ENERGY STORAGE IMPACT ON SYSTEMS WITH HIGH WIND ENERGY PENETRATION DINA KHASTIEVA

Transcription

1 ENERGY STORAGE IMPACT ON SYSTEMS WITH HIGH WIND ENERGY PENETRATION by DINA KHASTIEVA Submitted in partial fulfillment of the requirements for the degree of Master of Science Systems and Control Engineering CASE WESTERN RESERVE UNIVERSITY August, 2014

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Dina Khastieva candidate for the degree of Master of Science *. Committee Chair Kenneth A. Loparo Committee Member Vira Chankong Committee Member Marc Buchner Date of Defense 05/27/2014 *We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Contents LIST OF FIGURES... 4 LIST OF TABLES... 6 ACKNOWLEDGEMENT... 8 LIST OF SYMBOLS... 9 ABSTRACT CHAPTER Introduction Problem statement Purpose and significance of the study Literature review Contribution of study...19 CHAPTER Energy storage Organization and operation of electricity market

4 2.3 Reserves Optimal power flow Optimal power flow formulation OPF solving methods: Line stability index:...36 CHAPTER Introduction Formulation of Dynamic Optimal Power Flow for Day-Ahead market Optimal power flow for four hour-ahead Dynamic Optimization Problem CHAPTER Implementation Load Wind Generation Output Wind Based Generator Energy Storage System Reserve requirements Generation and energy storage cost Cost of Reserves Scenario

5 4.3 Scenario Scenario Contingency...59 CHAPTER Results Scenario Scenario Scenario Comparison Indices Capital cost: Conclusion...82 APPENDIX BIBLIOGRAPHY

6 List of Figures Figure 1 One day data for forecasted and actual wind generation output of PJM Figure 2 One day data for forecasted wind generation output and electricity demand of PJM Figure 3 Proposed location of Energy Storage...17 Figure 4 Operating principle of Energy Storage...21 Figure 5 Classification of energy storage systems...21 Figure 6 Classification of operating reserves Figure 7 Ramping requirements diagram Figure 8 IEEE 30 bus system diagram Figure 9 Forecasted and actual load curves for one day, PJM...47 Figure 10 Forecasted and actual load curves for the test system Figure 11 Forecasted and actual wind generation data for one day, PJM...49 Figure 12 Forecasted and actual wind generation...49 Figure 13 Generation capacity, scenario Figure 14 Generation by type,, scenario Figure 15 Generation capacity, scenario Figure 16 Generation by type, scenario Figure 17 Generation and storage capacity, scenario Figure 18 Generation by type, scenario Figure 19 Active power, scenario Figure 20 Active power reserves, scenario

7 Figure 21 Reactive power, scenario Figure 22 Active power for 4 hour-ahead optimization model, scenario Figure 23 Scheduled reserves and actual generation for 4 hour-ahead optimization model, scenario Figure 24 Reactive power for 4 hour-ahead optimization model, scenario Figure 25 Maximum L ij for 4 hour-ahead optimization model, scenario Figure 26 Maximum line loading for 4 hour-ahead optimization model, scenario Figure 27 Generation and load for contingency event. Scenario Figure 28 Active power, scenario Figure 29 Reactive power, scenario Figure 30 Consumed, forecasted and metered wind generation values, scenario Figure 31 Actual load, wind and generation, scenario Figure 32 Scheduled reserves and actual generation for 4 hour-ahead optimization model, scenario Figure 33 Active power for 4 hour-ahead optimization model., scenario Figure 34 Reactive power for 4 hour-ahead optimization model, scenario Figure 35 Maximum L ij for 4 hour-ahead optimization model, scenario Figure 36 Maximum line loading for 4 hour-ahead optimization model, scenario Figure 37 Scheduled reserves and actual generation for contingency event, scenario Figure 38 Percentage of curtailed wind, scenario Figure 39 Wind and Energy Storage dynamics, scenario Figure 40 Active power, scenario Figure 41 Reactive power, scenario

8 Figure 42 Active power for 4 hour-ahead optimization model, scenario Figure 43 Reactive power for 4 hour-ahead optimization model, scenario Figure 44 Scheduled reserves and actual generation for 4 hour-ahead optimization model, scenario Figure 45 Maximum line loading for 4 hour-ahead optimization model, scenario Figure 46 Maximum L ij for 4 hour-ahead optimization model, scenario Figure 47 Scheduled reserves and actual generation for contingency event, scenario Figure 48 Comparative diagram of maximum L ij Figure 49 Comparative diagram for maximum loading percentage

9 List of Tables Table 1 Values of Energy Storage parameters [10] Table 2 Applications of Energy Storage with benefits and disadvantages [19] Table 3 Classification of reserves according to time response [20] Table 4 Ramping capabilities of different power plants Table 5 Bus types Table 6 Loads in IEEE 30 bus system Table 7 Base generation in the IEEE 30 bus system Table 8 Generation cost Table 9 Cost for reserves Table 10 Generator parameters, scenario Table 11 Generator parameters, scenario Table 12 Generator parameters, scenario Table 13 Ramping requirements, scenario Table 14 Energy Storage capital cost Table 15 Capital cost of single transmission line Table 16 Cost of FGD

10 Acknowledgement First and foremost, I want to express my sincere gratitude to research advisor, Professor Kenneth A. Loparo, for his dedicated guidance, support and involvement in every step throughout the research process. Without an excellent working atmosphere he created, this thesis would have never been accomplished. I greatly appreciate Professor Buchner and Professor Chankong for their time and consideration in being a part of my master thesis defense committee. 8

11 List of Symbols NG NB G P i Number of generators Number of buses Active power generated at bus i D P i Active power demand at bus i inj P Active power injected at bus i i L P i Losses at bus i G Q i Reactive power generated at bus i D Q i Reactive power demand at bus i inj Q Reactive power injected at bus i i V i Voltage at bus i t T i Time Period of time Phase angle at bus i S ij Apparent power flow between bus i and j PU R Upward reserves provided by generator i i DU R Downward reserves provided by generator i i PU R Upward reserve requirements DU R Downward reserve requirements G S i Maximum apparent power provided by generator i 9

12 ESC State of charge of energy storage S Maximum apparent power provided by energy storage ES ESG P Active power provided or absorbed by energy storage Q ESG Reactive power provided by energy storage GSch P Scheduled generation i 10

13 Energy Storage Impact On Systems With High Wind Energy Penetration Abstract by DINA KHASTIEVA Renewable energy sources for electricity were introduced only a few decades ago and they are becoming an integral part of conventional power systems to meet increasing energy demands with reduced emissions. Their growth and penetration into power grid raises a concern about the impact of their intermittency on system stability and security as the capacity of the transmission system. The integration of large wind farm installations into utility service areas may require increases in available transmission systems capacity and the integration energy storage into the power system, resulting in large financial expenses that may make wind energy less attractive and affordable as an alternate source of energy. Energy storage systems integrated with renewable energy resources are considered to be an efficient and serviceable solution. They have multiple applications and may further provide an opportunity to reduce the capital cost necessary to modernize the system. This thesis proposes a new methodology for evaluating the impact and value of energy storage systems on power system with wind and storage using Dynamic Optimal Power Flow, solved using an interior point optimization method and implemented the MATPOWER package. 11

14 Chapter Introduction Driven by government incentives and promising low cost projections, wind-based electricity generation has been growing rapidly over the past 10 years The policies enacted by many First World countries to promote wind energy represent a sound indicator that this global trend is likely to continue at least another decade or two. The policies to promote wind energy include its regulations and targets, fiscal incentives and public financing activities. The EU has adopted a binding decision that by 2020, 20% percent of its energy supplies should come from wind and other renewable energy sources. The US Department of Energy is anticipating a scenario in which 20% percent of the total US energy supplies come from wind power by 2030 [1]. Increasing the demand for wind energy contributes to stronger competition among wind turbine manufacturers and leads to a steady decline in wind turbine costs, which is a major factor in establishing wind-based energy prices. Besides wind generation equipment there are great concerns about power system security and transmission system capacity. Investments required in these areas can cancel out all cost benefits gained from large wind generation installation projects. Energy generation from wind power is intermittent and non-dispatchable. Therefore managing wind energy is very straightforward: maximum production and consumption. However, such a strategy does not always comply with existing power grid regulations and may require operating conventional power system equipment in unintended ways. 12

15 Conventional power generation units primarily rely on coal or natural gas to produce electricity. Their dynamic response (ramping capability) to follow the wind is limited, and can create new problems in stability and security. Given restrictions in power grid management, it is sufficient to underline two main characteristics of wind-based generation that might create a challenge for power system operators, and require capital investments in grid modernization: Wind energy output is based on wind speed which is unpredictable and may change gradually in very short time periods thus requiring sufficient generation capacity with high enough ramping rate to follow changes in wind speed. Wind speed forecasting with high accuracy is difficult, so system operators will be required to increase their regulation reserve capacity to mange this uncertainty. These characteristics also affect transmission system capability. Transmission system capacity is limited so in situations when wind-based generation exceeds transmission limits it should be curtailed. In addition, the uncertainty and variability of wind generation might cause voltage instability. Historical data shows lack of correlation between wind-generated power and the load. Wind energy usually reaches its maximum output during the night while load is very low thus curtailment of the wind becomes unavoidable. 13

16 MW Hour Wind actual Wind forecast Figure 1 One day data for forecasted and actual wind generation output of PJM MW Load Wind Hour Figure 2 One day data for forecasted wind generation output and electricity demand of PJM. The challenges of high variability and uncertainty of the wind speed might be handled by a combination of additional generation units, dispatchable load, and transmission line upgrades; however energy storage systems could be a more practical solution. Energy 14

17 storage includes benefits for both generation and diapatchable load and can be used in multiple applications such as meeting peak load, load following, ancillary services support, or providing operating and planning reserves. 1.2 Problem statement At the utility scale, storage is invaluable to help control voltage and ramping issues, and in many cases it is a regulatory requirement such as California s storage mandate that requires the state's three major power companies to have electricity storage capacity that can provide 1325 megawatts by the end of 2020 [2]. By common expert consent, windbased energy generation can only reach its full potential if storage is available, otherwise large generating capacity with high ramping capability must be held in reserve for times when the wind does not blow or when wind speed changes too fast. Thus energy storage systems integrated with wind energy are considered as necessary solutions for economical, technical and other renewable energy integration related issues. However, as there are still few examples of large-scale energy storage integrations, it is necessary to develop a methodology to determine the capacity needs of energy storage in particular applications and to evaluate its impact on power system stability, security and economics. The first strategy is retention of transmission security constraints, where system operators coordinate power transmission in accordance with transmission capacity and the energy traded in compliance with the coordinated multilateral trade model. In the second model system operators have control over energy markets and they are required to create a competitive energy market place. Such a structure is based on the optimal power flow model (OPF) and it gives a better picture of the entire energy market. Moreover the OPF model allows dispatch of active and reactive power generation under security and 15

18 capacity constraints of the system. Therefore, the OPF model is a valuable tool for determining the impact of energy storage on power systems in both, economic and operating (stability, security and reliability) aspects. At the moment, the traditional OPF model is used as an approach for static optimization problems such as generation dispatch at given times. Integration of energy storage systems into the power system requires an extension of the conventional OPF model to the Dynamic Optimal Power Flow (DOPF) model. The DOPF model also needs to be modified to include additional parameters and constraints for a more precise assessment of the impact of energy storage on system operations. 1.3 Purpose and significance of the study The main purpose of this study is to evaluate energy storage system (ESS) performance in the presence of high wind energy penetration. We assume the ESS is located between the transmission and distribution systems. This location was chosen as the most suitable to evaluate the possible value of ESS to both the transmission and distribution systems together. 16

19 Figure 3 Proposed location of Energy Storage One of the challenges that large wind generation integration faces is limited electric supply reserve capacity and ramping capability of conventional generation units. When the penetration of intermittent generation increases, there is a rise in reserve requirements due to the unpredictable and uncontrollable nature of the intermittent generation source. Thus, the power system without sufficient dispatchable generation capacity requires installation of additional generation units. Besides the increase in reserve requirements, additional costly modifications and upgrades are also required for transmission lines and equipment. There are many possible applications of energy storage. However in this study we pay attention to 3 of them: Active Power Reserve Capacity Voltage support 17

20 Transmission, Generation and Distribution Upgrade Deferral The study of performance of energy storage system under these applications allows us to determine the avoided capital cost of additional upgrades that are required to integrate large wind generation units into utility service areas. In addition it also evaluates the ability of the energy storage system ability to provide reactive power reserves and support to improve voltage stability and security. 1.4 Literature review The National Renewable Energy Laboratory (NREL) as well as Sandia National Laboratories are highly involved in a variety of renewable energy studies and projects [3] [4] [5] [6]. In addition they have been investigating energy storage applications, benefits and costs [7] [8] [9]. Energy storage systems are interesting areas to many research institutions around the world [10], [11]. Previous work has provided a detailed overview of available energy storage technologies, their application and approximate financial and intangible benefits for power systems. The majority of these studies have used different approaches for evaluating energy storage technologies. However, they all agree that energy storage has a wide range of applications and provides remarkable benefits for power system operation. The focus of the research in [12], [13] is on the value and performance of energy storage technologies integrated into power systems with renewable generation. Interest towards the combination of ESS and large renewable generation supported by environmental policies such as the Mercury and Air Toxics Standards require incredibly costly upgrades for coal-fired power plants in order to reduce the negative impact on the 18

21 environment. As a consequence many coal power plants are scheduled to retire. According to the U.S Energy Information Administration (EIA) 27 GW of coal-fired generators are expected to retire between 2012 and Integration of energy storage dynamics into power system optimization models has also received attention. Various publications are dedicated to this problem. Markov Decision Processes are presented in [14] and [15] for energy storage dispatch. Others [16], [17], [18], prefer the multi-period Dynamic Optimal Power Flow model to simulate charge/discharge dynamics of energy storage. 1.5 Contributions of our study A vast number of studies have discussed integrated optimal power flow models for energy storage and considering the objective function of the optimization problem as a measure of the value of energy storage systems. The approximation of energy storage charge and discharge costs, however, does not always gives a true picture of the financial benefits that an energy storage system provides. Our study focuses on the capital costs and determines the value of energy storage using two different multi-period dynamic optimal power flow models; the day ahead optimization model based on forecasted load and wind generation curves and the 4 hour ahead model for actual load and wind generation data in order to evaluate performance of ESS given large forecast errors and reserve requirements. Furthermore, a line stability index was added into our analysis in order to evaluate the impact of additional reactive power generation from energy storage on voltage stability of given test system, the 19

22 percentage of line loading is used to assess the impact/value of energy storage heavily loaded transmission systems. 20

23 Chapter Energy storage The problem of storing electricity has been a big issue since the inception of power systems. In order to store electricity it has to be converted into another form of energy such as chemical, mechanical (kinetic or potential), and then converted back to electrical when it is needed. Hence, round trip efficient of EES is a critical factor for their success. Converting from electrical energy / Charging Storing energy (chemical energy, mechanical energy, etc ) Converting to electrical energy/discharging Figure 4 Operating principle of Energy Storage A widely-used approach for classifying EES systems is according to the form of energy used. Mechanical Chemical Electrochemical Electical Thermal Pumped hydro Compressed air Flywheel Batteries Hydrogen Capacitors Superconducting magnetic coil (SMES) Sensible heat storage Figure 5 Classification of energy storage systems 21

24 In order to classify and use energy storage devices the following parameters are used: Capacity; Efficiency; Time response; Discharge time; Power; Lifetime; Capital cost; Table 1 summarizes some of these parameters for different types of energy storage options. Technology Time response Power level Lifetime Capital cost Efficiency Pumped hydro >3 min > years 600$-1200$ 75%-82% Battery 1min-3hour years-10years 70%-80% CAES 3min-10min years >1000$ 60%-70% Flywheel 15ms -15min 0.005MW-5MW 15 years >500$ 80%-95% SMES 1ms -10ms 0.01MW-20MW 20 years 80%-90% 22

25 SCES 10ms-1min years >200$ 90%-94% Table 1 Values of Energy Storage parameters [10]. Each type of technology could be used for multiple applications such as energy management, backup power, load leveling, frequency regulation, voltage support, and grid stabilization. Importantly, not every type of storage is suitable for every type of application but energy storage systems can be designed with a broad portfolio of technologies. Combinations of different energy storage technologies with different performance characteristics give a single storage system a great opportunity to meet multiple requirements for different types of services. Other grid resources such as conventional generation units cannot achieve such flexibility. Table 2 summarizes possible applications, advantages and disadvantages of different types of energy storage technologies. Technology Application Advantage Disadvantage Pumped hydro Energy management Developed and Geographically limited Backup and seasonal mature Environmental reserves Very high ramp rate impacts Regulation service Most cost effective High overall project cos CAES Energy management Better ramp rates than Geographically limited Backup and seasonal gas turbine plants Low efficiency reserves Developed and Slow response time 23

26 Renewable mature Environmental impact integration Flywheel Load leveling Modular technology Rotor tensile strength Frequency regulation Proven growth limitations Peak shaving and off potential to utility Limited energy peak storage scale storage time due to Transient stability Long cycle life high frictional losses High peak power without overheating concerns Rapid response High efficiency SMES Power quality Highest round-trip Low energy density Frequency regulation efficiency from Material and discharge manufacturing cost prohibitive SCES Power quality Highly reversible and Currently cost Frequency regulation fast discharge prohibitive Flow battery Ramping Ability to perform high Developing Peak Shaving number of discharge technology Time Shifting cycles Complicated design Frequency regulation Lower Lower energy density Power quality charge/discharge efficiencies 24

27 Very long life Table 2 Applications of Energy Storage with benefits and disadvantages [19]. 2.2 Organization and operation of electricity market In the early days of power systems electricity was provided by a body of nonprofit electric providers and regulated by municipal or federal government agencies. This was a vertically established hierarchy where separate utilities were in charge of all electric power related activities such as generation, transmission, distribution, and retail markets. In turn, this gave them a monopoly over these fields. The state owned organization of power systems was challenged only two decades ago by the private energy sector. It began with the separation of electricity production and distribution activities. This introduction of competition between producers as well as less controlled trading and pricing gave rise to independent electricity markets. Although private electricity markets were implemented in different ways worldwide, they all share a number of common features: separation of generation, transmission, distribution, and retail activities. These new markets promote competition in production and retail except electricity transmission, which still remains operated by governmentregulated organizations. In order to manage effective transmission operations and overall stability of the system, independent system-operators (ISO) and regional transmission organizations (RTO) were developed. RTOs and ISOs do not own transmission or generation units; instead they are responsible for the maintenance of generation units and transmission equipment to ensure that all end users (customers) were served. 25

28 There is little practical distinction between an RTO and ISO. Both of them have to organize competitive market mechanisms to provide customers with stable and reliable electricity supplies. The main purpose of these markets is to help RTOs make operational decisions such as generation dispatch. There are three main marketplaces for electricity trading and they take place on different time frames. The first is the day-ahead market (forward market). In this market producers, retailers and large consumers participate in an auction where they submit their bids to sell (buy) required amounts of energy for a given price throughout the following day. The RTO then runs a computerized market model that matches buyers and sellers throughout the geographic market footprint for each hour. Based on the power flows needed to move the electricity throughout the grid from generators to consumers, the model evaluates the bids and offers of the participants. Additionally, the model must account for system performance that changes in line with the weather and equipment outages combined with the rules and procedures that are used to ensure system reliability. The purpose of the day-ahead market is to give generators and load-serving entities a means for scheduling their activities prior to their operations. It is based on the forecast of their needs and consistent with their business strategies. The day-ahead market allows participants to secure prices for electric energy the day before the operating day and hedge against price fluctuations that can occur in real-time. At the same time independent system operators may announce their demand for required reserve capacity and organize auctions for participants to bid their available capacity. The next level of trading energy is the real time-market that takes place after the day-ahead market and is aimed at covering unmatched energy supplies and demand over shorter time periods. The real-time market is used to balance the differences between the day-ahead 26

29 scheduled amounts of electricity based on the day ahead forecast and the actual real-time load. The real-time market is run hourly and in 5-minute intervals and clears a much smaller volume of energy and ancillary services than the day-ahead market. Prices resulting from the real-time market are only applicable to incremental adjustments to each of the resources associated with the day-ahead schedule. 2.3 Reserves Power system operators have a number of responsibilities for maintaining reliability and security of the power grid: Maintaining frequency very close to its nominal level-60 Hz in North America and 50 Hz in Europe and many other areas of the world. Keeping tie-line flows under their limits. Maintaining power flows below the maximum limits of transmission lines, transformers and other equipment. Maintaining voltage levels within nominal levels at all locations of the network. Providing necessary preparations for possible contingency events. All of the above-mentioned objectives can be easily achieved if system conditions are precisely forecasted. In reality, most power system operations are challenged by high unpredictability of some system properties including generation output, electricity demand, available transmission capacity, and disturbances and contingencies. Therefore, additional capacity above forecasted load is needed to meet actual demands and avoid system failure in case of contingency events. Available on-line generation units or 27

30 responsive load, referred to as reserves, could provide such capacity. These reserves could be created for many different reasons and come in different shapes and sizes, and could be provided both in terms of active and reactive power. Active power reserves also known as operating reserves are created to maintain stable frequency while reactive power reserves are useful for voltage control. Most systems consider both types of reserves to be ancillary services and directly involve them in daily operation of the system. There are some common categorizes such as primary, secondary and tertiary power system operations that depending on their function and their response times from fastest to slowest. Table 3 presents some common definitions for different categories of reserves. Frequency control reserves Primary local control that adjusts the active power dispatch and the dispatchable loads consumption to restore quickly the balance between load and generation Secondary centralized control that adjusts the active power output of the generating units to restore the frequency and the interchanges with other systems to their target values following an imbalance Voltage Tertiary Primary manual changes in the dispatching of generating units local control that maintains the voltage at a given bus control reserves Secondary centralized control that coordinates the actions of local regulators in order to manage reactive power dispatch within a regional voltage zone. 28

31 Tertiary manual optimization of the reactive power flows across the power system Table 3 Classification of reserves according to time response [20]. Active power reserves have broader applicability (e.g. power angle and frequency control) than reactive power reserves that are primarily used for voltage control. Therefore active power reserves have a more complex classification systems based on response time and target application. Operating reserves could be divided into non-event reserve and event reserve. Event reserves are usually used in response a contingency in the system such as generation or line outage or other emergency events that require immediate response or otherwise can cause system failure. Non-event reserves are aimed to cover day-to-day active power mismatches that are possible in the system. The diagram below presents classifications of operating reserves and their relationships. Operating reserves Event Non-event Regulating Following Contingency Ramping Figure 6 Classification of operating reserves. 29

32 The most important parts of the event and non-event based reserves are regulation and contingency reserves because very quick response is required to keep the system stable and reliable. There are no common rules for establishing required reserve capacity but most system operators prefer to keep from 40% to 100% of the largest single loss of generation as contingency reserves and from 5% to 10% of forecasted load level as regulating reserves [20]. Due to high forecast error and high variability, large wind generation integration requires gradual increases in regulating reserves. Many studies have evaluated the impact of renewable energy on reserve requirements [20]. One of the proposed methods is to use the standard deviation of hourly wind-based generation to create additional reserve capacity for the wind fluctuation and possible errors in the forecast. Another approach is to set a fixed percentage of the predicted wind generation and add it to the existing regulation requirements. For example, The Eastern Wind Integration and Transmission Study (EWITS) proposes the following method: Re greq3* 1%*( HourlyLoad) ( HourlyWind) (2.1) 2 2 ST Since the value of the forecasted load and wind generation output could be higher or lower than the actual load, reserve services should cover both of these situations. Therefore, generation units assigned for the reserve services should be able to ramp up or down for any required amount. 30

33 Most generation units have very limited ramping capability. The maximum ramping rate of a power plant depends on the type and size of the unit, and is usually described as some percentage of full or 50 % maximum power plant output. Type Max. ramp. rate (%/min) Gas fired plant <5% Coal fired plant <1% Nuclear plant 1%-5% Table 4 Ramping capabilities of different power plants. Ramping capability of the entire system should be able to cover all the anticipated and unpredicted changes in the load level and intermittent generation output. Ramping requirements Varibility Uncertanty Wind variability Load variability Wind forecast error Load forecast error Figure 7 Ramping requirements diagram. 31

34 2.4 Optimal power flow Optimal power flow formulation In deregulated electricity markets the goal of system operators is to obtain maximum profit under given operating conditions. In order to achieve this, power networks need to be operated in the most cost efficient way. In other words, system operators need to use different optimization methods to manage active and reactive power generation. One of these methods is based on the optimal power flow (OPF) model. The OPF model, first formulated in 1962 by Carpentier, has barely changed over the years. It is widely used by system operators to find the optimal solution for an objective function subject to power flow and other operational constraints, such as generator minimum output constraints, transmission stability and voltage constraints. There is a variety in OPF formulations with different constraints, objective functions, and solution methods. The objective function can include minimization of generation cost, minimization of power loss, and maximization of market surplus. The work in [21] presents a good survey of different OPF problem formulations. Mathematical formulation of the OPF could be written as a general constrained optimization problem. Min f x (2.2) Subject to: gx 0 (2.3) 32

35 hx ( ) 0 (2.4) Min Max x x x (2.5) This optimization problem has 4 main parts: An decision vector x; Objective function f x which also called the cost function; Inequality constraints (2.4) and (2.5) which limit the solution to a certain feasible set of variables; Equality constraints (2.3), which constrain the relationship between the decision variables. The objective function f x usually includes costs associated with active and reactive power generation and power loss other variables that are important to the optimization problem. The decision vector x includes 4 variables: Active power generation P Reactive power generation Q Voltage magnitude V Voltage angle δ Two of the four variables at each of the buses are known and the other two can be determined by solving the optimization problem. The combination of known and 33

36 unknown variables depends on the type of bus. The classification of busses is given in table 6. Bus type Specified Unknown Slack bus V, δ P,Q Generator bus/ P-V bus P, V Q, δ Load bus/ P-Q bus P, Q V, δ Table 5 Bus types. Besides the above-mentioned variables, optimal power flow may also include some additional variables such as: Active power reserves Reactive power reserves Transformer tap positions Phase shifter (quad booster) tap positions Equality constrains (2.3) usually include active and reactive power flow constraints based on Kirchhoff s law that requires that the sum of the power injected and withdrawn at any bus equals zero. G D inj L P P P P 0 (2.6) i i i G D inj L Q Q Q Q 0 (2.7) i i i P sin V V g cos b (2.8) inj i i j ij i j ij i j j 34

37 Q i ijcos i j V V g sin b (2.9) inj i i j ij j j Inequality constraints may include: Voltage magnitude constraint; V V V, Depending on the circumstances, voltage can vary; though, it Min Max i i i should remain within about 5% to 8% of the rated value. Active and reactive power generation constraints; P P P (2.10) Min G Max i i i Q Q Q (2.11) Min G Max i i i Line flow limits; S ( S ) 2 Max 2 ij ij (2.12) Other constraints depending on specific problem and variables OPF solution methods: The OPF problem is a non-convex and nonlinear optimization problem. Therefore, it is always challenging to find an optimal solution for this problem. A number of conventional solution approaches have been proposed to solve these OPF problems [21]: Linear programming methods Newton-Raphson methods Quadratic programming methods Nonlinear programming methods Interior point methods 35

38 Artificial intelligence methods Dynamic Optimal Power Flow (DOPF) is a dynamic optimization problem and has the same structure as the OPF. Although the DOPF seems to be similar to the Optimal Power Flow, it is different in one important aspect; unlike the conventional OPF that optimizes generation for a given moment of time, the DOPF optimizes generation output across a time horizon Therefore, the DOPF could be defined as a multi-period OPF problem that can include additional constraints, such as generator ramping limits and energy storage dynamics. 2.5 Line stability index: Voltage stability is one of the greatest concerns in terms of power system security assessment. In recent years electricity demands have increased gradually while transmission capacity remained the same. This imbalance can put stress on power system operations and increase the chance of contingency events such as line, generator and transformer outages. These events may cause significant voltage fluctuations that can ultimately lead to voltage collapse and a total blackout of the system. Voltage control for an AC power system is accomplished primarily by managing reactive power; changes in reactive power demand is accompanied by changes in voltage. The conditions for the voltage stability in a power system can be determined and maintained using voltage stability indices. These indices help system operators plan future operations. One of these indices is the line stability index. 36

39 The line stability index introduced by M. Moghavemmi et al. [22] measures the proximity to voltage collapse of each line of the system. For a typical transmission line, the index is calculated by the following formula: L ij 4XQj [Vsin( )] i 2 (2.13), where V i is the voltage magnitudes at the sending bus, is the difference between voltage phase angles, is the line impedance angle, X is the line reactance and Q j is the reactive power at the receiving end. The line stability index is used to find the stability index for each line connected between two buses of a system. The values of the L mn index increases with increasing power flow in the transmission system and varies from 0 when there is no load to 1, which represents a voltage collapse point. Another approach to calculate line stability index is to use the fast voltage stability index (FVSI) formula [23]. Similar to the line stability index value of FVSI, proximity to 1 shows that system approaches its instability point. FVSI could be calculated as: FVSI ij 2 4ZQj (2.14), where V i is the voltage magnitudes at sending end, X is the line V X 2 i reactance, Q j is the reactive power at the receiving end and Z is the line impedance. These indices can be effectively integrated into the OPF model in order to increase voltage stability of the optimized system and protect it from the voltage collapse. 37

40 Chapter Introduction At the operational level of a power system the OPF is solved in some form every year the planning purposes, every day for day- ahead markets, every hour, and finally every 5 minutes for real-time optimization. The day-ahead market is based on stochastic estimation of the load and intermittent generation units. Therefore it contains estimation/forecasting errors and uncertainties that should be covered by the regulating reserves, the amount cleared at the same time as generation. Each conventional generator unit participates simultaneously in both electricity and reserve markets. Errors in day-ahead wind forecast make it challenging for operators to dispatch power plants for the day-ahead market. But forecast accuracy increases in a four hour-ahead forecast compared with the 24 hour-ahead forecast. Therefore, solving the four hourahead optimization problem can help mitigate these prediction errors. It is reasonable to perform dynamic optimal power flow model for day-ahead optimization followed by 4- hour period optimization, prior to actual operation time, taking into account reserves determined from the day-ahead optimization and new forecasted load and wind data. 3.2 Formulation of Dynamic Optimal Power Flow for Day-Ahead market. Objective function min T NG Q f( x) [ P RPU RPD c c R c R t i ESP ESG ESQ ESG RUESP ESGU RDESP ESGD c P () t c Q () t c R () t c R () t G G PU PD Pi t c Qi t i t i t] i i i i (3.1) 38

41 The objective function in the proposed optimal power flow model includes cost functions of anticipated values of: G active power generation c P t NG i P i G reactive power generation c Q t NG i i Q i i reserve allocations NG i PU c RPU R RPD i c Ri c R t c R i i PD RUESP ESGU RDESP ESGD t t () () t charging and discharging costs of energy storage systems c ESP P ESG () t c ESQ Q ESG () t Power balance constraints: j inj Pi () t Vi() t Vj() t gijco s i() t j() t bijsin i() t j( t) i1... NB, j 1... NB (3.2) j j inj Qi (t) Vi(t) Vj( t) gijsin i( t) j( t) bijcos i( t) ( t) i1... NB, j 1... NB (3.3) G D inj P P () t P () t P () t 0 i 1... NB (3.4) i i i i G D inj Q Q () t Q () t Q () t 0 i 1... NB (3.5) i i i i Voltage limits: 39

42 Min Max V V() t V i 1... NB (3.6 a) i i i Line stability index: L ij L i1... NB, j 1... NB (3.6 b) Max ij Thermal limits: Power flow between buses i and j: P t V t g t V t V g t b t 2 ij () i () ii() i() j(t)[ ij cos( i() j(t)) ij sin( i() j(t))] i1... NB, j 1... NB (3.7) Q V t b V t V g t b t 2 ij (t) i ( ) ii i( ) j (t)[ ij sin( i( ) j(t)) ij cos( i( ) j(t))] i1... NB, j 1... NB (3.8) S P Q i1... NB, j 1... NB (3.9) ij ij ij S ( S ) i1... NB, j 1... NB (3.10) 2 Max 2 ij ij Generation limits: Min G PU Max P P () t R () t P i 1... NG (3.11 a) i i i i Min G PD Max P P () t R () t P i 1... NG (3.11 b) i i i i Min G Max Q Q () t Q i 1... NG (3.12) i i i Ramping constraints: 40

43 For a generator, the ramp rate is the rate at which the generator changes its output. A generator unit cannot provide reserve higher than its ramping rate. It is important to understand that depending on parameters of the generator these ramp rates constrain the scheduled reserves. RampDown G G PU RampUp P P () t P ( t1) R P i 1... NG (3.13 a) i i i i i RampDown G G PD RampUp P P () t P ( t1) R P i 1... NG (3.13 b) i i i i i Reserve requirement: The sum of allocated reserves should meet the required amount. PU PU Ri () t R () t i 1... NG (3.14) i PD PD Ri () t R () t i 1... NG (3.15) i Apparent power constraints: In order to establish relation between reactive and active power outputs, these two variables should be limited by the apparent power. Moreover, active power reserves should also be included in that constraint. S () t ( P () t R (t)) ( Q ()) t i 1... NG (3.16) G G P 2 G 2 i i i i G Rate S () t S i 1... NG (3.17) i i Energy storage constraints: 41

44 ESG P () t - charged/discharged active power. This variable can be positive when the energy storage system discharges or negative when it charges. ESG ESC(t) - energy storage state of charge at time t is changing according to P () t, state of charge at previous moment of time with self-discharge equal to (3.18). Also, the energy storage cannot exceed its maximum capacity (3.19). ESG ESC(t) ESC( t 1) P ( t) (3.18) 0 ESC(t) ESC Max (3.19) Energy storage systems as well as generators are able to produce reactive power and limits on the real and reactive power by apparent power are necessary. S () t ( P ) (Q ) ES ESG 2 ESG 2 (3.20) S () t S Rated (3.21) ES ES 3.3 Optimal power flow for four hour-ahead Dynamic Optimization Problem. Once the levels of power generation and reserve allocations are determined by the day-ahead optimization model, we can create the four hour-ahead optimization problem. In this four hour-ahead optimization model we introduce new constraints for conventional generation and energy storage units. Generation output should not exceed day-ahead scheduled generation and scheduled upward reserves assigned for a particular generation unit should not be lower than the scheduled generation and scheduled downward reserves (3.24). The combination of the day-ahead and four hour-ahead optimization problems is useful to determine the effectiveness of the reserve 42

45 requirements as well as the performance of energy storage under different load and wind power fluctuations. Objective function min t4 NG G Q G P RQ Q ESP ESG ESQ ESG f( x) P RP c Pi t c Qi t c Ri t c Ri t c P ( t) c Q ( t) i i i i (3.22) t i Subject to: (3.2)-(3.2), (3.13)-(3.21) and new active power generation limits: GSch PD G GSch PU P () t R () t P () t P () t R () t i 1... NG (3.23) i i i i i SchESG ESPD ESG SchESG ESPU P () t R () t P () t P () t R () t i 1... NG (3.24) i i i 43

46 Chapter Implementation The proposed DOPF for the day-ahead market and sequences of 4 hour-ahead optimal power flows for real-time optimization has been implemented using the open source package MATPOWER [24] written for MATLAB and designed for power system simulations. MATPOWER allows users to modify the existing code provided in the package. More importantly, it provides an extensible architecture for easy and structured modification of static optimal power flow models by adding additional linear constraints, variables and cost functions. While linear constraints and equations can be added using MATPOWER designed functions, all non-linear modifications must be done manually by altering the provided code. The package provides the optimization tool MIPS that implements the Primal-Dual Interior Point Algorithm that can be used externally as well as internally. The multi-period DOPF problem can be regarded as a sequence of static optimal power flow problems where for each hour the optimal power flow model represents an islanded power system with some connections through time constraints. In order to use MIPS it is necessary to provide the gradient and Hessian of the Lagrangian of the optimization problem. The basic calculations of both of these are provided in the MATPOWER package however they should be extended to the dynamic case model. The IEEE 30 bus test system was chosen for simulation of the proposed DOPF and it can also be found in MATPOWER package. 44

47 Figure 8 IEEE 30 bus system diagram. Bus P Q Bus P Q

48 Table 6 Loads in IEEE 30 bus system. Bus Pmin Pmax Qmin Smax a b c Table 7 Base generation in the IEEE 30 bus system. 46

49 4.1.1 Load Load variations in any time period have an important effect on power system operation. The generation has to be planned in advance in the day-ahead market based on forecasted values and then adjusted during the real-time operation in accordance with the actual electricity demand and reserve requirements. In order to model the load fluctuation, data from the day with the most extreme hourly load variations were chosen from PJM database. PJM provides both the forecasted and real load values, and based on these numbers we modeled the forecasted and real load variations for the IEEE 30 bus test system. MW Load PJM Day ahead Actual Figure 9 Forecasted and actual load curves for one day, PJM. 47

50 250 IEEE 30 bus 200 MW Forecasted Actual Figure 10 Forecasted and actual load curves for the test system Wind Generation Output Wind variations are modeled in the same way as the load fluctuations and based on the forecasted and actual wind based generation output. Similar to the load curve data, wind-based generation output data was selected from the daily wind generation values with the largest hourly changes in the wind. The initial level of the wind generator output was set to 80 MW, and the maximum output throughout the day will almost reach the wind-based generator s maximum output capacity. 48

51 Wind PJM MW Day ahead Actual Figure 11 Forecasted and actual wind generation data for one day, PJM Wind IEEE 30 bus MW Wind actual Wind forecast Figure 12 Forecasted and actual wind generation 49

52 4.1.3 Wind Based Generator The IEEE 30 bus test case has 2 large generators, Gen 1 and Gen 2 and they are located at bus 1 and bus 2 respectively. We assume that they are coal-fired plants and that can incur significant social cost. Due to negative environmental impact, coal power plants should be replaced or shut down first. In this study we assume that a large wind-based generator unit is placed at bus 2 along with Gen 2 and aimed to replace or reduce the use of the coal-fired generator at the given bus Energy Storage System The Energy Storage System (ESS) should be considered as a responsive load when being charged and as a generation source when discharged. In MATPOWER, a responsive load can be modeled as a generation unit, with negative minimum power output and zero maximum power capacity, thus the ESS could be modeled as a generator, with negative minimum power and positive maximum capability. The maximum and minimum active power values depend on the state of charge of the EES. For example half-charged 40 MW ESS will has -20MW as its minimum power output and +20MW as its maximum. Reactive Power Capability In most cases, storage systems by themselves do not have reactive power capability, however for a relatively modest incremental cost, reactive power capability can be added to most storage system types through power electronics [7]. Reactive power capability of ESS could be defined through the P-Q capability curve. 50