# Robust AC Optimal Power Flow

## TL;DR

This paper develops a tractable approximation method for the complex robust AC optimal power flow problem, enabling reliable operation of power systems with renewable energy uncertainties.

## Contribution

It introduces a finite-dimensional semidefinite programming approach with guarantees for feasible affine recourse policies in robust AC OPF.

## Key findings

- Effective on WSCC 9-bus system with renewable uncertainty
- Applicable to IEEE 14-bus test system with high renewable penetration
- Provides a sufficient condition for policy feasibility

## Abstract

There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty.