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Privacy-Preserving Distributed Optimal Power Flow with Partially Homomorphic Encryption

Tong Wu, Changhong Zhao, Ying-Jun Angela Zhang

TL;DR

A privacy preserving distributed optimal power flow (OPF) algorithm based on partially homomorphic encryption (PHE) that obtains the solutions that are very close to the global optimum, and converges much faster compared to competing alternatives.

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.

Privacy-Preserving Distributed Optimal Power Flow with Partially Homomorphic Encryption

TL;DR

A privacy preserving distributed optimal power flow (OPF) algorithm based on partially homomorphic encryption (PHE) that obtains the solutions that are very close to the global optimum, and converges much faster compared to competing alternatives.

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 -norm regularization. In addition, we transform the relaxed ADMM with the -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.

Paper Structure

This paper contains 25 sections, 7 theorems, 60 equations, 10 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Related Works
  4. Contributions
  5. Organization and Overview
  6. Preliminaries
  7. Definition
  8. Optimal Power Flow
  9. Partially Homomorphic Encryption
  10. Privacy-Preserving Distributed Optimal Power Flow
  11. Convex Relaxation
  12. Distributed Formulation
  13. Distributed Optimal Power Flow
  14. Privacy-Preserving Distributed Algorithm
  15. Privacy Analysis and Stopping Criterion
  16. ...and 10 more sections

Key Result

Lemma 1

We have the following relationship:

Figures (10)

  • Figure 1: The overview of the proposed method.
  • Figure 2: The flowchart of the proposed algorithm.
  • Figure 3: The 85-bus tree distribution system with three regions.
  • Figure 4: The evolution of $\mathbf{X}^r_{l, o}$.
  • Figure 5: The evolution of encrypt weighted differences (in ciphertext).
  • ...and 5 more figures

Theorems & Definitions (12)

  • Lemma 1
  • Proposition 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • ...and 2 more