Chance-constrained DC Optimal Power Flow with Non-Gaussian Distributed Uncertainties

TL;DR

This paper introduces a GMM-based chance-constrained DC optimal power flow model that effectively handles non-Gaussian uncertainties on both sides of the constraints, ensuring feasible solutions through a safe approximation.

Contribution

It develops a novel linearization technique and reformulation for non-Gaussian uncertainties in DC OPF, extending CCP applicability beyond Gaussian assumptions.

Findings

GMM effectively models non-Gaussian uncertainties.

The reformulated constraints are a safe approximation, guaranteeing feasibility.

The approach enhances robustness in power system optimization under uncertainty.

Abstract

Chance-constrained programming (CCP) is a promising approach to handle uncertainties in optimal power flow (OPF). However, conventional CCP usually assumes that uncertainties follow Gaussian distributions, which may not match reality. A few papers employed the Gaussian mixture model (GMM) to extend CCP to cases with non-Gaussian uncertainties, but they are only appropriate for cases with uncertainties on the right-hand side but not applicable to DC OPF that containing left-hand side uncertainties. To address this, we develop a tractable GMM-based chance-constrained DC OPF model. In this model, we not only leverage GMM to capture the probability characteristics of non-Gaussian distributed uncertainties, but also develop a linearization technique to reformulate the chance constraints with non-Gaussian distributed uncertainties on the left-hand side into tractable forms. A mathematical proof is further provided to demonstrate that the corresponding reformulation is a safe approximation of the original problem, which guarantees the feasibility of solutions.