Risk aversion for an electricity retailer with second-order stochastic dominance constraints

Carrión, Miguel; Gotzes, Uwe; Schultz, Rüdiger

doi:10.1007/s10287-008-0091-2

Cited by 20 publications

(7 citation statements)

References 29 publications

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“…The most typical application of stochastic dominance concepts in the power and energy systems area refers to risk-aversion modelling in electricity trading and portfolio optimization. The second-order stochastic dominance constraint has been imposed in [54] to reduce the risk of low profit for an electricity retailer, and in [55] for self-scheduling large consumers. In [56] portfolio optimization has been carried out by setting up a minimum tolerable CDF used as the reference; then, the CDF of the portfolio model is accepted if it exhibits second-order stochastic dominance over the reference CDF.…”

Section: Stochastic Dominance Applications To Power and Energy Systemsmentioning

confidence: 99%

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Chicco

Mazza

2019

Sustainable Energy, Grids and Networks

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Many optimization problems admit a number of local optima, among which there is the global optimum. For these problems, various heuristic optimization methods have been proposed. Comparing the results of these solvers requires the definition of suitable metrics. In the electrical energy systems literature, simple metrics such as best value obtained, the mean value, the median or the standard deviation of the solutions are still used. However, the comparisons carried out with these metrics are rather weak, and on these bases a somehow uncontrolled proliferation of heuristic solvers is taking place. This paper addresses the overall issue of understanding the reasons of this proliferation, showing a conceptual scheme that indicates how the assessment of the best solver may result in the unlimited formulation of new solvers. Moreover, this paper shows how the use of more refined metrics defined to compare the optimization result, associated with the definition of appropriate benchmarks, may make the comparisons among the solvers more robust. The proposed metrics are based on the concept of firstorder stochastic dominance and are defined for the cases in which: (i) the globally optimal solution can be found (for testing purposes); and (ii) the number of possible solutions is so large that practically it cannot be guaranteed that the global optimum has been found. Illustrative examples are provided for a typical problem in the electrical energy systems area -distribution network reconfiguration. The conceptual results obtained are generally valid to compare the results of other optimization problems.2

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Section: Stochastic Dominance Applications To Power and Energy Systemsmentioning

confidence: 99%

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Chicco

Mazza

2019

Sustainable Energy, Grids and Networks

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“…, π S > 0. Then (7) can be written as the following largescale mixed-integer linear program min c x + S ω=1 π ω q y ω :…”

Section: 2mentioning

confidence: 99%

Two-stage stochastic programs: Integer variables, dominance relations and PDE constraints

Schultz¹

2012

Numerical Algebra, Control &Amp; Optimization

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“…Research on stochastic dominance in optimization under uncertainty has seen a substantial increase during the last decade. Topics include basic analysis of models [16,14,29,26,25,15,20], algorithm development [36,19,22], and industrial applications, see for instance [10,23,21].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Dominance Constraints in Elastic Shape Optimization

Conti¹,

Rumpf²,

Schultz³

et al. 2018

SIAM J. Control Optim.

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This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from finite-dimensional stochastic programming to shape optimization. Rather than handling risk aversion in the objective, this enables risk aversion by including dominance constraints that single out subsets of nonanticipative shapes which compare favorably to a chosen stochastic benchmark. This new class of stochastic shape optimization problems arises by optimizing over such feasible sets. The analytical description is built on risk-averse cost measures. The underlying cost functional is of compliance type plus a perimeter term, in the implementation shapes are represented by a phase field which permits an easy estimate of a regularized perimeter. The analytical description and the numerical implementation of dominance constraints are built on risk-averse measures for the cost functional. A suitable numerical discretization is obtained using finite elements both for the displacement and the phase field function. Different numerical experiments demonstrate the potential of the proposed stochastic shape optimization model and in particular the impact of high variability of forces or probabilities in the different realizations.

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Risk aversion for an electricity retailer with second-order stochastic dominance constraints

Cited by 20 publications

References 29 publications

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Two-stage stochastic programs: Integer variables, dominance relations and PDE constraints

Stochastic Dominance Constraints in Elastic Shape Optimization

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