Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints

By Line A. Roald, Frauke Oldewurtel, B. V. Parys, Göran Andersson. 2015

86 citations recorded by the source corpus.

The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain in-feeds as random variables and formulate a security constrained optimal power flow using chance constraints. The chance constraints limit the probability of violations of technical constraints, such as generation and transmission limits, but require a tractable reformulation. In this paper, we discuss different analytical reformulations of the chance constraints, based on a given set of assumptions concerning the forecast error distributions. In particular, we discuss reformulations that do not assume a normal distribution, and admit an analytical reformulation given only a mean vector and covariance matrix. We illustrate our method with a case study of the IEEE 118 bus system, based on real data from the European system. The different reformulations are compared in terms of both achieved empirical violation probability and operational cost, which allows us to provide a suggestion for the most appropriate reformulation in an optimal power flow setting. For a large number of uncertainty sources, it is observed that the distributions of the line flows and generator outputs can be close to normal, even though the power injections are not normally distributed.

View Paper: https://www.semanticscholar.org/paper/d713fce36f3ccd5ae8030f7a5ac496231fadf8e3

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Citations in the corpus

Distributionally Robust Chance-Constrained Optimal Power Flow With Uncertain Renewables and Uncertain Reserves Provided by Loads (2017, background): “CC-OPF problems to manage renewable energy and load uncertainty have been posed in [10]–[15], though none of this work considers load reserves or their uncertainty.”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, background): “There are many works on solving OPF, unit commitment (UC) problem or reserve scheduling via stochastic programming [28, 32, 37], robust optimization [3, 11, 15, 16, 39, 40, 43, 49], and chance constrained program approaches [5, 4, 19, 27, 31, 35, 38, 44] (see [23] for some discussions).”