Hypergraph-Based Fast Distributed AC Power Flow Optimization

TL;DR

This paper introduces a hypergraph-based distributed optimization method for AC power flow problems, improving computational efficiency and convergence guarantees compared to existing algorithms.

Contribution

It proposes a novel hypergraph-based distributed sequential quadratic programming approach with proven convergence and reduced complexity for AC power flow optimization.

Findings

Achieves locally quadratic convergence rate.

Demonstrates lower computational complexity than existing methods.

Validated through numerical tests in open-source toolbox.

Abstract

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between subgrids can be expressed as hyperedges. Then, a hypergraph-based distributed sequential quadratic programming (HDQ) approach is proposed to handle the reformulated problems, and the hypergraph-based distributed sequential quadratic programming (HDSQP) is used as the inner algorithm to solve the corresponding QP subproblems, which are respectively condensed using Schur complements with respect to coupling variables defined by hyperedges. Furthermore, we rigorously establish the convergence guarantee of the proposed algorithm with a locally quadratic rate and the one-step convergence of the inner algorithm when using the Levenberg-Marquardt regularization. Our analysis also demonstrates that the computational complexity of the proposed algorithm is much lower than the state-of-art distributed algorithm. We implement the proposed algorithm in an open-source toolbox, i.e., rapidPF, and conduct numerical tests that validate the proof and demonstrate the great potential of the proposed distributed algorithm in terms of communication effort and computational speed.