61 CHAPTER 5 SOCIAL WELFARE MAXIMIZATION FOR HYBRID MARKET 5.1 INTRODUCTION Electricity markets throughout the world continue to be opened to competitive forces. The underlying objective of introducing competition to these markets is to make them more efficient. It is a general concept of capitalism that if fair and equitable market structures are created, which give all market participants incentives to maximize their own individual welfare, then the market as a whole will behave in a manner which maximizes welfare for everyone. If this objective is to be achieved, the electricity industry needs new algorithms to help market participants behave in an efficient manner, helping them maximize their own welfare. It is imperative that these algorithms model the economics of the electricity market while maintaining the detail necessary to represent the underlying engineering requirements. This dissertation presents a new algorithm, which determines the social welfare of the system with best feasible bilateral transaction, while taking into account the full model of the electrical transmission system. The electricity market architecture comprises of main four entities namely GENCOs, TRANSOs, DISCOs and an Independent System Operator (ISO). GENCO is not necessary to have its own generating plants, but it can negotiate on behalf of generating companies. In ancillary market GENCO has opportunity to sell its reserves and reactive power. The GENCO will try to maximize its own profit, whatever way it can, by selling the power in the
62 market. TRANSCO transmits the power from power producer to power consumer. It also maintains the transmission system to increase overall reliability of power system. DISCO distributes the power to retail companies, brokers or to its own consumers. ISO is an independent body which maintains the instantaneous power balance in the system. ISO is also responsible for secure operation of the grid. There could be two types of ISO, one is known as MinISO and the other is MaxISO (Shahidehpour et al 2002). While MinISO, looking after the grid security and has no role in power market, MaxISO model includes power exchange (PX). The function of power exchange is to provide a competitive market place for all the participant of the market. ISO uses the assets of TRANSCO for its functioning. The role of ISO also encompasses the fare use of transmission network, maximizing social welfare of the market, running Power Exchange (PX), and maintaining grid security and to run separate market for ancillary services. 5.1.1 Centralized Electricity Market (CEM) The structure of the forward market by examining the day-ahead is centralized electricity market, is sometimes called the pool market. In this market model, a pool operator takes bids from suppliers and consumers. In addition, dispatches generation and load in an economic manner based on the bids. The suppliers and consumers do not interact with one another directly, but only indirectly through the pool operator. The advantage of this arrangement is that the pool operator can internalize the problems of congestion management, loss allocation, and other ancillary services. The structure of CEM is shown in Figure 5.1. The pool operator is in charge of this market and uses auctions to determine the prices and quantities bought and sold for each hour of the next day in the day-ahead markets.
63 Sellers are generation entities and brokers/ marketers. Buyers are consumers, brokers/marketers, distribution entities and generation entities. Sellers and buyers in the market submit sealed offers and bids, respectively, specifying the price and quantity at which they are willing to sell/buy energy. The pool operator determines the successful offers and bids and the market clearing price by maximizing the social surplus. Figure 5.1 The structure of Pool market The pool operator in this model is responsible for the economic infrastructure of accepting and awarding bids, as well as the engineering
64 system infrastructure of maintaining the transmission system. The economic organization is called the power pool, or power exchange, while the engineering organization is called the Independent System Operator (ISO). In deregulated electric power systems operating with the pool type of structure, the ISO is responsible for carrying out market activities such as receiving bids from suppliers, unit commitment and dispatch simulations for the gencos and setting up the market clearing price. It also has the responsibility for ensuring system security and undertaking congestion management for which it has to procure ancillary services and also decide on the various control auction taken. The methods that have been used to dispatch generation and load in an economic manner and have been based on one of two methods: last accepted bid and spot pricing theory. In the last accepted bid method, market participants submit blocks of generation and sometimes load along with associated prices. All the supply bids are then aggregated and sorted by price in ascending order to create the aggregate supply curve. If consumer bidding is included, then all the demand bids are aggregated and sorted by price in descending order to create the aggregate demand curve. The curves are then plotted against one another, and the point were they cross defines the Market Clearing Price (MCP). All bids to the left of this point are then accepted and all suppliers are paid the MCP for the blocks of generation, which were bid, and all consumers must pay the MCP for the blocks of demand, which were bid. The other method used to dispatch generation and load in an economic manner is to use spot pricing theory as described in (Schweppe et al 1988). 5.1.2 Definition of Social Welfare Social welfare is defined as the total benefits of the buyers minus the total costs of the sellers. Maximization of a social welfare means to
65 formulate objective function to obtain the optimal dispatch schedules which is the common practice in most centralized power pools. Two cases may arise in this class of problems, one where the market operator receives both supply and demand bids and the system price is obtained by matching the highest priced sell bid to the lowest priced buy bid. The other is where only supply bids are received and the system price is obtained by finding the highest priced bid intersecting the system demand forecast (Bhattacharya 2001). Figure 5.2 Market settlements in double auction power pool Let us consider markets where both supply and demand bid is invited from participants. The system price is obtained by stacking the supply bids in increasing order of prices and the demand bids in decreasing order of their prices. The system price and the amount of energy cleared for trading is obtained from the crossing point of these curves as shown in figure. Such auction is called double auction and Figure 5.2 shows the typical market
66 clearing process in such power pools [Bhattacharya 2001]. The shaded area in Figure 5.2 denotes the social welfare from market based operation that the market operator seeks to maximize. The social welfare is a measure of the performance of the market as a whole, but, it fails to provide insights into the performance of the individual player. 5.1.3 Power Trading in Wholesale Electricity Market The restructured markets normally employ one or a combination of the following trading arrangements (Liu and Gross 2008). Pool Trading The pool trading involves bidding in the open market. The sellers have to bid their capacity and price, whereas buyers must bid their load requirement and, in addition, they can also bid the maximum price they can pay. The ISO and Power Exchange (PX) operate the electricity pool to perform a price based dispatch and provide a forum for major option. Market settlement takes place through posting the Market Clearing Price (MCP) in either Single Auction (in which only sellers bid the price) or in Double Auction market (in which both sellers and buyers bid their price). Alternatively the power exchange may settle the competitive bids and post the information about successful bidders and their price. Pool and Bilateral Trading This contains multiple separate energy markets, a pool market taken care of by the Power Exchange and bilateral contracts established by the scheduling coordinators (SCs). The ISO is responsible for system operation, guarantees system security, and in operational matters holds a superior
67 position over the PX and SCs. The existence of a power pool is not mandatory in this model. Multilateral Trading Multilateral trades are generalization of bilateral transactions where an SC or power broker puts together a group of energy producers and buyers to form a balanced transaction. In practice, multilateral and bilateral transactions may co-exist with a power pool. 5.2 MARKET MODEL FOR HYBRID TRANSACTION In a hybrid power market, market participants can buy/sell electric energy from the spot market and can also sign long-term bilateral contracts to reduce their price risk. In the spot market, suppliers submit their generation bids and customers submit their demand bids to the power pool. For a bilateral transaction, energy price is agreed by two contracted parties, and the contracted quantity and locations are provided to the ISO (Shahidehpour and Alomoush 2001). The ISO ensures that there are sufficient transmission resources to finalize the transactions. All bilateral transactions are then scheduled to meet their loads unless they incur network congestions. In order to maintain network security and reliability, all bilateral contract participants are required to submit curtailment bids which can be used to reschedule the bilateral transactions in case of congestion. With all the bids submitted by different market players, market clearing price and successful bids are determined using a security constrained OPF. The congestion problems are solved simultaneously through network constraints and elastic biddings during the solution process. The market model for congestion management of a hybrid power market is shown in Figure 5.3.
68 Figure 5.3 Hybrid power market This chapter proposes a methodology for determining social welfare of a hybrid power market that consists of a power pool and bilateral contracts between market participants and will be discussed in detail throughout. In this method, suppliers and sometimes consumers submit bid curves to the pool operator and an optimization routine is used to determine the dispatch results. Suppliers are then paid a price according to their bids and consumers must pay a price according to their bids. The proposed method is based on a modified Optimal Power Flow (OPF) model to maximize the social welfare. The HPSOCM technique is applied to solve the proposed OPF problem. 5.2.1 Cost of Active Power Generation The bidding strategy of a generation company is to maximize its profit. For a market without market power, a generator maximizes its profit when the bid equals its marginal cost. Under this assumption, the Cost function C(P ) g of real power for a generator at bus is given by,
69 ng C(P ) (a P b P c ) a (P ) b P c i1 ik 2 2 g gi gi gi gi gi gk gk,ipp gk gk,ipp gk (5.1) where P is the generated power at bus i, n gi g is the number of generators, P is the real power generation of IPP at bus k and a gk, IPP gi, b gi & c gi are the cost coefficients of generators and a gk, b gk & c gk are the cost coefficients of Independent Power Producer. 5.2.2 Benefit of a Pool Customer The power market provides customers an opportunity to participate in market trading based on their price and reliability requirements. The demand of a customer may change with the market-clearing price. Therefore, the load at each bus becomes a variable, which depends on the willingness of the customers to pay. Customer benefit is the value gained from using a certain amount of energy and therefore can be used to indirectly the willingness to pay. Mathematically, Customer Benefit function B(P d ) can be written as, nd 2 max 2 max B(P d ) (a dipdi b dipdi c di ) a dj (P dj,allow ) b djpdj,allow c dj (5.2) i 1 i j where P di is the demand at bus i, a b n d is the number of load, di, di & di c are the cost coefficient of the given demand, P dj,allow denotes allowable load at bus j and a dj, b dj & c dj are the cost coefficient of maximum demand of bus j.
70 5.3 FORMULATION OF OBJECTIVE FUNCTION The bidding problem consists of price offers and the amount of loads to be satisfied in the competitive market. All the participants submit a bidding strategy to maximize the social welfare while satisfying various constraints. The OPF model is formulated to maximize social welfare by maximizing allowable load at buyer bus is as follows, Objective: Maximize f (x) B(P ) C(P ) (5.3) subject to the following constraints d g The basic power flow equations are modified to include the power generation by IPP. Let Pi and Q i be two reformulated functions defined as: NB IPP max i i ij j ij j i Gi Gk di d j,allow j=1 P = V Y V cos( )-(P + P ) +(P P ) (5.4) k slack and j slack NB Q = i Vi Y i V j j sin( i j j i ) - Q Gi + QDi (5.5) j=1 i = l to n except slack bus and j = 1 to n IPP P P P P max Gi Gk di d j,allow (5.6) min Gi Gi max P P P (5.7) Gi min max Gi Gi Gi Q Q Q (5.8)
71 S l max l S (5.9) V min max i V i V i (5.10) where min PGi and generating unit at i th bus, max PGi minimum and maximum real power output of the max P is maximum real power flow on line l. l 5.3.1 Algorithm for Estimating Social Welfare The objective function is to maximize Social Welfare by maximizing allowable load at the buyer bus using HPSOCM. Load during each transaction is assumed as the particle to be optimized. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Suppliers and buyers in the power pool submit their generation bids and demand bids; bilateral contractors submit their contracted quantity and location. Specify the maximum and minimum limits of generation power of each generation units and IPP, maximum number of iterations to be performed. Particles are generated and initialized with position values and velocity. The fitness values for the particles are determined. If a particle does not satisfy the fitness requirement, it is regenerated. Execute the PSO operator on the particles. The optimal objective fitness values are calculated for all the particles. Then the values of position best and global best are determined.
72 Step 7: Step 8: Step 9: Position and velocities of particles are updated. Perform mutation process to replace the worst particles. If the maximum number of iteration exceeded or some pre specified an exit Criterion is satisfied, then goes further to step 10. Or else, update the time counter. Step 10: Output the particle with the maximum fitness values in the last generation. Calculate the optimum using HPSOCM. 5.4 CASE STUDY The IEEE 30 bus system and Indian utility 69 bus system are used to illustrate the proposed technique for the Social Welfare determination of a hybrid market and maximization of social welfare using HPSOCM method. The influence of the PSO parameters, the inertia weight, and population size, constants C 1 and C 2, on the convergence of the algorithm has been studied. The size of particles has been found to be 60, the inertia constant varied is found to be 0.5, Maximum number of iteration has been taken as 100. The minimum solution was obtained for 100 trial runs. The best results are considered as the solution of the particular algorithm. Parameter values for HPSOCM for the two test systems are shown in Table 4.1 in chapter 4. It is assumed that all components of the system are in service and that there are two bilateral transactions in the market. Let the BFT of power between seller at bus be10 and customer at bus be 5. The power dispatch, total generation cost, total benefit cost and social welfare are shown in Table 5.1. Consider the base case of market operation. Line flows under this case are all within their limits. The most economic dispatch is made to supply the pool demand. All the transactions in the bilateral market can be
73 transferred to the desired places without violating any network limit. In this hybrid market, the BFT of power between seller of 144.5 MW at bus 10 and customer of 98.91 MW at bus 5 has been fixed (The locations and value of buyer for BFT have found in chapter 3) and total demand is 288.11 MW. Table 5.1 The Social Welfare of hybrid transaction for IEEE 30 bus system Generation in MW Bus number (PSO) (HPSOCM) 1 95.4287 94.6970 2 34.8473 34.5763 13 13.7243 12.7267 22 0.0000 1.8712 23 0.0000 0.0000 27 0.0000 0.0000 10(IPP) 144.5000 144.5000 Total generation in MW 288.5000 288.3700 Total generation cost( C(P ) )(Min) $/hr 1026.7413 1024.6521 g Mean 1027.6440 1024.6631 Standard deviation 0.2307152 0.0028527 Total benefit cost ( B(P ) ) $/hr 12675.8595 12675.8595 d Social welfare[ B(P d ) C(P g ) ]$/hr 11649.1155 11651.2075 Computation time in sec 1.2071 0.9821 Number of iterations 29 23 From Table 5.1, it is evident that, in maximizing social welfare by HPSOCM outperforms the PSO in all aspects. Furthermore, the proposed HPSOCM and PSO algorithm are tested on Indian utility 69-bus system.
74 Table 5.2 The Social Welfare of hybrid transaction for Indian utility 69- bus system Generation in MW Bus number (PSO) (HPSOCM) 1 742.5857 741.4555 13 741.7762 741.5214 14 350.0000 349.9960 15 500.0000 500.0010 21 250.0000 250.0990 31 200.0000 199.9900 36 150.0000 150.0000 39 450.0000 450.0000 52 740.6381 741.0230 53 60.0000 60.0023 57 200.0000 200.0001 58 200.0000 200.0000 60 100.0000 100.0000 7(IPP) 260.3000 260.3000 Total generation in MW 4945.2991 4944.3972 Total generation cost( C(P ) )(Min)$/hr 34067.2412 34036.0672 g Mean 34067.7321 34036.0683 Standard deviation 0.02880629 3.137884691e -004 Total benefit cost ( B(P ) ) $/hr 138496.9271 138496.9271 d Social welfare[ B(P d ) C(P g ) ]$/hr 104429.6805 104460.8599 Computation time in sec 1.4986 1.219 Number of iterations 45 38 In this hybrid market, the BFT of power between seller of 260.3MW at bus 7 and customer of 202.02 MW at bus 2 has been fixed ( the locations and value of buyer for BFT have found already in chapter 3). The power dispatch, total generation cost, total benefit cost and social welfare are shown in Table 5.2. In this market, total demand is 4944.2MW. From Table 5.2, HPSOCM outperforms the PSO in all aspects.
75 5.5 CONCLUSION The Welfare Maximization algorithm for hybrid market is presented in this chapter will be of great use to pool market and bilateral market participants for market analysis. However, others, such as industry regulators, are interested in studying market equilibrium behavior. Using the hybrid market welfare Maximization algorithm, the entire market can be simulated with their bids with the objective of maximizing welfare. HPSOCM algorithm was shown to hold potential for helping to solve the welfare maximization problem. It was effective in increasing the probability of jumping out of the local optimum and overcome the premature convergence of the standard PSO. In this approach, each participant tries to maximize its profit with the help of information announced by operator. The market operator decisions are performed to keep system operation within security limits. The results are compared with the PSO. The results obtained using HPSOCM yields more profit.