Solving stochastic complementarity problems in energy market modeling using scenario reduction

Gabriel, Steven A.; Zhuang, Jifang; Egging, Ruud

doi:10.1016/j.ejor.2007.12.046

Cited by 60 publications

(30 citation statements)

References 18 publications

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“…Stochastic mathematical programs with equilibrium constraints are analyzed in [37,44,30]. For the natural gas market, the deterministic MCP model from [15] and [23] was revisited in a stochastic risk-neutral setting in [14]. For electricity markets, game-theoretical and MCP formulations have been considered in [27] and [17], respectively.…”

Section: Modelling Equilibrium Problems In the Presence Of Risk Aversionmentioning

confidence: 99%

“…In this section we use data from a real-world problem, the gas network specified in [23], with two particular goals. First, we analyze the agents' strategies regarding aversion to risk under different conditions of market volatility.…”

Section: Assessment On the European Natural Gas Networkmentioning

confidence: 99%

“…Following [23], when a pricesensitive demand curve is available, there are given intercept d 0 and matrix P defining the inverse demand function as P · +d 0 . In this case, for the MCP model the remuneration changes…”

Section: Remark 1 (Price Cap Regulatory Interventions and Market Pomentioning

confidence: 99%

“…In this work, we adopt the modeling of [32]. Our approach is comprehensive enough to include the electricity generation-capacity expansion model [17] and the European natural gas market model in [23], set in a stochastic environment.…”

Section: Introductionmentioning

confidence: 99%

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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: Modelling Equilibrium Problems In the Presence Of Risk Aversionmentioning

confidence: 99%

Section: Assessment On the European Natural Gas Networkmentioning

confidence: 99%

Section: Remark 1 (Price Cap Regulatory Interventions and Market Pomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…The MCP framework is convenient for this type of exercise, as it allows to include Cournot market power for certain suppliers, in contrast to welfare maximization or cost minimization problems. In addition, these models can easily be extended to include stochasticity (e.g., Gabriel et al, 2009) or two-level problems such as Stackelberg competition (e.g., Siddiqui and Gabriel, 2012).…”

Section: Introductionmentioning

confidence: 99%

Endogenous Investment Decisions in Natural Gas Equilibrium Models with Logarithmic Cost Functions

Huppmann

2012

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. November 13, 2012 Terms of use: Documents in AbstractThe liberalisation of the natural gas markets and the importance of natural gas as a transition fuel to a low-carbon economy have led to the development of several large-scale equilibrium models in the last decade. These models combine long-term market equilibria and investments in infrastructure while accounting for market power by certain suppliers. They are widely used to simulate market outcomes given different scenarios of demand and supply development, environmental regulations and investment options.In order to capture the specific characteristics of natural gas production, most of these models apply a logarithmic production cost function. However, no model has so far combined this cost function type with endogenous investment decisions in production capacity. Given the importance of capacity constraints in the determination of the natural gas supply, this is a serious shortcoming of the current literature. This paper provides a proof that combining endogenous investment decisions and a logarithmic cost function yields indeed a convex minimization problem, paving the way for an important extension of current state-of-the-art equilibrium models.

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Introduction and Motivation

Gabriel

Conejo

Fuller

et al. 2012

International Series in Operations Research &Amp; Management Science

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Solving stochastic complementarity problems in energy market modeling using scenario reduction

Cited by 60 publications

References 18 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

Endogenous Investment Decisions in Natural Gas Equilibrium Models with Logarithmic Cost Functions

Introduction and Motivation

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