Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty

Aigner, Kevin-Martin; Clarner, Jan-Patrick; Liers, Frauke; Martín, Alexander

doi:10.1016/j.ejor.2021.10.051

Cited by 14 publications

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References 42 publications

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“…in Carpentier (1962), Mary et al (2012), Aigner et al (2021a), also in their linearised version as DC networks, see e.g. Aigner et al (2021). Direct current networks with system voltages below (2019).…”

Section: Stability Of Lvdc Networkmentioning

confidence: 99%

Optimization over decision trees: a case study for the design of stable direct-current electricity networks

et al. 2023

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In many real-world mixed-integer optimization problems from engineering, the side constraints can be subdivided into two categories: constraints which describe a certain logic to model a feasible allocation of resources (such as a maximal number of available assets, working time requirements, maintenance requirements, contractual obligations, etc.), and constraints which model physical processes and the related quantities (such as current, pressure, temperature, etc.). While the first type of constraints can often easily be stated in terms of a mixed-integer program (MIP), the second part may involve the incorporation of complex non-linearities, partial differential equations or even a black-box simulation of the involved physical process. In this work, we propose the integration of a trained tree-based classifier—a decision-tree or a random forest, into a mixed-integer optimization model as a possible remedy. We assume that the classifier has been trained on data points produced by a detailed simulation of a given complex process to represent the functional relationship between the involved physical quantities. We then derive MIP-representable reformulations of the trained classifier such that the resulting model can be solved using state-of-the-art solvers. At the hand of several use cases in terms of possible optimization goals, we show the broad applicability of our framework that is easily extendable to other tasks beyond engineering. In a detailed real-world computational study for the design of stable direct-current power networks, we demonstrate that our approach yields high-quality solutions in reasonable computation times.

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Section: Stability Of Lvdc Networkmentioning

confidence: 99%

Optimization over decision trees: a case study for the design of stable direct-current electricity networks

et al. 2023

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Reliable–Economical–Social Equilibrium‐Based Scheduling of Hybrid Solar–Wind–Hydro System

2024

Sustainable Hybrid Energy Systems

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Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

et al. 2022

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We present a robust approximation of joint chance constrained DC optimal power flow in combination with a model-based prediction of uncertain power supply via R-vine copulas. It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in. This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (Eur J Oper Res (2022) https://doi.org/10.1016/j.ejor.2021.10.051). The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets. The resulting robust optimization problem has a known equivalent tractable reformulation. To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes. The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model. Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts. The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas. We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.

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Robust approximation of chance constrained DC optimal power flow under decision-dependent uncertainty

Cited by 14 publications

References 42 publications

Optimization over decision trees: a case study for the design of stable direct-current electricity networks

Optimization over decision trees: a case study for the design of stable direct-current electricity networks

Reliable–Economical–Social Equilibrium‐Based Scheduling of Hybrid Solar–Wind–Hydro System

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

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