Multiscale stochastic optimization: modeling aspects and scenario generation

Glanzer, Martin; Pflug, Georg Ch.

doi:10.1007/s10589-019-00135-4

Cited by 8 publications

(4 citation statements)

References 37 publications

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“…For a maximization problem, VSS is defined by the difference between the optimal value of the stochastic problem (RP) and the value of the objective function of the stochastic problem while applying the deterministic problem solution (EEV). For further details, see [20].…”

Section: Resultsmentioning

confidence: 99%

Considering Forward Electricity Prices for a Hydro Power Plant Risk Analysis in the Brazilian Electricity Market

et al. 2023

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The Brazilian Power System is mainly composed of renewable generation from hydroelectric and wind. Hence, spot and forward electricity prices tend to represent the inherently stochastic nature of these resources, while risk management is a measure taken by agents, especially hydro power plants (HPPs) to hedge against deep financial losses. A HPP goal is to maximize its profit considering uncertainties in forward electricity prices, spot prices, and generation scaling factor (GSF) for years ahead. Therefore, the objective of this work is to simulate the real decision-making process of a HPP, where they need to have a perspective of the forward market and future spot price assessment to negotiate forward electricity contracts. To do so, the present work models the uncertainty in electricity forward prices via two-stage stochastic programming, assessing the benefits of the stochastic solution in comparison to the deterministic one. In addition, different risk aversion levels are assessed using conditional value at risk (CVaR). An important conclusion is that the results show that the greater the HPP risk aversion is, the greater the energy selling via electricity forward contracts. Moreover, the proposed model has benefits in comparison to a deterministic approach.

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Section: Resultsmentioning

confidence: 99%

Considering Forward Electricity Prices for a Hydro Power Plant Risk Analysis in the Brazilian Electricity Market

et al. 2023

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“…The vast majority of articles favor the Wasserstein type distances resp. metrics (also Fortet-Mourier distance Kantorovich/Kantorovich-Rubinstein distance, earth mover distance, optimal transport distance) for scenario reduction, see Henrion et al (2009); Rujeerapaiboon et al (2017); Arpón et al (2018); Glanzer and Pflug (2020). This also holds for all applications mentioned in the first paragraph.…”

Section: Introductionmentioning

confidence: 82%

The energy distance for ensemble and scenario reduction

Ziel

2020

Preprint

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Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems. We propose a new method for ensemble and discrete scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy (MMD). We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures which allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it to a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario set tend exhibit better statistical properties for energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to binary trees and a real data based examples for electricity demand profiles.

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“…An important selection criterion is the choice of a distance (or metric) which characterizes to a certain extent how close the m selected trajectories are to the considered large set of n trajectories in the scenario set. The vast majority of articles favour the Wasserstein type distances respecting metrics (also Fortet-Mourier distance Kantorovich/Kantorovich-Rubinstein distance, earth mover distance, optimal transport distance) for scenario reduction, see [10,11]. This also holds for all applications mentioned in the first paragraph.…”

Section: Introductionmentioning

confidence: 99%

The energy distance for ensemble and scenario reduction

Ziel

2021

Phil. Trans. R. Soc. A.

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Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but are also used in probabilistic forecasting, clustering and estimating generative adversarial networks. We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy. We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data-based examples for electricity demand profiles and day-ahead electricity prices. This article is part of the theme issue ‘The mathematics of energy systems’.

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Multiscale stochastic optimization: modeling aspects and scenario generation

Cited by 8 publications

References 37 publications

Considering Forward Electricity Prices for a Hydro Power Plant Risk Analysis in the Brazilian Electricity Market

Considering Forward Electricity Prices for a Hydro Power Plant Risk Analysis in the Brazilian Electricity Market

The energy distance for ensemble and scenario reduction

The energy distance for ensemble and scenario reduction

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