Wasserstein Two-Sided Chance Constraints with An Application to Optimal Power Flow

TL;DR

This paper develops a Wasserstein-based approach to two-sided chance constraints for optimal power flow, providing scalable, conservative approximations with proven consistency and guarantees, demonstrated on large power systems.

Contribution

It introduces a novel Wasserstein two-sided chance constraint model with hierarchical conic approximations, tailored for optimal power flow applications.

Findings

Efficient conic approximations for joint chance constraints

Asymptotic consistency of the proposed approximations

Successful application to large IEEE power systems

Abstract

As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate, it is oftentimes much more challenging to compute than individual CCs. Motivated by the application of optimal power flow, we study a special joint CC, named two-sided CC. We model the uncertain parameters through a Wasserstein ball centered at a Gaussian distribution and derive a hierarchy of conservative approximations based on second-order conic constraints, which can be efficiently computed by off-the-shelf commercial solvers. In addition, we show the asymptotic consistency of these approximations and derive their approximation guarantee when only a finite hierarchy is adopted. We demonstrate the out-of-sample performance and scalability of the proposed model and approximations in a case study based on the IEEE 118-bus and 3120-bus systems.