Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions

Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions.Market power, Electricity, Networks, Numeric models, Model comparison

The More Cooperation, the More Competition? A Cournot Analysis of the Benefits of Electric Market Coupling

Market coupling in Belgian and Dutch markets would permit more efficient use of intercountry transmission, 1) by counting only net flows against transmission limits, 2) by improving access to the Belgian market, and 3) by eliminating the mismatch in timing between interface auctions and the energy spot market. A Cournot market model that accounts for the region’s transmission pricing rules and limitations is used to simulate market outcomes with and without market coupling. This accounts for 1) and 2). Market coupling improves social surplus in the order of 108 €/year, unless it encourages the largest producer in the region to switch from a price-taking strategy in Belgium to a Cournot strategy due to a perceived diminishment of the threat of regulatory intervention. Benefit to Dutch consumers depends on the behavior of this company. The results illustrate how large-scale oligopoly models can be useful for assessing market integration

The More Cooperation, the More Competition? A Cournot Analysis of the Benefits of Electric Market Coupling

Market coupling in Belgian and Dutch markets would permit more efficient use of intercountry transmission, 1) by counting only net flows against transmission limits, 2) by improving access to the Belgian market, and 3) by eliminating the mismatch in timing between interface auctions and the energy spot market. A Cournot market model that accounts for the region’s transmission pricing rules and limitations is used to simulate market outcomes with and without market coupling. This accounts for 1) and 2). Market coupling improves social surplus in the order of 108 €/year, unless it encourages the largest producer in the region to switch from a price-taking strategy in Belgium to a Cournot strategy due to a perceived diminishment of the threat of regulatory intervention. Benefit to Dutch consumers depends on the behavior of this company. The results illustrate how large-scale oligopoly models can be useful for assessing market integration.Electric power, Electric transmission, Liberalization, Oligopoly, Complementarity models, Computational models, Netherlands, Belgium, France, Germany, Market Coupling

Decomposition of Variational Inequalities with Applications to Nash-Cournot Models in Time of Use Electricity Markets

This thesis proposes equilibrium models to link the wholesale and retail electricity markets which allow for reconciliation of the differing time scales of responses of producers (e.g., hourly) and consumers (e.g., monthly) to changing prices. Electricity market equilibrium models with time of use (TOU) pricing scheme are formulated as large-scale variational inequality (VI) problems, a unified and concise approach for modeling the equilibrium. The demand response is dynamic in these models through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. An approximation of the welfare change for this analysis is also presented. Moreover, break-up of a large supplier into smaller parts is investigated. For the illustrative examples presented in the dissertation, overall welfare gains for consumers and lower prices closer to the levels of perfect competition can be realized when the retail pricing scheme is changed from single pricing to TOU pricing. These models can be useful policy tools for regulatory bodies i) to forecast future retail prices (TOU or single prices), ii) to examine the market power exerted by suppliers and iii) to measure welfare gains/losses with different retail pricing schemes (e.g., single versus TOU pricing). With the inclusion of linearized DC network constraints into these models, the problem size grows considerably. Dantzig-Wolfe (DW) decomposition algorithm for VI problems is used to alleviate the computational burden and it also facilitates model management and maintenance. Modification of the DW decomposition algorithm and approximation of the DW master problem significantly improve the computational effort required to find the equilibrium. These algorithms are applied to a two-region energy model for Canada and a realistic Ontario electricity test system. In addition to empirical analysis, theoretical results for the convergence properties of the master problem approximation are presented for DW decomposition of VI problems

Design and analysis of competitive electricity markets

This thesis focuses on the study of allocation mechanisms and pricing schemes for the design and analysis of competitive electricity markets. Motivated by the increasing demand-side participation in high- and low-voltage power grids, we consider two-sided competition models where a finite group of producers and consumers compete through scalar-parameterized supply offers and demand bids. Acting as a smooth approximation to supply offers used in practice, scalar-parameterized offers greatly facilitate mathematical analysis while preserving the primary determinants and mechanisms by which market power is exercised in electricity markets. In the framework of a pool-based market, characterized by a central dispatch and pricing mechanism, when strategic, capacity-constrained suppliers face strategic, price- responsive consumers, we show that market allocative efficiency loss and price markup at the Nash equilibrium are bounded. We demonstrate analogous efficiency bounds in the study of inter-area electricity markets where we exploit scalar-parameterized offers to model budget-constrained price arbitrageurs that compete against affine inter-area price spreads. Our analysis provides important insights on the type of behavior that may occur at the equilibrium including the pivotal role assumed by certain players, the impacts of aggregate liquidity and uncertainty as well financial positions in other electricity markets. Through the application of reinforcement learn- ing algorithms we demonstrate that players can discover their equilibrium actions even when they know little to nothing about the game setting. The simplicity of scalar-parameterized supply offers that grant market ac- tors’ one-dimensional action spaces while properly constraining their strategic flexibility, render such offer/bid structures an attractive candidate for the expansion of electricity markets to distribution grids. Motivated by the rapid proliferation of distributed energy resources that increasingly hold value for the grid either as power suppliers or flexible demand, we leverage scalar-parameterized supply offers together with appropriate pricing schemes to design a pool-based market for the retail sector. Our goal is complicated by the underlying physics of distribution grids that render the central dispatch problem, in its full generality, non-linear and non-convex. To get around this difficulty, we exploit semidefinite relaxations of the optimal power flow problem and leverage duality theory to define prices for electricity as the optimal Lagrange multipliers of nodal real and reactive power balance constraints. We demonstrate that such prices stand on sound economic principles that together with scalar-parameterized offers/bids, constitute a comprehensive mechanism for the expansion of markets to the low-voltage side of the electric power grid

Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context: Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported

DECENTRALIZED ALGORITHMS FOR NASH EQUILIBRIUM PROBLEMS – APPLICATIONS TO MULTI-AGENT NETWORK INTERDICTION GAMES AND BEYOND

Nash equilibrium problems (NEPs) have gained popularity in recent years in the engineering community due to their ready applicability to a wide variety of practical problems ranging from communication network design to power market analysis. There are strong links between the tools used to analyze NEPs and the classical techniques of nonlinear and combinatorial optimization. However, there remain significant challenges in both the theoretical and algorithmic analysis of NEPs. This dissertation studies certain special classes of NEPs, with the overall purpose of analyzing theoretical properties such as existence and uniqueness, while at the same time proposing decentralized algorithms that provably converge to solutions. The subclasses are motivated by relevant application examples

On the analysis of stochastic optimization and variational inequality problems

Uncertainty has a tremendous impact on decision making. The more connected we get, it seems, the more sources of uncertainty we unfold. For example, uncertainty in the parameters of price and cost functions in power, transportation, communication and financial systems have stemmed from the way these networked systems operate and also how they interact with one another. Uncertainty influences the design, regulation and decisions of participants in several engineered systems like the financial markets, electricity markets, commodity markets, wired and wireless networks, all of which are ubiquitous. This poses many interesting questions in areas of understanding uncertainty (modeling) and dealing with uncertainty (decision making). This dissertation focuses on answering a set of fundamental questions that pertain to dealing with uncertainty arising in three major problem classes: [(1)] Convex Nash games; [(2)] Variational inequality problems and complementarity problems; [(3)] Hierarchical risk management problems in financial networks. Accordingly, this dissertation considers the analysis of a broad class of stochastic optimization and variational inequality problems complicated by uncertainty and nonsmoothness of objective functions. Nash games and variational inequalities have assumed practical relevance in industry and business settings because they are natural models for many real-world applications. Nash games arise naturally in modeling a range of equilibrium problems in power markets, communication networks, market-based allocation of resources etc. where as variational inequality problems allow for modeling frictional contact problems, traffic equilibrium problems etc. Incorporating uncertainty into convex Nash games leads us to stochastic Nash games. Despite the relevance of stochastic generalizations of Nash games and variational inequalities, answering fundamental questions regarding existence of equilibria in stochastic regimes has proved to be a challenge. Amongst other reasons, the main challenge arises from the nonlinearity arising from the presence of the expectation operator. Despite the rich literature in deterministic settings, direct application of deterministic results to stochastic regimes is not straightforward. The first part of this dissertation explores such fundamental questions in stochastic Nash games and variational inequality problems. Instead of directly using the deterministic results, by leveraging Lebesgue convergence theorems we are able to develop a tractable framework for analyzing problems in stochastic regimes over a continuous probability space. The benefit of this approach is that the framework does not rely on evaluation of the expectation operator to provide existence guarantees, thus making it amenable to tractable use. We extend the above framework to incorporate nonsmoothness of payoff functions as well as allow for stochastic constraints in models, all of which are important in practical settings. The second part of this dissertation extends the above framework to generalizations of variational inequality problems and complementarity problems. In particular, we develop a set of almost-sure sufficiency conditions for stochastic variational inequality problems with single-valued and multi-valued mappings. We extend these statements to quasi-variational regimes as well as to stochastic complementarity problems. The applicability of these results is demonstrated in analysis of risk-averse stochastic Nash games used in Nash-Cournot production distribution models in power markets by recasting the problem as a stochastic quasi-variational inequality problem and in Nash-Cournot games with piecewise smooth price functions by modeling this problem as a stochastic complementarity problem. The third part of this dissertation pertains to hierarchical problems in financial risk management. In the financial industry, risk has been traditionally managed by the imposition of value-at-risk or VaR constraints on portfolio risk exposure. Motivated by recent events in the financial industry, we examine the role that risk-seeking traders play in the accumulation of large and possibly infinite risk. We proceed to show that when traders employ a conditional value-at-risk (CVaR) metric, much can be said by studying the interaction between value at risk (VaR) (a non-coherent risk measure) and conditional value at risk CVaR (a coherent risk measure based on VaR). Resolving this question requires characterizing the optimal value of the associated stochastic, and possibly nonconvex, optimization problem, often a challenging problem. Our study makes two sets of contributions. First, under general asset distributions on a compact support, traders accumulate finite risk with magnitude of the order of the upper bound of this support. Second, when the supports are unbounded, under relatively mild assumptions, such traders can take on an unbounded amount of risk despite abiding by this VaR threshold. In short, VaR thresholds may be inadequate in guarding against financial ruin