producing the electricity inside the regulatory framework. The 59

72 proposed model consist of three stages:1) electricity price forecasting for each hour during the time horizon, 2)calculation of gas margin for different available quantity of gas for producing electricity,3) optimum schedule of electricity production based on profit maximization, taking into account relevant technical and operational constraints of the generation system. In the first stage the hourly electricity price in the market for short term, midterm and long term is estimated by using stochastic model. The optimal allocation of gas quantity for electricity power production is done in the second stage by comparing the marginal value of gas in electricity market and the gas price in the gas market. The outputs of the first stage, electricity price, and the second stage, available gas quantity, are inputs for the third stag which is the single firm commitment problem with the maximization objective function (figure 3). Figure 3: multi stage production decision model We show that when the spot price of electricity is estimated in the first step, the marginal value of the gas can be calculated for different quantity of gas. The gas margin for each quantity should compare with gas price in the market. If the gas Margin is higher than the gas price then it is better to allocate more gas for electricity production instead of selling the raw gas in gas markets. After fixing the available quantity of gas for electricity production, again we should run the first step model to update the electricity price estimation; because when the electricity production is increased by using more gas, then the electricity price changes. The stage one and two behave like one loop. This procedure could be continued up to the point where the electricity price doesn t change significantly from one step to another. In the previous Market modeling with the price clearing process as exogenous to the firm s optimization program, the influence of the firm s decisions on the market clearing price neglects but in the proposed multi stage model this influence considers by considering a loop between the first and second stage of the proposed mode. As mentioned before, in the first stage the hourly electricity price in the market is estimated by using stochastic model and one of the input data for this step electricity price forecasting process is the available quantity of gas for producing electricity. The optimal allocation of gas quantity for electricity power production is done in the second stage by considering the output of the first stage electricity price and also comparing the marginal value of gas in electricity market and the gas price in the gas market we should put again this new quantity of gas in the first step in order to update the electricity price, this loop will continue up to get the equilibrium point 60

73 between electricity price and optimal quantity of gas. The outputs of the first stage, electricity price, and the second stage, available gas quantity, are inputs for the third stag which is the single firm commitment problem with the maximization objective function Figure 3 present the proposed procedure. As you can see there is a loop (go and back) between the first and second stage and the estimation of electricity price and available quantity of fuel are the input data for the third step. 3.2 Electricity generation using natural gas combined cycles Electricity generation using natural gas combined cycles is a technology which is not only one of the most efficient, but also that with the least environmental impact and applied worldwide. It is virtually the only technology used for electricity generation projects currently being implemented in the developed countries, and a system which will replace traditional systems, resulting in a drop in emissions into the atmosphere. This technology consists of utilizing natural gas combustion (turbine boiler) and steam produced by the exhaust gases (reheat boiler and steam turbine) to generate electricity. These two processes are complementary and enable very high energy performance levels to be reached as power is generated in two stages yet using a single energy source. Figure 4: Operating diagram of a combined-cycle plant Combined cycle power generation thus represents the ideal energy model as it is higher performing than other power generation systems while at the same time reduces any environmental impact using, as it does, a less polluting energy within a more efficient system. Combined cycle generator sets have a performance of over 57%, far superior to that of a conventional plant. This means that for every kilowatt/hour of electricity produced, a third less primary energy is required, i.e. natural gas. This technology produces notably low emissions: 60% less carbon dioxide and 70% less nitrogen oxides than in a conventional plant. Virtually no sulphur dioxide emissions and particles. 61

74 As stated in the study "Environmental Impacts of Electricity Production", published by the Institute for Energy Diversification and Saving (IDAE), electricity production using combined cycles has a lesser impact on the environment than photovoltaic and nuclear systems, or those using coal, oil or lignite. In addition, combined cycle generator sets consume only a third of the cooling water required by a conventional plant with the same output, and the installation takes up less space than a conventional plant. In the next parts three steps of proposed model will be explained in details. 3.3 Step one: Electricity price forecasting In liberalized electricity markets power producers face a wide range of decision problems that require modeling of electricity prices as a crucial input. In the highly liquid and developed financial markets the literature on price modeling is extensive. To predict future price developments analysts use both technical analysis based on patterns in historical market price movements and fundamental analysis based on expectations about the development in the underlying market price drivers. Electricity markets worldwide are still in the development phase and not surprisingly there exists conflicting views about the value of such modeling tools in electricity markets. In this chapter we look at how we could forecast the electricity price for the specific period of time An overview of electricity price modeling methodologies A useful way of categorizing price models is to look at the data used to model input parameters. In electricity markets one can distinguish between two main categories of data: 1. Market price data 2. Fundamental data about market price drivers With this distinction market price data includes both historical spot prices and derivative prices such as the forward curve. Fundamental data includes technical and market based information that can be used to construct the expected development of supply and demand curves in the market. The distinction between fundamental data and market data sets the stage for two different approaches towards electricity price modeling. The first approach is based on econometric models such as Stochastic Differential Equations (SDE) known from financial theory. In such 62

75 financial models market data is used to estimate a parametric structure adapted to fit the characteristics of electricity prices. The motivation is that of technical analysis where patterns in market data are assumed to be the most valuable predictor of future prices. The second approach is based on a technical bottom up modeling of the electricity system where data about supply, transmission, distribution and demand are used to model future market price dynamics (JACOB LEMMING, 2007).There is also the third approach which is called the combined approaches. The problems sketched with financial and fundamental models combine in this approach to explain why practitioners often prefer models that combine the two model types. These three approaches are explained in appendix A The first step objective In the short term, intervals ranging of one month, decision makers in electricity companies are faced with the problem of forecasting the electricity price for specific period of time. Based on this forecasting they will decide about its hourly production. In the competitive market this problem is more complicated. The amount of electricity production and its price are impact by the shape of the electricity demand curve over the time. Here the main Idea is to estimate the Average of the electricity price for specific periods of time, for instance one month, and then estimate the electricity price for each hour by using one of the electricity price modeling methodologies (part 3.1.1). Based on this Idea, in the first we should find one model for estimating the electricity average price and then in the second step find other model which could estimate the hourly electricity price based on this average. In next two parts we will explain these two steps in detail Average price In the first step, as mentioned before, we need to estimate the average electricity price. The estimation of the average electricity price in the spot market is accounted for by using MARAPE model. This model, which is referred to as the probabilistic production costing model, incorporates the stochastic features of load and generator availabilities (VAZQ, 05) The objective of this model is to allow the electricity company to evaluate the future evolution of the prices in the market in the middle term, i.e., ranging from one month to four or five years, both quantitatively and qualitatively. The model opts for a mixed approach, where the main risk factors (demand, hydro production,...) are studied through quantitative models (time series, ARIMA and GARCH models) that are used to generate future scenarios that feed a strategic production costing 63

76 model that computes the prices and productions in the market, simulating the producers' behavior. The output of this model is the electricity average price which we need for the second step Estimation price for each hour In this project in order to estimate the hourly electricity price we just focus on historical data. Based on that, the only input data for this stage are the average electricity price from MARAPE model and the available historical data. If we look at the electricity price modeling methodologies in part 3.1.1, the best methodology, which is fitted with these available input data, is the financial price models. In financial price models the time dynamics of market prices is driven by stochastic processes generally in the form of stochastic differential equations and parameters are estimated using market data such as historical spot and derivative prices. Applications of the spot price approach to electricity markets can be found in references such as Lucia & Schwartz (LUCI, 02). In their paper, they proposed one factor model for electricity price forecasting based on the spot price. The model describes the spot price P(t) dynamics along with other key state variables using a set of stochastic processes spilt into deterministic components f(t) modeling trends and cycles and we could consider the average electricity price to present this component, and a stochastic component ξ(t) modeling the uncertainty or distribution of prices. In order to Estimate the stochastic component ξ(t) by using discrete observations, we need to express them fully in discrete form. We choose the empirical estimation to be based on the following simple time series equation (1): ξ(t) = -A(2)* ξ(t-1) - A(3)* ξ(t-2) A(N+1)* ξ(t-n) (1) For t = 0,1,2,...,N, and where the innovations ξt are normal random variables with mean zero and variance σ 2. All A(i) coefficients, are estimated by using the historical data. We also estimate all parameters simultaneously by nonlinear least square methods to the maximum likelihood criterion in the case that the experimental errors have a normal distribution (KMAD, 04). 64

77 3.3.3 Conclusion The purpose of this step is to estimate the hourly electricity price for the second and third step. As explained in this part first we calculate the average electricity price by using MARAPE model and then we estimate the hourly electricity price by using financial model. In the next part the second step of the model will be explained in details. 3.4 Step two: Calculation of the marginal value of gas The second step of the proposed model is the calculation of the gas marginal value and its optimum allocation of gas for producing the electricity in the electricity market. In this stage first we propose the mathematical model for calculating the Marginal value of gas and Its optimum quantity for producing electricity and then we design a tool in order to use and implement this model in a user friendly way Objective In the short term, intervals up to one month, decision makers in the companies with two business line in gas and electricity are faced with the problem of the optimal allocation of gas to the gas market and electricity market. In the competitive market this problem is more complicated. The amount of electricity production and its price are impact by the shape of the electricity demand curve over the time. In the proposed model the demand curve considered in the first step (part 3.1) in order to estimate the electricity price so here we will consider the electricity price during the specific period instead of demand curve to calculate the optimal allocation of gas for producing the electricity. The objective of Gas model, therefore, is to obtain optimal allocation of gas for producing the electricity in thermal power plants so as to meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. The main idea is calculating the shadow price of Fuel balance equation, which is the marginal value of gas for producing the electricity or in the other words how much the benefit will change by adding one extra unit of gas for producing the electricity. In this way the company could compare the gas price in the gas market with this marginal value and if this marginal value is higher than the gas price in the gas market then it is better to allocate more gas for producing electricity instead of selling the original gas. Gas model cover: Calculation of Marginal value of gas in electricity market optimal allocation of gas for producing the electricity 65

78 It is possible to run the model for more than one month in case of significant CPU time. When the model become bigger and bigger then it is not easy to solve it in a short CPU time. The possible techniques for solving the problem, as described in the literature, are reviewed briefly below Model approach The second step is the single firm optimization problem (part ) in which the objective function is to maximize expected profits and the decisions, such as marginal value of gas, are required to meet technical characteristics and operating constraints such as capacity limits. The output of the first stage electricity price is an input data for this step. The most important model s characteristic is that the electricity price is estimated by using another tool in the first stage, which means price is an exogenous variable for second stage so in order to solve the problem the levels of market modeling which represents the price clearing process as exogenous to the firm s optimization program is needed. Consequently, as the price is fixed, the market revenue price times the firm s production becomes a linear function of the firm s production, which is the main decision variable in this approach. In view of that, traditional Linear Programming (LP) and Mixed Integer Linear Programming (MILP) techniques can be employed to obtain the solution of the model. In conclusion, the optimization model with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue is proposed to calculate the optimal allocation of gas for producing the electricity in thermal power plant, taking in to account the technical characteristic of thermal plants and limited gas fuel Representing time A chronological time chart is requisite to weekly modeling to incorporate the effect of timewise interconnections 1 (thermal set ramping up and down, start up and shutdown flexibility and so on) Figure 5: chronological representation of time 1 The notion of time wise interconnection means that the value adopted by decision variables in one hour affects the value that these same or other variables may adopt in subsequent hour. Before producing at full capacity, for instance, allowance must be made for the time needed to raise output, a necessarily gradual process. 66

79 Although the intervals used in this model are hourly, when a large scale generating system is to be modeled the size of the problem can be reduced by grouping consecutive hours with the similar characteristics. In such cases, periods may have a variable duration (JAVI, 07) Model assumptions The model assumptions are: We just consider one firm in optimization model The transmission grid is not included in the model We just consider the combined-cycle plants in the model That is called the single node approach The chronological evolution of the system hour by hour must be modeled. The time wise representation of hourly period is used A thermal set is not allowed to start up shut off at any time of day An uncertainty is not considered, a deterministic approach is used The efficiency curve (input output curve) for each thermal plant is considered as linear function Increasing in the gas consumption in each step of running the model is small Constant start up duration for startup ramp The model structure explained in the next part Model structure In order to build the Mathematical model it is necessary to know: what are the input data and criteria, which kinds of constraints does the system have, what are the interested outputs and result, finally what are the objective function, decision and state variables inside the model. In the following parts these four items will be explained Input data and criteria There are some criteria in all mathematical models and each model designed based on these criteria. In the third step of multistage decision model the model s criteria could be maximizing the benefit of the company and the optimal generation program inside the critical constraints. In addition, based on the experience and available historical data it is possible to provide some required technical information, which can be considered as an input data. In this model the input data could be categorized in 3 groups, a) technical characteristic of each thermal unit and their operational cost, b) available resources like amount of gas,c) the electricity Price which is estimated in the first step. These three groups are explained in the following parts: 67

80 Technical characteristic of thermal units A combined cycle is characteristic of a power producing engine or plant that employs more than one thermodynamic cycle. Heat engines are only able to use a portion of the energy their fuel generates (usually less than 50%). The remaining heat from combustion is generally wasted. Combining two or more "cycles", such as the Brayton cycle and Rankine cycle, results in improved overall efficiency. In a combined cycle power plant (CCPP), or combined cycle gas turbine (CCGT) plant, a gas turbine generator generates electricity and the waste heat is used to make steam to generate additional electricity via a steam turbine; this last step enhances the efficiency of electricity generation. Most new gas power plants in North America and Europe are of this type. In a thermal power plant, high temperature heat as input to the power plant, usually from burning of fuel, is converted to electricity as one of the outputs and low temperature heat as another output. As a rule, in order to achieve high efficiency, the temperature difference between the input and output heat levels should be as high as possible (see Carnot efficiency). This is achieved by combining the Rankine (steam) and Brayton (gas) thermodynamic cycles. Such an arrangement used for marine propulsion is called Combined Gas (turbine) And Steam (turbine) (COGAS). Each thermal unit has its own technical characteristics that have effects on outputs of unit. These characteristics are explained bellow: Gross and net power All plants in house facilities consume power that is taken directly from the plant generator, only part of the gross power produced is fed to the grid. The terms gross power and net power are generally used to distinguish between the power produced at the generator output terminals and the power available at the power plant bars, after deducting the internal load (usage). These two parameters are generally related via a coefficient K, known as the auxiliary load factor, as following 2 : Net power= Gross power*k If we have historical data just base on net power then it is not necessary to consider the coefficient K in the calculation. 2 In the company where the project is implemented, all data are base on the net power.input-output curve (efficiency curve) is also defined based on the net power, so all quantities are considered as the net power. 68

81 Upper and lower output limits Thermal set cannot produce power above their maximum capacity or below their minimum stable load. The existence of a maximum standard capacity (nominal) is a result of the design of the thermal unit itself. The minimum stable load is the outcome of combustion stability requirement in the boiler as well as to steam generator constraint. Ramping constraint Ramping constraints, which limit the capability of units to change production over short periods of time, can have an important impact on the short term generation scheduling. Large, efficient thermal units frequently have significant ramp limits. If the difference in system load in successive periods exceed the ramp limits of efficient units, those which are not significantly ramp limited gain additional value because of their ability to match the rapidly changing load. Such load following generation units are smaller (and less efficient) coal fired and oil fired thermal units, gas turbines, and especially hydro units. Moreover, ramping limits may also constrain the contributions of some units to spinning reserve and operating reserves. Therefore, an accurate modeling of ramping limitations is fundamental to achieve feasible as well as efficient schedules. According to the actual energy production process, the power output of an electric power unit is restricted by three kinds of ramp constraints (Javier Garcia Gonzalez, 2007). 1) Operating ramp constraints, also known as ramp up and ramp down rate limits. The increment or decrement of the generation level of a unit over any two successive online periods (except start up and shut down periods) is bounded by the ramp up (RU) and ramp down (RD) limits, respectively.in other word it shows the variation limit in power output in two consecutive periods. 2) Start up ramp constraint, which involves an increasing power trajectory. When a unit (that is off line) is started up, it should follow an increasing power trajectory from 0 to the minimum power output,during start up time periods, being the pre specified power output (data) in start up period i. 3) Shut down ramp constraint, which involves a decreasing power trajectory. When a unit (that is on line) is shut down, its generation level should be reduced to the minimum power output, subject to the operating ramp constraints defined above. Then, it should follow a shut down decreasing power trajectory during shutdown periods. 69

82 Minimum shut down and operating time characteristic This type of characteristics require for thermal units to remain on or off for certain number of hours after start up or shut down before being shut down or start up again. The aim is to prevent boiler wear and damage caused by changes in temperature Thermal generation cost The costs associated with thermal set operation consist of production cost, start up cost, and shutdown cost. The operation cost itself consists of the fuel cost and maintenance cost. In short term operation model the fuel cost is generally expected as a quadratic function of output and it is necessary to define the input output curve for calculating the fuel consumption and cost. The characteristic input output curve (efficiency of each thermal unit) that relate gross output to consumption in fuel may vary depend on the plant technology (coal, fuel oil, gas, CCGT). Efficiency of thermal unit The combustion turbine s energy conversion typically ranges between 25% to 35% efficiency as a simple cycle. The simple cycle efficiency can be increased by installing a recuperator or waste heat boiler onto the turbine s exhaust. A recuperator captures waste heat in the turbine exhaust stream to preheat the compressor discharge air before it enters the combustion chamber. A waste heat boiler generates steam by capturing heat form the turbine exhaust. These boilers are known as heat recovery steam generators (HRSG). They can provide steam for heating or industrial processes, which is called cogeneration. Highpressure steam from these boilers can also generate power with steam turbines, which is called a combined cycle (steam and combustion turbine operation). Recuperators and HRSGs can increase the combustion turbines overall energy cycle efficiency up to 80%. One way to calculate the efficiency of each thermal unit is using the historical data of net output power and its corresponded gas consumption for drying the Input output curve. This curve could present the net output powers [MW] correspond to consumption of Gas fuel [MW] and can be used to find the fuel expenditure corresponding to a certain output. In the proposed model we simplified this non linear function into linear (add curve) Maintenance cost Maintenance cost are generally regarded to depend linearly on the gross output [(O&M) Og [ /MWh]]. It could also define in another way for instance depend on equivalence operation 70

83 hour (EOH) which means it calculated based on hours generators produce electricity and it is not depend on production amount. The fuel price The main fuel in thermal units is Gas and the price of the Gas is determined in the market so it is vary from period to period and depend on market price but its changes during the month is not significant and we could consider it as an input constant value. In the gas model it is not necessary to consider it. In other word if we consider the zero value for it then the marginal value of the gas (shadow price of fuel balance equation) minuses the gas price in the market is equal to gas added value for producing electricity. Start up cost Start up cost Reflects the fuel consumption needed to reach the optimal conditions of temperature (T) and pressure (P) in the boiler. This fuel consumption is needed to reach a suitable boiler temperature and pressure. Since such start up cost obviously depend on initial thermal unit conditions, they maybe expressed in terms of an exponential function on the time the unit has been shut down. Figure 6: start up function In the proposed model we simplified this non linear function into linear. In fact the start up cost is related to start up ramp. In the startup period the efficiency of the thermal unit is different from normal condition. Each thermal plant consumes extra fuel (Gas) and produces the power with specific efficiency during the start up period in order to reach the base load level. This extra gas consumption could be considered as start up cost. It is easy to estimate this efficiency curve for each plan by analyzing the historical data. In some company there is also a fix start up cost per start up which we could add it in the model as a fix cost per start up decision. Shutdown cost Shutdown cost represents the amount of unburned fuel that goes to waste when a decision is made to shut down the generator set this cost usually consider as a fix and constant value. 71

84 There is another shut down opportunity which is related to shut down ramp. In the shutdown period, the efficiency of thermal units is different from normal condition but it still produces electricity. The company could earn revenue by selling this amount of production. The average production and the efficiency curve during this shutdown period could be calculated by analyzing the historical data. Factor Emission Each thermal unit consumes gas and produce CO2 emissions. There is a penalty in the market because of producing the co2 emission (Cp [ /ton]). This cost is also an input data. Factor emission ([ton/ MWHpcs]) times co2 cost ([ /ton]) is equal to co2 cost for each unit of gas consumption. THIRD PARTY ACCESS COST (ATR ) Another Input data is ATRg ([ /MWh_PCS]) cost. This cost is the amount of money that the company pays to Gas suppliers /system, for getting access to the gas network; it is paid per MWh_PCS and is different for each thermal Plant. Initial amount of Gas and its Price In the gas model the total amount of available gas (GAS) for producing the electricity is fixed in each time of running the model but the idea is defining specific range for the gas with the maximum and minimum limits then run the gas model for different quantity of the gas inside the predefined range, which means run the model for minimum limit of the gas then increase it with small changes and again run the model and record the marginal value of gas for relevance quantity then continue this procedure up to maximum limit of the gas inside the range. The company could compare these marginal valu with gas price in its market and allocate the optimal quantity of gas for each market. Electricity Price Electricity price (EP p [ /MWh]) is an input data which is calculated in the first step (part 3.2), this price is calculated at the first of each month pare hour for each day and it could be updated during the month by using the new market data State Variables, objective function, In the proposed model the state variables are the generation power: q pg Power generated in period p with thermal plant g [MW]. Start up and shut down decision variables or unit 72

85 commitment decision: u pg Commitment state of thermal plant t in period p (0, 1), y pg Startup decision in thermal plant g at the beginning of period p (0, 1), z pg Shutdown decision in thermal plant t at the beginning of period p. In addition it is possible to consider the state variables like: c p Operational cost in period p [ ] or fuel consumption Q g. The objective function is the maximization of benefit in electricity market by considering the revenue and the operation cost. So the total benefit is equal to Revenue minus the total production cost witch defined in previous part Model formula In this optimization model there are some constraints which are related to limited resources and time. This part describes these constraints Objective function The objective function is the maximization of benefit in electricity market by considering the revenue and the operation cost. Maximize π = Revenue [ ] cost [ ] Revenue [ ] itself is equal to Electricity price in each period (EP p ) multiplied by power produce (q gp ) in each period (p) by each thermal plant (g). Revenue [ ] = [ /MWh]* [MWh] Total Operation Cost [ ] consist of two parts. The first part depends on amount of gas consumption and power production but the second part does not depend on gas consumption. The first part is equal to total cost per unit of gas consumption multiplied by gas consumption but we can eliminate this amount and just consider it zero. In this case the shadow price of the fuel balance equation shows the gas added value and its price together. Total cost per unit of gas consist of the cost for getting access to the gas network for each plant (ATR g, [ /MWhpcs]) plus emission cost which is Factor emission (FE g, [ton/mwhpcs]) multiplied by Co2 cost (CO, [ /ton]). The total amount of gas consumption is calculated by using the Input Output (efficiency) curve. The characteristic input output curve (efficiency of each thermal unit) that relate gross output to consumption in fuel vary depend on the plant technology (coal, fuel oil, gas, CCGT). In short term operation model the fuel cost is generally expected as a quadratic function of output. We use the historical data of net power output and the corresponded 73

86 gas consumption in the case company in order to draw this curve. The result shows the linear relation between gas consumption and power generation 3. B g is the fix term of the input output (efficiency) curve [MWhpcs] and α g is the linear term of the input output (efficiency) curve [MWhpcs/ MWh]. The second part of the cost is equal to start up cost for each plant (γ g ) multiplied by start up decision in each period for each plant (y pg ) plus shutdown cost for each plant (θ g ) multiplied by shutdown decision in each period for each plant (Z gp ) and pluse operation cost for each plant (O g ) multiplied by working hour of each plant (U gp ) Model Constraints In this part all model technical constraints will be explained. Fuel balance equation Total amount of Gas which is available for consuming in thermal units (GAS) for producing electricity during the specific period is fixed and predetermined in step two, so the total amount of gas consumption which is calculated by using the linear input output curve(part ) should be lower than total amount of available gas (GAS) during the given period. The following constraint is defined in order to satisfy this condition: Where p is a period, g is a generator, β g is a fix term of the input output (efficiency) curve [MWhpcs], α g is a Linear term of the input output (efficiency) curve [MWhpcs/ MWh], q gp is a Power produced by thermal plant g in period p, U gp is a Commitment decision variable (0, 1) and finally GAS is a available amount of gas for intra period. Upper and lower output limits Thermal set cannot produce power above their maximum capacity or below their minimum stable load. 3 In fact it is not linear but we consider the linear approximation 74

87 A binary variable, U gp, is introduced the thermal unit connection or disconnection.the variable adapt the value of one when unit g connected in period p, otherwise it is zero. When the thermal unit is connected (after the start up and before the shutdown ramp period) its output only adapts values within the minimum stable load (qmin g ) and its maximum capacity (qmax g ). The following constraint is defined in order to satisfy this condition. If the working condition (U gp ) is equal to zero then the output power should be zero otherwise it should be between the Maximum and minimum limits. In order to define the ramp constraint another variable could be defined to make the deference between the production in the ramp period and other period.this variable is defined as follow: Or q gp is the power above the minimum stable load. This formulation is very useful to split the input output curve or define the start up and shutdown ramp. Maintenance program The maintenance program could be included in the model by simply setting the connection variable (unit commitment decision variable) is equal to zero during the maintenance period. If is the set of period in which unit t is unavailable for maintenance, the constraint could be defined as follow: Ramp up and down constraint These constraints, also known as load gradient constraints, limit the variations in power output in two consecutive periods. The ramping up and down constraints is formulated as bellow: 75

88 Start up and shutdown ramp constraint There is start up cost which is related to start up ramp. In the startup period the efficiency of the thermal unit is different from normal condition. In order to reach the base load level, during this start up period the thermal unit consume fuel (Gas) with specific efficiency. The startup duration depends on the shut down duration before start up decision. In the case study at the company if the shot off duration is less than 8 hours then start of period is 2 hours with the average power production of OU1, if the shot off duration is less than 47 and more than 8 hours then the start up duration is 3 hours with the average production of ou2 and finally if the shot off duration is between 47 and 72 hours then the start up duration is 3 hours with the average power production of ou3. The following constraints describe this start up condition. If DFg 8 then Sg =2 ; OUig = ou1 else If 8 DFg 47 then Sg =3 ; OUig = ou2 else If 47 DFg 72 then Sg =3 ; OUig = ou3 else Sg =3 ; OUig = ou4 End If. If ygp =1 then DFg =0 else DFg = DFg =1 End If. This way of defining the start up and shutdown ramp is not linear. In order to simplify the model we define it in a linear way as follow. By analyzing the historical data, in the company as a case study, we have just considered 3 hours for startup ramp in all plant without considering the shutdown duration before start up, and one hour for shutdown ramp. This assumption doesn t have huge effect on the result because the shutdown duration more than 47 hours is seldom so it will happen just in the fundamental maintenance problem. 76

89 We define Rmax gp and Rmin gp for each plant in each period to show the maximum and minimum limit of power production. The following constraint is defined in order to satisfy this condition. Where s is equal to 3 hours for startup ramp If we define Rmax and Rmin by using the above formula then it is not necessary to consider the Upper and lower output limits constrains: Logic coherence start up, commitment and shutdown constraint The following constraint represents the relation between, start up (y pg ), shutdown (Z pg ) and unit commitment (U pg ) decision variables: Minimum shut down and operating time characteristic This type of constraints requires for thermal units to remain on or off for certain number of hours after startup or shut down before being shut down or start up again. The aim is to prevent boiler wear and damage caused by changes in temperature. It could be formulated linearly with the binary variables which relate start up and shut down decision to connection status when τg is defined as the minimum shut down time for set g and Ωg as minimum operating time: 77

90 Start up limit Sometimes there is a limit for startup decision, for instance to limit the number of startup per day in each thermal plant or to limit the time for start up the plant in each day (for instance we cannot turn on the plant after 4 PM in each day). These kinds of constrains could be present as follow: Where P is the first period of each day, which means this constrain is define for each day. The first constrain shows that, the total number of starts per day should be lower than 3 times. And the second constrain shows there isn t any start up after specific hour of each day (RI), Daily benefit Each thermal unit starts to produce electricity just in the condition that the profit for day is positive otherwise it will not generate. The following constraint presents this condition Model Outputs In this step we are interested to know b) the added Value of the gas by allocating one extra unit of gas for producing the electricity in order to do the tradeoff between producing the electricity and selling the gas in the gas market. 78

91 3.4.6 Design of the Tool In order to implement the mathematical model we need to design a tool. GAMS is a good software for simulating and running the optimization model but it doesn t have a good interface. It is possible to make a connection between GAMS and excel so excel could be a good interface. We simulate the objective function and all defined constrains in GAMS. It is very easy to translate these mathematical equations in to the GAMS format. In this part the structure of the designed tool will be explained which is consisting of three parts: Modification of input data, running the model and finally getting and analyzing the result Modification of input data The proposed model has several input data (part ). It is necessary to import all these data before running the model in GAMS. It is very easy to write all these data in the excel file so we define a specific range in Excel sheet for writing and saving the input data and we call this excel sheet INPUT_DATA (figure 7). 79

92 Figure 7: excel sheet INPUT_DATA The input data which we record in the excel sheet consist of: the minimum and the maximum range of gas consumption and the step for increasing it in each step. the name of each thermal plants, specific period that we want to run the model for instance from 3/3/2009 to 15/3/2009,availability of each plant for each day (maintenance program), The minimum shut down time, the minimum operating time, shutdown cost [ per shutdown], Electricity Price in period P [ /MWh], slope Coefficient of input output (Efficiency) curve [MWhPCS/MWh], Vertical axes intercept of input output (Efficiency) curve [MWhPCS], Fixed START UP COST[ per start up], Maximum out power of generator g [MW], Minimum out power of generator g in the base load [MW], fuel cost (Gas Price)[ /MWhPCS] if we like or set it zero, factor emission [ton/mwhpcs], Operation & maintenance cost [ per hour], Cost for getting access to the gas network [ /MWhPCS], generation in shutdown ramp [MW], generation in the first hour of startup ramp [MW], generation in the second hour of startup ramp [MW], generation in the second hour of startup ramp [MW], CO2 cost [ /Ton]. Next step after recording all data in the excel sheet is exporting them with the specific format which is readable for GAMS. One of the best format is the INC format because it is easy to export the excel file to INC format and also it is very easy to Import them in the GAMS file. We define the write data() module in excel worksheet for exporting the data from excel sheet to INC file format. 80

93 Running the Model After importing the input data, which is the initial step, we should run the GAMS model. In order to run the model we define another excel sheet in the same worksheet and we call it RUN_ GAMS. In this sheet first we should write three important data. The first one is the route where we install the GAMS software; the second one is the route where we save the GAMS file and finally its name. We define a module FinalExecution() in this excel sheet in order to run the GAMS File. After activating this module just by pressing a simple button which is design in the excel sheet, GAMS start to run. After running the model GAMS could easily read all input data from INC file just by using the simple code which is $INCLUDE MAGAS_DAT.INC.In this way we could import all input data from INC file in to the GAMS file (figure 8). Figure 8: the excel sheet of running the model After running the GAMS model, it will provide all results. This result should save in the specific format which could be read able for excel. We can use a simple code which is $INCLUDE MAGAS_RES.INC to export and save the result in the INC file format. Finally at the end of this step we have the result of optimization model in INC file format Getting and analyzing the result 81

94 After running the model and saving the result in INC file, we should import them in the excel sheet. We define another excel sheet for this purpose in the same worksheet and we call it RESULT. In this sheet we define another module ImportResultdata() in order to Import the result from INC File. After activating this module just by pressing a simple button which is design in the excel sheet, all results will import to the excel sheet in the predetermined range. Results consist of the Marginal value of gas, gas consumption, available amount of gas and the benefit for each level of gas picture shows this interface Size of the model Figure 9: Import data excel sheet as an interface In order to determine the size of the model, the number of variables and constrains should be determined. The gas model is run just for one month, in the one month model, there are 744 period (hour ) and 9 thermal plants, 2 variables per period and per thermal plants, 2 binary variables again per period and per thermal plants, 3 free variables and 2 variables per period. The total numbers of variables are by adding all together. 82

95 The model consist of several constrains, 6 constrains per period per thermal plants, 2 constrains per period and 4 free constrains, which means the total number of constrains are equal to The gas model runs for several quantity of gas. The running duration for each quantity is 45 second but if it runs for 10 replications then the running duration will increase more or less to 10 minutes. This model also runs for 19 thermal plants instead of 9 thermal plants but in general the total running duration significantly depends on number of replication. 3.5 Step three: Optimal schedule of electricity production The third step of the proposed model is the calculation of the optimal electricity production schedule. In this stage first we propose the mathematical model for calculating the production schedule, start up and shutdown decision for each thermal plant and then we design a tool in order to use and implement this model in a user friendly way Objective In the short term, intervals ranging from one week to one month, decision makers are faced with the problem of optimal hourly scheduling for thermal plant. In the competitive market this problem is more complicated. Set start up and shutdown decisions are impact by the shape of the electricity demand curve over the time. The demand curve considered in the first step in order to estimate the electricity price so here we will consider the electricity price during the specific period instead of demand curve to calculate the optimal schedule of electricity production. The objective of monthly model, therefore, is to obtain an hourly schedule for each thermal power plant so as to meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. Monthly scheduling models cover: Generating set operation, including startup and shout down decisions and provisional hourly scheduling for all generator set. Economic considerations, with operating and marginal cost forecasting. It is possible to run the model for more than one month in case of significant CPU time. When the model become bigger and bigger then it is not easy to solve it in the short CPU time. 83

96 The possible techniques for solving the problem, as described in the literature, are reviewed briefly below Model approach The third step is the single firm optimization problem (part ) in which the objective function is to maximize expected profits and the decisions, such as production schedule, are required to meet technical characteristics and operating constraints such as capacity limits. The outputs of the first stage electricity price and the second stage available quantity of gas are input data for this step. The most important model s characteristic is that the electricity price is estimated by using another tool in the first stage, which means price is an exogenous variable for third stage so in order to solve the problem the levels of market modeling which represents the price clearing process as exogenous to the firm s optimization program is needed. Consequently, as the price is fixed, the market revenue price times the firm s production becomes a linear function of the firm s production, which is the main decision variable in this approach. In view of that, traditional Linear Programming (LP) and Mixed Integer Linear Programming (MILP) techniques can be employed to obtain the solution of the model. In conclusion, the optimization model with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue is proposed to calculate the hourly schedule of electricity production for each plant, taking in to account the technical characteristic of thermal plants and limited gas fuel Representing time A chronological time chart is requisite to weekly modeling to incorporate the effect of timewise interconnections 4 (thermal set ramping up and down, start up and shutdown flexibility and so on) Figure 10: chronological representation of time Although the intervals used in this model are hourly, when a large scale generating system is to be modeled the size of the problem can be reduced by grouping consecutive hours with 4 The notion of time wise interconnection means that the value adopted by decision variables in one hour affects the value that these same or other variables may adopt in subsequent hour. Before producing at full capacity, for instance, allowance must be made for the time needed to raise output, a necessarily gradual process. 84

97 the similar characteristics. In such cases, periods may have a variable duration Javier Garcia Gonzalez, 2007) Model assumptions The model assumptions are: We just consider one firm in optimization model The transmission grid is not included in the model That is called the single node approach We just consider the combined-cycle plants in the model The chronological evolution of the system hour by hour must be modeled. The time wise representation of hourly period is used A thermal set is not allowed to start up shut off at any time of day An uncertainty is not considered, a deterministic approach is used The Constant start up duration for startup ramp The efficiency curve (input output curve)for each thermal plant is considered as linear function Model structure In order to build the Mathematical model it is necessary to know: what are the input data and criteria, which kinds of constraints does the system have, what are the interested outputs and result, finally what are the objective function, decision and state variables inside the model. In the following parts these four items will be explained Input data and criteria There are some criteria in all mathematical models and each model designed based on these criteria. In the third step of multistage decision model the model s criteria could be maximizing the benefit of the company and the optimal generation program inside the critical constraints. In addition, based on the experience and available historical data it is possible to provide some required technical information, which can be considered as an input data. In this model the input data could be categorized in 3 groups, a) technical characteristic of each thermal unit and their operational cost, b) available resources like amount of gas and its value, c) the electricity Price which is estimated in the first step. These three groups are explained in the following parts: 85

98 Technical characteristic of thermal units As explained before, a combined cycle is characteristic of a power producing engine or plant that employs more than one thermodynamic cycle. Heat engines are only able to use a portion of the energy their fuel generates (usually less than 50%). The remaining heat from combustion is generally wasted. Combining two or more "cycles", such as the Brayton cycle and Rankine cycle, results in improved overall efficiency. In a combined cycle power plant (CCPP), or combined cycle gas turbine (CCGT) plant, a gas turbine generator generates electricity and the waste heat is used to make steam to generate additional electricity via a steam turbine; this last step enhances the efficiency of electricity generation. Most new gas power plants in North America and Europe are of this type. In a thermal power plant, high temperature heat as input to the power plant, usually from burning of fuel, is converted to electricity as one of the outputs and low temperature heat as another output. As a rule, in order to achieve high efficiency, the temperature difference between the input and output heat levels should be as high as possible (see Carnot efficiency). This is achieved by combining the Rankine (steam) and Brayton (gas) thermodynamic cycles. Such an arrangement used for marine propulsion is called Combined Gas (turbine) And Steam (turbine) (COGAS). Each thermal unit has its own technical characteristics that have effects on outputs of unit. These characteristics are explained bellow: Gross and net power All plants in house facilities consume power that is taken directly from the plant generator, only part of the gross power produced is fed to the grid. The terms gross power and net power are generally used to distinguish between the power produced at the generator output terminals and the power available at the power plant bars, after deducting the internal load (usage). These two parameters are generally related via a coefficient K, known as the auxiliary load factor, as following 5 : Net power= Gross power*k If we have historical data just base on net power then it is not necessary to consider the coefficient K in the calculation. 5 In the company where the project is implemented, all data are base on the net power.input-output curve (efficiency curve) is also defined based on the net power, so all quantities are considered as the net power. 86

99 Upper and lower output limits Thermal set cannot produce power above their maximum capacity or below their minimum stable load. The existence of a maximum standard capacity (nominal) is a result of the design of the thermal unit itself. The minimum stable load is the outcome of combustion stability requirement in the boiler as well as to steam generator constraint. Ramping constraint Ramping constraints, which limit the capability of units to change production over short periods of time, can have an important impact on the short term generation scheduling. Large, efficient thermal units frequently have significant ramp limits. If the difference in system load in successive periods exceed the ramp limits of efficient units, those which are not significantly ramp limited gain additional value because of their ability to match the rapidly changing load. Such load following generation units are smaller (and less efficient) coal fired and oil fired thermal units, gas turbines, and especially hydro units. Moreover, ramping limits may also constrain the contributions of some units to spinning reserve and operating reserves. Therefore, an accurate modeling of ramping limitations is fundamental to achieve feasible as well as efficient schedules. According to the actual energy production process, the power output of an electric power unit is restricted by three kinds of ramp constraints. a. Operating ramp constraints, also known as ramp up and ramp down rate limits. The increment or decrement of the generation level of a unit over any two successive on line periods (except start up and shut down periods) is bounded by the ramp up (RU) and ramp down (RD) limits, respectively.in other word it shows the variation limit in power output in two consecutive periods. b. Start up ramp constraint, which involves an increasing power trajectory. When a unit (that is off line) is started up, it should follow an increasing power trajectory from 0 to the minimum power output,during start up time periods, being the pre specified power output (data) in start up period i. c. Shut down ramp constraint, which involves a decreasing power trajectory. When a unit (that is on line) is shut down, its generation level should be reduced to the minimum power output, subject to the operating ramp constraints defined above. Then, it should follow a shut down decreasing power trajectory during shutdown periods [1]. Minimum shut down and operating time characteristic 87

100 This type of characteristics require for thermal units to remain on or off for certain number of hours after start up or shut down before being shut down or start up again. The aim is to prevent boiler wear and damage caused by changes in temperature Thermal generation cost The costs associated with thermal set operation consist of production cost, start up cost, and shutdown cost. The operation cost itself consists of the fuel cost and maintenance cost. In short term operation model the fuel cost is generally expected as a quadratic function of output and it is necessary to define the input output curve for calculating the fuel consumption and cost. The characteristic input output curve (efficiency of each thermal unit) that relate gross output to consumption in fuel may vary depend on the plant technology (coal, fuel oil, gas, CCGT). Efficiency of thermal unit The combustion turbine s energy conversion typically ranges between 25% to 35% efficiency as a simple cycle. The simple cycle efficiency can be increased by installing a recuperator or waste heat boiler onto the turbine s exhaust. A recuperator captures waste heat in the turbine exhaust stream to preheat the compressor discharge air before it enters the combustion chamber. A waste heat boiler generates steam by capturing heat form the turbine exhaust. These boilers are known as heat recovery steam generators (HRSG). They can provide steam for heating or industrial processes, which is called cogeneration. Highpressure steam from these boilers can also generate power with steam turbines, which is called a combined cycle (steam and combustion turbine operation). Recuperators and HRSGs can increase the combustion turbines overall energy cycle efficiency up to 80%. One way to calculate the efficiency of each thermal unit is using the historical data of net output power and its corresponded gas consumption for drying the Input output curve. This curve could present the net output powers [MW] correspond to consumption of Gas fuel [MW] and can be used to find the fuel expenditure corresponding to a certain output. In the proposed model we simplified this non linear function into linear (add curve) Maintenance cost Maintenance cost are generally regarded to depend linearly on the gross output (O&M) Og [ /MWh]. It could also define in another way for instance depend on equivalence operation hour (EOH) which means it calculated based on hours generators produce electricity and it is not depend on production amount. The fuel price 88

101 The main fuel in thermal units is Gas and the price of the Gas is determined in the market so it is vary from period to period and depend on market price but its changes during the month is not significant and we could consider it as a constant value in input data. Start up cost Start up cost Reflects the fuel consumption needed to reach the optimal conditions of temperature (T) and pressure (P) in the boiler. This fuel consumption is needed to reach a suitable boiler temperature and pressure. Since such start up cost obviously depend on initial thermal unit conditions, they maybe expressed in terms of an exponential function on the time the unit has been shut down. Figure 11: start up function In the proposed model we simplified this non linear function into linear. In fact the start up cost is related to start up ramp. In the startup period the efficiency of the thermal unit is different from normal condition. Each thermal plant consumes extra fuel (Gas) and produces the power with specific efficiency during the start up period in order to reach the base load level. This extra gas consumption could be considered as start up cost. It is easy to estimate this efficiency curve for each plan by analyzing the historical data. In some company there is also a fix start up cost per start up which we could add it in the model as a fix cost per start up decision. Shut down cost Shutdown cost represents the amount of unburned fuel that goes to waste when a decision is made to shut down the generator set this cost usually consider as a fix and constant value. There is another shut down opportunity which is related to shut down ramp. In the shutdown period, the efficiency of thermal units is different from normal condition but it still produces electricity. The company could earn revenue by selling this amount of production. The average production and the efficiency curve during this shutdown period could be calculated by analyzing the historical data. Factor Emission Each thermal unit consumes gas and produce CO2 emissions. There is a penalty in the market because of producing the co2 emission (Cp [ /ton]). This cost is also an input data. 89

102 Factor emission ([ton/mwhpcs]) times CO2 cost ([ /ton]) is equal to CO2 cost for each unit of gas consumption. Third party access cost (ATR COST) Another Input data is ATRg ([ /MWhPCS]) cost. This cost is the amount of money that the company pays to Gas suppliers/system, for getting access to the gas network; it is paid per MWhPCS and is different for each thermal Plant. Initial amount of Gas and its Price Total amount of available gas (GAS) for producing electricity in market is fixed for each month and is determined in the second step. The initial estimation of Gas price (GP [ /MWhpcs]) is an input data which is determined by expertise in the company but the uncertainty about this initial estimation is high so it is risky to consider it as a fixed input value. The different scenarios based on the different gas price will be defined in order to manage and threat this high degree of uncertainty about gas price. Electricity Price Electricity price (EP p [ /MWh]) is an input data which is calculated in the first step (part 3.2), this price is calculated at the first of each month pare hour for each day and it could be updated during the month by using the new market data Decision and state Variables, objective function, In the proposed model the decision variables are the generation power: q pg Power generated in period p with thermal plant g [MW]. Start up and shut down decision variables or unit commitment decision: u pg Commitment state of thermal plant t in period p (0, 1), y pg Startup decision in thermal plant g at the beginning of period p (0, 1), z pg Shutdown decision in thermal plant t at the beginning of period p. In addition it is possible to consider the state variables like: c p Operational cost in period p [ ] or fuel consumption Q g. The objective function is the maximization of benefit in electricity market by considering the revenue and the operation cost. So the total benefit is equal to Revenue minus the total production cost defined in previous part. 90

103 Model formula In this optimization model there are some constraints which are related to limited resources and time. This part describes these constraints Objective function The objective function is the maximization of benefit in electricity market by considering the revenue and the operation cost. Maximize π = Revenue [ ] cost [ ] Revenue [ ] itself is equal to Electricity price in each period (EP p ) multiplied by power produce (q gp ) in each period (p) by each thermal plant (g). Revenue [ ] = [ /MWh]* [MWh] Total Operation Cost [ ] consist of two parts. The first part depends on amount of gas consumption and power production but the second part does not depend on gas consumption. The first part is equal to total cost per unit of gas consumption multiplied by gas consumption.total cost per unit of gas itself consist of Gas price (GP, [ /MWhPCS]) per unit of gas plus cost for getting access to the gas network for each plant (ATR g, [ /MWhPCS]) plus emission cost which is Factor emission (FE g, [ton/mwhpcs]) multiplied by CO2 cost (CO, [ /ton]). The total amount of gas consumption is calculated by using the Input Output (efficiency) curve. The characteristic input output curve (efficiency of each thermal unit) that relate gross output to consumption in fuel vary depend on the plant technology (coal, fuel oil, gas, CCGT). In short term operation model the fuel cost is generally expected as a quadratic function of output. We use the historical data of net power output and the corresponded gas consumption in the case company in order to draw this curve. The result shows the linear relation (is not exactly linear, we consider an approximation) between gas consumption and power generation. B g is the fix term of the input output (efficiency) curve [MWhPCS] and α g is the linear term of the input output (efficiency) curve [MWhpcs/MWh]. The second part of the cost is equal to start up cost for each plant (γ g ) multiplied by start up decision in each period for each plant (y pg ) plus shutdown cost for each plant (θ g ) multiplied by shutdown decision in each period for each plant (Z gp ) and plus operation cost for each plant (O g ) multiplied by working hour of each plant (U gp ). 91

104 Model Constraints In this part all model technical constraints will be explained. Fuel balance equation Total amount of Gas which is available for consuming in thermal units (GAS) for producing electricity during the specific period is fixed and predetermined in step two, so the total amount of gas consumption which is calculated by using the linear input output curve(part ) should be lower than total amount of available gas (GAS) during the given period. The following constraint is defined in order to satisfy this condition: Where p is a period, g is a generator, β g is a fix term of the input output (efficiency) curve [MWhPCS], α g is a Linear term of the input output (efficiency) curve [MWhPCS/MWh], q gp is a Power produced by thermal plant g in period p, U gp is a Commitment decision variable (0, 1) and finally GAS is a available amount of gas for intra period. Upper and lower output limits Thermal set cannot produce power above their maximum capacity or below their minimum stable load. A binary variable, U gp, is introduced the thermal unit connection or disconnection.the variable adapt the value of one when unit g connected in period p, otherwise it is zero. When the thermal unit is connected (after the start up and before the shutdown ramp period) its output only adapts values within the minimum stable load (qmin g ) and its maximum capacity (qmax g ). The following constraint is defined in order to satisfy this condition. If the working condition (U gp ) is equal to zero then the output power should be zero otherwise it should be between the Maximum and minimum limits. In order to define the ramp constraint another variable could be defined to make the deference between the production in the ramp period and other period.this variable is defined as follow: Or 92

105 q gp is the power above the minimum stable load. This formulation is very useful to split the input output curve or define the start up and shutdown ramp. Maintenance program The maintenance program could be included in the model by simply setting the connection variable (unit commitment decision variable) is equal to zero during the maintenance period. If is the set of period in which unit t is unavailable for maintenance, the constraint could be defined as follow: Ramp up and down constraint These constraints, also known as load gradient constraints, limit the variations in power output in two consecutive periods. The ramping up and down constraints is formulated as bellow: Start up and shut down ramp constraint There is start up cost which is related to start up ramp. In the startup period the efficiency of the thermal unit is different from normal condition. In order to reach the base load level, during this start up period the thermal unit consume fuel (Gas) with specific efficiency. The startup duration depends on the shut down duration before start up decision. In the case study at the company if the shot off duration is less than 8 hours then start of period is 2 hours with the average power production of OU1, if the shot off duration is less than 47 and more than 8 hours then the start up duration is 3 hours with the average production of ou2 and finally if the shot off duration is between 47 and 72 hours then the start up duration is 3 hours with the average power production of ou3. The following constraints describe this start up condition. If DFg 8 then Sg =2 ; OUig = ou1 else If 8 DFg 47 then Sg =3 ; OUig = ou2 else If 47 DFg 72 then Sg =3 ; OUig = ou3 else Sg =3 ; OUig = ou4 End If. If ygp =1 then DFg =0 else DFg = DFg =1 End If. 93

106 This way of defining the start up and shutdown ramp is not linear. In order to simplify the model we define it in a linear way in the following way. By analyzing the historical data we have just consider 3 hours for startup ramp in all plant without considering the shutdown duration before start up, and one hour for shutdown ramp. This assumption doesn t have huge effect on the result because the shutdown duration more than 47 hours is seldom so it will happen just in the fundamental maintenance problem. We define Rmax gp and Rmin gp for each plant in each period to show the maximum and minimum limit of power production. The following constraint is defined in order to satisfy this condition. Where s is 3 (hours) for startup ramp If we define Rmax and Rmin by using the above formula then it is not necessary to consider the Upper and lower output limits constrains: 94

107 Logic coherence start up, commitment and shut down constraint The following constraint represents the relation between, start up (ypg), shutdown (Zpg) and unit commitment (Upg) decision variables: Minimum shut dawn and operating time characteristic This type of constraints requires for thermal units to remain on or off for certain number of hours after startup or shut down before being shut down or start up again. The aim is to prevent boiler wear and damage caused by changes in temperature. It could be formulated linearly with the binary variables which relate start up and shut down decision to connection status when τg is defined as the minimum shut down time for set g and Ωg as minimum operating time: Start up limit Sometimes there is a limit for startup decision, for instance to limit the number of startup per day in each thermal plant or to limit the time for start up the plant in each day (for instance we cannot turn on the plant after 4 PM in each day). These kinds of constrains could be present as follow: Where P is the first period of each day, which means this constrain is define for each day. The first constrain shows that, the total number of starts up per day should be lower than 3 times. And the second constrain shows there isn t any start up after specific hour of each day (RI), Daily benefit 95

108 Each thermal unit starts to produce electricity just in the condition that the profit for day is positive otherwise it will not generate. The following constraint presents this condition Model Outputs The company is interested to know a) the optimum amount of gas which should be assign to each plant for producing electricity (fuel consumption), b) the hourly schedule of each plant and start up shutdown planning, for a given period of time, c) the estimated benefit and added value of each scenario based on gas price and available amount of fuel. The model could easily provide these results Design of the Tool In order to implement the mathematical model we need to design a tool. GAMS is a good software for simulating and running the optimization model but it doesn t have a good interface. It is possible to make a connection between GAMS and excel so excel could be a good interface. We simulate the objective function and all defined constrains in GAMS. It is very easy to translate these mathematical equations in to the GAMs format. In this part the structure of the designed tool will be explained which is consisting of three parts: Modification of input data, running the model and finally getting and analyzing the result Modification of input data The proposed model has several input data (part ). It is necessary to import all these data before running the model in GAMS. It is very easy to write all these data in the excel file so we define a specific range in Excel sheet for writing and saving the input data and we call this excel sheet INPUT_DATA (figure 12). 96

109 Figure 12: Import data excel sheet as an interface The input data which we record in the excel sheet consist of : the name of each thermal plants, specific period that we want to run the model for instance from 3/3/2009 to 15/3/2009,availability of each plant for each day (maintenance program), available amount of gas for intra period [MWhPCS], The minimum shut down time, the minimum operating time, shutdown cost [ per shutdown], Electricity Price in period P [ /MWh], slope Coefficient of input output(efficiency) curve [MWhPCS/MWh], vertical axes intercept of input output (Efficiency) curve [MWhPCS], Fixed START UP COST[ per start up], Maximum out power of generator g [MW], Minimum out power of generator g in the base load [MW], fuel cost (Gas Price)[ /MWhPCS], factor emission [ton/mwhpcs], operation & maintenance cost [ per hour], Cost for getting access to the gas network [ /MWhPCS], generation in shutdown ramp [MW], generation in the first hour of startup ramp [MW], generation in the second hour of startup ramp [MW], generation in the second hour of startup ramp [MW], CO2 cost [ /Ton]. Next step after recording all data in the excel sheet is exporting them with the specific format which is readable for GAMS. One of the best format is the INC format because it is easy to export the excel file to INC format and also it is very easy to Import them in the GAMS file. We define the write data () module in excel worksheet for exporting the data from excel sheet to INC file format. 97

110 Running the Model After importing the input data, which is the initial step, we should run the GAMS model. In order to run the model we define another excel sheet in the same worksheet and we call it RUN_ GAMS. In this sheet first we should write three important data. The first one is the route where we install the GAMS software; the second one is the route where we save the GAMS file and finally its name. We define a module FinalExecution() in this excel sheet in order to run the GAMS File. After activating this module just by pressing a simple button which is design in the excel sheet, GAMS start to run. After running the model GAMS could easily read all input data from INC file just by using the simple code which is $INCLUDE MAGAS_DAT.INC.In this way we could import all input data from INC file in to the GAMS file (figure 13). After running the GAMS model, it will provide all results. This result should save in the specific format which could be read able for excel. We can use a simple code which is $INCLUDE MAGAS_RES.INC to export and save the result in the INC file format. Finally at the end of this step we have the result of optimization model in INC file format. Figure 13: the excel sheet of running the model Getting and analyzing the result After running the model and saving the result in INC file, we should import them in the excel sheet. We define another excel sheet for this purpose in the same worksheet and we call it RESULT. 98

111 In this sheet we define another module ImportResultdata() in order to Import the result from INC File. After activating this module just by pressing a simple button which is design in the excel sheet, all result will import to the excel sheet in the predetermined range. The result consists of power production in each period for each thermal plant (production schedule), benefit of each thermal plant per day, Gas consumption of each thermal plant per day. After importing the result in this excel sheet, we export the production schedule of each plant to separates excel sheets in the same work sheet so we have one sheet for each plant production schedule. It is possible to do extra analysis over these data for instance we calculate the total benefit for working day, Saturday and Sunday separately and also the benefit per gas consumption per day. These kinds of data will help the decision maker to manage both electricity and gas market. Figure 14: excel sheet INPUT_DATA We design the tool for different time horizontal.fist for one month or less with 2 minutes CPU time, then for three month or less with 12 minutes CPU time and finally the model for 6 month with 20 minutes CPU time Size of the model The model is solved by using the mixed integer linear programming based on branch and bound algorithm. In this way of programming, the number of binary variables has a 99

112 significant effect on running duration. In order to solve the model as fast as possible we should reduce the number of binary variables in the model by using the efficient formulas. For presenting the minimum operation and shout down duration we could use formula with several binary variables. Instead of using the formula with several binery variables we use following ones in order to reduce the number of binary variables. Consequently, the running duration decreased significantly. In order to determine the size of the model, the number of variables and constrains should be determined. The Monthly model, consist of 744 periods (hour ) and 9 thermal plants, 2 variables per period and per thermal plants, 2 binary variables again per period and per thermal plants, 3 free variables and 2 variables per period. The total numbers of variables are by adding all together. The model consist of several constrains, 6 constrains per period per thermal plants, 2 constrains per period and 4 free constrains, which means the total number of constrains are equal to The monthly model runs in 45 second and it takes 65 second for reading the data from GAMS and import them in excel. The model is quite fast, especially for one month when the company is interested to running the model several times for checking different changes in parameters and input data. The model for three months, consist of 744*3 periods (hour ) and 9 thermal plants, 2 variables per period and per thermal plants, 2 binary variables again per period and per thermal plants, 3 free variables and 2 variables per period. The total numbers of variables are by adding all together. The model consist of several constrains, 6 constrains per period per thermal plants, 2 constrains per period and 4 free constrains, which means the total number of constrains are equal to

113 This model runs in 12 minutes for running the model and reading the data from GAMS and import them in excel. This time duration is quite good, especially when the company is interested to running the model several times for checking different changes in parameters and input data. Finally the model for 6 months, consist of 744*6 periods (hour ) and 9 thermal plants, 2 variables per period and per thermal plants, 2 binary variables again per period and per thermal plants, 3 free variables and 2 variables per period. The total numbers of variables are by adding all together. The model consist of several constrains, 6 constrains per period per thermal plants, 2 constrains per period and 4 free constrains, which means the total number of constrains are equal to This model runs in 15 to 20 minutes for running the model and reading the data from GAMS and import them in excel. This time duration is also quite good. This model also runs for 19 thermal plants instead of 9 thermal plants but in general the total running duration significantly depends on number of replication. The models are quite fast, especially for one month when the company is interested to running the model several times for checking different changes in parameters and input data. 3.6 Conclusion In this chapter the proposed model, new multi stage production decision model for companies with multi business line gas and Electricity generation in a deregulated market, and the tools for implementing and using the mode were explained. The model consists of three stages: 4. The electricity price forecasting 5. The calculation of the marginal value of the gas 6. The optimal schedule of electricity production In the first stage the hourly electricity price in the market for short term, midterm and long term is estimated by using stochastic model. For this purpose, first we need to estimate the 101

114 average electricity price and then forecast hourly electricity price by considering average electricity price estimation. There are different methods in the literature for average electricity price forecasting. We used MARAPE model for this purpose. This model, which is referred to as the probabilistic production costing model, incorporates the stochastic features of load and generator availabilities (VÁZQ, 05). The objective of this model is to allow the electricity company to evaluate the future evolution of the prices in the market in the middle term, i.e., ranging from one month to four or five years, both quantitatively and qualitatively. In the proposed model the average electricity price is not useful and we need hourly electricity price estimation. We suggest using financial price approach to estimate hourly electricity price by using historical data and average electricity price estimation as an input data. Finally the output of this step is hourly electricity price estimation (part 3.3). The second step of the proposed model is the gas model to calculate the gas marginal value and its optimum allocation for producing the electricity in the electricity market. we proposed the optimization mathematical model to calculate this gas marginal value. The objective of Gas model, therefore, is to obtain optimal allocation of gas for producing the electricity in thermal power plants so as to meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. The main idea is calculating the shadow price of Fuel balance equation, which is the marginal value of gas for producing the electricity or in the other words how much the benefit will change by adding one extra unit of gas for producing the electricity. In this way the company could compare the gas price in the gas market with this marginal value and if this marginal value is higher than the gas price in the gas market then it is better to allocate more gas for producing electricity instead of selling the original gas (part 3.4). The third step of the proposed model is the calculation of the optimal electricity production schedule. In this stage we propose the optimization mathematical model. The objective of this model, therefore, is to obtain an hourly schedule for each thermal power plant so as to meet the system limits at a maximum benefit, maintaining a suitable level of reliability and guaranteeing compliance with system (technical, environmental and regulatory) constraints. The optimization method with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue is proposed to calculate the hourly schedule of electricity production for each plant, taking in to account the technical characteristic of thermal plants and limited gas fuel (part3.5). In order to implement the mathematical model we need to design a tool. GAMS is a good software for simulating and running the optimization model but it doesn t have a good interface. It is possible to make a connection between GAMS and excel so excel could be a good interface. 102

115 The main Idea is to use excel as an interface. The user can import all data in excel sheets and then transfer them from excel sheet into INC file format.gams could easily import and read data from INC file format and also it could export the result into INC file format. After that we can import the result in to excel sheet from INC file format. In this way we designed the tool to implement and use the mathematical model. 4 Model testing Investigating the suitability of a model for intended objective is very crucial part of our model study. We use the available model and methodology for the first step of proposed model electricity price forecasting which is presented by other researcher (CARL, 05), the evaluation of this model had don by authors so it is not necessary to evaluate it again. The new parts of this project are steps two and three in proposed model. We test these two steps by using two methodologies, verification and validation, in order to evaluate the suitability of the proposed model. This chapter consists of two main parts. In part 4.1 the result of testing the step two of proposed model is explained. The result of testing the third step of proposed model is presented in part Step two: Gas Model The second step of proposed model is the gas model in order to calculate the optimal quantity of gas for electricity production. To test this part of the model verification and validation are taken into account. The term verification is used to refer to consistency and validation refers to tests that contribute to building confidence in a model. This chapter consists of four parts. Part shows the reference behavior of the model. Part discusses the verification. Part discusses the validation. Part contains the conclusion Reference behaviour of the model In the first stage of testing the model we draw the reference behavior of the model for gas marginal value. For this purpose we set the input data in the realistic way. The input data consist of data related to the technical characteristic of thermal plants, electricity price and available quantity of Gas. We used the spot price for electricity during March 2008 as the real electricity price. The available gas quantity and technical characteristic of thermal plants are determined by using the historical data and expertise s Idea, who knows the system very well, consequently the uncertainty related to this part of input data is low. The normal behavior by considering a real input data can be seen in figure

116 Figure 15: reference behaviour for Gas Margin The Marginal value increased when the electricity price goes up which means for a good price of electricity, by adding one extra unit of gas the objective function which is the benefit of the company will increased more and by adding more and more gas the marginal value will decrease. The Gas value (marginal value) more depends on the hourly electricity price and available quantity of Gas Verification The verification tests of a model entails whether the model has been coded correctly and consistently. They are aimed solely at the question of whether the model has made the correct transition from concept to verification. Following are the tests that will be performed during verification phase Code check One of the best ways to check whether model has been coded correctly is to isolate sections of model and test them. After that it is necessary to check the equations of the model one by one. This has all been done and no mistakes have been found. This increases confidence in the model Dimension analysis The aim of this test is to check dimensional consistency of model. The units of model correspond with what the variables represents in the real world. Our model has been created with dimensions that correspond to the real world. The list of all these important units is given in the following table. Table 4.1.1: The model parameters 104

117 Parameter q min, q max Γ g ϴ g O g rs g, rb g α g Β g S g OU ig rsu t, rsd t τ g Ω g FE g GP EP p ATR g CO p GAS Rmax gp Rmin gp unit Net maximum and minimum power [MW] Fix Start up cost related to maintenance cost [ / start up] Fix shutdown cost related to maintenance cost [ / shut down] Operation & Maintenance variable cost [ /h] Ramp rate limits (up & down) [MW/h] Linear term of the input output (efficiency)curve [MWhpcs/ MWh] Fix term of the input output (efficiency) curve [MWhpcs] Start up duration of thermal unit [h] The average output of thermal unit g in i th hour of startup ramp [MW] Start up and shutdown Ramp [MW/h] the minimum shutdown time [h] The minimum operating time [h] Emission factor [Ton/MWhpcs] Estimation of gas Price for period [ /MWhpcs] Estimation of Electricity Price in period P [ /MWh] Cost for getting access to the gas network [ /MWhpcs] Co2 cost for each period [ /Ton] Available amount of gas for each month [MWhpcs] Maximum range of production in each period in each plant [MW] Minimum range of production in each period in each plant [MW] Numerical error analysis The proposed methodology for solving the model is the optimization with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue. MILP is based on branch and bound algorithm with discrete variables. For integer and discrete solution we can check whether the solution meets the relative and absolute optimality tolerances or not. There is a termination criteria set by options optcr or optca in GAMS to check these 105

118 tolerances. This option sets a relative termination tolerance for problems containing discrete variables, which means that the solver will stop and report on the first solution found whose objective value is within 100*optcr of the best possible solution. Beside that there is a parameter named GAP in the output file of GAMS which is provide the information about how close obtained solution is to the relaxed solution. In the proposed model we set the optcr option very small (optcr =1e 12) and We tested the model for 12 months during 2008 and the result for gap value during each month was zero which means the solution satisfies the termination criteria Validation During the validation phase the aim is to check both the model structure and model behavior. For checking model structure we have performed a direct extreme condition test and for testing behavior of the model we have performed sensitivity analysis Extreme analysis In this test model is evaluated under extreme conditions. This is done by determining whether the resulting values are plausible when compared to the knowledge of expectations of what would happen in real situation. It is often easier to imagine what could happen in reality under extreme conditions that could happen in reality without extreme conditions. In our research two extreme analysis tests have been done. The first test assumes thermal plants are not available. The model behaves realistic. When thermal plants are not available the hourly production of all plants and the gas margin became zero. Figure 15 shows the reference behavior and figure 16 shows this extreme condition. Figure 16: Extreme condition in the case of non available thermal plants 106

119 The second test assumes the available quantity of gas becomes zero. In this case the electricity production becomes zero but the marginal value of gas is not zero and equal to [ /MWHpcs] which means by adding one unit of gas the company has this opportunity to earn more money and the benefit will increase Sensitivity analysis A sensitivity analysis is designed to determine the elements in the model to which the model is sensitive and that have major influence on the behavior when they are changed. The goal of this test is to find out how sensitive the model is to plausible changes in data. In our research this test is aimed at locating changes in the system that have the desired influence on the system s behavior and in this way it helps in contribution for users to define possible strategy for the company. In this sensitivity analysis we check what kind of affect an increase and decrease of ten percent of every variable has on start up decision in the morning and afternoon. If the change (of the reference variable) is lower than 0.5 % the variable is not sensitive. If the change lies between 0.5 and 2.5 % the variable is marginally sensitive. If the change lies between 5 and 10 percent the variable is moderately sensitive. If the change is higher than 10 % it is extremely sensitive. Two variables have been find that have such a strong effect, that they can be used as steering parameters. These parameters are: Electricity Price Gas Price There is of course always some uncertainty in the values used for each parameter. For most of the parameters however the uncertainty should be higher than 10 percent or even higher to show a significant change in system behavior but the uncertainty about other parameters is not significant because the expertise know the system very well. The result shows the model is sensitive to electricity price and the Marginal value of gas will change by changing the electricity price by 10 %. The behavior of model before and after changes is the same but the values change and they shown in appendix B. When we change the gas price, the gas margin will change but the changes are equal to changes in gas price so its changes could recognize easily. 107

120 4.1.5 Conclusion Several tests have been performed on Gas model. The model has passed them all; therefore it is suitable for its purpose. The most sensitive factor is electricity price which depend on the quality of output in the First step of proposed model. With the better model for forecasting the electricity price the efficiency of gas model also will increase. 4.2 Step three: optimum schedule of electricity production The third step of proposed model is the optimal schedule of electricity production. To test this part of the model verification and validation are taken into account for monthly model. The term verification is used to refer to consistency and validation refers to tests that contribute to building confidence in a model. This chapter consists of four parts. Part shows the reference behavior of the model. Part discusses the verification. Part discusses the validation. Part contains the conclusion Reference behavior of the model In the first step of testing the model we draw the reference behavior of the model for electricity production. For this purpose we set the input data in the realistic way. The input data consist of data related to the technical characteristic of thermal plants, electricity price and available quantity of Gas. We used the spot price of electricity during March 2009 as the real electricity price. The available gas quantity is taken from the step two of proposed model. Technical characteristic of thermal plants are determined by using the historical data and expertise Idea, who know the system very well, consequently the uncertainty related to this input data is low. The normal behavior of hourly electricity production in each thermal plant by considering a real input data can be seen in figure 17 to 25.The Production increased when the electricity price goes up and if it goes down the production will reduce. The Production quantity more depends on the hourly electricity price and available quantity of Gas. Beside that the technical characteristics of thermal plants like maximum production limit is also has effect on production schedule. 108

121 Figure 17: reference behaviour of hourly production Figure 18: reference behaviour of hourly production in Figure 19: reference behaviour of hourly production 109

122 Figure 20: reference behaviour of hourly production in Figure 21: reference behaviour of hourly production in Figure 22: reference behaviour of hourly production in 110

123 Figure 23: reference behaviour of hourly production in Figure 24: reference behaviour of hourly production in Figure 25: reference behaviour of hourly production in 111

124 4.2.2 Verification The verification tests of a model entails whether the model has been coded correctly and consistently. They are aimed solely at the question of whether the model has made the correct transition from concept to verification. Following are the tests that will be performed during verification phase Code check One of the best ways to check whether model has been coded correctly is to isolate sections of model and test them. After that it is necessary to check the equations of the model one by one. This has all been done and no mistakes have been found. This increases confidence in the model Dimension analysis The aim of this test is to check dimensional consistency of model. The units of model correspond with what the variables represents in the real world. Our model has been created with dimensions that correspond to the real world. The list of all these important units is given in the following table. Table 4.2.1: the model parameters Parameter q min, q max Γ g ϴ g O g rs g, rb g α g Β g S g OU ig rsu t, rsd t τ g Ω g FE g GP Unit Net maximum and minimum power [MW] Fix Start up cost related to maintenance cost [ / start up] Fix shutdown cost related to maintenance cost [ / shut down] Operation & Maintenance variable cost [ /h] Ramp rate limits (up & down) [MW/h] Linear term of the input output (efficiency)curve [MWhpcs/ MWh] Fix term of the input output (efficiency) curve [MWhpcs] Start up duration of thermal unit [h] The average out put of thermal unit g in i th hour of start up ramp [MW] Start up and shutdown Ramp [MW/h] the minimum shutdown time [h] The minimum operating time [h] Emission factor [Ton/MWhpcs] Estimation of gas Price for period [ /MWhpcs] 112

125 EP p ATR g CO p GAS Rmax gp Rmin gp Estimation of Electricity Price in period P [ /MWh] Cost for getting access to the gas network [ /MWhpcs] Co2 cost for each period [ /Ton] Available amount of gas for each month [MWhpcs] Maximum range of production in each period in each plant [MW] Minimum range of production in each period in each plant [MW] Numerical error analysis The proposed methodology for solving the model is the optimization model with Mixed Integer Linear Programming (MILP) techniques for maximizing the Market revenue to calculate the gas value. MILP is based on branch and bound algorithm with discrete variables. For integer and discrete solution we can check whether the solution meets the relative and absolute optimality tolerances or not. There is a termination criteria set by options optcr or optca in GAMS to check these tolerances. This option sets a relative termination tolerance for problems containing discrete variables, which means that the solver will stop and report on the first solution found whose objective value is within 100*optcr of the best possible solution. Beside that there is a parameter named GAP in the output fileof GAMS which is provide the information about how close obtained solution is to the relaxed solution. In the proposed model we set the optcr option very small (optcr =1e 12) and We tested the model for 12 month during 2008 and the result for gap value for each month was zero which mens the solution satisfies the termination criteria Validation During the validation phase the aim is to check both the model structure and model behavior. For checking model structure we have performed a direct extreme condition test and for testing behavior of the model we have performed sensitivity analysis and comparison with real data Extreme analysis In this test model is evaluated under extreme conditions. This is done by determining whether the resulting values are plausible when compared to the knowledge of expectations of what would happen in real situation. It is often easier to imagine what could happen in reality under extreme conditions that could happen in reality without extreme conditions. In our research two extreme analysis tests have been done. The first test assumes that thermal plants are not available. The second test assumes that the available quantity of gas becomes Zero. 113

126 The model behaves realistic. When thermal plants are not available the hourly production of all plants became zero. It also happened for Zero quantity of gas which are the realistic behavior Sensitivity analysis A sensitivity analysis is designed to determine the elements in the model to which the model is sensitive and that have major influence on the behavior when they are changed. The goal of this test is to find out how sensitive the model is to plausible changes in data. In our research this test is aimed at locating changes in the system that have the desired influence on the system s behavior and in this way it helps in contribution for users to define possible strategy for the company. In this sensitivity analysis we check what kind of effect an increase and decrease of ten percent of every variable has on start up decision in the morning and afternoon. If the change (of the reference variable) is lower than 0.5 % the variable is not sensitive. If the change lies between 0.5 and 2.5 % the variable is marginally sensitive. If the change lies between 5 and 10 percent the variable is moderately sensitive. If the change is higher than 10 % it is extremely sensitive. Two variables have been find that have such a strong effect, that they can be used as steering parameters. These parameters are: Electricity Price Gas Price There is of course always some uncertainty in the values used for each parameter. For most of the parameters however the uncertainty should be higher than 10 percent or even higher to show a significant change in system behavior but the uncertainty about other parameters is not significant because the expertise know the system very well. The result shows the model is sensitive to electricity price and the production schedule will change by changing the electricity price by 10 %, but if the electricity price changes with the same behavior and stable trend then the production schedule is more or less the same. The behavior of model before and after changes is shown in appendix B. When we change the gas price by 10 %, the production schedule will change but the changes are not significant from the expertise point of view. In fact, in some points the production will decreased when the electricity price is not high enough compare to gas price. 114

127 4.3 Conclusion Several tests have been performed on our model. The model has passed them all; therefore it is suitable for its purpose. As mentioned before the most sensitive factor is electricity price which depend on the quality of output in the First step of proposed model. We use the available model and methodology for the first step of proposed model electricity price forecasting which is presented by other researcher [CARL, 05]. If we could find better model for forecasting the electricity price then the efficiency of model will increase. 4.4 Future Research In this Project we consider several assumptions. For future work it will be interesting to work on these assumptions. For instance we considered the linear start up ramp but it is not real case. The startup ramp depends on shutdown duration before start up but in the proposed model the start up ramp is defined linear in order to solve the model with mixed integer linear programming. For future work it is interesting to define it as a non linear function and try to solve the model with other methodology. On the other hand, in the proposed model there are three steps and each of them solves one after another but the best case is to solve them at the same time. For this purpose we need a very complicated non linear model which could calculate the electricity price and production schedule simultaneously. It could be an interesting work for future research in order to get more realistic results. 115

128 Bibliography [BAIL, 01] Baillo, A., Ventosa, M., Ramos, A., Rivier, M., Canseco, A., 2001, Strategic unit commitment for generation companies in deregulated electricity markets, In: Hobbs, B., Rothkopf, M., O Neil, R., Chao, H. (Eds.), The Next Generation of Unit Commitment Models, Kluwer Academic Publishers, Boston,pp [BALD, 01] Baldick,R.,Hogan,W.W.,2001. Capacity Constrained Supply Function Equilibrium Models of electricity markets: stability, non decreasing constraints, and function space iterations, Program on Workable Energy Regulation (POWER) PWP 089, University of California Energy Institute, Berkeley, CA. [BALD, 00] Baldick,R.,Grant,R.,Kahn,E.,2000. Linear supply function equilibrium: generalizations, application and limitations, Program on Workable Energy Regulation (POWER) PWP 078, University of California Energy Institute, Berkeley, CA. [CLEW, 99A] Clewlow, L. & Strickl and, C. (1999a), A multi factor model for energy derivatives, Working paper, School of Finance and Economics Technical University of Sydney. [CLEW, 99] Clewlow, L. & Strickland, C. (1999 b), Valuing energy options in a one factor model fitted to forward price s, Working paper, School of Finance and Economics, Technical University of Sydney. [CLEW, 00] Clewlow, L. & Strickland, C. (2000), Energy Derivatives: Pricing and Risk Management, Lacima Publications, London. [DAVI, 00] David, A.K. Fushuan Wen, Strategic bidding in competitive electricity markets: a literature survey, Power Engineering Society Summer Meeting, 2000.IEEE. [DAY_, 02] Day, C.J., Hobbs,B.F.,Pang,J. S.,2002. Oligopolistic competition in power networks: a conjectured supply function approach. IEEE, Transactions on Power Systems 17 (3), [DENG, 00] Deng, S. (2000), Stochastic models of energy commodities prices and their application: Mean reversion with jumps and spike snote, Working pap e r, POWER, University of California Energy Institute, Berkeley, California. [DEJO, 02] DeJong, C. & Huisman, R. (2002), Option formulas for mean reverting power prices wit h spikes, Working paper, Rotterdam school of Management at Erasmus University Rotterdam, Netherlands. 116

129 [EURO, 00] European Communities, 2000, Competition policy in Europe and citizen, Official Publications of the European Communities, [EURE, 04] EURELECTRIC, 2004, EURELECTRIC report on Regulatory Models in a Liberalised European Electricity Market, EURELECTRIC SG Regulatory Models. [GARC, 99] Garcia,J. Roman, J.Barquin,J.Gonzalez,A.,1999, Strategic bidding in deregulated power systems, Proceedings 13th PSCC, Conference, Norway, July. [GEOR, 00] George Gross, David Finlay 2000, Generation Supply Bidding in Perfectly Competitive Electricity Markets, Computational & Mathematical Organization Theory archive, Volume 6, Issue 1. [GREE, 92] Green, R.J.,Newbery,D.M.,1992, Competition in the British electricity spot market. Journal of Political Economy 100 (5), [GREE, 96] Green, R.J., 1996, increasing competition in the British electricity spot market. Journal of Industrial Economics (44), [GROS, 96] Gross, G.,Finlay, D.J.,1996, Optimal bidding strategies in competitive electricity markets, Proceedings of the 12th PSCC Conference, Germany, July. [JACO, 07] Jacob Lemming, 2007, Electricity Price Modelling For Profit at Risk Management, Systems Analysis Department Risø National Laboratory, DK 4000 ROSKILDE. [JAVI, 07] Javier Garcia Gonzalez (2007), decision support model in electricity power system, Pontifical University of Comillas. [JOHN, 00] Johnson, B. & Barz, G. (2000), Selecting Stochastic Processes for Modelling Electricity Prices, Published in : Energy Modelling and the Management of Uncertainty, Risk Books, Lon don 2000 pp [JOY_, 00] Joy, C. (2000), Pricing Modelling and Managing Physical Power Derivatives, Published in: Energy Modelling and the Management of Uncertainty, Risk Books, London 2000 pp [JUAN, 03] Juan Rivier, 2003, Restructuring and regulation of the electricity industry, Traditional regulation of the electricity industry, Comillas Spain [KMAD, 04] K. Madsen, H.b. Nielsen, O. Tingleff, 2004, Methods for non linear least squares problems, Technical university of Denmark informatics and mathematical modelling 117

130 [KELL, 01] Kellerhals, B.P. (2001), Pricing electricity forwards under stochastic volatility, Working paper, POWER, Department of Finance, College of Economics and Business Administration Eberhard Karls University Tubingen, Germany. [KNIT, 00] Knittel, C. R. & Roberts, M. (2000), financial models of deregulated electricity prices I: Discrete time models, Working paper, Department of Finance and Economics, Boston University. [KOEK, 01] Koekebakker, S. & Ollmar, F. (2001), forward curve dynamics in the Nordic electricity market, working paper, Agder University College, Norway. [LUCI, 02] Lucia, J. J. & Schwartz, E. S. (2002), Electricity prices and power derivatives: Evidence from the Nordic power exchange, Review of Derivatives Research 5(1 ), [IGNA, 06] Ignacio J. Pérez Arriaga, 2006, Redesigning competitive electricity markets: The case of Spain,Instituto de Investigación Tecnológica (IIT), Comillas University, Madrid [PERE, 99] Pereira, M.V., 1999, Methods and tools for contracts in a competitive framework, Working Paper CICRE Task Force M [PILI, 98] Pilipovi c, D. (1998), Energy Risk: Valuing and Managing Energy Derivatives, Mc Graw Hill, New York. [RUDK, 98] Rudkevich,A.,Duckworth,M.,Rosen,R.,1998, Modelling electricity pricing in a deregulated generation industry: the potential for oligopoly pricing in a Poolco. Energy Journal 19 (3), [RAJA, 01] Rajamaran,R.,Kirsch,L.,Alvarado,F.,Clark,C.,2001, Optimal self commitment under uncertain energy and reserve prices. In: Hobbs, B.F., Rothkopf, M.H., O Neill, R.P., Chao, H. P. (Eds.), the Next Generation of Electric Power Unit Commitment Models, International Series in Operations Research & Management Science. Kluwer Academic Publishers, Boston,pp [SHRE, 01] Shrestha, G.B.Song Kai Goel, L., 2001, Strategic bidding for minimum power output in the competitive powermarket, Nanyang Technol. University [SPAN, 05] Spanish electric power act, 3rd edition 2005, Madrid [STEI, 03] Stein W. Wallace, Stein Erik Fleten, 2003, Stochastic Programming Models in Energy, Handbooks in OR & MS, Vol. 10 [TOMA, 03 1] Tomás Gómez San Román,2003 1,Course on Regulation and restructuring of the electricity industry,the economics of regulation: monopolistic activities, Comillas University, Spain 118

131 [TRAI, 03] training course for energy regulators (3rd), European University Institute Florence, background reading material For Generation & the wholesale market, 2003 Madrid [UNGE, 02] Unger, G.,2002. Hedging strategy and electricity contract engineering, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich. [VARI, 92] Varian, H.R., 1992, Microeconomic Analysis, W.W. Norton & Company, New York, studies & semi; a sample of numerical results are presented to illustrate the robustness and superiority of the analytically developed bidding strategies. [VAZQ, 05] C. Vázquez and C. Batlle, 2005, Strategic medium term model for the Spanish electricity market, developed for: Gas Natural Electricidad,Madrid spain. 119

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133 Appendix A: Financial models In financial price models the time dynamics of market prices is driven by stochastic processes generally in the form of stochastic differential equations and parameters are estimated using market data such as historical spot and derivative prices. As described in Clewlow & Strickland (1999b) most literature on financial price models falls into one of two main categories. The first category of models describe the spot price P(t) dynamics along with other key state variables using a set of stochastic processes. These processes are generally spilt into deterministic components f(t) modeling trends and cycles and a stochastic component S(t) modeling the uncertainty or distribution of prices. The second category of models uses a similar set up but focuses directly on the dynamic evolution of the entire forward price curve. The two approaches are interrelated as forward prices can be derive d from the risk adjusted or risk neutral version of a spot price process provide d that an explicit solution to the stochastic differential equation governing the spot price can be obtained analytically (see Clewlow & Strickland (2000) for an example ). Applications of the spot price approach to electricity markets can be found in references such as Lucia & Schwartz (2002), DeJong & Huism an (2002), Pilipovic (1998), Deng (2000), Kellerhals (2001), Knittel & Roberts (2000) and Johnson & Barz (2000). References that apply the forward price approach to electricity pricing include Clewlow & Strickland (1999 b), Koeke bakker & Ollmar (2001), Clewlow & Strickland (1999 a ) and Joy (2000). The main strength of financial models lies with the use of realized prices, which include information about less tangible factors such as speculation, market power and general trader physiology. The main weakness is the potential lack of predictive power with historical data in developing markets such as the electricity market. Fundamental models Fundamental models constitute a category of engineering models based on a technical bottom up modeling of the production, transmission and consumption parts of the system. This form of modeling tends to be rather complex since it requires an accurate description of a large technical system including factors such as production capacity, production costs, transmission constraints and consumption patterns. Modeling the development in average levels in such factors over time is generally a data intensive task and the large amount of stochastic fluctuations place an even higher demand on the amount and quality of input data required. 121

134 In fundamental models prices pikes and seasonal variations are a direct result of movements in a set of underlying variables that must be modeled with a considerable degree of accuracy. The number of such underlying price driving variables far exceeds the number of variables used in any financial model. As a result no two fundamental models will generally be based on the exact same data set making them much harder to verify and compare than financial models. In addition to the complex technical modeling, the main challenge with fundamentally based price modeling lies with the translation of modeling results into credible market price scenarios. The preferences of suppliers and consumers must be accurately reflected through the modeling, which is difficult task. Combined approaches The problems sketched above with financial and fundamental models combine to explain why practitioners often prefer models that combine the two model types. Fundamental data contains invaluable information about short term weather related changes in supply and demand, which generally cannot be found in market data. In the very long term market data will also tend to be insufficient, because the number of yearly observations required to statistically estimating how fluctuations in annual hydrologic al conditions (wet years vs. dry years) affects average annual prices would lack predictive power by the time it became available. On the other hand market price data such as forward price curves represents important information about the comprised expectations and risk aversion of market players. This kind of data cannot be modeled from technical factors in any meaningful way. An approach that combines the two types of models can be formed by using a bottom up model to construct price scenarios and then calibrate these such that expected prices in the set of scenarios fit the observed forward price curve in the market. If desired such calibration can include extrapolation of patterns found in historical data or parameters inferred from other derivative prices e.g. volatilities from options. 122

135 Appendix B: Gas Model: Main constraints Maxπ= GP = π/gc 123

136 Monthly Model: Main constraints Maxπ= 124

137 Sensitivity analysis: Gas Model Changes in electricity price by 10% FigureB1: Original behaviour before changes Gas available[mwhpcs Gas Margin[ /MWHpcs] Figure B2: Gas margin after 10% increase in electricity price Gas available[mwhpcs Gas Margin[ /MWHpcs]

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139 Monthly Model Changes in electricity price by 10% 127

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