Statistical Learning For DC Optimal Power Flow

TL;DR

This paper develops a statistical learning approach to create control policies for real-time optimal power flow in electric systems, effectively handling renewable energy uncertainty by combining a few key basis policies.

Contribution

It introduces an ensemble control policy framework that learns and combines a small number of basis policies to efficiently approximate optimal solutions under uncertainty.

Findings

Ensemble policies with about ten bases achieve high-probability optimality.

Only a few basis policies are relevant despite exponential possibilities.

The approach is validated with theoretical and empirical results.

Abstract

The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly in real-time. In this paper, we aim at developing control policies that are able to track the optimal set-point with high probability. The approach is based on the observation that the OPF solution corresponding to a certain uncertainty realization is a basic feasible solution, which provides an affine control policy. The optimality of this basis policy is restricted to uncertainty realizations that share the same set of active constraints. We propose an ensemble control policy that combines several basis policies to improve performance. Although the number of possible bases is exponential in the size of the system, we show that only a few of them are relevant to system operation. We adopt a statistical learning approach to learn these important bases, and provide theoretical results that validate our observations. For most systems, we observe that efficient ensemble policies constructed using as few as ten bases, are able to obtain optimal solutions with high probability.