A Comparison of Electricity Market Designs in Networks

Ehrenmann, Andreas; Neuhoff, Karsten

doi:10.1287/opre.1080.0624

Cited by 74 publications

(52 citation statements)

References 30 publications

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“…This yields highly nonlinear VI operators in Proposition 3. We first note that the stopping test for the smoothing method was triggered after six VI solves on average: j ≤ 6 in (16). The second observation is a noticeable difference in the total solution time: with our approach the average time spent in each scenario was about half a second, while the AVaR reformulation needed more than eight seconds per scenario.…”

Section: Performance Of the Smoothing Approachmentioning

confidence: 94%

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An approximation scheme for a class of risk-averse stochastic equilibrium problems

2016

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We consider two models for stochastic equilibrium: one based on the variational equilibrium of a generalized Nash game, and the other on the mixed complementarity formulation. Each agent in the market solves a single-stage risk-averse optimization problem with both here-and-now (investment) variables and (production) wait-and-see variables. A shared constraint couples almost surely the wait-and-see decisions of all the agents. An important characteristic of our approach is that the agents hedge risk in the objective functions (on costs or profits) of their optimization problems, which has a clear economic interpretation. This feature is obviously desirable, but in the risk-averse case it leads to variational inequalities with set-valued operators -a class of problems for which no established software is currently available. To overcome this difficulty, we define a sequence of approximating differentiable variational inequalities based on smoothing the nonsmooth risk measure in the agents' problems, such as average or conditional value-at-risk. The smoothed variational inequalities can be tackled by the PATH solver, for example. The approximation scheme is shown to converge, including the case when smoothed problems are solved approximately. An interesting by-product of our proposal is that the smoothing approach allows us to show existence of an equilibrium for the original problem. To assess the proposed technique, numerical results are presented. The first set of experiments is on randomly generated equilibrium problems, for which we compare the proposed methodology with the standard smooth reformulation of average value-at-risk minimization (using additional variables to rewrite the associated max-function). The second set of experiments deals with a part of the real-

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Section: Performance Of the Smoothing Approachmentioning

confidence: 94%

“…Among related literature, however mostly casting the problem in deterministic or risk-neutral settings, we refer to [11,25,1,35,36,38,26,16,10,48]. We also mention [9], which emphasizes the tradeoff between maximal profit and minimal risk for thermal power producers in a pool-based electricity market.…”

Section: Introductionmentioning

confidence: 99%

An approximation scheme for a class of risk-averse stochastic equilibrium problems

2016

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“…Continuing with comparisons between implicit and explicit auctions for electricity trade and transmission, Ehrenmann and Neuhoff [27] extend the equilibrium problem formulation introduced by Cardell et al [28] -a Stackelberg game -to represent an integrated market design, and the mixed complementarity problem formulation in Hobbs et al [29] -a Cournot game -to represent a separate market design, in the presence of market power. They show that in a simple two-node network, the integrated market design reduces the exercise of market power; however, for more complicated networks they are unable to determine a general ranking.…”

Section: Literature Reviewmentioning

confidence: 99%

Does size matter? Simulating electricity market coupling between Colombia and Ecuador

Ochoa

Ackere

2015

Renewable and Sustainable Energy Reviews

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“…We will focus here on game-theoretic formulations, although other approaches such as bi-level programming and mathematical programs with equilibrium constraints are also possible. References on the topic are numerous; with no claim of being exhaustive we mention [3,4,19,23,24,28,29,31,[60][61][62]77,91,109,110].…”

Section: Example 5 (Rolling Horizon Decomposition For Risk Averse Mulmentioning

confidence: 99%

Divide to conquer: decomposition methods for energy optimization

Sagastizábal

2012

Math. Program.

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Modern electricity systems provide a plethora of challenging issues in optimization. The increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting. The liberalization of the electricity sector brought the need of designing sound markets, ensuring capacity investments while properly reflecting strategic interactions. In all these problems, hedging risk, possibly in a dynamic manner, is also a concern. The fact of representing uncertainty and/or competition of different companies in a multi-settlement power market considerably increases the number of variables and constraints. For this reason, usually a trade-off needs to be found between modeling and numerical tractability: the more details are brought into the model, the harder becomes the optimization problem. For structured optimization and generalized equilibrium problems, we explore some variants of solution methods based on Lagrangian relaxation and on Benders decomposition. Throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems.

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A Comparison of Electricity Market Designs in Networks

Cited by 74 publications

References 30 publications

An approximation scheme for a class of risk-averse stochastic equilibrium problems

An approximation scheme for a class of risk-averse stochastic equilibrium problems

Does size matter? Simulating electricity market coupling between Colombia and Ecuador

Divide to conquer: decomposition methods for energy optimization

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