Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning

TL;DR

This paper introduces a scalable, data-driven method for improving joint chance constraints in AC optimal power flow, reducing conservativeness and enhancing voltage regulation in distribution networks with renewable energy.

Contribution

It develops an iterative, learning-based approach that refines bounds on joint chance constraints, outperforming traditional union bound methods in power system optimization.

Findings

Reduces conservativeness compared to Boole's inequality.

Efficiently approximates bounds on joint chance constraints.

Successfully applied to IEEE 37-node test feeder.

Abstract

This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance constraints, which satisfy multiple constraints simultaneously with a prescribed probability, are one way to incorporate uncertainty across sets of constraints, leading to a chance-constrained optimal power flow problem. Departing from the computationally-heavy scenario-based approaches or approximations that transform the joint constraint into conservative deterministic constraints, this paper develops a scalable, data-driven approach which learns operational trends in a power network, eliminates zero-probability events (e.g., inactive constraints), and accurately and efficiently approximates bounds on the joint chance constraint iteratively. In particular, the proposed framework improves upon the classic methods based on the union bound (or Boole's inequality) by generating a much less conservative set of single chance constraints that also guarantees the satisfaction of the original joint constraint. The proposed framework is evaluated numerically using the IEEE 37-node test feeder, focusing on the problem of voltage regulation in distribution grids.