Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow

TL;DR

This paper introduces a new, tighter upper bound for joint chance constraints in AC optimal power flow problems, improving efficiency and accuracy in managing uncertainties in power systems with high renewable penetration.

Contribution

The paper develops a novel, less conservative upper bound for joint chance constraints, enhancing solution efficiency in stochastic optimal power flow problems.

Findings

The new upper bound reduces conservativeness compared to traditional methods.

Simulation results demonstrate improved voltage regulation under uncertainty.

Method effectively handles high photovoltaic penetration scenarios.

Abstract

Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Efficient solution methods for single chance constraints in optimal power flow problems have been considered in the literature; however, joint chance constraints have predominantly been solved via scenario-based approaches or by utilizing the overly conservative Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem which maintain desired levels of voltage magnitude in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound.