A Generalized Framework for Chance-constrained Optimal Power Flow

TL;DR

This paper introduces a versatile framework for chance-constrained optimal power flow that handles uncertainties without assuming specific distributions, using polynomial chaos expansion to derive affine feedback policies.

Contribution

It presents a general, distribution-agnostic approach to chance-constrained OPF problems, leveraging polynomial chaos expansion for constructing affine feedback policies.

Findings

Random-variable minimizers lead to affine feedback policies.

The framework is applicable regardless of the uncertainty distribution.

Validated on a 300-bus test case.

Abstract

Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to guarantee power balance while maintaining economic and secure operation. In the presence of Gaussian uncertainties affine feedback policies are known to be viable options for this task. The present paper advocates a general framework for chance-constrained OPF problems in terms of continuous random variables. It is shown that, irrespective of the type of distribution, the random-variable minimizers lead to affine feedback policies. Introducing a three-step methodology that exploits polynomial chaos expansion, the present paper provides a constructive approach to chance-constrained optimal power flow problems that does not assume a specific distribution, e.g. Gaussian, for the uncertainties. We illustrate our findings by means of a tutorial example and a 300-bus test case.