FICA: Faster Inner Convex Approximation of Chance Constrained Grid Dispatch with Decision-Coupled Uncertainty

TL;DR

This paper introduces FICA, a novel method that significantly accelerates solving power dispatch problems with chance constraints by exploiting problem structure, achieving up to 500x speedup with minimal loss in solution quality.

Contribution

FICA is a new inner convex approximation technique that leverages one-dimensional problem structure to greatly improve computational efficiency in chance-constrained power dispatch.

Findings

FICA achieves up to 500x speedup over CVaR in large problems.

The approximation quality of FICA is within 1% of exact solutions.

FICA's speedup is most significant when half of the constraints have the one-dimensional structure.

Abstract

This paper proposes a Faster Inner Convex Approximation (FICA) method for solving power system dispatch problems with Wasserstein distributionally robust joint chance constraints (WJCC) and incorporating the modelling of the automatic generation control factors. The problem studied belongs to the computationally challenging class of WJCC with left-hand-side uncertainty (LHS-WJCC). By exploiting the special one-dimensional structure (even if only partially present) of the problem, the proposed FICA incorporates a set of strong valid inequalities to accelerate the solution process. We prove that FICA achieves the same optimality as the well-known conditional value-at-risk (CVaR) inner convex approximation method. Our numerical experiments demonstrate that the proposed FICA can yield 40x computational speedup compared to CVaR, and can even reach up to 500x speedup when the optimisation horizon exceeds 16 time steps. This speedup is achieved when only 50% of constraints in a WJCC have the one-dimensional structure. The approximation quality is numerically verified to be the same as CVaR, and the quality gap is below 1% when compared to the computationally demanding exact reformulation of the LHS-WJCC in most cases. We also discuss the applications of FICA in optimisation problems from other domains that (partially) exhibit the one-dimensional structure.