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Privacy-Preserving Power Flow Analysis via Secure Multi-Party Computation

Jonas von der Heyden, Nils Schlüter, Philipp Binfet, Martin Asman, Markus Zdrallek, Tibor Jager, Moritz Schulze Darup

TL;DR

This work presents a tailored solution to the power flow problem building on an SMPC implementation of Newton’s method, allowing multiple parties to jointly evaluate functions of their private inputs without revealing the latter.

Abstract

Smart grids feature a bidirectional flow of electricity and data, enhancing flexibility, efficiency, and reliability in increasingly volatile energy grids. However, data from smart meters can reveal sensitive private information. Consequently, the adoption of smart meters is often restricted via legal means and hampered by limited user acceptance. Since metering data is beneficial for fault-free grid operation, power management, and resource allocation, applying privacy-preserving techniques to smart metering data is an important research problem. This work addresses this by using secure multi-party computation (SMPC), allowing multiple parties to jointly evaluate functions of their private inputs without revealing the latter. Concretely, we show how to perform power flow analysis on cryptographically hidden prosumer data. More precisely, we present a tailored solution to the power flow problem building on an SMPC implementation of Newtons method. We analyze the security of our approach in the universal composability framework and provide benchmarks for various grid types, threat models, and solvers. Our results indicate that secure multi-party computation can be able to alleviate privacy issues in smart grids in certain applications.

Privacy-Preserving Power Flow Analysis via Secure Multi-Party Computation

TL;DR

This work presents a tailored solution to the power flow problem building on an SMPC implementation of Newton’s method, allowing multiple parties to jointly evaluate functions of their private inputs without revealing the latter.

Abstract

Smart grids feature a bidirectional flow of electricity and data, enhancing flexibility, efficiency, and reliability in increasingly volatile energy grids. However, data from smart meters can reveal sensitive private information. Consequently, the adoption of smart meters is often restricted via legal means and hampered by limited user acceptance. Since metering data is beneficial for fault-free grid operation, power management, and resource allocation, applying privacy-preserving techniques to smart metering data is an important research problem. This work addresses this by using secure multi-party computation (SMPC), allowing multiple parties to jointly evaluate functions of their private inputs without revealing the latter. Concretely, we show how to perform power flow analysis on cryptographically hidden prosumer data. More precisely, we present a tailored solution to the power flow problem building on an SMPC implementation of Newtons method. We analyze the security of our approach in the universal composability framework and provide benchmarks for various grid types, threat models, and solvers. Our results indicate that secure multi-party computation can be able to alleviate privacy issues in smart grids in certain applications.

Paper Structure

This paper contains 29 sections, 2 theorems, 20 equations, 2 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Contributions
  4. Preliminaries
  5. The power flow problem
  6. Overview of secure multi-party computation
  7. Instantiation of SMPC
  8. Tailored power flow analysis
  9. Discussion of different formulations
  10. Cartesian power flow formulation
  11. Line search
  12. Privacy-preserving power flow analysis
  13. Gradient vector and Jacobian
  14. Solving the system of linear equations
  15. Direct solver
  16. ...and 14 more sections

Key Result

Theorem 1

Let the composition of $\Pi_\mathcal{F}\xspace$ and $\mathcal{R}$ be a protocol instantiating a functionality $\mathcal{F}$ with perfect/statistical/computational security, and let $\Pi_\mathcal{R}\xspace$ be a protocol instantiating the functionality $\mathcal{R}$ with the same type of security. Th

Figures (2)

  • Figure 1: Privacy preserving computation via secret sharing in a smart grid with $n=3$ prosumers. Each prosumer $\mathsf{P}_i$ has $3$ shares and is connected via a point to point connection (gray lines) to all other prosumers.
  • Figure 2: Semi-urban network topology with 44 nodes, of which 39 represent prosumers. The face color of the $i$-th node corresponds to the magnitude $|s_i(\mathbf{v})|$, whereas orange node outlines and edges indicate voltage and current constraint violations \ref{['eq:constraints']}, respectively.

Theorems & Definitions (5)

  • Definition 1: UC-security, Def. 4.19 in Cramer2015secure
  • Theorem 1: Composition Theorem, Thm. 4.20 in Cramer2015secure
  • Definition 2: $\mathcal{F}\xspace_{\mathsf{ABB}}$, KellerOS16
  • Definition 3: Ideal functionality of power flow analysis $\mathcal{F}\xspace_{\mathsf{PFA}}$
  • Theorem 2