CONTINGENCY OPTIMIZED ENERGY_ RESERVE CAPACITY AND REACTIVE POWER SCHEDULING AND PRICING IN AN ELECTRICITY POOL

CONTINGENCY OPTIMIZED ENERGY, RESERVE CAPACITY AND REACTIVE POWER SCHEDULING AND PRICING IN AN ELECTRICITY POOL DISSERTATION Submitted in partial fulfilment of the requirements of Master of Engineering in Electrical Power Engineering Hitendra Dev Shakya Department of Electrical and Electronics Engineering School of Engineering Kathmandu University December 2005 CONTINGENCY OPTIMIZED ENERGY, RESERVE CAPACITY AND REACTIVE POWER SCHEDULING AND PRICING IN AN ELECTRICITY POOL DISSERTATION Submitted in partial fulfilment of the requirements of Master of Engineering in Electrical Power Engineering By Hitendra Dev Shakya Under Supervision of: Dr Bhupendra Bimal Chhetri Associate Professor and Mr. Roshan Bhattarai, Assistant Professor Department of Electrical and Electronics Engineering School of Engineering Kathmandu University Department of Electrical and Electronics Engineering School of Engineering Kathmandu University December 2005 DEDICATION With a prayer I dedicate it to my mother Laxmi Kumari Shakya and to the memory of my father late Dr Janak Dev Shakya. ACKNOWLEDGEMENT I gratefully acknowledge the supervisory support and guidance provided throughout the thesis by Associate Professor Dr. Bhupendra Bimal Chhetri, Head of Department, Electrical and Electronics Engineering Department, and also Assistant Professor Roshan Bhattarai, Electrical and Electronics Engineering Department, for the kind supervisory assistance. I must also acknowledge the great help that was the information received from the emails from Prof. Carlos E Murillo Sanchez, Cornell University, and Dr Ray Zimmerman, PSERC, Cornell University, both of whom had together developed the program package MATPOWER and the particular MINOPF program that is used in this thesis. This is the place for acknowledging with thanks. So I wish to thank Kathmandu University, the NORAD organization and Norwegian University of Science and Technology (NTNU) for once again granting me the opportunity to complete the degree that actually started in Trondheim in 1998 and also let me not forget to add to Prof. Arne T Holen and Dr Kjetil Uhlen (NTNU) that it is a continuation to what I have learnt with you. The list is long but I should not shrink from mentioning at least the following – Mr Mahesh Acharya, Nepal Electricity Authority for giving me initial guidance and suggestion, Mr Morten Husom, our NETBAS instructor, colleagues in NEA, Bigyan Shrestha, Mr. Rajeswor M Sulpia, Jayendra Shrestha, my seniors in Chilime Dr Damber Bahadur Nepali and Lila Nath Bhattarai. Not to forget, my NORAD fellow mates of this MEPE degree, particularly, I acknowledge the various suggestions received from Chandan, Herbert, Manohar, Pramod and Vijaykumar. Last but not least, I thank my wife and my son and daughter for bearing with me and understandingly supporting me throughout the course and this thesis in particular. ABSTRACT Electricity is a 'product' which has unique characteristics obeying certain laws of physics. Hence, the market has to adapt to its needs. Introduction of competition into the electricity sector has not been smooth in most of the countries. In Nepal also, we must prepare ourselves and design a market amenable to our particular constraints. The Generation business requires large investments from scarce government resources. The private sector must participate to satisfy the increasing demands. There is ample experience about competition in this sector in Nepal. Hence, it is submitted that Electricity Pool model is appropriate for Nepal with single-ended competition in generation sector with a single buyer. In this particular Pool model, the Independent System Operator (ISO) acts as both the system operator and market operator including grid operator and manages the ancillary services. I requires spinning reserve for system security. In a market, t reserve energy has a price. This thesis has proposed a method to optimize both energy (P) and reserve (R) considering also the contingencies. After designing an objective function and solving for the test case, total cost and energy and reserve allocation are compared against a Fixed Reserve scheduling, proving that the Reserve responds to the costs. It is hence termed here as 'Responsive Reserve' OPF (RROPF). The solution is also 'contingency secure'. In a Market Power test case, the Reserves were found to be shifted within 'contingency constraints'. A method of de-committing unnecessary expensive generators during Off Peak load is tested, showing its applicability for realtime OPF. The RROPF m ethod sends correct signals to consumers by reducing R prices when there is less load increase during peak, and to the ISO to forecast the load and contingency probability correctly. Finally, the optimization includes Reactive Power (Q), using a New conversion method from the generator cost function which removes the need for a Separate Market for Q. The results show that the allocated Q is optimized, responds to the prices and also it is contingency secure. Inclusion of Reserve Q can also be done but not included in this method. Pricing of the P, R and Q is done easily from the Lagrangian multipliers at the buses. The thesis discusses a Perturbation method for finding ‘P only’ price at the nodes, and finally, presents the Pool model with given methodology. Further market simulation tests need to be done to prove its usefulness hopefully for the South Asian region. TABLE OF CONTENTS GLOSSARY OF ABBREVIATIONS ............................................................................i LIST OF SYMBOLS .....................................................................................................ii LIST OF FIGURES ......................................................................................................iii LIST OF TABLES ........................................................................................................iv Chapter 1: INTRODUCTION................................................................................1 1.1 Introduction................................................................................................1 1.1.1 Objective of the Thesis ....................................................................3 1.1.2 Organization of the Thesis ...............................................................3 1.1.3 Limitations of the thesis ...................................................................5 1.2 General Overview......................................................................................6 1.2.1 The Electricity Sector in Nepal........................................................6 1.2.3 The American Experience - Competition in Electricity Comes Full Circle ................................................................................................7 1.2.5 Restructuring and Competition.......................................................8 1.2.7 Electricity Market and Restructuring in Developing Countries- ..10 1.2.8 Model Proposal for Nepalese Electricity Sector – Pool Model ....12 Chapter 2: LITERATURE REVIEW.....................................................................14 2.1 Ancillary Services in an Electricity Pool Market.................................14 2.1.1 Reliability, Security and Adequacy: ..............................................14 2.1.2 Operating Reserve..........................................................................16 2.1.3 Payment for Capacity:....................................................................17 2.1.4 Contingency and Local Reliability Costs and the Thesis ..............18 2.2 The Optimal Power Flow Paradigm ......................................................20 2.2.1 Economic Dispatch........................................................................20 2.2.2 Optimal Power Flow – ...................................................................20 2.2.3 MINOPF Using NEWTONs Method.............................................21 2.2.4 Security Constrained Economic Dispatch (SCED)and Real time Optimal Power Flow (RTOPF) ......................................................22 2.3 Tools Used- MatlabTM, MATPOWER, MINOPF. ................................23 2.3.1 MatlabT M ........................................................................................23 2.3.2 MATPOWER.................................................................................23 2.3.3 MINOPF.........................................................................................24 Chapter 3: THE CONTINGENCY OPTIMIZED INTEGRATED ENERGY, RESERVE CAPACITY AND REACTIVE POWER SCHEDULING AND PRICING.......................................................26 3.1 The Concept..............................................................................................26 3.1.1 Simultaneous Offer of Energy and Reserve ...................................26 3.1.2 Contingency Optimization (CON-OPT) ........................................28 3.1.4 Contingency Optimized Energy and Reserve Scheduling .............29 3.2 Optimized Reactive Power Flow and Scheduling .................................30 3.2.1 One Regulation for Q.....................................................................30 3.2.2 Single Commodit y– The Capacity Curve ......................................31 3.2.3 The Objective Function and OPF ..................................................31 3.3 Methodology Adopted for Implementation of the Exposition.............36 3.3.1 System Description and Test Cases ...............................................36 3.3.2 The OPF Software Program...........................................................37 3.3.3 The Generation Cost Curves:.........................................................38 3.3.4 Market Power Test Case ................................................................39 3.3.5 Decommitment and Other Test Cases............................................40 3.3.6 Simplification of the Objective Function.......................................40 3.3.7a Option 1 of Solving the Contingencies .........................................43 3.3.7b Option 2 of Solving the Contingencies .........................................45 3.3.8 The Contingencies and the Network ..............................................46 3.3.9 Responsive Reserve Optimal Power Flow (RROPF): ...................46 3.3.10 Fixed Reserve Objective Function (FROPF) .................................47 3.3.11 Reactive Power Co-Optimization ..................................................48 Chapter 4: ANALYSIS OF THE CASE-RESULTS AND DISCUSSION .......50 4.1 Case Discussion .......................................................................................50 4.1.1 Case1: Initial Peak Load Case– Combined Network Option.........50 4.1.2 Fixed Reserve OPF Case ...............................................................51 4.1.3 Case 2 – Market Power Test ..........................................................55 4.1.4 Load Decrease by 2% Case............................................................58 4.1.5 Decommitment...............................................................................60 4.1.6 Final CCOPF with Reactive Power Included to the Energy and Reserve:..........................................................................................61 4.2 Discussion on the Methods for Pricing of the Energy and Reserve ....62 4.2.1 Pricing by Perturbation Method .....................................................63 4.2.2 Pricing of the P, R and Q with the COPRQ Scheduling ................65 4.2.3 Pricing Based on Zones..................................................................66 4.2 Summary of Results .................................................................................67 4.2.1 Result of Contingency Optimization: ............................................67 4.2.2 Results for Fixed vs. Responsive Reserve ....................................67 4.2.3 Market Power Test.........................................................................67 4.2.4 Reactive Power Co-Opt Test: ........................................................67 4.2.5 Expected Cost ................................................................................68 4.3 Conclusion ................................................................................................68 4.4 Pool Design with the Above Mechanism................................................68 4.5 Limitation and Further Work ................................................................69 REFERENCES ...........................................................................................................70 Appendix A: Case-Data.............................................................................................74 Appendix B: Use of OPF with the Data Files ..........................................................76 Appendix C: Result Details .......................................................................................78 Appendix D: The Californian Experience ...............................................................91 Appendix E: Competition in Electricity Comes Full Circle -The American Experience: .........................................................................................93 Appendix F: Better Regulation or Deregulation ...................................................95 Appendix G: Looking for Solutions within the Restructuring and Deregulation Problems .............................................................................................97 Appendix H: Attributes of Electricity as a Product.............................................100 Appendix I: Ancillary Services in an Electricity Pool Market..........................102 Appendix J: Economic Dispatch & Optimal Power Flow..................................106 Appendix K: The Generation Cost Curves...........................................................113 GLOSSARY OF ABBREVIATIONS Abbreviation AGC AS CAS CCOPF CCOPRQF CON-OPT COPRQ DISCO ECMP FACTS FROPF GENCO IEEE INPS ISO LDC LOLP MATPOWER MCP MINOPF MVAR MW NEA NERC OPF PJM PPA PSERC RCMP RROPF RRQOPF RTOPF SARI SCADA SCED SCOPF SLP USA VOLL Full-Form Automatic Generation Control Ancillary Services Capacity Ancillary Services Contingency Constrained Optimal Power Flow Contingency Constrained Optimal Energy, Reserve and Reactive Power Flow Contingency Optimization Contingency Optimized Energy, Reserve and Reactive Power Distributing Company Energy Market Clearing Price Flexible AC Transmission Systems Fixed Reserve Optimal Power Flow Generating Company Institute of Electrical and Electronics Engineers Integrated Nepal Power System Independent System Operator Load Dispatching Centre Loss of Load Probability A software for power system from Cornell University Market Clearing Price An OPF software from Cornell University Megavar Megawatt Nepal Electricity Authority North American Electric Reliability Council Optimal Power Flow Pennsylvania, New Jersey, Maryland Electricity Pool Power Purchase Agreement Power Systems Engineering Research Centre Reserve Market Clearing Price Responsive Reserve Optimal Power Flow Responsive Reserve and Reactive Power Optimization Real time optimal power flow South Asian Regional Initiative Supervisory Control and Data Acquisition Security constrained economic dispatch Security Constrained Optimal Power Flow Successive Linear Programming United States of America Value of Lost Load i LIST OF SYMBOLS Symbol Pi Qi Ct PD PL Pik ? Vi µi Sij Gi R pk ? ? ? ? Ri Pi RRi Qi Meaning Active power at bus I Reactive Power at bus i Cost function Power Demand (load) Active power loss Active power at bus I for the kth contingency Lagrangian Multiplier Voltage at bus I Lagrangian Multiplier for the inequality constraint where used Apparent Power Flow from bus i to j Generating Capacity of ith generator Reserve Capacity Probability of the kth contingency Lagrangian for Reserve capacity at bus i Lagrangian for Active power at bus i Lagrangian for (Active power-Responsive Reserve) at bus i Lagrangian for Reactive power at bus I ii LIST OF FIGURES Figure No. Caption Page Figure 2.1 – The Reserve Capacity Pyramid and the Responsive Reserve Optimization ....................................................................................................................15 Figure 3 - Cost curve of Q dependent on P cost and P value .......................................35 Figure 4- Generator cost curves...................................................................................39 Figure 5 -Theoretical Cost curves of P, R and P +R in a generator ( R decrease with P increase)..................................................................................................42 Figure 6 – Actual Cost curve of P, R and Q in a generator .........................................43 Figure 7 – Response vs Fixed Reserve – P and R allocations .....................................54 Figure 8- 6 cases – P allocation to get Pmax.............................................................55 Figure 9 – P and R allocation in Fixed vs Responsive Reserve with Market Power case.............................................................................................................58 Figure 10 – Comparison of P and G(Pmax) in Market Power case vs Load Incr 2% .59 Figure 11 – Comparison of Lambda P at buses – MP case vs load incr 2% ...............60 Figure 12 - P and Q allocation - with Q and without Q Optimization........................62 iii LIST OF TABLES Table No. Caption Page Table 1 - Pmax set received from option 1 - higher than other case ..............................50 Table 2- The solution from the simplified objective function- base case 0 .................51 Table 3 - Solution of Pg, Pmax from the Responsive Reserve case ............................51 Table 4 6 Cases – P allocation to get Pmax..............................................................55 Table 5- Comparison of the Fixed Reserve and Responsive Reserve OPF for Market Power Test case.............................................................................................57 Table 6 – Compare –when load decrease by 2% .........................................................59 Table 7 – Power allocation and obj.fn. Cost with G5 decommitted ............................60 Table 8 – P,R and Q optimization-results after RROPF ..............................................61 Table 9 – Pricing comparision – lambda P of Initial, Market Power, Decommitted...64 Table 10 – Pricing of P and Q – after P R Q optimized solution.................................66 iv Chapter 1: 1.1 INTRODUCTION Introduction The monopolistic Electricity industry has been deregulated in many of the developed countries and it is being introduced in many developing countries like Nepal. Maturing of the technology and the market has made it possible. Government resource scarcity has accelerated it with the concept that market competition will force economic efficiency. Initially, the private sector was invited to participate in the generation sector. As the general capacity and confidence of the private sector increased, there have been gradual efforts in deregulation and introduction of competition in the whole of the electricity sector. Hence, Restructuring and Deregulation are the pertinent issues in today’s electricity sector. High electricity tariff and the scarcity of capital to meet the increasing demand in Nepal probably caused electricity policies of 1992 and 2001 to introduce competition in the electricity sector. The international development agencies such as World Bank and the donor countries have also influenced the process. The national utility Nepal Electricity Authority has been preparing for restructuring by practicing internal unbundling. Further progress is expected in restructuring and deregulation soon. Hence it is high time to think towards deregulating and designing a market for electricity. Market design for electricity is very complex and there is no unique proposal or solution. Every market design must be suited to the physical, geographical, financial, economical and political conditions of the area. Removing regulation creates a free Market. Creating a competitive market is more difficult. This dissertation seeks to propose a market design for Nepal taking into account its present characteristics and vulnerabilities. The Pool market has been proposed. Based upon this model, the thesis proposes the methodology and a mechanism of Market Operation. 1 Optimal Power system operation based on economic scheduling and merit order dispatch is a regular practice even in vertically integrated sectors. In a market, the scheduling depends not on the inherent cost characteristics of the generators but on the price offers made by the generators for the energy. The author had the opportunity to work in the national Load Dispatching Centre for three years, implement a SCADA system in there, and be involved in system operation. Additionally, during more than ten years of experience in power plant operation, maintenance, construction and design in the national utility including a semi-private power producer, some insights were gained into the electricity sector of Nepal. The author had been particularly involved with the System Stability and had done study work on small signa l stability of Integrated Nepal Power System (INPS) during an earlier post- graduate study. The observations and the perceptions gained have enforced the concept that an Electricity Pool Market that included Energy and Reserve capacity in a single-settleme nt clearing mechanism is suitable for Nepal. Load variation and disturbances in a power system can not be prevented or predicted. It necessitates Reserve capacity in the system, a capacity available to produce when necessary, and a market where such a Reserve capacity is paid. Capacity payment also ensures adequacy of supply. The market should determine the role of capacity as a hedge for the risk of high prices due to ‘an obligation to serve’, albeit at a high price. In this Pool model, the market to determine the capacity price and reserve price is the bid offer by the generators themselves. In addition to the Reserve capacity, which may consist of spinning reserve, nonspinning reserve, or regulation capacity, there are other ancillary services like voltage support or reactive power, black start capability and line charging capacity, dynamic scheduling, energy imbalance, regulation etc. From a steady state stability point of view and from a system operator’s point of view, one of the most important ancillary services would be reactive power or the voltage support. Hence, it is aga in natural that this should be not free but priced. But pricing of reactive power has remained a complex issue and creating a market for it is a challenge to the market designers. Regulatory practices have mostly determined the price of such services. Here, the combined Optimal Power Flow solution is proposed which provides a reliable method 2 to optimize the system operation based on its price and at the same time, determines the predictable and rational price for the Reactive Power. Thus, a single-ended generating market that included not only energy but also reserve capacity and reactive power and a single settlement clearing mechanism is proposed for Nepalese ‘Electricity Pool’. 1.1.1 Objective of the Thesis The objectives can be outlined as a) To study the evolution of deregulation and the experiences worldwide in electricity sector and propose a market design suitable for Nepalese power sector restructuring and deregulation. b) To test a method for contingency constrained energy and reserve optimization and scheduling for a Pool market and to verify the benefits of the proposed method c) To test the mitigation of market power evident in Pool markets by above method d) To include in a single Contingency Constrained Optimal Power Flow (CCOPF) the three products provided by a single entity viz. Active Power, Reactive Power and Reserve Capacity which are valued and hence, offered with a price, in the market, and discuss the results. e) To discuss the proposed Pool model mechanisms in view of the Contingency Constrained Optimal Energy, Reserve and Reactive Power scheduling. 1.1.2 Organization of the Thesis The first chapter introduces the electricity market, the pertinent issues of deregulation and the Electricity Pool model. The concept of capacity payment is discussed and its use as hedge against load fluctuation and contingency. It gives a general overview of the electricity sector, the subject of deregulation and regulation, and understanding of 3 the market economics applied to electricity; with respect to experiences in California. It then discusses the Pool model and restructuring vis a vis Nepal. The second chapter gives an overview of the literature review done while carrying out the dissertation work. The rationality of capacity payment and the utilization of reserve for contingency security are discussed. The market power problem and its solution in a reserve market and reactive power payment are discussed. The Optimal power flow theory is introduced and economic dispatch and security constrained dispatch as well as the contingency optimization of energy and capacity is introduced. The tools used for optimal power flow (OPF: MINOPF and MATPOWER) are explained in brief. In the third chapter, the formulation of the objective function and the implementation of contingency constrained optimization of energy, reserve and reactive power are described in detail. The theory and the methodology are described as follows. 3.1– The theory of the method proper – Contingency Constrained Optimal Power Flow (CCOPF) and the Objective Function 3.2– The theory of including the reactive power in the CCOPF. 3.3- The Description of the Methodology adopted for implementation of the theory The final chapter analyses the Results and discusses the import of the results towards the conclusion. The verification of the RROPF and the Contingency Optimized Energy Reserve and Reactive Power scheduling is done and is recommended for implementation. Discussion about locational Pricing of the energy, reserve and reactive power is done, while also mentioning the mechanisms in the Pool model with this method. Further study area is suggested. The appendix contains elaboration on some of the issues related to the thesis such as California crisis analysis, Ancillary services, Optimal Power Flow method, Generation cost curves etc. for easier understanding of the subject. It also includes the References, the Input Data to the Case files, the Output data detail. 4 1.1.3 Limitations of the thesis The thesis has been limited to the formulation and testing of the methods as mentioned above and the market simulation of the method has not been undertaken to provide further proof as it requires more economic theory than possible in this treatise. The complexity of writing a program for OPF meant that a ready software had to be used. Modification of the codes was not possible and hence, direct nodal pricing of energy using dual lagrange multipliers for capacity was not done. The contingency optimization may be solved using stochastic multi-objective optimization methods but which was out of scope of this thesis. Price elastic demand was not included in the method. It is possible to simulate a demand behaviour by adding a generator but this thesis has not tested this implementation. The reserve capacity for reactive power is an interesting extension of this method but which has not been used. 5 1.2 General Overview Electricity being a part of the basic infrastructure for a country’s development, governments have tended to regulate it rigorously and keep it vertically integrated. The electricity industry is capital intensive and technology intensive. It means the government has to support and initiate many of the projects. Hence, Electricity has been a natural monopoly industry for long. While deregulating the industry and creating a market for it, the unusual set of physical and economic attributes of Electricity must be recognized and incorporated into the successful design of competitive market and regulatory institutions to avoid performance failures. 1.2.1 The Electricity Sector in Nepal It is a much-repeated fact that Nepal has the second highest water storage and generating capacity in the world. In terms of generating capacity, 83,000 MW theoretical is not such a large capacity when we compare with electricity consumption of the two neighbouring countries, India and China, considering them as its market. It is also well known that we have developed less than 1% of this potential. Nepal ventured into electricity generation in 1911. Since then it has been a part of the government’s business to provide electricity to the people, to the privileged few. In almost a century of its history, it has grown from 500 kW to a little more than 500 MW only. Notwithstanding the difficulties in developing hydro-power within a framework of poor, technologically backward and mountainous country, it raises many questions about the efficacy of the government involvement in this sector. Looking for alternative solutions in Nepalese electricity sector, therefore, should not be evaded longer. In fact, it has become imperative to think of restructuring and deregulation as a distinct possibility. In that respect, it is wise to study experiences in other countrie s and follow their discussions in order to learn from their mistakes and wisdom, and to chart a path that is suitable and effective. The American case study presents the evolution appropriately. 6 1.2.3 The American Experience - Competition in Electricity Comes Full Circle The electricity market began as a free market in the 1880s in the USA, one of the first countries where electricity started as an industry. It had private entrepreneurs who invested in electricity and provided it as a luxury good to the people. Within 25 years, suppliers pleaded for regulation, arguing that they faced ruinous competition. The public was not served well either.[34,Lester] A consensus emerged that verticallyintegrated companies should be granted monopoly status within a geographical area in exchange for regulation that obliged them to serve consumers at low prices but gave them essentially guaranteed rates of return that could attract capital. Coming Full circle towards competitive Electricity sector: A combination of factors contributed to rising prices. Many utilities had made unsound investments resulting in high costs, especially for nuclear plants, and were unable to operate the new plants efficiently. Consumers protested that they should not have to pay for bad investment. Left to its own devices, a monopoly might take advantage of its market power to raise price. These reasons contributed to the Deregulation movement in USA which was in full force in 1990s. Better Regulation or Deregulation: As can be seen from various countries’ experiments with deregulation, it is a very treacherous path and in many countries than not, the answer is not deregulation, but reforming regulation. Making deregulation work requires better regulation. When a market where one or more sellers have market power is freed of regulation, prices are likely to rise far above marginal cost and other problems will occur. If deregulation is to bring benefits to consumers, the markets it creates must be competitive. Creating new institutions: Deregulation requires new institutions, primarily to perform functions formerly carried out by vertically integrated utilities. An independent systems operator is 7 needed to coordinate supply and demand. A regional transmission operator is needed to manage transmission. Regulators need effective tools to monitor the system operation and the market and to test and simulate market behaviour to determine market power. An important component is training individuals and acquiring hardware and software. Therefore, the costs of setting up new market institutions must be accounted for in determining whether restructuring yields a net social benefit. Capital Costs: If a deregulated company has to renegotiate its loans at market rates of return, accounting for risk, total costs would increase. The current uncertainty about industry restructuring will force borrowing rates to be higher. In a competitive market, the participants must see themselves as price takers, not price setters. Since electricity cannot be stored, designing a market that prevents a company from having market power is much more difficult for electricity than for other goods and services. 1.2.5 Restructuring and Competition It should not be summarily concluded that deregulation is an unacceptable risk for Nepal. Learning from others’ experiences, we can design and modify the industry to be more efficient and growing. Hence, some of the weaknesses known should be scrutinized to find a solution. The performance improvements can come from a combination of institutional reforms: Vertical and horizontal restructuring to facilitate competition and mitigate crosssubsidization problems, good market designs that facilitate efficient competition among existing generators, competitive entry of new generators, and retail competition for industrial customers. Market Models: The most efficient design of wholesale energy markets continues to be a subject of dispute among interest groups and independent experts.[3,Stoft]. Should the market be built around a pool or rely on bilateral contracts? Should there be locational pricing 8 of energy and operating reserves? How should transmission capacity be allocated? Should transmission rights be physical or financial? There are many architectures implemented and some are a mixture of them. Mainly, there have been two discussions for competitive markets. 1. Bilateral markets and centralized markets 2. The Pool model and the Exchange model Bilateral markets are those where consumers directly purchase from the generators and use the trans mission lines for a wheeling charge. These markets are good for the bulk supply of energy. But due to the intrinsic nature of the product ‘electricity’, ancillary products like reactive power, stability reserve and inter-dependent losses, wholly bilateral markets are not possible. The latter two models are the two models of centralized market. Exchange model is a double-ended with retail consumer as well as whole-sale distribution competition. For an Exchange model, with retail participation in bidding for energy, it requires very robust market economy, sound communication and information system and efficient financial institution for settling the financial issues. The information about the market and the power system has to be free, accessible and there sho uld be no information asymmetry. Strong regulatory body should be there to protect the consumers from harm as any preventive or corrective regulation has to be very fast to be effective. For these reasons, Exchange model is not yet suitable for developing countries and Nepal. Experience in Deregulation - the Californian Experience The Californian power market fiasco at the end of last century has been useful as a case study for many of the other deregulating countries. Some of the features evident from the study of the Californian experience are as follows 1. Price of supply was not allowed to transfer to the consumer- regulated tariff. 2. Capacity was separately traded, so capacity withholding occurred driving spot market prices high. 9 3. Incentive for investment in generation was low, the market was capacity deficient. It imported lots of energy, so suppliers went to others during peak- load when price caps were introduced. 4. Price caps and other regulations were counter productive. Resulting in rolling black-out.[38,Clark] Lessons Learnt: From these observations some inferences can be drawn. Few necessary features for a competitive power market are 1. Retail Prices Must Reflect Costs 2. There must be competitive markets for regulation, spinning and non-spinning reserves, and reactive power. 3. Timing of Market Clearance is important 4. Transmission must facilitate Competition 5. There must be sufficient number of generators and none should have a domineering presence. 6. The total capacity in the system should be sufficiently bigger than the load demand and there must be price signals to encourage investment. 1 .2.7 Electricity Market and Restructuring in Developing Countries- Electricity is a high value infrastructure in developing countries, and part of the governments’ responsibility. Leaving it to the market requires strong market development which is normally absent in such countries. Hence, deregulation must be cautiously applied. 10 The Pool Model with Adaptations: A pool model with the correctly designed mechanisms is suggested for the developing countries. The detail mechanisms can be country and economy specific but a general methodology as outlined here is recommended. An Independent System Operator has become a necessity for avoiding the conflict of interest in vertically integrated utility with private sector participation in the system. Hence, in many countries facilitation is being done to isolate the System Operator and allow full access of the transmission lines to the generators. The Electricity Pool: The electricity pool model is a single side competitive market with competition at the seller side. The particular market design involves generators participating in a singleended market competing with their price offers of generation. The Independent System Operator with integrated Grid Operator provides the services of clearing the Market as well as Optimal system operation and transmission of ‘the commodity’ up to the Distributing companies. Distribution is envisaged as a State / private / public monopoly. Wholesale and retail buyer competition can be introduced after the proper infra-structure and market development has occurred. Tariff is designed as flexible, zonal and periodically updated according to the Market Clearing Prices by the Distributing companies, but which is regulated and supervised by a Regulating authority. In such a Pool market design, experience in other markets have shown that there are some inherent weaknesses, such as market power of pivo tal players, disincentive for investment in generation and perverse signals for congestion and scarcity. On the other hand, complete deregulation, as discussed, has more complexities and incurs more costs with few benefits in the short run. Underdeveloped electricity sectors like ours can not aspire to such competitive markets at once. Hence, Pool model being an intermediate necessity, the challenge is to overcome or mitigate the weaknesses to suit the needs. In this intermediate stage, without demand side participation, there may be regulation on maximum price for energy (caps), and monitoring of supply competition to check market power is also necessary. 11 Costly Market Structures: Every time a new market is created, new opportunities are created to exercise market power. Each must be monitored to detect and punish fraud and collusion. Each of these new markets must be structured to facilitate competition. Location is important in all these markets. For example, the market for real power depends on the capacity and location of the transmission links. The value of reserves depends on the location of the generating plant providing the reserves and reactive power is very locational. 1.2.8 Model Proposal for Nepalese Electricity Sector – Pool Model There are various models of power market in the paradigm of Restructuring and Deregulation of Electricity Sector. Designing an electricity market for Nepal firstly involves 1.Restructuring 2. Formation of ISO and Grid Operator 3. Formation of Regulatory Commission 4. Acceptance of locational monopoly of DISCO 5. Introduction of Generation competition but no retail competition 6. Possible and recommended introduction of variable tariff, periodic and depending on metering technique, particularly to large consumers. High tariff, lack of government capital with many demanding sectors, and encouraging private sector participation are the factors driving Nepal towards restructuring. To use the Indian power sector as a market, a Pool model market in Nepal will facilitate to determine the price of our Generation. It is a fact though that to avoid being exploited by the Indian monopsony, SARI grid or market integration within India is necessary. Undeveloped market and economy, weak technology base, small size of market, lack of experience, an encouraging private sector participation in generation business, and a well- equipped Load Dispatching Centre are the reasons for believing that a Pool model will be successful here. Unbundling: Regarding restructuring of the utility and eventual market creation, questions abound about whether a single holding organization is better or it should be disbanded into small generating and distributing companies. Economists require that in order to have 12 a competitive buyers’ market, there must be sufficient number of sellers. This would lead us to believe that the utility should be broken down to small companies. But electricity is a capital intensive and technology heavy business. Hence, economy of scale and institutional strength matters in a country like Nepal. While the discussion goes on, this thesis, assuming a healthy competitive generation market in a Pool model, goes on to propose a Contingency Constrained Energy, Reserve and Reactive Power Optimized scheduling and pricing methodology for the Electricity Pool of Nepal. Price signals from Market Clearing Price for capacity increase and consumer behaviour has to be studied during any method application in a Pool model. Marginal Cost price by generators and protection against withholding by pivotal player has to be ensured. In this design, price is transferred from GENCO to ISO to DISCO to Consumers and market price is reflected in demand, allowing for demand response to price. Incentive for load curve optimization for DISCO is included but regulation is necessary in distribution side for determining tariff and, hence, profit to DISCO. Locational Marginal Pricing in a Pool model solves the problem of congestion and this is an answer to Nepalese Geographical and physical compulsion. Chapter 1 Summary The Electricity Sector of Nepal is preparing itself for restructuring. The need for restructuring and gradual deregulation has been brought on due to prevalent high electricity prices and government resource scarcity and also the worldwide trend. The restructuring and electricity market has to be designed suiting the particular conditions of Nepal. Single-ended competition in a Pool model with independent ISO acting also as market operator and including the transmission Grid operator is recommended. Market design is very critical to its success. The market mechanisms should be designed with experiences gained from the world wide deregulation. Once the market players are entrenched in any mechanism and learn to benefit from it, any change will be opposed and difficult to bring. 13 Chapter 2: LITERATURE REVIEW 2.1 Ancillary Services in an Electricity Pool Market In the Electricity Pool model, generators compete in the market to supply power at a price determined by the demand and the offered bids. The power demand and the offer of supply is matched and dispatched in real time by the Independent System Operator (ISO) and the Grid Operator (single or separate). When ancillary services or reliability products are priced and requires a market, the ISO integration with the Pool Market operator is a logical design. The ISO is the power system operator and carrier of the power to the Distributing companies which are wholesale and retail sellers of power to the consumer. The ISO employs Optimal Power Flow tools to optimize the operation of the Power system. The optimal power system operation means not only merit order dispatch based on the cost of power but also optimal operation while ensuring security and reliability of the system. It is found that Optimality is obtained in terms of cost of power generated and Security constrained OPF are used for maintaining the voltage at bus and power flow in line / transformer within the security limits. Operating reserve and reactive power are the main Ancillary services traded in the market to help the reliability and security of the system. Ancillary services are required for every market independent of the price volatility. 2.1.1 Reliability, Security and Adequacy: Reliability of a system is a combination of adequacy and security.[15.Scmuel] Reliability encompasses two attributes of electricity system – Security, which describes the ability to withstand disturbances (contingencies) and Adequacy, which represents the ability of the system to meet the aggregate power and energy requirements of all consumers at all times. Security procedures include Security Constrained Dispatch and requires ancillary services such as voltage support, regulation, capacity, spinning reserves, black start 14 capability etc. Adequacy represents the system ability to meet the system demands on a longer time scale. Capacity-Based Ancillary Services (CAS) 1. Frequency response - It depends on the speed droop and power- frequency droop of the generators, and the response period is usually up to a few seconds and it is paid additional to the energy costs as a service add-on to the generators who provide it. 2. Regulation – It includes the basic Automatic Generation Control (AGC) service to track the load with the generation (non-automatic) so as to ensure that the frequency stays within a predefined frequency band, and which may be made mandatory by regulation. A 10-minute overload of generator or over-draw of water from Run of River (ROR) hydro-power plants can be classified as Regulation reserve. 3. Reserves – It includes the Capacity available within the specified response time to withstand unexpected generation or demand variation, and it may be provided by either on- line generators (spinning) or off- line generation sources (non-spinning). Responsive Reserve Optimization Non-Spinning Reserve Figure 2.1 – The Reserve Capacity Pyramid and the Responsive Reserve Optimization 15 2.1.2 Operating Reserve This paper identifies the 10 minute spinning reserve for optimization. When the hour ahead market is cleared, the energy and the 10 minute spinning reserve is allocated and market clearing price fixed. In subsequent hour market, if the spinning reserve is used due to any contingency, then further spinning reserve is allocated either from the non-spinning reserve or other capacity such as import contracts. Start-up costs for non-spinning units can be traded and fixed in the hour ahead market. Market for Reserve Capacity Ancillary services should be priced over multiple dimensions, if it is to be priced efficiently and that requires multiple and related markets. [12,Schuler] The services with the shortest response time are assigned highest priority. Price for Reserve Capacity In some of the Pool and exchange markets, the acquisition of CAS is considered once the energy markets have cleared and the congestion management issues have been addressed. The energy required during real-time operation can be purchased in real time from the generators in the price dictated by the suppliers. This price, known as the Spot Price, has been shown to have volatile nature and be much higher than the marginal cost of production. The payment to Operating reserve can be avoided if the price volatility is accepted. In a Pool model, which are more vulnerable to market power by the generators, reserves, pre-paid as call-options, provide hedging against price rises to some extent. The amount of capacity, location and types of reserve procured are normally determined by experience of system operation and statistical forecast rather than any mathematical formulation. Overlap of Market and Real-Time Energy and Reserve: At some time before real- time, the market ends, fixes its prices and hands it over to the System Operator in the control room to implement the solution reliably. The system operator will use the market energy and reserve and as the real- time reliability 16 demands, can procure additional reserves and balancing energy and other ancillary services such as reactive power. Capacity Withholding Despite day ahead procurement, Pool model and Exchanges have suffered from high prices for energy during peak loads due to the practice called capacity withholding. In many markets [10,chen], the reserve capacity purchased is settled separately than the energy market. The suppliers, after r petitive visiting of the market, estimate the e reserve required for a given situation and withhold the capacity to increase the Market Clearing Price, in short indulging in co-operative gaming. To counter such gameplaying, price caps may be necessary as a safety valve for the regulators. 2.1.3 Payment for Capacity: Generators get compensated for cost of capacity either through scarcity rents that arise in the energy markets (spot prices) or through premiums for availability in terms of call options and agreed strike prices. In energy only markets like Nordpool, Australian Victoria pool etc, capacity or reserve payments are absent from market design. In California, reserve capacity is traded separately in a secondary market as short term or long term contracts. In UK, Spain and some South American countries (e.g. Argentina), generators are paid according to their availability based on generated energy as an uplift to the energy market clearing price (ECMP). In Spain capacity charges are indistinguishable from stranded investment compensation. In Philadelphia, New J ersey, Maryland region (PJM), New York and New England, the distributing companies (DISCO) are required to have reserve capacity contracts with generating companies (GENCO). These capacity markets provide incentives for building of reserves. The Basis of Capacity Payment and Reserve Capacity Payment The optimal capacity is such that the incremental cost of a capacity unit equals the shadow price on the constraint that is active during the peak. This shadow price reflects the incremental value of unserved load as measured by willingness to pay net 17 of marginal energy cost.[15,Shmuel] Paying generators this price (spot price) during supply scarcity periods will provide them with the same income as capacity payment. In the particular design of Pool market (discussed in section 3) with market decided reserve capacity pricing, the capacity cost is recovered from the difference of the marginal cost of reserve and the Reserve market clearing price (RCMP). The marginal cost of reserve will depend upon the long run marginal cost of investment for capacity expansion. The payment will depend upon operation and availability so it sends the right signals to the generators to ensure optimal operation and pricing strategy. POOL MODEL and Market Power In the demand-inelastic markets due to tariff fixing, it is possible to play co-operative games without explicit collusion, but which can be monitored by regulators. Studies have shown, [36,Thomas] using simulations of experimental results, that the power flow on any line in an electric network is linearly proportional to the total system load when that system is optimally dispatched using accurate generator cost data. By comparison, when offers from generators obtained in a wholesale market that is not perfectly competitive are used to dispatch the system, that relationship between line flow and system load becomes nearly random. Using such engineering models, it can be determined whether market power is evident in the system and if so, regulatory actions can be taken. But depend ing upon the efficiency of the regulator is against the spirit of the deregulation. Hence, it is necessary to employ better methods of operating a power system under a Pool model that mitigates market power and avoids the need for Regulation. 2.1.4 Contingency and Local Reliability Costs and the Thesis Studies have shown that ancillary services increase local costs when transmission is constrained. [43.Arce] When reserves are market based and the ene rgy and reserve prices are affected by the transmission constraints, the question arises how to reflect these costs adequately in the pricing method. Present practices of pricing energy may not justify or reveal the correct energy prices at different locations in this case. One fundamental question arises. Is the reliability within the constrained region equivalent 18 to the reliability of the remainder of the system? Is there some additional reliability cost that should be included in the local price of the constrained region? Is it fair for those paying higher prices to receive less reliable energy? When the constraints are applicable during contingencies only, there is a need for a method which correctly allocates the energy and reserves and optimizes the total cost. This is the problem which the thesis proposes to solve. The method proposed provides a solution for pricing the energy and reserve obtained from contingency optimized power flow. The method is described in Chapter 3 which will mitigate the market power problem as well as the locational reliability costs and solve the optimal operation issue in one single solution. 19 2.2 The Optimal Power Flow Paradigm 2.2.1 Economic Dispatch The optimization in power system operation was initially limited to economic dispatch of the most efficient power plants in merit order. Later the model included optimization of the transmission losses in the system along with the efficiency of the plants. The efficiency is expressed in terms of cost per unit increment of output. The scheduling involves those plants that are determined to be operated a priori. The objective function optimized in economic dispatch (ED) is expressed as Ct = min ∑ C i ( Pi ) i =1 ng (1.1) Ci = Cost function, Pi = Generation, ng = no of generators Normally, Economic Dispatch problem is solved by using the Lagrange multiplier method. The Pgi solution satisfying the minimum of Cgi ( Pgi ) is the Economic Dispatch method. There may be different optimization techniques developed till now for different problems and complexities of the optimization. 2.2.2 Optimal Power Flow – The main objective function of the basic Optimal Power Flow (OPF) problem is the same as Economic Dispatch, which is the minimum of Operating Cost Ct . But in an OPF, the control variables are not only Pgi (the generation of power plants) but also many other variables in a power flow, such as Voltage magnitude and angle, capacity commitment, lambda vector etc. In an optimal power flow, the Objective function is the Total cost of the power required for the system operation Ct = min ∑ C i ( Pi ) i =1 ng subject to the constraints 20 Fj(?,V,P,Q)= 0, j=1…nb ; power balance equation for the network at each bus Pi = Qi = ∑ V V [G i j j∈nb i j j ∈nb ij cos(δi − δj ) + Bij sin( δi − δj )] sin( δi − δj ) − Bij cos(δi − δj )] ∑ V V [G ij Vmin ≤ Vi ≤ Vmax |Sjk |=Sjmax the inequalities of the voltage limit and the power flow limit in the lines The solution of the Objective function can be obtained using different methods similar to Economic Dispatch. 2.2.3 MINOPF Using NEWTONs Method The software MINOPF, used in this work, employs amongst others the Newton’s method to the OPF problem. A power system OPF analysis can have many different goals and corresponding objective functions. One possible goal is to minimize the costs of meeting the load on a power system while maintaining system security. Another goal of an OPF analysis could be the determination of system marginal costs. This marginal cost data can aid in the pricing of MW transactions as well as in the pricing of ancillary services such as voltage support through MVAR support. In solving the OPF using Newton’s method, the marginal cost data is determined as a by-product of the solution. [29, Sun] A brief overview of the OPF solution method is given in Appendix N. Linear Programming Method: LP based techniques utilizes piecewise linear cost curve representations very efficiently. But their main problem is that LP tends to set the control variables at breakpoints of the piecewise linear cost curves. This may cause relatively large jumps in the optimal solutions even for small change in load. Successively refining the piecewise approximation of the cost curve around an intermediate solution solves the problem. But it also makes it very slow and may be unacceptable for real time optimal 21 control. Besides, the Participation factors or the incremental price (lambda) can not be obtained in a straightforward way.[25,Bacher] 2.2.4 Security Constrained Economic Dispatch Optimal Power Flow (RTOPF) (SCED) and Real ti me Although SCED has different meanings [24,Vargas], generally it deals with optimal allocation of generators in a power system subject to transmission and generation constraints. There are two parts to this problem, network modelling and mathematical modelling. Network modelling problem is specific to the particular network components. There are many formulations proposed for mathematical modelling and solution. Linear Programming [27,Stott], recursive quadratic programming [28.Biggs], Newton-Raphson techniques [29,Sun], Successive Linear Programming (SLP)[24,Vargas] etc. Important assumption in SCED scheduling is that once the active power is scheduled reactive power optimization does not change the operating point of the system significantly and if there are violations of the constraints, they may be corrected by changing the reactive control variable of the system. Real Time Optimal Power Flow (RTOPF) and Security Constraints [25,Bacher] The classical RTOPF uses firstly the State Estimator solution as its base data. The state estimator is another software tool used by ISO or Load Dispatching Centre to find the correct Power Flow solution using the P, Q Generation, line parameters and line flow and bus voltage measurements. The errors in measurements are smoothed out and any missing data is estimated by running the load flow and adjusting the unknown values against the measured and known parameters.[[2],p454] The state estimator data of the network is used to solve an AC OPF in a costoptimization mode. This OPF identifies binding and near binding constraints set ( e.g. branches carrying load 80% of the limit). This near limit constraint set is used for the second stage Linear programming. The constraints are linearized as a linear relation between changes in network MW flow and changes in nodal power. These constraints are used in a Security constrained Economic Dispatch (SCED) and an optimum disp 22 atch is determined. Using the constraints of the first stage, a trajectory of SCED optimum is found with variable load. This solution provides the real time operation dispatch. [25,Bacher] The RTOPF is repeated periodically, and the frequency may be increased during rapid load changes or during contingencies. Since the computation speed in present day have increased tremendously, other methods of computation heavy algorithms are also implemented to achieve any small improvements possible in the solution. 2.3 Tools Used- MatlabTM, MATPOWER, MINOPF. 2.3.1 Matlab TM This is a well known programming and simulation software used by scientists, engineers and students. The version used is 6.5.0.1809131 Release 13 The software copyright is held by The MathWorks Inc. 2.3.2 MATPOWER MATPOWER uses many of the functions available in Matlab’s Optimization Tool Box to work different optimization techniques for optimal power flow. Amongst the methods available for optimal power flow solvers are DC power flow, AC Power flow using Linear Programming, AC OPF using Quasi-Newton method and AC OPF using a generalized gradient method. MATPOWER - A MatlabT M Power System Simulation Package Version 3.0 (February14 2005) – This program was developed by Ray D Zimmerman, Carlos E.Murillo Sanchez and Dequiang Gan of Power Systems Engineering Research Centre (PSERC), School of Electrical Engineering, Cornell University, USA. The software is freely downloadable with acknowledgement of the same. The homepage of MATPOWER’s website is http://www.pserc.cornell.edu/matpower/ 23 2.3.3 MINOPF The objective function for this thesis is solved mainly using the MINOPF program which is a separate sub-program developed also by Cornell University, School of Engineering, originally coded in FORTRAN, and transported to Matlab. The version used is m.v 1.4 2005/2/14. The copyright is by Power System Engineering Research Centre (PSERC) 2005. The codes were prepared by Ray Zimmerman. The software is freely downloaded from its homepage http://www.pserc.cornell.edu/minopf/ The codes for this solver is not modifiable and hence the objective function has to be modified to suit one’s needs. This program is very robust, and it uses the sparse matrix for speed in solving. x    f = min ∑ [ f 1i ( Pgi ) + f 2i (Qgi )] + c y   x , y, z i =1 z    θ    V x =  . − − x min ≤ x ≤ x max  Ps    Qs  ng The generalized AC OPF formulation as used by MINOPF is shown Subject to Voltage and generation var limits gp (x)=P(?,V) - Pg +Pd = 0 (active power balance) gq (x)= Q( ?.V) – Qg + Qd = 0 ( reactive power balance) gsf (x)= Sf(? ,V)= Smax (apparent P flow limit from end of branch)===? ? gst (x)= St (? ,V)= Smax (apparent P flow limit to end of branch)  x l ≤ A y  ≤ u   z   general linear constraints 24 When there is no cost optimization required for Q (reactive power), then there are only rows for generation P in the cost curve matrix and for Q it is kept empty. To include Reactive Power optimization, additional cost curves in terms of polynomials have to be given. MINOPF u the general non- linear problem minimizer program called MINOS ses which is sold by Stanford University, but which is transportable to Matlab. It does simplex-like iterations on the linearization of the general problem, and it does major iterations that resemble quasi-Newton updates. It exploits sparsity in both cases, and it works on a reduced order dense system. The evaluation routine for the Jacobian of the constraints and the cost calculations are all done in FORTRAN and then transported to Matlab for the auxiliary functions. For this reason, modifying the code for adapting to different objective functions is difficult. But since this program is very robust and tested for large systems, it is used for testing my formulations. The results are adequately output and can be stored in text files as well as the variable matrices can be copied to excel files for analysis. 25 Chapter 3: THE CONTINGENCY OPTIMIZED INTEGRATED ENERGY, RESERVE CAPACITY AND REACTIVE POWER SCHEDULING AND PRICING 3.1 The Concept This thesis proposes the method of Optimization of Energy and Reserve together in one settlement as the best method for Pool model market for system operation. The method of Optimized scheduling and pricing of Energy and Reserve is developed and implemented using an Optimal Power Flow program based in Matlab. The MATPOWER program is a collection of Matlab-coded programs designed to carry out Optimal power flow using different techniques such as DC Power Flow, Linear Power Flow, Quasi Newton Method based OPF, General gradient method program etc. Generally, Energy and Reserve are offered at different rates and price curves. The Reserve offer price is based on the return rates on the capital investment and other fixed costs. The actual pricing from the Generators’ side is not discussed here. Energy and Reserve cost curves – Generally the cost of production is non- linear and slightly increasing for thermal generators but almost linear for hydro generators. Nonlinear cost curves can be linearized piece-wise for a linear function. The program used for OPF is able to handle non-linear functions and hence, the generation cost curves are designed as polynomials with very small quadratic coefficient for hydro-generator model. 3.1.1 Simultaneous Offer of Energy and Reserve When the generators make offer of prices for generation and reserve, it is designed and assumed that blocks of energy and price are quoted with maximum power available, the capacity offer, for the hour (energy for one hour). The offer can include a minimum power that can be accepted, below which the unit has to be decommitted, that is no power nor reserve can be used from this plant. When a block of power is 26 offered, it is possible to take some of the capacity offered as Power and others as reserve. Since both power and reserve is offered in one set, this mechanism will reduce the opportunity to exploit the reserve market. Option 1: The optimization of energy and reserve can be done sequentially. Using a standard OPF program, the energy from generators can be optimized with the objective function C gt = min ∑ C gi ( Pi ) i =1 ng with the usual constraints and get the optimal solution of [ Pi ]. After obtaining the [ Pi ], the reserve can be optimized using any standard Economic Dispatch program Crt = min ∑C i =1 ng ri ( Pi ) with the equality constraint and the inequality constraint capacity ? Ri = k* ?Pi Ri + Pi= Pimax with k normally taken as 0.1 Pimax is the offered block of This sequential optimization can be iterated to give the Pareto Optimal solution. Option 2: The same optimization can be done by dual-optimization. The two variables are optimized together in one objective function. By this method, the optimum combination of energy and reserve is achieved for operation. The Objective function is Ct = min ∑ [C gi ( Pi ) + C ri ( Ri )]. i =1 ng 27 s.t. Fj(?,V,P,Q)= 0, j=1…nb ; power balance equation for the network at each bus Pimin = Pi = P imax Generation limit Ri + Pi= Pimax Vmin ≤ Vi ≤ Vmax |Sjk |=Sjmax lines the inequalities of the voltage limit and the power flow limit in the Capacity limit The drawback of this method is that reserve allocation is done with a view to replenishing power during contingencies but the network condition of the contingencies are not accounted in the optimization. This is one of the reasons why reserve allocation has remained judgmental and not mathematically proven or transparent. The selection of reserve should be dictated by the line flow limits and voltage limits when it is called on to produce during the contingencies. Hence, the selection of reserve is not independently optimizable. 3.1.2 Contingency Optimization (CON-OPT) Security constrained optimal power flow (SCOPF) has many interpretations. Optimal power flow with line flow limits and voltage limits is said to be security constrained. Optimal power flow with steady state stability and voltage stability constraints can also be obtained. There is marginal difference between SCED and SCOPF. Security Constrained Optimal Power Flow (SCOPF) The SCOPF starts by solving an OPF with (n-0) constraints only. Once the Optimal Constrained condition is solved (SCED), the contingency analysis is executed. The contingency analysis starts by screening the power system for potential worstcontingency cases. Each contingency case will require a full AC Power Flow to find 28 the new constraints. But since there may be numerous contingencies, the cases have to be limited to most likely ones. When all the n-1 contingencies are selected, each contingency is done a power flow and if any limit violations are detected, then the constraint sensitivities are saved for the final OPF. All the contingencies are then added to the OPF to arrive at a solution which will give a solution which is safe for all the contingencies. When Reserve Capacity allocation is included, the connotation of the term is varied. In this context, the Power Flow solution should optimize the different power flows possible in the most possible contingencies and determine the optimum reserve capacity to cover all the contingencies and thus provide an Optimized solution with an Expected Cost. Therefore, the formulation here for obtaining the Optimum operating solution is termed as 3.1.4 Contingency Optimized Energy and Reserve Scheduling Responsive Reserve: The Reserve allocated after Contingenc y Optimization (CON_OPT) can be called RESPONSIVE RESERVE. The total capacity requirement for each unit obtained from CON_OPT is set as the limits for each generator and the combined Energy and Reserve Optimization is carried out. These reserves respond to the different possible contingencies with an optimum mixture of energy and reserve. The energy and cost curves and their mutual ratios may be different from generator to generator. The second OPF can thus be called Responsive Reserve OPF (RROPF). The complete Objective function for such an Optimization can be expressed as Ct = min [ ∑ p j ∑ [C pi ( Pgi ) + C ri ( Rgi )].] P, R j =1 i =1 k ng Where ∑ K pk = 1 is sum of the probabilities of the different contingencies. k =0 29 This function takes care of the contingencies in a probabilistic manner and the total cost is optimized with related weightage given to individual function costs. 3.2 Optimized Reactive Power Flow and Scheduling Many proposals exist on how to deal with reactive power issues, but no market has addressed the problem of market-based reactive management comprehensively. It is important but there is no consensus about the mathematical solution. [18 Carlos]Reactive power can not be transported long distance and has locational constraints. Active power optimization is constrained and modified by reactive power requirements of the network. ‘All network intricacies, including topology and reactive dispatch, must be an integral part of the market clearing mechanism’. [18 Carlos] As Reactive power is interrelated and dependent on P and is regarded as ancillary product of the same generator, they should be priced, and hence, it is only proper to include it in the optimization method. Reactive Power has locational constraints and hence, the pricing is locational. 3.2.1 One Regulation for Q In a Pool model, the reactive power optimization can be taken up by the ISO with the regulation that any generator participating in the system at the period be obliged to produce reactive power as dispatched by ISO with a compensation according to the Nodal Price for the same. Locational prices(criteria) of the reactive power are obtained from the LaGrange multiplier or the shadow prices at the related bus. The measure of the value of the reactive power due to conditions like voltage instability proximity are taken care by the ISO which determines the amount of reactive power necessary by varying the voltage limits and flow limits in the OPF. 30 The reactive power costs will be very non- linear, as shown later, and monotonically increasing. This means the reactive power drawn from a generator will cost more and more as the Q/P ratio increases. This cost behaviour will automatically address the increased value of Q , in and around the Reactive power crises or voltage instabilities. This mechanism is readily applicable in POOL models and ISO controlled ancillary service markets, but same can not be true in double-ended markets, which require spot markets. ‘Spot pricing of Q is very disputable’ and there are many research works going on about how to implement it.[21, Weber] Another question to answer while deciding the pricing method and the market design for Q is whether to create a free market for the sake of creating it or to create a market where the product is valued by competitive forces. In case of Q, it must be decided on the latter side. There is no need for Q to be independently marketed and traded in the spot market. Due to its very dependence with P, the pricing should be related to it. It is submitted here that by allowing competitive market by indirect pricing, the purpose of market efficiency is served while also fulfilling the technical requirements of the system. Locational pricing resulting from Optimal Power Flow solutions will ensure that the generators do not suffer due to the loss of opportunity to sell energy. In fact, the method proposed below takes care of exactly this ‘lost opportunity’ to evaluate the price of Reactive Power. 3.2.2 Single Commodity– The Capacity Curve This means there is a single commodity offered by the generators to the market. The rates are different for energy and reserve but they are quoted beforehand. For reactive power, the generators have to quote their fuel prices and which will moderate the conversion rate from active power (Mwh) to reactive power (Mvarh) along with the amount of ‘paid’ reserve. 3.2.3 The Objective Function and OPF The objective function can be modified to include the Reactive power produced by generators and an optimization based on the cost curve of Q can be done. 31 Ct = min [∑ p j ∑ [ C pi ( Pgi ) + C ri ( Rgi ) + f i (Qgi )] P , R ,Q j =1 i =1 k ng The objective function will again assume certain simplifications. The capacity curve limits which is itself a non- linear function of active power produced is neglected and a constant apparent power limit is assumed with Q max also specified. This is a clo se approximation of the actual capacity curves as can be seen from one sample curve. Lambda Q can not be directly used to cost when reserve is being paid. The ratio of the bus lambda to the weighted average lambda will give the index with which the opportunity cost of Q has to be moderated. It may be >1 or <1 depending upon the location. From the figure, it is seen that when Active power P and reactive power Q is being generated, the virtual power is thus S = (P1 +dP ) Mwhr. Fig.3.2: Approximate capacity curve of a generator Now, from the above diagram, if the generator is paid for P1 = CP1 (P1 ) energy and R1 Reserve Capacity R1 = CR1 (R1 ) then the price to be paid for Q is given as CQ= Cq1 – (C R1 – C’R1 ) CR1 – C’R1 = cr(R1)-cr( R1 ’) capacity where cr (R1) is the cost function of the reserve 32 And CR1 – C’R1 is the deduction for paid reserve deducted after the Cq1 ’ is found from OPF. Cq1 =? ri * Q= k’* CP1 (?P) is the mount that would be paid if there is no reserve. If allowed to generate the generator would be paid CP1 (?P) but there would be tradeoff for fuel. Where Cq1 = k’* CP1 is a moderated rate of Reactive Power . k’ is determined by the fuel cost and the efficiency reduction for operating at the given operating point. For simplicity, CP1 can be approximated to a linear function of the energy ?P not generated. From the capacity curve given in fig.2, the thermal heating limit curve is a parabolic curve given by S2 = P2 + Q 2 , S is the capacity of the generator in MW at unity power factor. The curve can be approximated to cover the full operating region neglecting the reduction in Q due to rotor heating at low power factors ( normally no-operation zone). Q 2 = S2 - P2 Q =v( S2 - P2 ) ; P =v( S2 - Q2 ) Given the cost curve of Energy , C(P)= a P = a * v( S2 - Q2 ) ( C(P) approximated to a linear curve, non- linear curve can be treated in piecewise linear mode) The Cost function of Reactive Power is dependent upon the energy sacrificed C(Q) = a (S-P) = a *(S- v( S2 - Q2 ) If we represent the cost curve by a monotonically increasing second order polynomial then C(Q) = a + ß Q + ? Q2 = a *(S- v( S2 - Q2 ) 33 Putting Q=0, And putting Q=S, a=0 ß +?S=a (1) (2) Putting Q = 1, ß + ? = a *[S- v( S2 -1)] Solving the two equations, we get the two coefficients ß and ? ? = a *[1-S+ v( S2 – 1)]/(S-1) ß = a *[1- S{1-S+ v( S2 – 1}/(S-1)] So the cost function is dependent upon a (the cost coefficient of CP Energy cost curve) and the maximum capacity offered S = P max . Before we use the cost curve, it is realized that if the generator was really called upon to generate ?P energy, then it would incur fuel costs. So it must be adjusted into the cost curve by a modifier k. We assume that for Hydro plants there is no fuel cost but there is some trade-off in efficiency and thermal heating of the rotor and stator. Hence, we take kh =0.9 Similarly, assuming the fuel cost of the energy is about 70%, the modifier kt = 0.3 for thermal generators. Then the cost curve is given by Cq = kh/t (ß*Q + ?* Q2 ). The cost curve of Reactive Power is shown in fig.3. We can now use this curve in the OPF program to obtain the solution of Ct = min [∑ p j ∑ [ C pi ( Pgi ) + C ri ( Rgi ) + f i (Qgi )] P , R ,Q j =1 i =1 k ng Actual method to solve the above objective function can be many. Using state of the art Multi-objective weightage optimization or stochastic weightage optimization theories are available for solving them. 34 Further work can be done in actually developing a relevant software employing any of the new methods and algorithms. In this thesis, the methodology is simplified and a near optimal process is sought. The cost of Reactive power given by ? ri * Q is a good measure for locating a new source of Q. It also provides the financial analysis tool for such a decision. Reactive power reserve can also be used in a similar fashion to responsive reserve, but in the given POOL model, it is assumed that transmission services are within the ISO and hence, such ancillary services shall be provided by ISO. Cost curve of Reactive Power dependent upon P and cost of P 180000 160000 140000 120000 100000 80000 60000 40000 20000 0 0 20 40 60 Mvarh 80 100 120 NRs. Figure 3 - Cost curve of Q dependent on P cost and P value 35 3.3 Methodology Adopted for Implementation of the Exposition 3.3.1 System Description and Test Cases A case study network is prepared based on the IEEE 14 bus network. The system is not representative of Integrated Nepalese Power System (INPS) as the INPS is elongated from east to west with very sparse connectivity except in Kathmandu valley. The total load and generation in this network is derived from the Nepalese system (INPS) for the year 2010 from the present status of 550 MW peak load in December 2004 and 612 MW installed capacity. The Nepalese sector is, as mentioned earlier, undergoing restructuring process, which is slow but steady. The earliest time for any implementation of a Pool model market design is assumed to be appx. 2010, 5 years from hence. Assuming Unconstrained growth rate of 8 % till 2010, the load is approximately 875MW. Predicted generation capacity addition, from available predictions (ref- NEA F.Y. review 2004 [40,NEA] and T and D Plan report, NEA 2004 [42,NEA] ) is approximately 1150 MW. Therefore, a load estimate and generation forecast is made for that scenario. But due to implementation and testing simplicity, the buses have to be reduced to a simple network. There are five generators in the IEEE 14 bus network Hence, following five types of generators are assumed. 1. 2. 3. 4. 5. Reservoir type Peaking ROR type Run-of River type – Gen1 (total – 300MW) - Gen2 (total – 200MW) - Gen3 (total – 250 MW) Peaking ROR other area- Gen4 ( total – 300 MW) Thermal and PROR combined – Gen5 ( total – 100MW) The 5 generating bus in IEEE 14 bus network can be related to a real market where there are numerous generators but which can be lumped to 5 groups and belonging to each Generating companies. The response behaviour of each group of generators are hence generalized into one lumped generator. 36 From market design study, it is known that in order for the Pool market to function properly and behave as an efficient market, there must be a number of players and no single generator should have dominant size ( 20% of the market) . Market Power may be exercised if the generator is larger than 20 % and that there should be six or more players to reduce market power [Appendix M]. Hence, in a 5 generator system, the market power will be prominent and its impact can be more directly seen and the effect of the methodology in mitigating such power can be tested. The system model of 14 bus ( 5 generating nodes, 8 load nodes) is assigned load and generation with generation surplus in one region and deficit in another to simulate the practical scenario of East and West of Nepal. This helps to elucidate the results. 3.3.2 The OPF Software Program The Optimal Power Flow is a very complex and computationally difficult problem to be implemented in program. There are many optimal power flow programs available in the market. Hence, a readily available and tested software is used. For the purposes of this study, a Matlab TM based software, MATPOWER [2], from Cornell University, School of Electrical Engineering, was downloaded from the University website. The codes can be used freely with acknowledgements where used. MINOPF is a sub-program of MATPOWER developed particularly for power system markets. Since this program, as already described, is very robust and suitable for OPF problem solving, it has been used although it constrains the user from modifying any of its codes. Due to this limitation, the objective functions have to be formulated to fit into the given model. Using the MATPOWER Program The MINOPF program requires the input data in a given format. The sample input data for IEEE 14 bus network is given in the package. This case file is modified according to requirement to get the solution of the Objective function. For the Test case, load data and generation data is prepared. The data are entered in Excel sheet in a format suitable to transport to case14.m file. The primary data of a test system is loaded in case14p0.m file. Separate m- files for input data are prepared. All the variation in load, generation, branch, generation cost and reserve cost data are 37 prepared in concerned Excel files first. These data are easily transported to the m-case file. This input file is used by the ‘runopf.m’ program by calling ‘runopf(case file)’ in Matlab. The output matrices are stored in workspace and a standard output is printed to file. The important messages from command window are copied to a MsWord file for documentation. The runopf.m file loads the input data and prepares it in a format used by MINOPF and calls the function minopf.m. The calling of the different OPF programs are in a sequential priority unless the method is specified while calling the ‘runopf.m’. The load data is put in the bus matrix and the generator data is in the gen matrix. The bus voltages and angles and the load P and Q have to be first obtained from a Power flow program so that convergence can be achieved. When the data is varied far away from a feasible solution, the OPF may not converge. In such conditions, bus voltages and/or generation voltage and power has to be iterated back with an input data which is closer to a feasible solution. The output solution is printed to the screen. The information includes bus voltages, angles, power loss, and power flow from and to the bus. Flow constraints, if constrained, are also shown. Most important information available are: 1. Total Objective Function Cost in $/Mwhr 2. The optimum Generation and Reactive Power allocation 3. The incremental generation and reactive power cost (lambdaP and lambdaQ) at individual nodes. 4. Losses in the branches and the Total system loss. The procedure of preparing the input data file and calling the OPF program is manually done each time. An interactive program can be prepared to load the data but transferring data from excel sheet is an easier way. 3.3.3 The Generation Cost Curves: The energy and reserve cost curves are represented by two polynomials but both assumed to be almost linear. The cost curve simplification does not affect the test of the scheduling optimization. A common practice in industry is to represent the cost function of each generator through a mo notonically increasing second order or third order polynomial. [26] 38 The generator cost curve Cgi(Pi) = a+aPi+bPi2 And the reserve cost curve Cri(Ri) = ß+cRi+dRi2 Generator 1 Energy cost Generator 2 Energy cost Generator 3 Energy cost Generator 4 Energy cost Generator 5 Energy cost 5000 P1 +0.02Pi2 4000 P2 +0.01P22 3500 P3 +0.001P32 4500 P4 +0.001 P42 10000 P5 +0.08 P52 Reserve cost Reserve cost Reserve cost Reserve cost Reserve cost 400Ri+0.02Ri2 250R2 +0.01R2 2 1050R3 +0.01R3 2 500 R4 +0.01 R4 2 400 R5 +0.08 R5 2 The figures for the assumed cost curves [Appendix O]. are given in figure .1 ENERGY COST CURVE - INITIAL CASE 2000000 1800000 1600000 1400000 COST NRs/HR 1200000 1000000 800000 GEN1 GEN2 GEN3 GEN4 GEN5 600000 400000 200000 0 0 20 40 60 80 100 MWHR 120 140 160 180 200 Figure 4- Generator cost curves 3.3.4 Market Power Test Case It is intended to test the effect of some of the generator trying to exercise market power. When after repetitive visits, the reserve required is estimated, the generator with more reserve tends to increase its reserve price. The cost of reserve of the reservoir type G1 is increased to a high level to reflect exercise of market power. 39 Energy cost 5000 P1 +0.02Pi2 Reserve cost 1050Ri+0.02Ri2 3.3.5 Decommitment and Other Test Cases During off-peak cases, the expensive generators should be excluded from the OPF since including the minimum amount from these generators will increase the market clearing price to its levels. Hence, after RROPF results are obtained, if the generator is found to be in the minimum and without any reserve allocation, the whole CON-OPF and RROPF should be repeated with this generator considered as decommitted and find the new operating cost f1 and accept this new solution if f1 < f0 . This is shown to be the case in decreased load when G5 is decommitted. Other Cases – Load decrease by 2% There may be several cases of cost curves. It is not intended to check all the combinations. The effect of prudent behaviour, by ISO and from the consumers, is tried to show by reducing the load. The effect of price elastic demand is checked here also. If demand is responsive to price, then the contingency of load increase will be reduced. This will ultimately affect the total reserve capacity requirement. Hence, the reserve cost uplift, and the cost of energy per unit both will reduce significantly, thus sending the correct signal to the consumers for a rational demand behaviour. The effect on the price due to the correct estimation by the ISO will also be proved by this test. This will provide the correct incentive for the ISO to behave efficiently and rationally which should thus be monitored by regulators. 3.3.6 Simplification of the Objective Function Ct = min [ ∑ p j ∑ [C pi ( Pgi ) + C ri ( Rgi )].] P, R j =1 i =1 k ng Five contingencies of equal probability have been taken. 80% of the time (pk =0.8) the system remains in the base case and there is a 0.2 probability that one of the 40 contingencies will occur. The contingency will return to base condition before another contingency, which means only n-1 contingency is considered. Here, the pk needs to be evaluated only to find the Expected Cost of the Objective Function. Modified Objective Function for Energy and Reserve Firstly the two variables, energy and reserve capacity, which are interdependent have to be merged into one single function. This is done to use the OPF program without modifying the code. Consider the objective function for any one case of power flow, Ct = min ∑ [C gi ( Pi ) + C ri ( Ri )]. i =1 ng s.t. Fj(?,V,P,Q)= 0, j=1…nb ; power balance equation for the network at each bus Pimin = Pi = P imax Pimax is the capacity offered by each of the generators for the next hour Ri + Pi= Pimax Vmin ≤ Vi ≤ Vmax |Sjk |=Sjmax lines Here, the two functions Cgi and Cri are given as The generator cost curve Cgi(Pi)= aPi represented by a linear curve And the reserve cost curve Cri(Ri) = cRi represented by a linear curve Hence, the objective function to be solved can be reduced to the inequalities of the voltage limit and the power flow limit in the Capacity limit 41 Cgi(Pik ) + Cri(Rik ) = (a-c)Pik = Cprk (Pik ) where Cprk is a combined function for kth case. The linear curve can be expressed in a quadratic form with a very small second order co-efficient. The generator cost curve Cgi(Pi) = a+aPi+bPi2 And the reserve cost curve Cri(Ri) = ß+cRi+dRi2 Cgi(Pik ) + Cri(Rik ) = a+aPik +bPik2 + ß +cRik +dRik 2 = Pimax ) = (a+ ß)+aPik +c (Pimax –Pik ) +bPik2 +d (Pimax –Pik )2 In an almost linear cost curve (approximate) and with no starting costs, (a+ ß)=0 and the quadratic coefficient can also be neglected. Gi is a constant for a given case. In our case, we have used a polynomial with a very small quadratic coefficient. The combined cost curve of P and R of a generator is shown in a chart when a highly quadratic polynomial curve is used for P and R ( Rik = Pimax –Pik and Gik 2500000 THEORETICAL - P+R COST CURVE P -MW R -MW 2000000 P+R COST 1000000 C S N SH O T R / R 1500000 500000 0 0 20 40 60 80 100 MW 120 140 160 180 200 Figure 5 -Theoretical Cost curves of P, R and P +R in a generator ( R decrease with P increase) But using the given cost curve of Gen1 , following almost linear curve is obtained. 42 ENERGY, RESERVE AND TOTAL COST CURVE- GEN1 1000000 900000 800000 700000 600000 NRs/HR G1-ENERGY G1-RES P+R COST 500000 400000 300000 200000 100000 0 0 20 40 60 80 100 MW ->P, <-R 120 140 160 180 200 Figure 6 – Actual Cost curve of P, R and Q in a generator With the above modified function, the OPF program can now be tricked into solving it as C prt = min ∑ [C pri ( Pi )]. i =1 ng In order to co-optimize the energy and reserve for the reserve case as well as the contingencies with five probability cases, a simplification is sought. 3.3.7a Option 1 of Solving the Contingencies Two possible methods are discussed. In one of the possible methods, the network is duplicated and the network of base case is then connected in a star topology with other five identical networks in a single network. The load and installed capacity are according to the contingencies predicted in each of the cases. The five contingency networks are connected to bus 1 (base network) through a very high impedance line ( 0.8 pu resistance and reactance) and a flow limit of 0.1 MW, which means they are virtually isolated. During a power flow, the six networks should be balanced with themselves as inter-tie flow would be very costly and limited. This design is made to use the same OPF program to consider the whole network as one and optimize the six 43 cases simultaneously. In this design of testing, the optimum power flow, the power assigned to the generators, will reflect the capacity required for different contingencies. The base case and five contingency cases give a set of Pik (k = 0…5) solutions for each generator. In the base case, the system has a peak load of 875 MW and 5 generators have offered capacities of 1150 MW. In the five contingencies, worst cases of generation loss, line outage and load increase are considered with equal probability of pk =0.04 such that ? p k = 1 ( p0 = 0.8 base, and p1…5 = 0.04 x 5= 0.2). The cost curves of the five contingency curves are weighted with the pk to reflect proportionately in the Expected Cost. E(Ct ) = p0 Ct0 + p1 Ct1 +p2 Ct0 + p3 Ct3 +p4 Ct4 +p5 Ct5 First, the integrated network is tested with above Objective Function. Second, the base case has the reserve modified cost curve, while the other five cases do not consider the reserve, as these cases are expected to return to normal. Maximum of the six contingencies Pik max is the committed capacity for a second iteration of optimization with the new limits for Unit Commitment with only the base (real) network. The new Gik = max(Pik ) With the capacity limits Ginew = Pik max , the second Optimization should, therefore, give an optimum combination of energy and reserve for the real network, while covering the contingency security. Here, it is seen that the Capacity required and hence the energy and reserve is optimized with respect to the contingencies. There is no arbitrary reserve allocation and the location of the reserve is also determined by the combined optimization. In the contingency case, the reserve is called on to produce and the solution is already constrained by the voltage, active and reactive power, and line flow limits. This 44 ensures that the Final Solution with the reserves thus allocated is the best solution regarding security in contingency as well as the total cost of operation. 3.3.7b Option 2 of Solving the Contingencies The purpose of the above method of simultaneous solution is to give the Ginew for the second Optimization. But with a trivial simplification of the formulation, an easier method can be implemented. To simplify the solving method, the objective function can be simplified as Ct = min [ ∑ p j (.C1T + C 2T + C3T ...C 5T )] P, R j =1 k where C1T is the optimized solution of case1 and C2T is the solution of case2 and so on. In the case of unequal probabilities, the comp lete function has to be solved. Since the pk of each of the contingency is assumed equal, if all of the cases are independently optimized, the whole objective function is optimized. It is seen that the above assumption is made only to simplify the problem, since the objective is not to develop a solver program but to test the proposition. As the most probable and worst possible single contingency cases are considered with equal probability, the [ Pik ] solution from the k cases solved independently should give the Optimum set of generator maximum capacity [Gi ] required for any contingency, starting from a given Base condition. Therefore, firstly, a base case where the system has a peak load of 875 MW and 5 generators have offered capacities of 1150 MW is solved with the regular constraints and the capacity constraint from the initial Offers received. Pimin = Pik = Pimax With six OPF solutions for six of the cases, Ginew is obtained similar to previous method. 45 Comparison: Since the objective of the above process is to identify the Gi for the final OPF only, we compare the Pik max received from the two processes to decide which method gives a more economic solution while maintaining Security for all the five contingencies. 3.3.8 The Contingencies and the Network The base case network has two identifiable areas of load which are interconnected with four trans mission lines but are constrained during contingency. There is a net power surplus in area 1 with generator G1, G2 and G4 and a net load excess in area 2 with generator G3 and G5. The generators are assumed as lumped and representing themselves a sub- network with net-generation and connected through the virtual tie- line. The actual system can be expanded to include all the lines and generators. Five contingencies are considered. a. Largest unit failure – Consider 10 % of the generation capacity loss in one generator of Area 2 = G3 – 87.5 MW generation loss b. Largest unit failure – Consider 10 % of the generation capacity loss in one generator of Area 1 = G2 – 87.5 MW generation loss c. Largest unit failure – Consider 10 % of the generation capacity loss together in two generators of Area 1 and 2 = G1 and G5 – 87.5 MW generation loss d. Heaviest loaded line failure – Branch 3-4 with pre- fault flow of 145 MW. e. Sudden load increase of 5% in the total network. The load increase is generalized into all the load buses. 3.3.9 Responsive Reserve Optimal Power Flow (RROPF): From the Contingency Optimized solutions, the new Optimization is done for final Energy and Reserve allocation. Here, the objective is to optimize the reserves which 46 can respond to the contingencies and yet be most economic. Hence, they are called Responsive Reserves. The Optimization is hence, termed Responsive Reserve OPF (RROPF). Ct = min ∑ [C gi ( Pi ) + C ri ( Ri )]. i =1 ng The required objective function is modified into the following C prt = min ∑ [C i =1 ng pri ( Pi )]. s.t. Pimin = Pik = Gi and the equality constraint Pi+Ri = Gi embedded in the modified function. For simplicity, we do not impose any restrictions in R. To include such a restriction, i linear constraints would have to be added into the MINOPF program which is said to have bugs in the present version for this. 0= Ri = Gi The [Pi] solution is the required solution and [Ri ] is obtained by Ri = Gi - Pi which gives the [ Ri ] solution. 3.3.10Fixed Reserve Objective Function (FROPF) For simulating the Fixed Reserve optimization, the objective function has to be modified in a different way. Since the reserve is fixed in this case, there is no need for Contingency Optimization and FROPF is carried for the Peak load case with fixed reserves. The capacity limits are changed in this case. Ri = 0.1*Pi Pi = GiF 47 GiF = Gi / 1.1 Pimax (The Pimax has to be reduced as reserve is allocated in each generator.) Energy cost curve CPi(Pi) = a+aPi+bPi2 And the reserve cost curve Cri(Ri) = ß+cRi+dRi2 Cgi(Pik ) + Cri(Rik ) = a+aPik +bPik2 + ß +cRik +dRik 2 and Gik = Pimax ) = (a+ ß)+aPik +c *0.1Pik ) +bPik 2 +d *0.01Pik 2 = (a+ ß) + (a+c *0.1)Pik +(b+d *0.01)Pik 2 = CPRi(Pik ) Hence, the cost curve for Fixed Reserve case is modified accordingly to use the same Optimization program. ( Rik = 0.1*Pik 3.3.11Reactive Power Co-Optimization Since Reactive power is also interrelated and dependent on P and is regarded as ancillary product which is priced in many markets, it is only proper to include it in the optimization method. Reactive Power has locational cons traints and hence, the pricing is locational. The objective function can be modified to include the Reactive power produced by generators and an optimization based on the cost curve of Q can be done. Ct = min [∑ p j ∑ [ C pi ( Pgi ) + C ri ( Rgi ) + f i (Qgi )] P , R ,Q j =1 i =1 k ng The objective function will aga in assume certain simplifications. The exact capacity curve limits which can be best represented by piece-wise quadratic curve is approximated with one single quadratic equation. The small error in the low power factor region is neglected. It is practical to assume this because a generator is rarely called to produce in such low power factors except for short periods during contingencies. Hence, a constant apparent power limit is assumed with Q max also 48 specified. This is a close but not exact approximation of the actual capacity curves as can be seen from one sample curve given. 49 Chapter 4: 4.1 ANALYSIS OF THE CASE-RESULTS AND DISCUSSION Case Discussion 4.1.1 Case1: Initial Peak Load Case– Combined Network Option The Base case data and the five contingenc y cases are input sequentially to simulate a single network. The 5 swing buses of the network are connected in a star to the swing bus of the base case, but the five networks can have only one swing bus. The generation cost curve is concatenated and similarly the branch data is also stringed together. The cost curve of the five contingencies are weighted with the pk =0.04 and for the base case with p0 =0.8. Solving all the five networks in one single network gives a near optimal solution. It can be seen that the program tries to optimize the total cost and hence, the solution of individual generators in individual contingencies may not be minimized. Since, this combined optimization is only to find the maximum commitment Gi required for the final Responsive Reserve, the Gi solution obtained from this procedure may not be optimal. From the results in Table -1, it is seen that the total cost is higher than that received from the second option. Table 1 - Pmax set received from option 1 - higher than other case Combined network contingency - Pmax result. Gen1 Gen2 Gen3 Gen4 Case 0 98.345 200 250 Case 1 198.94 200 162.5 Case 2 235.12 112.5 219.98 Case 3 159 200 219.56 Case 4 146.54 200 219.64 Case 5 188.08 200 224.11 Max 235.12 200 250 300 191.93 94.746 200 250 250 Gen5 Total 30 878.345 30 891.44 30 897.6 18.75 897.31 30 896.18 30 942.19 30 1015.12 total 300 30 974.746 MarktPowerTstcase 300 30 971.93 Initial Peak Case 300 300 300 300 300 300 300 Second option This procedure is a simplification of the actual objective function 50 Ct = min [ ∑ p j (.C1T + C 2T + C3T ...C 5T )] P, R j =1 k The base case and 5 individual contingencies are solved for the input data of ‘peak load case’. The [Pi ] set solution of each case available from the ‘gen’ matrix of ‘workspace’ is stored in a table and the a [Pimax] set is obtained for the RROPF problem. Solving with this simplified objective function, the solution is stored for comparison with Fixed reserve case. Table 2Pg 103.31 200 250 300 30 The solution from the simplified objective function- base case 0 300 200 250 300 100 Pmin 30 30 75 60 30 Qg Qmax Qmin Vg mBase status Pmax 19.76 180 -90 1.1 100 1 65.27 120 -60 1.1 100 1 74.14 150 -75 1.1 100 1 36.9 180 -90 1.1 100 1 42.32 60 -30 1.1 100 1 Table 3 - Solution of Pg, Pmax from the Responsive Reserve case PEAK RESPONSIVE RESERVE RESULTS Obj Cost 3429405 GEN DATA Pg Qg Qmax Qmin Vg 103.36 21.551 115.16 -57.579 1.0985 200 70.895 120 -60 1.0954 250 71.439 150 -75 1.1 300 8.0258 180 -90 1.1 30 18 18 -9 1.0935 RESULT Gen 1 2 3 6 8 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 191.93 200 250 300 30 Pmin 30 30 75 60 30 4.1.2 Fixed Reserve OPF Case A similar OPF is solved for a system with Fixed reserves, where reserves are predetermined with a view to obtain security. For the case of Fixed reserve, there is no particular method to optimize the reserve, except the requirement that the total reserve should be 10% of the system power at the moment. The generators are assumed as lumped within a sub-network. It is therefore logical that such an apportioning of 10% reserve in each generator group can occur. With such fixed reserves, there may even 51 be system violations for some of the contingencies, which will indicate vulnerability of the system and opportunity for price spikes or load shedding. It is simulated to find the total operation cost for Fixed Reserve versus Responsive Reserve cases for one Peak load scenario with a given set of Offers from the generators. It is tried to show that RROPF gives economic operation of the system. The result below shows the solutions from the two methods. The table shows the Pg and Qg allocation and the Pmax which gives the Reserve allocated to the particular generator. 52 Table– 4 Responsive vs. Fixed Reserve – Optimization of P and R in INITIAL CASE PEAK CASEComparison of cost and P and R required for the two methods GenCostCoeff FixedReserve case RespReserve case aP bP^2 cR dR^2 G=capact P=enrgy R=reserv G=capact P=enrgy R=reserv 5000 0.02 400 0.02 189.64 172.4 17.24 191.93 103.36 88.57 4500 0.01 250 0.01 200.002 181.82 18.182 200 200 0 3500 0.001 1050 0 249.997 227.27 22.727 250 250 0 4500 0.03 500 0.03 300.003 272.73 27.273 300 300 0 Fixed Respnsv 10,000 0.08 400 0.02 33 30 3 30 30 0 972.642 884.22 88.422 971.93 883.36 88.57 4056350 3429405 MW change FR-RR 0.712 0.86 -0.15 Analysis % change 0.1% 0.1% G=capacity required is decreased in RR compared to FR , although small 0.1% 3E+06 P = energy used is decreased in RR compared to FR , although small 0.1% Reduction Loss - the co-optimization has reduced system loss. The expensive Reserves in FR of G3 (1050Rs/MW) and G5 (500 Rs./MW) has shifted to G1 which has P cost more than G2 and G3. G2 and G3and G4 having cheaper energy than G1 have taken up all the load and shifted the reserve. Conclusion : Responsive reserve is more economic than Fixed Reserve. The P and R allocation in the two cases are presented in a chart 53 responsive vs fixed -P & R allocation 350 300 250 200 MW 150 100 50 0 g1r g1f g2r g2f g3r g3f g4r g4f g5r g5f Rg Pg Figure 7 – Response vs. Fixed Reserve – P and R allocations 54 4.1.3 Case 2 – Market Power Test As natural with generators lying in load pocket areas, they will try to exercise market power. Especially, when reserve capacity is to be scheduled, the profit making intent will be more singular on reserve pricing as “a single capacity is to be offered” and generators will offer to produce at the lowest prices for ‘Energy’ to be selected at first. Therefore, a simulation with FROPF and RROPF was done with one Generator G3 in load pocket (area2) offering high price for reserve. The [Pi ] solution set obtained from the CON-OPT gives the [Pimax ] set for the RROPF Table 4 6 Cases – P allocation to get Pmax Comparison of the Pi from six cases to get Pimax for Market Power test case (RROPF) Pg Pg Pg Pg Pg Pg Pimax 276.77 300 290.39 250 300 300 300 Gen1 30 94.746 16.875 67.436 48.335 51.937 94.746 Gen2 250 162.5 250 250 219.74 250 250 Gen3 300 300 300 300 300 300 300 Gen4 30 30 30 18.75 30 30 30 Gen5 886.77 887.246 887.265 886.186 898.075 931.937 974.746 Max Committed capacity required 974.746 The Pi solution from the six contingency cases are presented in a chart Pi soultion from Contingency cases Market Power case 350 300 250 M W 200 150 100 50 0 1 2 3 Generators 4 5 Pg Pg Pg Pg Pg Pg Figure 8- 6 cases – P allocation to get Pmax 55 Table- 6 Results of RROPF with new Market Power cost curve from Generator 1 MARKET POWER TEST CASE RESPONSIVE RESERVE - WITH NEW Gimin and Gimax GEN DATA Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax Pmin 1 276.86 29.93 180 -90 1.1 100 1 300 30 2 30 56.85 56.85 -28.4 1.08 100 1 94.746 30 3 250 86.96 150 -75 1.1 100 1 250 75 6 300 13.25 180 -90 1.1 100 1 300 60 8 30 18 18 -9 1.09 100 1 30 30 886.86 974.746 Similarly, the results from Fixed Reserve OPF for the Market Power test case is as shown Table – 7 Results for Fixed Reserve OPF with Market Power cost curve from Generator 1 MARKET POWER TEST CASE Fixed Res Pi result Pg Active Power Limits Qg Qmax Qmin Vg mBase status 192.63 47.134 163.6 -81.8 1.0992 100 181.8 109.1 109.1 -54.5 1.0855 100 219.47 28.282 136.4 -68.2 1.1 100 272.7 18.283 163.6 -81.8 1.1 100 30 54.5 54.5 -27.3 1.0962 100 Bus 1 2 3 6 8 1 1 1 1 1 Pmax Pmin 272.7 181.8 227.3 272.7 90.9 30 30 75 60 30 Comparing the two results, it is tried to show that in such Market power situation, RROPF gives much better solution than Fixed Reserve case. 56 Table 5- Comparison of the Fixed Reserve and Responsive Reserve OPF for Market Power Test case MARKET POWER CASE Cost coeff-P Cost coeff-R 5000 0.02 1050 0.02 4500 0.01 250 0.01 3500 0.001 1050 0.001 4500 0.03 500 0.03 10,000 0.08 400 0.02 FixedReserve case RespReserve case G=capactP=enrgy R=reservG=capact =enrgy R=reserv P 189.64 172.4 17.24 300 276.86 23.14 200.002 181.82 18.182 94.746 30 64.746 250 250 249.997 227.27 22.727 0 OBJ FN COST 300.003 272.73 27.273 300 300 0 Fixed Respsv 33 30 3 30 30 0 972.642 884.22 88.422 974.75 886.86 87.886 4130135 3426131 MW change FR-RR -2.104 -2.64 0.536 % change -0.2% -0.3% %change in Fixed Rescase 0.018 -0.001 Analysis %change in Resp Rescase 1 G=974.75 capacity required is increased due to Market Power exercise P = energy used is increased in RR compared to FR Loss is increased due to transportation of power from less expensive ones (considering Reserve Price also) 2 The expensive Reserves in FR of G1 (1050Rs/MW) caused little reserve in G1 and big increase in G2 3 The total P and R itself is not indicative. The total cost can not be compared directly due to the design of But comparitive increase is analysed the Objective function which is additive in Fixed Res case and subtractive in Resp Res case. Even with increase in P, the increase in operating cost is less in Responsive Reserve case than Fixed Reserve case. Conclusion : Responsive reserve is more economic than Fixed Reserve. 57 With these two cases in a peak load scenario, it is shown that the proposed methodology for the Contingency Optimized Energy and Reserve Scheduling is the best mecha nism in a POOL model – regarding not only security, but also adequacy, market power, and proper signals to investment in capacity, and pricing for energy by generators. The P and R allocation obtained from the two Responsive and Fixed methods are presented in a chart below. Responsive vs. Fixed P,R allocation Market Power case 350 300 250 MW 200 150 100 50 0 1 2 Gen 1-53 4 5 FG=capacity FP=energy FR=reserve RG=capacity RP=energy RR=reserve Figure 9 – P and R allocation in Fixed vs. Responsive Reserve with Market Power case 4.1.4 Load Decrease by 2% Case The test case for Load variation is checked with load decrease of 2% in al buses. The objective function cost will be certainly lower , and the P and R allocation will also be lower. But the indicator of the Cost is the Bus Lambda, which ultimately reflects the Operation optimality. We see that the lambdaP has decreased significantly and hence, it can be concluded that this method will send correct price signals to consumers as well as ISO and distributing companies to show more restraint and responsible behaviour during Peaks. Table of data compared to the base of Market Power case is shown 58 Table 6 – Compare –when load decrease by 2% Comparision when load decrease by 2% ld2% MP case ld 2% MP case ld 2% Mpcase Pg Pg Pmax Pmax lambdaP lambdaP 258.9 276.86 300 300 3960.4 3961.1 30 30 94.746 77.246 4095.6 4106.2 250 250 250 250 4013.7 4031.3 300 300 300 300 4175.9 4194.3 30 30 30 30 4118.9 4131 868.9 886.86 957.246 974.746 4099.7 4116.7 4189.9 4206.8 4189.7 4206.6 4190.8 4207.6 4225.4 4244 4203.7 4222.7 4174 4192.8 4182 4200.9 4245.8 4264.9 Load at bus decr 2% Load P LoadQ 0 0 117.6471 39.21569 88.23529 39.21569 117.6471 44.11765 117.6471 51.96078 117.6471 9.803922 0 0 0 0 49.01961 44.11765 39.21569 17.64706 78.43137 13.72549 58.82353 11.76471 39.21569 9.803922 34.31373 9.803922 The chart to compare the Power allocation and the lambda vectors are given below Comparison after Load decr2% - P and G(capacity) 350 300 250 MW 200 150 100 50 0 1 2 Generators 3 4 5 Pg Pg Pmax Pmax Figure 10 – Comparison of P and G(Pmax) in Market Power case vs. Load Incr 2% 59 Comparison of LambdaP at buses - LD by2% & MP case 4300 4250 4200 4150 4100 4050 4000 3950 3900 3850 3800 1 lambdaP lambdaP NRS/Mwhr 2 3 4 5 6 BUS no 7 8 9 10 11 12 13 14 Figure 11 – Comparison of Lambda P at buses – MP case vs. load incr 2% 4.1.5 Decommitment Further to the above mechanism, decommitment of the expensive generators can be incorporated to the CCOPF. This is done by removing the expensive generator from the network (status = 0) and doing the CON-OPT and RROPF completely. It must be checked whether generation allocated to it if removed, remaining capacity will be enough for the load. Table shows the comparison between Initial Peak case without and with G5 Decommitted- Allocation of P and Total Cost Table 7 – Power allocation and obj.fn. Cost with G5 decommitted PK w/oG5 PEAK with G5 179.67 103.36 200 200 219.98 250 300 300 30 899.65 883.36 obj cost 3419237 3429405 Although generation and loss is increased Total cost has decreased g1 g2 g3 g4 g5 60 4.1.6 Final CCOPF with Reactive Power Included to the Energy and Reserve: To include the Reactive Power as per our formulation, some modification to the network was necessary. 1. The generation Pmax and Qmax is given. Hence, for PRQ optimization, as explained in the formulation, S (Maximum MVA of the machines offered) needs to be calculated. S2 = P2 + Q2 The new max S is also the Pmax for all the base case and contingencies because a generator can be loaded up to S at unity power factor if it can be loaded up to Pmax while giving Qmax at a lower power factor, 2. Since the MINOPF does not allow to have Smax limit on generators, a new generator bus is added and linked by a negligible impedance line to the actual bus. This branch will be limited by the Smax limit. This modification solves the Apparent power capacity just the way it is required. 3. The cost curve prepared as explained in the formulation part, is added to the ‘gencost’ matrix. With the above modifications, CON-OPT is carried out to get [Gi] solution set from the Pimax . It is to be noted that if within a generator, when capacity required is reduced, generators may be shutdown due to Generator’s own unit scheduling. When Gi is obtained at the same time Qimax must be obtained for the given Gi by the same relation. Hence, Qimax is also modified. Responsive Reserve and Reactive Power Optimization (RRQOPF ) is done with the above data. The results are presented below. Table 8 – P,R and Q optimization-results after RROPF 3446201 Responsive Reserve of P,Q,R Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status 15 22.41 43.947 57.616 -33.596 1.0666 100 1 16 196.57 50.964 120 -79.834 1.0585 100 1 17 287.43 48.844 150 -100.64 1.0583 100 1 18 348.13 34.725 180 -121.83 1.1 100 1 8 30 18 18 -10.496 1.0668 100 1 Pmax Pmin 111.99 22.41 266.11 30 335.45 75 406.1 60 34.986 30 61 The load and generation cost curve data used are same as Initial Peak Load case. The total cost has increased compared to Initial case. It is natural because the Q is to be paid here. The cheaper generator G4 is used more than Pmax with better power factor and the reactive load is shifted to G3 and G2. The results show that the formulation has Optimized the P, R and Q as required. The P(R) and Q allocation with and without Q Optimization is shown in chart 400 350 300 MW/Mvar 250 200 150 100 50 0 1 2 Gen w/o Q and3 Q opt w. 4 5 P and Q comparison with and without Q OPTimization Pg (w.QOPT) Pg(w/oQOPT) Qg(w QOPT) Qg(w/o QOPT) Figure 12 - P and Q allocation - with Q and without Q Optimization The P,R,Q solution is the Contingency Optimized Energy, Reserve and Reactive Power (COPRQ) scheduling for the system. 4.2 Discussion on the Methods for Pricing of the Energy and Reserve Locationa l and zonal pricing of the energy and reserve – separate mechanisms for GENCO and DISCO. The bus lambda ? RRi obtained from the RROPF gives the incremental price of converting one unit of reserve into energy. The ?RRi = ?Pi – ? Ri . where ?Pi is the incremental price of energy and ?Ri is the incremental price of the reserve at bus i. Since there is no reserve allocated in the load-bus itself, the load bus has ?Pi but since the DISCO should pay for the reserve capacity also, an uplift charge has to be paid for it. ? Disco*PD = ?P *PD + ? R *RD = ? RRi *PD + ? R *PD + ? R *(GD -PD ) = ? RRi *PD + ? R *GD 62 From above it is clear that the DISCO are effectively paying the price of converting one unit of reserve into energy and additionally a ‘capacity charge’ but which is dependent upon the ‘actual system reserve employed the for the hour’ and not the installed capacity. Similar statement is valid also for GENCOs also. 4.2.1 Pricing by Perturbation Method To obtain ? P and ? R, it requires again a perturbation analysis. The complete optimization process is repeated for each bus by adding one unit of energy at the bus ? PDi and obtaining new Gimax and solving the RROPF, which gives the system cost fi . ? Pi = fi (the cost from perturbation in bus i) – f0 (the cost of main RROPF) Then it is easy to get ?Ri = ?Pi – ? RRi which is the incremental reserve price. The nodal prices indicated by the bus lambda vector for the different cases are shown on the next page. 63 Table 9 – Pricing comparison – lambda P of Initial, Market Power, Decommitted Lambda P vector at the nodes from the different cases Initial Market Decommit Peakcase Power test ted G5 6000 lambdaP lambdaP lambdaP 4604.1 3961.1 4607.2 5000 4627.1 4106.2 4651.5 4560.9 4031.3 2450.4 4000 4753.1 4194.3 5077.1 4714.3 4131 4812.3 3000 4687.7 4116.7 4853.7 4771.5 4206.8 5094.2 2000 4771.3 4206.6 0 4772.6 4207.6 5095 4818.6 4244 5109 1000 4803.1 4222.7 5018.3 4773.2 4192.8 4952 0 4781.3 4200.9 4969.6 1 4841.8 4264.9 5143 Lambda Pfor Initial/MarketP/Decommit Cases lambdaP lambdaP lambdaP NRs./Mwh 2 3 4 5 6 Bus 1-14 7 8 9 10 11 12 13 14 64 4.2.2 Pricing of the P, R and Q with the COPRQ Scheduling For pricing the reactive power at the nodes, it is to be noted here that the there is no reserve Q allocation in the scheduling. It can be easily added similar to the Energy reserve. Here, since there is no reserve, the lambda Q vector represents the actual nodal price of reactive power for both the generators and load. To get the ? P and ? R, it requires again a perturbation analysis. The complete optimization process is repeated for each bus by adding one unit of energy at the bus ? PDi and obtaining new Gimax and solving the CCPRQ, which gives the system cost fi . The cost reflects the additional system cost not only due to energy but a small portion of Q required to supplement the reactive loss due to ?PDi. This again is logical and it should reflect the additional cost. Hence, the incremental energy cost ? Pi = fi (the cost from perturbation in bus i) – f0 (the cost of main CCPRQ) Then it is easy to get ? Ri = ? Pi – ? RRi which is the incremental reserve price. The Generator gets paid for CG = ? Pi x PGi + ? Ri x (Gi - PGi ) + ? Qi x QGi Payment to generators The payment form DISCO are little different due to the reserve costs. CD = ?Pi x PDi + ?Qi x QDi + Reserve uplift x PDi Payment by distributing companies Where the reserve uplift is the weighted average of ? ? Ri x (Gi - PGi ) The bus lambda matrix is shown below with the cost (payment) accordingly. Following Table shows Nodal price of Reactive power for DISCO and GENCO (The active and reserve price have to be calculated with another perturbation analysis) 65 Table 10 – Pricing of P and Q – after P R Q optimized solution Bus 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Lambda P LambdaQ Pload Qload CostPload CostQloadCost(P-R)Gen CostQgen 4311.1 1311.3 0 0 0 0 4255.9 1372.1 120 40 510708 54884 3934.9 1479.3 90 40 354141 59172 4423.6 1491.8 120 45 530832 67131 4428.5 1379.5 120 53 531420 73113.5 4314.2 961.83 120 10 517704 9618.3 4617 1394.3 0 0 0 0 4616.7 1394.1 0 0 0 0 138501 25093.8 4635.1 1393.3 50 45 231755 62698.5 4684.8 1314.1 40 18 187392 23653.8 4572.6 1115.5 80 14 365808 15617 4482.3 999.35 60 12 268938 11992.2 4506.8 1031.8 40 10 180272 10318 4751.5 1280.8 35 10 166302.5 12808 4310.9 1310.9 0 0 0 0 96607.269 57610.122 4253.9 1371.5 0 0 0 0 836189.123 69897.126 2450.6 1227 0 0 0 0 704375.958 59931.588 4020.9 932.15 0 0 0 0 1399795.917 32368.909 The table shows the lambda P and lambda Q for each of the bus. While lambda Q is the price of Q / mvarh directly chargeable, for lambdaP given is actually lambda(P-R) as is already expla ined. From this lambda P-R index, actual locational prices can be easily found. 4.2.3 Pricing Based on Zones Locational prices for each and every node in the network is a good solution and gives a correct price but it is hard to implement and invites many real- life problems. Any constraint violation and adjustment in Optimal Power Flow due to such constraints means the nodal prices are changed in all the nodes of the Network. Along with the energy prices, the reserve and reactive power prices also change. A weighted average price for a similarly constrained and within distinct network subsections gives a better solution. The consumers within such networks get the average price and also due to similar constraints get equal quality power. To do this, first the nodes of each sub-networks have to be identified. The lambda P,R and Q for these nodes are weight-averaged and applied to all. This solution basically makes no difference to the ISO or the system operation. However, there must Not be large variance in the nodal prices within one sub- network. The five generators, eight load buses in the network are assumed here to represent such sub-networks or zones. This assumption requires initial reduction of the network, rest of the procedure is same. 66 4.2 Summary of Results 4.2.1 Result of Contingency Optimization: It is seen that simultaneous optimization with duplicated network (Option1) gives a higher amount of Capacity commitment than separate OPFs (Option2). Hence, for further RROPF, the results from second option (Pi = Gi , Gi = Pimax ) was carried on. The RROPF results are stored with [Pi] and [Ri] found. 4.2.2 Results for Fixed vs. Responsive Reserve Since the reserve is fixed in this case, there is no need for Cont ingency Optimization and FROPF was carried for the Peak load case with fixed reserves. The result in the first case of peak load – The responsive Reserve is found to be shifted and allotted to the cheapest one while also optimizing the energy allocation. Therefore, the total cost is reduced. The total reserve allocation is approximately 10 %, which is the generation loss used in the contingency and which is also the contingency used as a thumb rule for Fixed Reserve. Whereas the Fixed Reserve case may violate some constraints, the solution does not violate any constraints during any of the contingencies. 4.2.3 Market Power Test In order to test the reserve response to high pricing by generators, the reserve price was increased in the swing- bus , the generator which had large reserve in the First Peak case. It is seen that when reserve price increased, the allocation is shifted to other generators. Here it is important to observe that the new solution is still ‘contingency secure’. This may not be the case with a Fixed Reserve case. In both cases, the total operating cost is compared with the Fixed Reserve case and it is observed that it results in more economic solution. 4.2.4 Reactive Power Co-Opt Test: The results show that the reactive power is optimally distributed and the P is rescheduled compared to the first RROPF result without cost for Reactive power. The cost results are in line with the expected values. The pricing of Q is straight forward, and addition of Q does not affect the pricing of P and R. 67 4.2.5 Expected Cost The expected cost for these contingencies can be calculated with sufficient data for the involved parameters which is the sum of the expected costs given by individual costs of the base case and the individual contingency cases multiplied with their probabilities. The individual contingency costs have to be calculated first by using the Perturbation method to find the Energy cost and subsequently reserve cost and total cost. 4.3 Conclusion From the above results, it can be concluded that above method of optimized scheduling and pricing results in simple single-stage market. This can mitigate Market Power and is recommended for Electricity Pool model type small markets, especially those which are not yet ready for double sided market with retail seller competition. The above results also establishes the applicability of the method of CONTINGENCY OPTIMIZED ENERGY, RESERVE AND REACTIVE POWER SCHEDULING . The method used here can be suitably termed as CONTINGENCY CONSTRAINED OPTIMAL ENERGY, RESERVE AND REACTIVE POWER FLOW (CCOPRQPF). 4.4 Pool Design with the Above Mechanism The Pool design with above design will require a separate Regulator similar to the Nepal Electricity Regulatory Commission proposed in the modification of the existing law. The structure also requires an Independent System Operator with Grid Operator integrated. Without an Independent ISO, the Pool Market Operator can not function and the Pool model can not exist. Similarly, to avoid market power, there must be 5 or 6 large generating companies and the reservoir type Generator, with the Reserve capacity for Peak load, should preferably be with a government authority or the ISO. However, the generating and distributing company may be under one single holding company or the same organization with total financial and administrative separation for independent interaction in the market. The Tariff should be variable in the time of day and period of the year with regular supervision of the pricing method adopted by the distributing company. The variable 68 tariff may be applied to large industrial and commercial consumers. To make the demand responsive to price, the expected price received from the above CCOPRQF should be published and notified to the large consumers by internet and daily TV/radio broadcast. The actual price is determined post-event when all the generation and transmission surcharges are calculated. Further detail of the mechanism may be worked out as necessitated by the above proposed method, but this not being the intention of the thesis, it is rested here. 4.5 a) Limitation and Further Work Simulation and Testing of the method proposed above by standard testing and simulation packages to find the behaviour of the Market Players and test for Market Power indices. This is a very important follow- up to this work. The Regulators will need such tools and the information as they have to watch and pre-empt any collusive acts by the generators before they actually disrupt the market. Suggested areas of further research related to the above work: b) Implementation of the Real- Time Contingency Optimized Optimal Power Flow including the Reserve and Reactive Capacity. This is very important to the ISO for system operation when the market starts to operate under the regime as proposed by this wo rk. c) Solve the Contingency Optimization problem through state of the art MultiObjective Weightage Method or other adaptive learning methods and compare the performances. For developing markets like ours which can not go to full market for a considerable time to come, we have to find more efficient and effective OPF methods. This is an area of further research which will meet our concerns. d) Extend the RROPF to include the reactive power reserve also, especially SVCs, synchronous condensers and FACTS to pay for their investment. e) The optimal operation of FACTS and Series Capacitors according to the Optimal power, reactive power and reserve capacity exchange through the tielines between Areas. 69 REFERENCES [1] DP Kothari, JS Dhillon Power System Optimization, Eastern Economy Edition, Prentice Hall India [2] Allen J Wood, Bruce F Wollenberg ‘Power Generation, Operation and Control’ Wiley Student Edition, 2005 [3] S Stoft ‘Power System Economics: Designing Markets for Electricity’WileyIEEE Press, May 2002 [4] [5] H Saadat ‘Power System Analysis’ Tata-McGrawHill 2002 CL Wadhwa, ‘Electrical Power Systems’, New Age Internatinal Limited, Publishers 1997 [6] [7] T W Berrie “Power System Economics” Peter Peregrinus Ltd, 1983 Belegundu AK, Chandrupatla TR ‘Optimization Concepts and Applications in Engineering’ Pearson Education Pvt Ltd, 2003 [8] Mathews JH, Fink KD ‘Numerical Methods Using Matlab’ Eastern Economy Edition, Prentice Hall of India, 2005 [9] Geoffrey Rothwell, Tomas Gomez “Electricity Economics, Regulation and Deregulation” Wiley Interscience Ltd, IEEE Press 2003 [10] Jie Chen, James S Thorp, Robert J Thomas, Timothy D Mount ‘Locational Pricing and Scheduling for an Integrated Energy Reserve Market’ Proceedings of the 36th Hawaii International Conference on System Sciences-2003 [11] Robert J Thomas, Thomas R Schneider “Underlying Technical Issues in Electricity Deregulation” PSERC 97-18 Proceedings of the Hawaii International Conference of System Sciences, January 6-9, 1997, Kona, Hawaii [12] Richard Schuler, ‘Electricity and Ancillary Services Markets in New York State: Market Power in Theory and Practice,’ 34th Annual Hawaii Conference on Systems sciences, January 3-6,2001 [13] [14] Howard F Illian , ‘Completing the Market Design’ IEEE, November 2004 Richard Schuler ‘Self-Regulating Markets for Electricity : Letting Customers into the Game’ IEEE Power Systems Conference and Exposition, October 1013, 2004, NY 70 [15] Shmuel Oren, ‘Capacity Payments and Supply adequacy in competitive electricity markets’ VII Symposium of specialists in electric operational and expansion planning, Curitiba, Brasil, May21-26, 2000 [16] Takahide Hori ‘Creating the Wholesale market for electricity in Japan: What should Japan learn from Major Markets in the United States and Europe’ Electric Power Development Co.Ltd.Japan June 2001 [17] Simon Ide, Timonthy Mount, William Schultze, Robert Thomas, Ray Zimmerman ‘Experimental tests of competitive markets for electric power’ Proceedings of 34th Hawaii International conference of system sciences 2001 [18] Carlos E Murillo Sanchez, Ray D Zimmerman, Robert J Thomas ‘Kirchoff vs. Competitive Markets : A few examples’ 0-7803-6672-7/01/2001 IEEE [19] C E Murillo Sanchez, SM Ede, T D Mount, RJ Thomas and RD Zimmerman ‘An engineering approach to monitoring market power in restructured markets for electricity’ Cornell University and PSERC [20] John Bower ‘Why did Electricity Prices Fall in England and Wales? Market Mechanism or market structure?’ Oxford Institute for Energy Studies 2002 [21] James D Weber, Thomas J Overbye, Peter W Sauer, Christopher L De Marco ‘ A simulation based approach to Pricing Reactive Power’ IEEE 1998, published in Proceedings of the Hawaii International Conference on System Sciences, January6, 1998, Hawaii [22] Tim Mount, Yumei Ning, Hyungna Oh, ‘An analysis of price volatility in different spot markets for electricity in the USA’ Department of Agricultural Resource and Managerial Economics, Cornell University [23] R J Thomas, TD Mount, R Zimmerman, WD Schultze, R E Schuler, L D Chapman ‘Testing the effects of Price Responsive Demand on Uniform price and soft-cap electricity auctions’ Proceedings of the 35th Hawaii International Conference on system sciences 2002 [24] Luis S Vargas, Victor H Quintana, Anthony Vanelli, ‘A tutorial description of an interior point method and its applications to security constrained economic dispatch,’ IEEE Transactions on Power systems vol8, no3, august 1993 [25] Rainer Bacher, Hans P Van Meeteren, “Real time optimal power flow in automa tic generation control’ IEEE Transactions on Power Systems. Vol 3 No4 , November 1988 71 [26] Shoults RR and Mead MM, ‘Optimal Estimation of piecewise linear incremental cost curves for EDC’ IEEE transactions on Power Apparatus and systems, vol PAS 103, No 6, pp 1432-1437, June 1984 [27] Stott B and Alsac O, ‘Experience with successive linear programming for optimal rescheduling of active and reactive power’, paper 104-01, Proceedings of CIGRE, Florence, Italy, 1983 [28] Biggs MC and Laughton MA, ‘Optimal Electric Power Rescheduling: A large non- linear programming test problem solved by recursive quadratic programming’ Mathematical Programming 13, pp.167-182,1977 [29] Sun DI, Ashley B, Brewer B, Hughes A and Tinney WF ‘ Optimal Power flow by Newton Approach’ IEEE Tran. On Power Apparatus and Systems vol PAS 103,No10, pp1248-1259 October 1984 [30] M Huneault, FD Galiana ‘A Survey of Optimal Power Flow Literature’ IEEE Transactions on Power Systems, vol.6,No.2, May 1991 [31] Gianfranco Chicco, George Gross ‘Competitve Acquisition of Prioritizable Capacity-based Ancillary services” Publication of PSERC and CERTS [32] Peter W. Sauer,Thomas J. Overbye,George Gross,Fernando Alvarado,Shmuel Oren, James Momoh “Reactive Power Support Services in Electricity Markets , Costing and Pricing of Ancillary Services, Final Project Report,”PSERC Publication 01-08, May 2001 [33] Nodir Adilov, Thomas Light, Richard Schuler, William Schultz, David Toomey, Ray Zimmerman ‘Self- Regulating Markets?’ Advanced workshop in Regulation and competition , Rutgers center for research in regulated industries 17th annual western conference, CA June 24, 2004 [34] Lester B. Lave, Jay Apt, and Seth Blumsack “Rethinking Electricity Deregulation” Carnegie Mellon Electricity Industry Center Working Paper CEIC-04-03 [35] Nopporn Leeprechanon, A Kumar David, Selva S Murthy, Fubin Liu ‘Transition to an Electricity Market : A model for Developing Countries’ IEEE Transactions on Power systems ,vol 17, no3, August 2002. [36] Thomas RJ, Zimmerman RD, Murillo-Sancgez, Ede SM, Mount ‘An Engineering Approach to Monitoring Market Power in Restructured Markets for Electricity’ Cornell University, and PSERC 72 [37] Pedro Correia, Thomas Overbye, Ian Hiskens ‘Supergames in Electricty Markets : Beyond the Nash Equilibrium concept’ Presentation at 14th Power Systems Computation Conference, Seville, Spain, June 2002 [38] Buddy Clark and Diana Liebmann “Power Restructuring Experience In California Will Not Occur In Texas” Houston Business Journal. August 17, 2001 [39] Bigyan P Shrestha, Rabin Shrestha “Pricing Transmission Services under Competitive Market Structure: A Case of Nepal” International Conference on Power Systems, Kathmandu, 2004 [40] ‘Nepal Electricity Authority, Fiscal Year 2004/05 – A year in Review ’ A utility annual review publication of Nepal Electricity Authority, August 2005 [41] ‘Nepal Electricity Authority, Generation’ – An annual publication of the generation business of Nepal Electricity Authority, Third issue, August 2005 [42] ‘Transmission and Distribution Plan F.Y. 2004/05 Nepal Electricity Authority’ A report of system planning department, Nepal Electricity Authority, 2004 [43] JR Arce, MD Ilie, FF Garces, “Managing Short term Reliability related Risks” IEEE summer Power Meeting , Vancouver, Canada, July 15-19, 2001, Paper 0-7803-7031 73 Appendix A: Case-Data An approximate representation of The Integrated Nepal Power System of 2005 – with lumping of some of the generators and load buses 74 TEST CASE INPUT DATA PREPARATION 2 Branch Data distance (km) fbus tbus r x From To 60 double 1 2 0 60 double 1 5 0 100 single 2 3 0 100 double 2 4 0 60 double 2 5 0 60 double 3 4 0 100 double 4 5 0 0 trf 4 7 0 0 trf 4 9 0 0 trf 5 6 0 60 double 6 11 0 60 double 6 12 0 60 double 6 13 0 10 double 7 8 0 10 double 7 9 0 60 double 9 10 0 60 double 9 14 0 150 double 10 11 0 60 double 12 13 0 100 single 13 14 0 b 0 0 0 0 0 0 0 0.20912 0.25202 0.25202 0.05917 0.05917 0.05917 0.05001 0.05001 0.05917 0.05917 0.05917 0.05917 0 0 0 0 0 0 0 0 0 0 0 0.0528 0 0 0 0 0.0528 0 0.0528 0 0 rateA 300 300 150 250 300 300 250 300 300 300 300 300 300 300 300 300 300 250 300 300 rateB 300 300 150 250 300 300 250 250 250 250 300 300 300 300 300 300 300 250 300 300 rateC 300 300 150 250 300 300 250 0 0 0 300 300 300 300 300 300 300 250 300 300 ratio 0 0 0 0 0 0 0 0.92 0.95 0.97 0 0 0 0 0 0 0 0 0 0 angle 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 status 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 132 kV double circuit Duck r/km p.u x/km p.u. b/km p.u. base 100MVA 0.000258 0.001243 0.001051 300MW 132 kV single circuit duck 0.000516 0.0022 0.000522 150MW 75 Appendix B: Use of OPF with the Data Files Matlab Program – some sample case files used function [baseMVA, bus, gen, branch, areas, gencost] = case14 %CASE14 Power flow data for IEEE 14 bus test case. % -Peak,Base,ContingencyCombinedFn % This data was converted from IEEE Common Data Format % (ieee14cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11 % Converted from IEEE CDF file from: % http://www.ee.washington.edu/research/pstca/ % 08/19/93 UW ARCHIVE 100.0 1962 W IEEE 14 Bus Test Case % MATPOWER % $Id: case14.m,v 1.5 2004/09/21 01:46:23 ray Exp $ %%----- Power Flow Data -----%% %% system MVA base ('this is case Peak -Reactive Power') baseMVA = 100; %% bus data %bus_i type Pd bus = [ 1 1 0 2 1 120 3 1 90 4 1 120 5 1 120 6 1 120 7 1 0 8 2 0 9 1 50 10 1 40 11 1 80 12 1 60 13 1 40 14 1 35 15 3 0 16 2 0 17 2 0 18 2 0 ]; %% generator data % bus Pg gen = [ 15 200 68.852 16 190 50 17 240 34.273 18 240 59.239 8 116.62 Qd 0 40 40 45 53 10 0 0 45 18 14 12 10 10 0 0 0 0 Gs 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 0 20 0 0 0 0 Bs area Vm Va baseKV 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.0634 1.0529 1.0412 1.0095 1.0314 1.0729 1.0365 1.0365 1.0346 1.0313 1.0463 1.0644 1.0595 1.0479 1.0635 1.0531 1.0415 1.0732 -0.0060638 -1.7583 0 -0.31814 0 -3.9927 0 -2.9883 0 -2.5216 0 -6.2304 0 -6.2283 0 -6.6082 0 -7.1734 0 -5.9055 0 -4.8723 0 -5.1552 0 -8.1125 0 0 0 1 -1.7553 0 -0.30986 0 -2.5058 0 zone 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1.1 1 1 1 1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.9 1.1 1.1 1.1 Vmax 1.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 ; 0.9 0.9 0.9 0.9 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Vmin ; Qg Qmax Qmin Vg mBase status Pmax Pmin 57.6162-33.59572906 1.1 100 1 111.9857635 22.41 ; 120 -79.83389477 1.0756 100 1 266.1129826 30 ; 150 -100.6363988 1.0787 100 1 335.4546625 75 ; 180 -121.8307427 1.1 100 1 406.1024757 60 ; 42.187 18 -10.49571341 0.94493 100 1 34.98571137 30 ; 76 ]; %% branch data % fbus tbus r xb rateA rateB rateC ratio branch = [ 1 2 0.016320.066 0.0624 250 250 250 0 0 1 1 5 0.016320.066 0.0624 250 250 250 0 0 1 1 15 0.0001 0.0001 0 111.9857635 111.9857635 2 3 0.0545 0.22 0.0515 130 130 130 0 0 1 2 4 0.032640.132 0.1248 200 200 200 0 0 1 2 5 0.016320.066 0.0624 250 250 250 0 0 1 2 16 0.0001 0.0001 0 233.2380758 233.2380758 3 4 0.016320.066 0.0624 250 250 250 0 0 1 3 17 0.0001 0.0001 0 291.5475947 291.5475947 4 5 0.032640.132 0.1248 200 200 200 0 0 1 4 7 0 0.209120 300 250 0 0.95 0 4 9 0 0.252020 300 250 0 0.95 0 5 6 0 0.252020 300 250 0 0.97 0 6 11 0.016320.066 0.0624 250 250 250 0 0 1 6 12 0.016320.066 0 250 250 250 0 0 1 ; 6 13 0.0272 0.11 0 200 200 200 0 0 1 ; 6 18 0.0001 0.0001 0 349.8571137 349.8571137 7 8 0.0001 0.0001 0 34.98571137 34.98571137 7 9 0 0.011 0 300 300 300 0 0 1 ; 9 10 0.016320.066 0.0624 250 250 250 0 0 1 9 14 0.032640.132 0 200 200 200 0 0 1 ; 10 11 0.0272 0.11 0.104 200 200 200 0 0 1 12 13 0.016320.066 0 250 250 250 0 0 1 ; 13 14 0.081750.33 0.07725100 100 100 0 0 1 ]; %%----- OPF Data -----%% %% area data areas = [ 1 1; ]; %% generator cost data % 1 startup shutdown n x0 y0 ... xn % 2 startup shutdown n c(n-1) ... c0 gencost = [ 2 0 0 3 0.02 4600 0 ; 2 0 0 3 0.01 4250 0 ; 2 0 0 3 0.001 2450 0 ; 2 0 0 3 0.03 4000 0 ; 2 0 0 3 0.08 9600 0 ; 2 0 0 3 15 -7.525062709 0 ; 2 0 0 3 13.52257519 -6.772556438 2 0 0 3 12.6253011 -6.325275903 2 0 0 3 13.52257519 -7 0 ; 2 0 0 3 30.15151136 -15.15113634 ]; return; yn angle status ; ; 111.9857635 ; ; ; 233.2380758 ; 291.5475947 ; 1 ; 1 ; 1 ; ; 349.8571137 34.98571137 ; ; ; 0 0 1 ; 0 0 0 0 1 1 ; ; 0 0 0 0 1 1 ; ; 0 0 0 ; ; ; 77 Appendix C: Result Details CONTINGENCY CONSTRAINED ENERGY, RESERVE AND REACTIVE POWER OPTIMIZATION RESULTS cost 3447728 Case 0 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 1 15 30 42.787 180 -90 1.0651 100 1 349.86 2 16 188.59 49.605 120 -60 1.0564 100 1 233.24 3 17 287.65 47.542 150 -75 1.0567 100 1 291.55 4 18 348.23 33.717 180 -90 1.1 100 1 349.86 cost 5 8 30 22.518 60 -30 1.0695 100 1 116.62 3641319 Case 1 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 15 91.492 44.356 180 -90 1.0721 100 1 349.86 16 228.19 48.276 120 -60 1.0589 100 1 233.24 17 185.22 39.614 97.32 -48.66 1.0406 100 1 189.41 18 348.16 34.387 180 -90 1.1 100 1 349.86 cost 8 30 23.359 60 -30 1.0659 100 1 116.62 3472148 Case 2 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 15 96.027 45.029 180 -90 1.0686 100 1 349.9 16 122.77 46.265 67.5 -33.75 1.0528 100 1 131.2 17 287.59 47.885 150 -75 1.0551 100 1 291.5 18 348.21 33.906 180 -90 1.1 100 1 349.9 cost 8 30 23.602 60 -30 1.0693 100 1 116.6 3390563 Case 3 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 15 25 43.362 150 -75 1.0656 100 1 291.5 16 205.24 50.287 120 -60 1.0577 100 1 233.2 17 287.55 48.107 150 -75 1.0568 100 1 291.5 18 348.21 33.863 180 -90 1.1 100 1 349.9 cost 8 18.8 22.823 60 -30 1.0685 100 1 86.6 3698785 Case 4 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 15 73.654 56.66 180 -90 1.0632 100 1 349.86 16 224.78 62.223 120 -60 1.0499 100 1 233.24 17 219.92 45.576 150 -75 1.1 100 1 291.55 18 346.34 49.502 180 -90 1.1 100 1 349.86 cost 8 30 31.667 60 -30 1.0513 100 1 116.62 3645668 Case 5 Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status Pmax 15 35.348 45.288 180 -90 1.0683 100 1 349.86 16 227.75 50.28 120 -60 1.0596 100 1 233.24 17 287.49 48.492 150 -75 1.0576 100 1 291.55 18 348.22 33.785 180 -90 1.1 100 1 349.86 8 30 23.784 60 -30 1.0705 100 1 116.62 Pmin 30 30 75 60 30 Pmin 30 30 48.75 60 30 30 16.9 75 60 30 25 30 75 60 18.8 30 30 75 60 30 30 30 75 60 30 Pmin Pmin Pmin Pmin 78 3446201 Responsive Reserve of P,Q,R Gen Bus Pg Active Power Limits Qg Qmax Qmin Vg mBase status 15 22.41 43.947 57.616 -33.596 1.0666 100 16 196.57 50.964 120 -79.834 1.0585 100 17 287.43 48.844 150 -100.64 1.0583 100 18 348.13 34.725 180 -121.83 1.1 100 8 30 18 18 -10.496 1.0668 100 1 1 1 1 1 Pmax Pmin 111.99 22.41 266.11 30 335.45 75 406.1 60 34.986 30 Final Result of the CCPRQ optimal flow – P and Q allocation have changed from the Initial case with all the others remaining same. BUS OUTPUT DATA bus. type Pact Qact G 1 1 0 0 2 1 120 40 3 1 90 40 4 1 120 45 5 1 120 53 6 1 120 10 7 1 0 0 8 2 0 0 9 1 50 45 10 1 40 18 11 1 80 14 12 1 60 12 13 1 40 10 14 1 35 10 15 3 0 0 16 2 0 0 17 2 0 0 18 2 0 0 Lambda P LambdaQ B 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 0 20 0 0 0 0 stat 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Vm Va 1.0665 0.001085 1.0583 0.86627 1.058 4.9772 1.0236 -0.51764 1.0401 -1.2129 1.0997 -0.3304 1.0668 -3.6415 1.0668 -3.6409 1.0644 -3.9743 1.061 -4.5808 1.0748 -3.489 1.0923 -2.5637 1.0875 -2.8179 1.0784 -5.4815 1.0666 0 1.0585 0.87371 1.0583 4.9894 1.1 -0.31555 Vmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 Vmin 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 4311.1 4255.9 3934.9 4423.6 4428.5 4314.2 4617 4616.7 4635.1 4684.8 4572.6 4482.3 4506.8 4751.5 4310.9 4253.9 2450.6 4020.9 1311.3 1372.1 1479.3 1491.8 1379.5 961.83 1394.3 1394.1 1393.3 1314.1 1115.5 999.35 1031.8 1280.8 1310.9 1371.5 1227 932.15 gen5 gen1 gen2 gen3 gen4 79 Simultaneous Contingencies optimization – all contingencies in one network Flow between the contingency networks constrained to 0.1 MW. bus Base case 1 2 3 6 8 15 16 17 20 22 29 30 31 34 36 43 44 45 48 50 57 58 59 62 64 71 72 73 76 78 Pg 98.345 200 250 300 30 198.94 200 162.5 300 30 235.12 112.5 219.98 300 30 159 200 219.56 300 18.75 146.54 200 219.64 300 30 188.08 200 224.11 300 30 Qg 18.079 62.895 72.606 9.3374 27.296 25.921 99.974 30.906 12.901 57.947 67.841 67.5 37.612 21.692 60 44.519 114.68 29.299 28.502 37.5 48.076 94.758 30.299 14.039 60 42.388 110.71 29.936 19.216 60 Qmax 180 120 150 180 60 180 120 97.5 180 60 180 67.5 150 180 60 150 120 150 180 37.5 180 120 150 180 60 180 120 150 180 60 Qmin -90 -60 -75 -90 -30 -90 -60 -48.75 -90 -30 -90 -33.75 -75 -90 -30 -75 -60 -75 -90 -18.75 -90 -60 -75 -90 -30 -90 -60 -75 -90 -30 Vg 1.0893 1.0865 1.0953 1.1 1.0979 1.0939 1.0862 1.1 1.1 1.1 1.0939 1.0662 1.1 1.1 1.0937 1.0939 1.0834 1.1 1.1 1.0757 1.0939 1.0813 1.1 1.1 1.1 1.0939 1.082 1.1 1.1 1.0971 mBase 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 status 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Pmax 300 200 250 300 100 300 200 162.5 300 100 300 112.5 250 300 100 250 200 250 300 62.5 300 200 250 300 100 300 200 250 300 100 Pmin 30 30 75 60 30 30 30 48.75 60 30 30 16.875 75 60 30 25 30 75 60 18.75 30 30 75 60 30 30 30 75 60 30 878.345 Conting 1 891.44 Conting 2 897.6 Conting 3 897.31 Conting 4 896.18 Conting 5 942.19 80 Simultaneous Contingencies optimization – all contingencies in one network Flow between the contingency networks constrained to 0.1 MW. Case 1- with Reserve included in base case only and Case 2 - with objective function same in all cases RESULT OF CONTINGENCY OPTIMIZATION FOR GETTING MAX CAPACITY COMMITMENT Case with Reserve included in base case only Gen1 Gen2 Gen3 Gen4 Gen5 case0 122.02 195.66 245.66 293.05 31.75 888.14 case0 98.345 200 250 300 30 878.35 case1 230.00 197.83 161.41 263.50 31.78 884.52 case1 198.94 200 162.5 300 30 891.44 case2 227.41 99.72 248.04 293.05 39.88 908.11 case2 235.12 112.5 219.98 300 30 897.6 case3 151.98 197.19 222.46 273.94 21.28 866.85 case3 159 200 219.56 300 18.75 897.31 case4 87.14 195.47 245.52 292.92 41.13 862.17 case4 146.54 200 219.64 300 30 896.18 case5 138.10 200.00 250.00 300.00 30.00 918.10 case5 188.08 200 224.11 300 30 942.19 Gi=maxPi 230.00 200.00 250.00 300.00 41.13 1021.13 Gi=maxPi 235.12 200 250 300 30 1015.12 Gi=maxPi 300 94.746 250 300 30 974.75 marktPowcase Combined network model gives a higher commitment requirement. Gi=maxPi 191.93 200 250 300 30 971.93 peak case Case with objective function same in all cases Gen1 Gen2 Gen3 Gen4 Gen5 81 Comparing the commitment for capacity (Gi) , simultaneous solution gives higher value than Separate solution for both Initial and Market Power cases. CONTINGENCY CONSTRAINED ENERGY, RESERVE AND REACTIVE POWER OPTIMIZATION RESULTS cost 3447728 Case 0 Gen 1 2 3 4 5 Case 1 Gen Bus cost 3641319 Active Power Limits 15 16 17 18 8 Pg 30 188.59 287.65 348.23 30 Qg 42.787 49.605 47.542 33.717 22.518 Qmax 180 120 150 180 60 Qmin -90 -60 -75 -90 -30 Vg 1.0651 1.0564 1.0567 1.1 1.0695 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 349.86 233.24 291.55 349.86 116.62 Pmin 30 30 75 60 30 Bus cost 3472148 Case 2 Gen Active Power Limits 15 16 17 18 8 Pg 91.492 228.19 185.22 348.16 30 Qg 44.356 48.276 39.614 34.387 23.359 Qmax 180 120 97.32 180 60 Qmin -90 -60 -48.66 -90 -30 Vg 1.0721 1.0589 1.0406 1.1 1.0659 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 349.86 233.24 189.41 349.86 116.62 Pmin 30 30 48.75 60 30 Bus cost 3390563 Case 3 Gen Active Power Limits 15 16 17 18 8 Pg 96.027 122.77 287.59 348.21 30 Qg 45.029 46.265 47.885 33.906 23.602 Qmax 180 67.5 150 180 60 Qmin -90 -33.75 -75 -90 -30 Vg 1.0686 1.0528 1.0551 1.1 1.0693 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 349.9 131.2 291.5 349.9 116.6 Pmin 30 16.9 75 60 30 Bus Active Power Limits 15 16 17 18 Pg 25 205.24 287.55 348.21 Qg 43.362 50.287 48.107 33.863 Qmax 150 120 150 180 Qmin -75 -60 -75 -90 Vg 1.0656 1.0577 1.0568 1.1 mBase 100 100 100 100 status 1 1 1 1 Pmax 291.5 233.2 291.5 349.9 Pmin 25 30 75 60 82 8 Case 4 Gen 18.8 22.823 60 -30 1.0685 100 1 86.6 18.8 Cost 3698785 Bus Active Power Limits 15 16 17 18 8 Pg 73.654 224.78 219.92 346.34 30 Qg 56.66 62.223 45.576 49.502 31.667 Qmax 180 120 150 180 60 Qmin -90 -60 -75 -90 -30 Vg 1.0632 1.0499 1.1 1.1 1.0513 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 349.86 233.24 291.55 349.86 116.62 Pmin 30 30 75 60 30 Cost 3645668 Case 5 Gen Bus Active Power Limits 15 16 17 18 8 Pg 35.348 227.75 287.49 348.22 30 96.027 228.19 287.65 348.23 30 Qg 45.288 50.28 48.492 33.785 23.784 Qmax 180 120 150 180 60 Qmin -90 -60 -75 -90 -30 Vg 1.0683 1.0596 1.0576 1.1 1.0705 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 349.86 233.24 291.55 349.86 116.62 Pmin 30 30 75 60 30 cost 3446201 Final Responsive Reserve of P,Q,R Gen Bus Active Power Limits 15 16 17 18 8 Pg 22.41 196.57 287.43 348.13 30 Qg 43.947 50.964 48.844 34.725 18 Qmax 57.616 120 150 180 18 Qmin 33.596 79.834 100.64 121.83 10.496 Vg 1.0666 1.0585 1.0583 1.1 1.0668 mBase 100 100 100 100 100 status 1 1 1 1 1 Pmax 111.99 266.11 335.45 406.1 34.986 Pmin 22.41 30 75 60 30 83 Output results with Decommitment of G5 – The whole process is repeated with Generator 5 removed from the network CASE0 Gen OBJ COST Bus Limits 3286157 Active Power 1 2 3 6 Pg 134.81 200 250 300 884.81 3483211 1 2 3 6 224.12 200 162.5 300 886.62 3324160 223.84 112.5 250 300 886.34 3286158 134.81 200 250 300 884.81 3416949 179.38 200 10.82 89.36 85.922 23.834 180 120 97.32 180 -90 -60 -48.66 -90 1.1 1.0944 1.0891 1.1 100 100 100 100 1 1 1 1 300 200 162.5 300 30 30 48.75 60 Qg 19.878 80.941 81.393 19.882 Qmax 180 120 150 180 Qmin -90 -60 -75 -90 Vg 1.1 1.0965 1.1 1.1 mBase 100 100 100 100 status 1 1 1 1 Pmax 300 200 250 300 Pmin 30 30 75 60 CASE 1 OBJ COST OBJ COST CASE 2 1 2 3 6 26.41 67.5 91.503 23.464 180 67.5 150 180 -90 -33.75 -75 -90 1.1 1.0865 1.1 1.1 100 100 100 100 1 1 1 1 300 112.5 250 300 30 16.875 75 60 OBJ COST 1 2 3 6 OBJ COST CASE4 1 2 CASE3 19.879 80.939 81.393 19.882 150 120 150 180 -75 -60 -75 -90 1.1 1.0965 1.1 1.1 100 100 100 100 1 1 1 1 212.5 200 250 300 25 30 75 60 66.631 120 180 120 -90 -60 1.1 1.0823 100 100 1 1 300 200 30 30 84 3 6 OBJ COST CASE 5 1 2 3 6 219.6 300 898.98 3621715 221.34 200 224.25 300 945.59 29.795 55.367 150 180 -75 -90 1.1 1.1 100 100 1 1 250 300 75 60 74.824 120 32.003 64.317 180 120 150 180 -90 -60 -75 -90 1.1 1.0778 1.1 1.1 100 100 100 100 1 1 1 1 300 200 250 300 30 30 75 60 COMPARISON FOR PMAX CASE0 134.81 200 250 300 CASE1 224.12 200 162.5 300 CASE2 223.84 112.5 250 300 CASE3 134.81 200 250 300 CASE4 179.38 200 219.6 300 CASE5 221.34 200 224.25 300 pmax 224.12 200 250 300 974.12 DECOMMIT RESPRES 1 2 3 6 OBJ COST 179.67 200 219.98 300 899.65 3419237.1 107.14 67.5 37.725 63.927 180 67.5 150 180 -90 -33.75 -75 -90 1.1 1.066 1.1 1.1 100 100 100 100 1 1 1 1 224.12 200 250 300 22.41 30 75 60 85 Case of Load Decreases of 2% - Outputs for all contingencies and Responsive Reserve optimization Cost 3254582 Case 0 Bus 1 2 3 6 8 1 2 3 6 8 1 2 3 6 8 1 2 3 6 8 1 2 3 6 8 1 2 Pg 258.84 30 250 300 30 300 77.246 162.5 300 30 272.42 16.875 250 300 30 250 50.05 250 300 18.75 300 32.305 218.03 300 30 880.335 300 33.656 Qg 23.759 67.775 71.08 6.5356 24.68 25.633 71.239 59.116 7.4512 34.514 24.841 67.5 71.126 6.8362 25.449 23.27 67.585 71.635 6.1959 26.348 46.569 100.46 31.951 11.844 58.789 23.851 74.558 Qmax 180 120 150 180 60 180 120 97.5 180 60 180 67.5 150 180 60 150 120 150 180 37.5 180 120 150 180 60 180 120 Qmin -90 -60 -75 -90 -30 -90 -60 -48.75 -90 -30 -90 -33.75 -75 -90 -30 -75 -60 -75 -90 -18.75 -90 -60 -75 -90 -30 -90 -60 Vg 1.1 1.0831 1.0949 1.1 1.097 1.1 1.0811 1.0744 1.1 1.0985 1.1 1.0817 1.0941 1.1 1.0971 1.1 1.0842 1.0951 1.1 1.0973 1.1 1.0763 1.1 1.1 1.1 1.1 1.0815 mBase 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 status 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Pmax 300 200 250 300 100 300 200 162.5 300 100 300 112.5 250 300 100 250 200 250 300 62.5 300 200 250 300 100 300 200 Pmin 30 30 75 60 30 30 30 48.75 60 30 30 16.875 75 60 30 25 30 75 60 18.75 30 30 75 60 30 30 30 3404079 Case 1 3252587 Case2 3196778 Case 3 3349105 Case4 3433185 86 case 5 3 6 8 3254832 1 2 3 6 8 Bus data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 250 70.355 150 300 9.0749 180 30 29.528 60 913.656 300 77.246 250 300 30 957.246 Load decrease 2% onmp case 258.9 34.818 30 250 300 30 3 2 2 1 1 2 1 2 1 1 1 1 1 1 46.348 85.188 10.369 18 0 117.65 88.235 117.65 117.65 117.65 0 0 49.02 39.216 78.431 58.824 39.216 34.314 -75 -90 -30 1.0913 1.1 1.0984 100 100 100 1 1 1 250 300 100 75 60 30 180 46.348 150 180 18 0 39.216 39.216 44.118 51.961 9.8039 0 0 44.118 17.647 13.725 11.765 9.8039 9.8039 RROPF -90 23.174 -75 -90 -9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Pmax 1.1 100 1.0782 1.1 1.1 1.0914 0 0 0 0 0 0 0 0 0 0 0 20 0 20 100 100 100 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.1 1.078 1.1 1.054 1.063 1.1 1.09 1.091 1.087 1.078 1.082 1.095 1.091 1.097 300 77.246 250 300 30 0 -3.718 -1.418 -5.566 -4.268 -6.753 -9.13 -8.971 -9.481 -10.28 -9.61 -8.894 -9.093 -11.14 30 30 75 60 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 87 ENERGY AND RESERVE SCHEDULING - IEEE 14 BUS NETWORK TOTAL SYSTEM LOAD –875 MW TOTAL GENERATION CAPACITY (installed / offered) – 1150 MW INITIAL PEAK LOAD CASE G G G G G BASE CASE – GENERATION G1 (HM1) G2(HM2) G5(HM8) Base Case P= Contingency 1 P= Contingency 2 P= Contingency 3 P= Contingency 4 P= Contingency 5 P= RESPONSIVE RESERVE CASE G= P= R= FIXED RESERVE CASE G= P= R= G3(HM3) G4(HM6) 88 REACTIVE POWER – ENERGY – RESRVE COOPTIMIZATION files in C14Q1.M, C14PN.XL (SHEET- Q-Pk1 input data) print in CASE14Q0.DOC >> [a,busk,genk,gncostk,f]=runopf('c14q1'); ans = this is case Peak -Reactive Power Output = RESults-OPF Sheet Q1-res ) Converged in 0.10 seconds Objective Function Value = 3447727.96 $/hr ================================================================================ | System Summary | ================================================================================ How many? How much? P (MW) Q (MVAr) --------------------- ------------------- ------------- ----------------Buses 18 Total Gen Capacity 1341.1 -345.0 to 690.0 Generators 5 On-line Capacity 1341.1 -345.0 to 690.0 Committed Gens 5 Generation (actual) 884.5 196.2 Loads 11 Load 875.0 297.0 Fixed 11 Fixed 875.0 297.0 Dispatchable 0 Dispatchable 0.0 of 0.0 0.0 Shunts 2 Shunt (inj) 0.0 47.2 Branches 24 Losses (I^2 * Z) 9.47 41.81 Transformers 3 Branch Charging (inj) 95.4 Inter-ties 0 Total Inter-tie Flow 0.0 0.0 Areas 1 Minimum Maximum ------------------------- -------------------------------Voltage Magnitude 1.023 p.u. @ bus 4 1.100 p.u. @ bus 18 Voltage Angle -5.60 deg @ bus 14 4.86 deg @ bus 17 P Losses (I^2*R) 3.93 MW @ line 3-4 Q Losses (I^2*X) 15.90 MVAr @ line 3-4 Lambda P 2450.58 $/MWh @ bus 17 4735.88 $/MWh @ bus 14 Lambda Q 904.88 $/MWh @ bus 18 1447.59 $/MWh @ bus 4 ================================================================================ | Bus Data | ================================================================================ Bus Voltage Generation Load Lambda($/MVA -hr) # Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q ----- ------- -------- -------- -------- -------- -------- ------- ------1 1.065 0.001 - 4296.4981276.513 2 1.056 0.700 120.00 40.00 4255.6611335.288 3 1.056 4.852 90.00 40.00 3936.3411439.705 4 1.023 -0.666 120.00 45.00 4417.8891447.585 5 1.039 -1.315 120.00 53.00 4419.8801341.804 6 1.100 -0.429 120.00 10.00 4307.332 933.026 7 1.069 -3.780 - 4605.1001342.961 8 1.070 -3.779 30.00 22.52 - 4604.7881342.727 9 1.067 -4.111 50.00 45.00 4622.4891342.604 10 1.063 -4.704 40.00 18.00 4670.9541268.585 11 1.075 -3.596 80.00 14.00 4561.1631080.147 12 1.092 -2.664 60.00 12.00 4472.703 968.771 13 1.088 -2.920 40.00 10.00 4496.669 999.917 14 1.080 -5.603 35.00 10.00 4735.8791234.799 15 1.065 0.000 30.00 42.79 - 4296.2031276.093 16 1.056 0.707 188.59 49.60 - 4253.7721334.791 89 17 1.057 4.864 287.65 47.54 - 2450.5751194.139 18 1.100 -0.414 348.23 33.72 - 4020.894 904.878 -------- -------- -------- -------Total: 884.47 196.17 875.00 297.00 ================================================================================ | Branch Data | ================================================================================ Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z) # Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ----- ----- -------- -------- -------- -------- -------- -------1 1 2 -16.27 14.80 16.36 -21.47 0.086 0.35 2 1 5 46.27 27.99 -45.82 -33.07 0.451 1.82 3 1 15 -30.00 -42.78 30.00 42.79 0.002 0.00 4 2 3 -34.31 6.85 34.93 -10.09 0.621 2.51 5 2 4 24.65 13.83 -24.35 -26.09 0.304 1.23 6 2 5 61.86 10.36 -61.27 -14.83 0.588 2.38 7 2 16 -188.56 -49.57 188.59 49.60 0.034 0.03 8 3 4 162.64 17.56 -158.70 -8.40 3.933 15.90 9 3 17 -287.57 -47.47 287.65 47.54 0.076 0.08 10 4 5 5.76 -20.10 -5.69 7.12 0.068 0.27 11 4 7 29.91 4.55 -29.91 -2.90 0.000 1.65 12 4 9 27.39 5.04 -27.39 -3.35 0.000 1.69 13 5 6 -7.22 -12.22 7.22 12.67 0.000 0.44 14 6 11 103.34 13.76 -101.85 -15.14 1.483 6.00 15 6 12 70.03 -3.89 -69.36 6.57 0.664 2.68 16 6 13 47.54 1.08 -47.03 0.97 0.509 2.06 17 6 18 -348.13 -33.62 348.23 33.72 0.101 0.10 18 7 8 -30.00 -22.52 30.00 22.52 0.001 0.00 19 7 9 59.91 25.42 -59.91 -25.01 0.000 0.41 20 9 10 18.32 -1.40 -18.27 -5.47 0.049 0.20 21 9 14 18.98 -15.24 -18.81 15.92 0.170 0.69 22 10 11 -21.73 -12.53 21.85 1.14 0.124 0.50 23 12 13 9.36 5.29 -9.35 -5.23 0.016 0.06 24 13 14 16.38 -5.74 -16.19 -2.58 0.186 0.75 Total: 9.467 41.81 ================================================================================ | Voltage Constraints | ================================================================================ Bus # Vmin mu Vmin |V| Vmax Vmax mu ----- -------- ----- ----- ----- -------18 0.900 1.100 1.100505033.900 ================================================================================ | Generation Constraints | ================================================================================ Gen Bus Active Power Limits # # Pmin mu Pmin Pg Pmax Pmax mu ---- ----- ------- -------- -------- -------- ------1 15 304.997 30.00 30.00 349.86 5 8 5000.012 30.00 30.00 116.62 ================================================================================ | Branch Flow Constraints | ================================================================================ Brnch From "From" End Limit "To" End To # Bus |Sf| mu |Sf| |Smax| |St| |St| mu Bus ----- ----- ------- -------- -------- -------- ------- ----9 3 291.46 291.55 291.55 1503.116 17 17 6 349.75 349.86 349.86 284.287 18 >> 90 Appendix D: The Californian Experience In Californian Power exchange model, there were two prices, capacity reservation fee which is paid in advance, and energy payment for the reserve “called” on to generatelike the ‘call option’. Under the California plan, utilities sold off their power plants to independents and began to purchase their power on a day to day – or hour to hour –basis from the California Power Exchange and the California Independent System Operator. Both were intended to ensure that adequate supplies of power were available and delivered to meet consumer demand. Had the California market been opened with adequate supply and under modified market rules, deregulation there might have been successful. The California market, however, lacked rules which would encourage continued investment in supply, give market participants the ability to site plants easily and provide long-term risk management tools for market participants. For these reasons, the simultaneous opening up of both the wholesale and retail power markets in California was unsuccessful. California is faced with insufficient generating capacity, and the entire state is now scrambling to avert a power crisis this summer. California has not invested in its power infrastructure over the last decade, relying instead on its neighbors to provide the additional power supplies that it requires. At the same time, overall demand for electricity in California increased 24% from 1995 to 2000, nearly twice the national average for electrical demand growth. Unfortunately for California and its neighbours, hydropower, a primary source of power generation in the northwest, literally dried up due to two years of drought. Given the increased demand for natural gas fuel to replace the hydropower, California's pipelines have to operate at maximum capacity. The lack of capacity and bottlenecks lead to power shortages. Not only did California fail to invest in its own power generating capacity, it lacked the infrastructure to access its natural resources. California market was not designed to allow power companies to hedge their costs. Instead, the California structure mandated the use of a spot market for all sales of electricity. Market entrants could not engage in long-term contracts for the sale of 91 electricity. Long-term contracts benefit both buyers and seller and ultimately consumers by allowing buyers to take advantage of fuel diversity. The inability to fix long-term prices of the commodity exposed the utilities to high price spikes for power costs over the year. In the year 2000, without long-term contracting authority, utilities were forced to purchase their immediate power needs on the spot markets at high rates. Given the nature of the California market – with spiralling wholesale power costs and inelastic tariffed retail rates – there has been no margin, commonly referred to as “headroom,” within which retail providers could enter the market and successfully compete. As a result, many retail marketers did not engage in competition in California. Many that did compete withdrew shortly thereafter, leaving the existing utilities to offer retail service at rates that were lower than the rates they paid for wholesale power. (monopoly, vertically integrated, infrastructure, basic facility, subsidy, 92 Appendix E: Competition in Electricity Comes Full Circle - The American Experience: One of the first countries where electricity started as an industry, the United States had private entrepreneurs who invested in electricity and provided it as a ‘luxury good’ to the people. The electricity market in the USA began as a free market in the 1880s. Within 25 years, suppliers pleaded for regulation, arguing that they faced ‘ruinous’ competition. The public was not served well either.[34,Lester] It is enlightening to learn about the conversion of this ‘competitive’ sector into a monopoly and into public sector by public demand. Writing for New York’s Public Service Commission in 1908, Commissioner Maltbie Stated “The whole electric history of New York points out the futility of competition…It is coming to be generally recognized that monopoly control of electric light, heat and power may be very beneficial to the public if one company or the few non-competing companies can be placed under such public regulation and control as will secure for the public a fair share in the many benefits arising from unified management. That competition cannot be depended upon to protect the consumer from high prices and poor service has been fully demonstrated.” [34,Lester] A consensus emerged that vertically- integrated companies should be granted monopoly status within a geographical area in exchange for regulation that obliged them to serve consumers at low prices but gave them essentially guaranteed rates of return that could attract capital. Coming Full circle towards competitive Electricity sector : The above system thrived in the USA until 1970, when real electricity prices began to rise. A combination of factors contributed to rising prices, which ultimately led to the deregulation movement in the 1990s. Many utilities had made unsound investments resulting in high costs, especially for nuclear plants, and were unable to operate the new plants efficiently. Consumers protested that they should not have to pay for bad investment. 93 Economists regarded electricity supply as a natural mo nopoly. In these developed countries, even today the distribution system connecting customers to the transmission lines is too costly to permit multiple lines to each residential or other small customer. The transmission system has some of the same characteristics, but there is some possibility for competition. Generation, the part of the supply chain most amenable to competition, has limited economies of scale. The economies of scale mean that giving a single company the franchise to serve an area would result in lower costs for transmission and distribution and, up to a certain extent, for generation. Left to its own devices, a monopoly might take advantage of its market power to raise price. One solution is to create a regulatory agency that controls price. But efficient regulation is difficult. Since regulators must set price to give a fair return on the company’s investment and it must ensure that the company operates efficiently without excess costs. Regulators often make decisions on the basis of public desire (such as cross-subsidized tariff for the customers who are too poor to pay the real cost of electricity) The regulatory regime was desirable for utilities (who earned reasonable profits with little risk), regulators (who faced few difficult decis ions), and for customers (who had subsidized prices). Everyone avoided taking risks, since there was no premium if you succeeded and you were likely to lose your job if you failed. 94 Appendix F: to serve at a price’. Better Regulation or Deregulation In an electricity market, ‘obligation to serve’ electricity is replaced by an ‘obligation As long as the price remains low, the existing regime whether monopoly or competition gets accepted and hence, electricity remained as monopoly. Alternatives are sought and when prices rise, looking for the cause and trying to change the existing system. As prices rose swiftly in the US, consumers thought that the sellers and the utilities, rather than customers, should pay for bad decisions. The solution was sought in introducing competition and deregulation. As can be seen from various countries’ experiments with deregulation, it is a very treacherous path and in many countries than not, the answer is not deregulation, but reforming regulation. Even the most zealous deregulation proponents recognize the need for regulation of the distribution system, as well as the need to set rules for restructured markets. Making deregulation work requires better regulation. Describing a market as “free” and “competitive” is not the same thing. When a market where one or more sellers have market power is freed of regulation, prices are likely to rise far above marginal cost and other problems will occur. The realistic choice is how much authority to retain in an imperfect regulatory system and how much to transfer to an imperfect market for generation. Economists stress that if deregulation is to bring benefits to consumers, the markets it creates must be competitive. A competitive market structure often incurs large costs. If a competitive market cannot be achieved, prices are likely to be high and creating a free market is likely to result in higher prices than imperfect regulation, meaning that costs will rise. Regulators can require that retail prices fall, but efficiency gain in the short term will not compensate for the additional costs and so, eventually, prices will have to reflect the higher costs. Creating new institutions: Deregulation requires new institutions, primarily to perform functions formerly carried out by vertically integrated utilities. An independent systems operator is needed to coordinate supply and demand. A regional transmission operator is needed to manage transmission. Creating an effective new institution is 95 expensive and time consuming. Regulators need effective tools to monitor the system operation and the market for an optimal operation and to test and simulate market behaviour to determine market power. An important component is training individuals and acquiring hardware and software. These costs must be charged back to consumers as surcharges. The ISOs cover their operating costs through fees imposed on system participants and congestion payments. Therefore, the costs of setting up new market institutions must be accounted for in determining whether restructuring yields a net social benefit. Capital costs: The risks associated with deregulation in particular have led investors to demand much higher rates of return, although often they are not willing to supply the investment at any reasonable rate. The result is an increase in the cost of capital and hence the cost of new plant and equipment. When a capital- intensive company faces sharply higher costs for securing new capital, total costs rise significantly. If a deregulated company has to renegotiate its loans and bonds at market rates of return, accounting for risk, total costs would leap-frog. Under deregulation with fixed retail prices, the risks are shifted to investors. The current uncertainty about industry restructuring will force borrowing rates to be higher. Summing up deregulation: Eliminating regulation creates a free market. Creating a competitive market is more difficult. It requires that no seller have the ‘market power’ to increase profit by raising price. In other words, market participants must see themselves as price takers, not price setters. In a market, with inelastic demand, a company tends to bid their capacity at a high price. Since electricity cannot be stored, designing a market that prevents a company from having market power is much more difficult for electricity than for other goods and services. 96 Looking for Solutions within the Restructuring and Deregulation Problems Appendix G: From worldwide experience, it is seen that restructuring and deregulation has to be cautiously treated. There have been many problems a. Market power in spot wholesale power and operating reserve markets are quite significant. The problems can be attributed to too few competing generating companies, wholesale market design flaws, vertical integration between transmission and generation, excessive reliance on spot markets rather than forward contracts, and limited diffusion of communications and control technology that facilitates the participation of demand in wholesale spot markets. As a result, market power mitigation strategies ha ve become an important component of wholesale market reforms. However, efforts to mitigate market power with restrictions on bidding behaviour and price caps, rather than with structural remedies, may cause more harm than good and adversely affect investments in new generating capacity. b. The most efficient design of wholesale energy markets continues to be a subject of dispute among interest groups and independent experts.[3,Stoft]. Should the market be built around a pool or rely on bilateral contracts? Should there be locational pricing of energy and operating reserves? How should transmission capacity be allocated? Should transmission rights be physical or financial? Markets for energy and ancillary services (day-ahead and real time balancing) that accommodate bilateral contracts; locational pricing reflecting the marginal cost of congestion and losses at each location; an active demand side that can respond to market price signals, are some of the measures to ensure efficient system. c. No market design will work well if there are not an adequate number of competitive suppliers of generation service or the market power of dominant firms is not mitigated in some way. For this there should be a large number of competing suppliers of generation, which requires large investment. Creating appropriate investment incentives for new generating capacity is a growing problem in many countries. Investors look for stable market rules and longer term contractual 97 commitments before they commit capital. Financing investments in peaking capacity, which relies heavily on wholesale market prices creating “scarcity rents” to support fixed investment costs in a relatively small number of hours is especially problematic. There is not any uniq ue solution to restructuring nor deregulation. The sector is complex. Hence, many subtle variations and models can be seen in many countries that are having the competitive markets. There are many architectures implemented and some are a mixture of them. Mainly, there have been two discussions for competitive markets. 1. Bilateral markets and centralized markets 2.The Pool model and the Exchange model Bilateral markets are those where consumers directly purchase from the generators and use the transmission lines for a wheeling charge. These markets are good for the bulk supply of energy. But due to the intrinsic nature of the product ‘electricity’, ancillary products like reactive power, stability reserve and inter-dependent losses, wholly bilateral markets are not possible. The latter two models are the two models of centralized market. MARKET POWER : Market power refers to the concentration of resources in the hands of a single Producer or an insu? cient number of producers. One of the most common means for measuring market power is the Her?ndahl- Hirschman Index (H) [1]. This index is denned as follows: where the summation is over all N participants in the market and s refers to the market share of each. The share can be expressed in per unit (in which case the maximum value of H is 1) or in percent (in which case the maximum value of H is 10000). Other measures of market concentration are possible. Two other common measures of 98 concentration are the 4-firm and 8- firm concentration ratio (defined as the fraction of the total market held by the 4 or 8 largest Firms). Yet another index is the entropy coefficient E, defined as: Each market concentration index has advantages and disadvantages. It is impossible to establish a clear value below or above which market power exists for any index2. Many other aspects of a market not directly captured by these indices (most notably, ease of entry into a market) pla y heavily into the significance of specific quantitative values of an index. The greatest usefulness of these indices may be their value as relative market power indicators: a larger value of H indicates greater market concentration (and therefore the potential for greater market power) that a smaller value. The true measure of market power is the ratio between actual prices and the prices that would arise from true marginal cost pricing. Only market power as measured by H is considered here. 99 Appendix H: Attributes of Electricity as a Product Electricity has an unusual set of physical and economic attributes that significantly complicate the task of successfully replacing hierarchies (vertical and horizontal integration) with decentralized market mechanisms. These attributes must be recognized and incorporated into the successful design of competitive market and regulatory institutions to avoid performance failures. The attributes of electricity as a product are: a. Electricity cannot be stored economically and demand must be cleared with “just- in-time” production from generating capacity available to the network at exactly the same time that the electricity is consumed. Non-storability of electricity requires that supply and demand be cleared continuously at every location on the network. Network congestion, combined with non-storability, constrains the ability of remote suppliers to compete, further enhancing market power problems. Creating a set of complete markets that operate this quickly, at so many locations, and without creating market power problems is a significant challenge. b. The demand elasticity for electricity is very low but then supply gets very inelastic at high demand levels as capacity constraints are approached. As a result, spot electricity prices are inherently very volatile and unusually susceptible to the creation of opportunities for suppliers to exercise market power unilaterally. c. The combination of non-storability, real time variations in demand, low demand elasticity, random real time failures of generation and transmission equipment, the need to continuously clear supply and demand at every point on the network to meet the physical constraints on reliable network operations, means that some source of real time “inventory” is required to keep the system in balance. This “inventory” is generally provided by “standby” generators that can respond very quickly to changing supply and demand conditions, though demand side responses can also theoretically provide equivalent services as well. Compatible market mechanisms for procuring and effectively operating these “ancillary services” are therefore necessary but difficult to design. These attributes affect the design of efficient market and regulatory institutions. The failure to carefully integrate these 100 attributes into the design of regulatory and market institutions has created market performance problems. 101 Appendix I:Ancillary Services in an Electricity Pool Market In the Electricity Pool model, generators compete in the market to supply power at a price determined by the demand and the offered bids. The power demand and the offer of supply is matched and dispatched in real time by the Independent System Operator (ISO) and the Grid Operator (single or separate). The market operator in the Pool may be separate or integrated with ISO. When ancillary services or reliability products are priced and requires a market, the ISO integration with the Pool operator is a logical design. In such design, the reliability concerns of mid-term (month or day ahead) and short-term (hour ahead and real-time) can be addressed within one solution for the market. The solutions are then transferred continuously and post-event adjustments can be integrated for the final payments by the distributing companies (DISCO) and to the generating companies (GENCO). The ISO is the power system operator and carrier of the power to the Distributing companies which are wholesale and retail seller, in many cases, of power to the consumer. The ISO is a government regulated authority without any profit motive and which has to operate the system at the most optimum condition. Therefore, the ISO in a pool model has to employ Optimal Power Flow tools to optimize the operation of the Power system. The optimal power system operation normally means not only merit order dispatch based on the cost of power but also minimization of losses, ensuring security and reliability of the system. These requirements are met by different ISOs in different ways. It is found that Optimality is obtained methodically in terms of cost of power generated and distributed by using OPF programs and Security constrained OPF are used for maintaining the voltage at bus and power flow in line / transformer within the security limits. The North American Electric Reliability Council (NERC) has identified 12 Interconnected Operations Services (IOS) which can be commonly called as Ancillary services for system operation 102 1) Regulation support / reserve 2) Load Following 3) Energy Imbalance 4) Operating Reserve – Spinning 5) Operating Reserve – Supplemental 6) Backup Supply 7) System Control 8) Dynamic Scheduling 9) Reactive Power and Voltage Control from Generation Sources 10) Real Power Transmission Losses 11) Network Stability Services from Generation Sources 12) System Black start Capability Out of the above, operating reserve and reactive power are traded as separate products in the market to help the reliability and security of the system. Other services are available as by-products and not quantifiable for trade in the market, but as they are necessary f r system operation, they are procured by ISO and paid surcharges or o regulated as mandatory. Ancillary services are required for every market independent of the price volatility. Reliability, Security and Adequacy : Reliability of a system is a combination of adequacy and security.[15.Scmuel]Reliability is defined as the ‘degree to which the performance of the elements of the technical system results in power being delivered to consumers within accepted standards and in the amount desired.’ It encompasses two attributes of electricity system – Security, which describes the ability to withstand disturbances ( contingencies) and Adequacy, which represents the ability of the system to meet the aggregate power and energy requirements of all consumers at all times. Security is provided by means of operation standards and procedures that include Security Constrained Dispatch and the requirement for the ancillary services such as : voltage support , regulation capacity, spinning reserves, black start capability etc. The notion of adequacy represents the system ability to meet the system demands on a longer time scale. Capacity-Based Ancillary Services (CAS) The services included in AS are: 103 Frequency Response : This service requires both the up and the down shifting of the output level of the unit that provides the service. The speed droop and power – frequency droop of the generators are the inherent characteristics which provide frequency response. The response period is usually up to a few seconds. This service is pre-determined and required according to system stability by the ISO and is paid additional to the energy costs as a service add-on to the generators who provide it. Regulation: The basic Automatic Generation Control (AGC) service to track the load with the generation so as to ensure that the frequency stays within a predefined band of the system synchronous frequency. It is a non-automatic response of the generating units to the ISO signals to maintain supply-demand balance in actual operations, with positive and negative variation in the real power generation of the contributing units. This is again a SCADA based facility built- in in the plants and controllable by remote control center which may be made mandatory by regulation. A 10- minute overload of generator or over-draw of water from Run of River (ROR) hydro-power plants can be classified as Regulation reserve. These plants can provide up to 10% overload of their maximum continuous capacity for short time drawing extra water up to 10 minutes, which then has to be replaced by 10-minute spinning reserves. These services are also pre-determined before unit-commitment as required by system stability. The ISO has to pay the generators the excess at the spot price in case of the energy drawn from those generators which are not paid for their operating reserves. Reserves : Capacity available within the specified response time required for system operations to withstand unexpected generation outages and increases in the forecast demand, and used to allow the continued operation after system undergoes outages and/or 104 unexpected variations in the demand; reserves may be provided by either on- line generators loaded below their maximum capacity (spinning) or off- line generation sources having a response capability to meet requirements (non-spinning). 105 Appendix J: Economic Dispatch & Optimal Power Flow The optimization in power system operation was initially limited to economic dispatch of the most efficient power plants in merit order. Later the model included optimization of the transmission losses in the system along with the efficiency of the plants. The efficiency is expressed in terms of cost per unit increment of output. The scheduling involves those plants that are determined to be operated a priori. The objective function optimized in economic dispatch (ED) is expressed as Ct = min ∑ C i ( Pi ) i =1 ng (1.1) Ci = Cost function, Pi = Generation, ng = no of generators The objective function is limited by the following constraints Equality constraints PD + PL . = ∑ P as the power balance equation and i i =1 ng The inequality constraints as the plant capacity constraints. Pik , Qik = Active & Reactive power of ith generator at kth cont ingency, here k=0 base case. In a security constrained economic scheduling (SCED), the branch flow, bus voltage and angle limits are also employed as constraints Vmin ≤ Vi ≤ Vmax 106 |Sjk |=Sjmax Sjmax = Line flow limit of the branch from jth bus The Objective Function may be linear or non- linear Cost function of generation Cgi(Pgi)=k+aPgi+bPgi2 The constrained function is converted to unconstrained objective function optimization. Normally, Economic Dispatch problem is solved by using the Lagrange multiplier method. The augmented function using Lagrange multiplier to include an Equality constraint is L(Pgi )=Cgi(Pgi )+?(Pd+PL-? Pgi) (1.2) for The Pgi solution satisfying the minimum of Cgi ( Pgi ) is the Economic Dispatch method. There may be different optimization techniques developed till now for different problems and complexities of the optimizatio n. Classical method (Lambda Iteration Method)– Ct = min ∑ C i ( Pi ) i =1 ng ng Such that PD + PL . = ∑ P i i =1 and Pimin <= Pi <= Pimax PD =Load , PL = Loss, P I = Power generation, ?, µi max, µi min = Lagrangian multipliers The Lagrange function is given by L= Ct + ?(PD + PL - ? i=1 P i ) + ? i=1µi max (Pi-Pimax ) + ? i=1µi min (Pi-Pimin ) 107 The latter constraint terms are known as Kuhn-Tucker conditions. The minimum of this function is found where the partial of the function to its variables are zero. ∂L =0 ∂Pi ∂L =0 ∂λ ∂L = Pi − Pimax = 0 ∂µ i max ∂L = Pi − Pi min = 0 ∂µ i min ∂C t ∂P + λ ( L − 1) = 0 ∂Pi ∂Pi ∂C 1 ∂C 2 = ∂P1 ∂P2 ∂C i ∂P + λ L = λ ____ i = 1.....ng ∂Pi ∂Pi ∂C i ( ∂Pi 1 )=λ ∂PL 1− ∂Pi 1 ) The penalty factor Lpi is ( ∂PL 1− ∂Pi Now the cost is given by a polynomial of the second order. Ci= a+bPi + cPi2 . b + 2cPi + 2λ ∑ Bij Pj + Boi λ = λ j =1 ng c ( + Bii ) Pi + λ 1 b ∑≠Bij Pj = 2 (1 − Boi − λ ) j =1, j i ng Bij , B 0i = Loss coefficients Solving for the Pi at the kth iteration, Pik = λk (1 − Boi ) − b − 2λk ∑ Bij Pjk j ≠i ∑ i =1 ng λ (1 − Boi ) − b − 2λk ∑ Bij Pjk k j ≠i 2( c + λ Bii ) k 2( c + λ Bii ) k = PD + PL k This in short can be written as f(?)k = PD + PLk . 108 ? ? k = ?Pk / {df(?)/d ?}k . And ? k+1 = ? k + ??k . ? Pk = PD +PLk - ? i=1 P ik . Starting with a good estimate of ?k the iteration will be carried till ?Pk is less than a specified value e. If convergence is achieved, the Pi set is the required solution. [5,CLW p284] Optimal Power Flow – The main objective function of the basic Optimal Power Flow (OPF) problem is the same as Economic Dispatch, which is the minimum of Operating Cost Ct . But in an OPF, the control variables are not only Pgi (the generation of power plants) but also many other variables in a power flow, such as Voltage magnitude and angle, capacity commitment, lambda vector etc. In an optimal power flow, the Objective function is the Total cost of the power required for the system operation Ct = min ∑ C i ( Pi ) i =1 ng subject to the constraints Fj(?,V,P,Q)= 0, j=1…nb ; power balance equation for the network at each bus Pi = Qi = ∑ V V [G i j j∈nb i j j ∈nb ij cos(δi − δj ) + Bij sin( δi − δj )] sin( δi − δj ) − Bij cos(δi − δj )] ∑ V V [G ij Vmin ≤ Vi ≤ Vmax |Sjk |=Sjmax lines Fj(?,V,P,Q)= 0 can be restated as g(x,u,p) = 0, where x is the vector of dependent variables (di for PV bus, di and Vi for PQbus) and u is control variable and p is independent variables. the inequalities of the voltage limit and the power flow limit in the 109 L(x,u,p)= Ct (x,u) +? T g(x,u,p) Where ? T is a vector of LaGrange vectors of same dimension as g(x,u,p). (1.3) The solution of the Objective function can be obtained using different methods similar to Economic Dispatch. OPF using NEWTONs method The software MINOPF, used in this work, employs amongst others the Newton’s method to the OPF problem. A power system OPF analysis can have many different goals and corresponding objective functions. One possible goal is to minimize the costs of meeting the load on a power system while maintaining system security. The relevant costs for a power system analysis will depend on the nature of the analysis; for the OPF analysis used in this work, the relevant costs are the costs of generating power (MW) at each generator. It will be shown that the objective function ultimately becomes a function of only the generated power, although there will certainly be other control variables . With an OPF analysis, satisfying a system security requirement means keeping the devices in a power system within a desired operation range at steady state. These ranges could include maximum and minimum outputs for generators, maximum MVA flows on transmission lines and transformers, and maximum and minimum system bus voltages. An OPF only addresses steady-state operation of the power system. Topics such as transient and dynamic stability are not addressed. Another goal of an OPF analysis could be the determination of system marginal costs. This marginal cost data can aid in the pricing of MW transactions as well as in the pricing of ancillary services such as voltage support through MVAR support. In solving the OPF using Newton’s method, the marginal cost data is determined as a by-product of the solution. A brief overview of the OPF solution method is given below. [29, Sun] 110 A general minimization problem can be written in the following form: The solution of this problem by Newton’s method requires the creation of the Lagrangian: , A gradient and Hessian of the Lagrangian may then be defined as: gradient = ? (z) = ? L The OPF solution is obtained by solving ? L(z) = 0. The Hessian is used in the iterative process of Newton’s method. The Lagrangian only includes those inequalities that are being enforced. For example, if a bus voltage is within the desired operating range, then there is no need to activate the inequality constraint associated with that bus voltage. For this Newton’s method formulation, the 111 inequality constraints are handled by separating them into two sets: active and inactive. The objective function for the OPF reflects the costs associated with generating power in the system. The following quadratic cost model for generation of power is utilized: where P gi is the amount of generation in MW at generator i. The objective function for the entire power system can then be written as the sum of the quadratic cost model for each generator. Using this objective function in the OPF will minimize the total system costs. The OPF is able to model system security issues including line ove rloads, and lowvoltage and high- voltage problems. Besides, the OPF also yields information concerning the economics of the power system. The Lagrange multiplier associated with each constraint can be interpreted as the marginal cost associated with meeting that constraint. Therefore, the Lagrange multipliers can be interpreted as the marginal cost of real and reactive power generation at bus i in NRs/Mwh and NRs/Mvarh. These marginal costs could then be used to determine locational / nodal prices at bus i. On a larger level, the Lagrange multiplier associated with the area interchange constraint can be seen as the marginal cost of the area relaxing its interchange constraint. If this cost is positive, then the area would benefit from buying electricity, while if it is negative, the area would benefit from selling electricity. These costs may be of use in determining the price which one area would charge for a MW transaction with another area. 112 Appendix K: The Generation Cost Curves The energy and reserve cost curves are represented by two polynomials but both assumed to be almost linear. The cost curve simplification does not affect the test of the scheduling optimization. A common practice in industry is to represent the cost function of each generator through a monotonically increasing second order or third order polynomial. [26] The generator cost curve Cgi(Pi) = a+aPi+bPi2 And the reserve cost curve Cri(Ri) = ß+cRi+dRi2 The following cost curves are approximation only. The energy cost for Run-of River (ROR) type hydro projects are lower than Reservoir types and also lower than Peaking ROR (PROR). I have taken Nrs 3500 / MWhr as the cost of energy which is the price being charged to Nepal Electricity Authority (NEA) for bulk sale to rural consumers. a, ß = 0 There are no start- up costs for hydro-plants. Due to the cavitation zones of Francis turbines, low efficiency for Pelton turbine at low outputs and similarly for thermal units, certain minimum outputs are assumed for all generators. The start-up costs for thermal units are assumed included in the minimum capacity. Generator 1 – G1 is a reservoir type, controlled by state, generator. The energy cost is high but reserve cost is low as the unserved energy remains in the reservoir. Energy cost 5000 P1 +0.02Pi2 Reserve cost 400Ri+0.02Ri2 Here the second order term is added only to fit in as a polynomial for the OPF program handling. Generator 2–G2 is a Peaking ROR, controlled by state, generator. The energy cost is lower and reserve cost is also low as it can store energy for peak loads. This curve 113 does not represent a whole day cost curve, as reserve can not be stored for whole day in a PROR. These cost curves, at best, can be assumed for four hour blocks. If the four hour block reserve is not used during the real time operation, then the generator has to offer energy at a lower price in the next block and increase the Reserve price just like ROR generators. Energy cost 4000 P2 +0.01P22 Reserve cost 250R2 +0.01R2 2 Generator 3 – G3 is a ROR generator. The energy cost is low and since no reserve can be stored, it is priced very high. Energy cost 3500 P3 +0.001P32 Reserve cost 1050R3 +0.01R3 2 Generator 4 – G4 is a PROR with a higher operating cost than G2 and reserve is priced low as energy can be stored. Energy cost 4500 P4 +0.001 P42 Reserve cost 500 R4 +0.01 R4 2 Generator 5 – G5 is a mix of thermal power plant and PROR. The import from neighbouring grid can also be assumed to be in this model instead of PROR. Therefore, its energy is priced very highly. With 10 minute spinning reserve, gas turbines can start from standstill and provide the reserve. Hence, reserve is priced very low to reflect only the scarcity rent, the compensation required for the capacity investments. Energy cost 10000 P5 +0.08 P52 Reserve cost 400 R5 +0.08 R5 2 These cost curves are for the Initial Test case. 114