Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints

TL;DR

This paper develops a distributionally robust chance-constrained optimal power flow model to handle uncertainties from renewable energy sources, providing analytical reformulations that do not assume normal distributions, and evaluates their performance on a real-world case study.

Contribution

It introduces new analytical reformulations of chance constraints for power flow optimization that are distributionally robust and applicable with limited distributional assumptions.

Findings

Reformulations effectively control violation probabilities and costs.

Normal distribution approximations are valid for line flows and generator outputs.

The proposed methods outperform traditional approaches in uncertain power system operations.

Abstract

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.