Privacy-Preserving Distributed Optimal Power Flow with Partially Homomorphic Encryption

TL;DR

This paper introduces a privacy-preserving distributed optimal power flow algorithm using partially homomorphic encryption and ADMM, ensuring sensitive grid data remains confidential while solving the OPF problem efficiently.

Contribution

It develops a novel privacy-preserving distributed OPF method combining PHE, ADMM, and SDP transformation, with proven privacy guarantees and exactness.

Findings

Effective privacy preservation in distributed OPF.

Exact transformation of relaxed ADMM to SDP.

Numerical validation confirms approach's effectiveness.

Abstract

Distribution grid agents are obliged to exchange and disclose their states explicitly to neighboring regions to enable distributed optimal power flow dispatch. However, the states contain sensitive information of individual agents, such as voltage and current measurements. These measurements can be inferred by adversaries, such as other participating agents or eavesdroppers. To address the issue, we propose a privacy-preserving distributed optimal power flow (OPF) algorithm based on partially homomorphic encryption (PHE). First of all, we exploit the alternating direction method of multipliers (ADMM) to solve the OPF in a distributed fashion. In this way, the dual update of ADMM can be encrypted by PHE. We further relax the augmented term of the primal update of ADMM with the $\ell_1$-norm regularization. In addition, we transform the relaxed ADMM with the $\ell_1$-norm regularization to a semidefinite program (SDP), and prove that this transformation is exact. The SDP can be solved locally with only the sign messages from neighboring agents, which preserves the privacy of the primal update. At last, we strictly prove the privacy preservation guarantee of the proposed algorithm. Numerical case studies validate the effectiveness and exactness of the proposed approach.