Models of supply function equilibrium with applications to the electricity industry (original) (raw)
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Supply function equilibrium analysis for electricity markets
2009
The research presented in this Thesis investigates the strategic behaviour of generating firms in bid-based electricity pool markets and the effects of control methods and network features on the electricity market outcome by utilising the AC network model to represent the electric grid. A market equilibrium algorithm has been implemented to represent the bi-level market problem for social welfare maximization from the system operator and utility assets optimisation from the strategic market participants, based on the primal-dual interior point method. The strategic interactions in the market are modelled using supply function equilibrium theory and the optimum strategies are determined by parameterization of the marginal cost functions of the generating units. The AC power network model explicitly represents the active and reactive power flows and various network components and control functions. The market analysis examines ii 2.12 Existence and multiplicity of pure equilibria in linear SFE models 60 2.13 Stochastic optimisation with linear supply function bidding 64 2.14 Numerical methods for SFE solutions 66 Chapter 3: Methodology and implementation of the electricity market SFE algorithm 3.1 The work in this Thesis 71 3.2 The primal-dual interior point method 76 3.3 Applications of the primal-dual interior point method 81 3.4 Introduction to the implemented market equilibrium algorithm 83 3.5 Modelling of the electricity network 84 3.5.1 Representation of the transmission line branch 84 3.5.2 Representation of the transformer 86 3.5.3 Formulation of the power flow and power mismatch equations 89 3.6 Electricity market assumptions and ISO obligations 90 3.7 The optimisation problem of the ISO 94 3.8 The optimisation problem of the generating firms 95 3.9 The solution for the SFE market problem 95 3.9.1 Reformulation of the ISO optimisation problem 96 3.9.2 Introduction of the complementarity constraint 98 3.9.3 Formulation of the combined optimisation problem for the SFE solution 99 3.9.4 Linearization of the market problem's KKT system 102 3.9.5 Formulation of the Newton matrix equation 105 3.10 Implementation issues for the primal-dual interior point algorithm 109 3.11 Conclusions for Chapter 3 112 Chapter 4: The impact of transformer tap-ratio control on the electricity market equilibrium 157 6.2.1 The interactions between the new firm and the existing firms 160 6.2.2 The choice for the best location for the new generating unit 161 6.2.3 The effects of the new entry on the nodal prices and the social welfare 162 6.3 Conclusions for Chapter 6 163 iv Chapter 7: Modelling of grid-connected photovoltaic systems in the electricity market equilibrium algorithm 7.1 Introduction to photovoltaic (PV) technology 165 7.2 Modelling the economic aspects of grid-connected PV systems in the electricity market model 167 7.3 Numerical results using the PV systems economic model 168 7.4 Discussions on the PV economic model 172 7.5 Modelling the operational aspects of grid-connected PV systems in the electricity market model, in terms of active and reactive PV power output 173 7.5.1 Experimental PV equipment 174 7.5.2 Processing the data collected from the experimental PV park 174 7.5.3 Modelling the PV output performance in the electricity market algorithm 176 7.6 Numerical results using the economic-operational PV systems model: the effect of the solar irradiance-dependent PV active and reactive power generation on the electricity market 177 7.6.1 Numerical results on the 5-bus system 178 7.6.2 Numerical results on the IEEE 57-bus system 183 7.6.3 Discussion on the impact of solar irradiance on the electricity market equilibrium and the significance of PV reactive power modelling 185 7.7 Conclusions for Chapter 7 186 Chapter 8: Parameterization of supply functions in AC electricity market equilibrium models References 226
Equilibrium and non-equilibrium models of the power markets
African Journal of Business Management, 2012
The competition trend within the electricity segment has motivated the research community efforts and directed them towards investigations of deregulation of the electricity markets. This underlines significant research needs to insure providing appropriate design and functioning, as well as analysis support models that would fit to recent electricity market settings. Thus, this work focuses on facets of the deregulated electricity markets and on modeling the power market. It aims primarily at identifying, classifying and characterizing the quite bewildering multiplicity of the methods available in the specialized literature on the topic. This study offers review of the most appropriate works related to electricity market models, like the equilibrium and non-equilibrium models, and some other related areas of research, like optimization as an exogenic variable or firm decisions function. The agent and Cournot based supply function has non-equilibrium and equilibrium simulation models under the conditions of both imperfect and perfect competition. Lastly, it characterizes the approaches most suitable for implementing different types of market analysis and planning studies in the electricity sector for new setting.
Linear supply function equilibrium: generalizations, application, and limitations
PWP078, University of California …, 2000
We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players all having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and the choice of affine marginal costs is reviewed in the context of the existing literature.
Modeling Electricity Markets: A Brief Introduction
Momoh/Economic Market Design Planning, 2009
This chapter provides a comprehensive overview of the economic structure of present and future electricity markets from the combined perspectives of economics and electrical engineering. It describes the basic structure of an electricity market and defines concepts such as consumer surplus, congestion rents, and market power. Furthermore, it outlines the mechanisms resulting in strategic bidding by generators and provides definitions and applications of the different equilibrium models to effectively analyze associated outcomes (prices and quantities). Examples from different equilibrium models (e.g. Cournot, auction-based) are presented. LMP calculations are then described via examples and economic dispatch formulation. Finally, their possible extension in stochastic and dynamic markets is highlighted via adaptive dynamic programming.
A Supply Function Competition Model for the Spanish Wholesale Electricity Market
2005
We model the Spanish wholesale market as a multiplant linear supply function competition model. According to the theory, the larger generators should have supply curves for each plant which are to the left of the supply curves of plants owned by smaller generators. We test this prediction for fuel plants using data from the Spanish Market Operator (OMEL) from May 2001 to December 2003. Our results indicate that the prediction of the model holds.
Energy Studies Review, 2009
Research into modeling electricity markets is continuing and the subject of many debates. All types of competition (Cournot, Bertrand, supply function) are utilized and have their advantages and disadvantages for electricity markets. It is well-recognized that models cannot address all questions of interest; however they appear as an interesting tool for gleaning insights into the complexity of electricity markets and whether electricity markets may deliver the expected benefits of liberalization. In particular, proving the existence of market power is a very complex task. Market simulation models should not be seen as the ultimate solution but as one powerful tool. While it is extremely difficult to prove if any market participants were manipulating markets, simulation models can show (under certain assumptions) if it would have been profitable to do so. Such models can be used in addition to traditional competition analysis. For instance, a model can estimate different benchmarks (competitive, supply function) against which actual market prices may be compared. This paper provides a practical application of the SFE concept and how such theoretical approach can be used in practice. The model combines the supply function equilibrium approach in an expanded version of the Baldick et al. model (2000) with forward contracting based on the model of Newbery (1998). We also discuss the different options for market modeling with respect to strategic variables and forward contracting. Finally, we present an application of this model to the Dutch electricity market.
Supply Function Competition in the Spanish Wholesale Electricity Market
The Energy Journal, 2010
Financial support from Ministerio de Ciencia e Innovación (SEJ2006-06309 and ECO2009-09120), Gobierno Vasco DEUI (IT-313-07), BBVA and IVIE is gratefully acknowledged. We thank Jorge de la Cruz for his helpful research assistance, and seminar participants at the IDEI Conference on Competition and Coordination in the Electricity Industry (Toulouse), Universidad Autónoma de Barcelona and Universidad de Alicante, the editor and three anonymous referees for comments and suggestions. We are especially indebted to Eva Ferreira, M. Cruz Loyo and Enrique Pastor for their invaluable 1. Appendix 1 gives a brief description of the day-ahead market. An overview can be found in Crampes and Fabra (2005).
Problems of the Supply Industry in Wholesale Electricity Markets
Social Science Research Network, 2022
This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors.
Equilibrium in wholesale electricity markets
2003
We develop game theoretic models to evaluate strategic behavior in deregulated electricity markets, with particular attention given to the market rules in place in California through the summer of 2000. We prove existence of a Nash equilibrium under two particular sets of market rules used by the CALPX and CAISO respectively. Next we derive a lower bound (strictly above marginal cost) on average equilibrium prices when there is a positive probability that at least one generator is capacity-constrained. Finally, we compare two competing methods for modelling competition in power markets: supply function equilibrium and discrete, multi-unit auctions and illustrate shortcomings of both approaches.