A Quadratically-Constrained Convex Approximation for the AC Optimal Power Flow

TL;DR

This paper presents a new quadratically-constrained convex approximation for the AC optimal power flow problem that does not rely on common simplifying assumptions and maintains the original problem's structure, enabling decentralized optimization.

Contribution

The authors introduce a novel QCAC model for AC-OPF that preserves problem structure and does not depend on typical assumptions, improving accuracy and applicability.

Findings

Outperforms existing conic relaxations in accuracy.

Effective for large-scale power systems with up to 30,000 buses.

Shows advantages over second-order conic relaxations in case studies.

Abstract

We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance ratio, near-nominal voltage magnitudes, or small angle differences, and preserves the structural sparsity of the original AC power flow equations, making it suitable for decentralized power systems optimization problems. To achieve this, we reformulate the AC-OPF problem as a quadratically constrained quadratic program. The nonconvex terms are expressed as differences of convex functions, which are then convexified around a base point derived from a warm start of the nodal voltages. If this linearization results in a non-empty constraint set, the convexified constraints form an inner convex approximation. Our experimental results, based on Power Grid Library instances of up to 30,000 buses, demonstrate the effectiveness of the QCAC approximation with respect to other well-documented conic relaxations and a linear approximation. We further showcase its potential advantages over the well-documented second-order conic relaxation of the power flow equations in two proof-of-concept case studies: optimal reactive power dispatch in transmission networks and PV hosting capacity in distribution grids.