Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Synthesizing Grid Data with Cyber Resilience and Privacy Guarantees

Shengyang Wu, Vladimir Dvorkin

TL;DR

This work tackles the dual challenge of privacy and cyber resilience in releasing synthetic OPF data. It introduces Cyber Resilient Obfuscation (CRO) and an exponential-mechanism variant (CRO-Exp) that embed attack-optimization into post-processing, recasting the difficult tri-level problem as a tractable robust optimization framework. The methods maintain DP guarantees while explicitly penalizing attack damage under load-redistribution scenarios, using a robust optimization (RO) surrogate to bound adversarial effects. Experimental results on standard testbeds demonstrate that CRO can preserve data fidelity while dramatically reducing vulnerability to attacks, and CRO-Exp significantly lowers computational burden without compromising resilience. The approach offers a practical pathway for sharing realistic yet secure grid models for analysis and validation.

Abstract

Differential privacy (DP) provides a principled approach to synthesizing data (e.g., loads) from real-world power systems while limiting the exposure of sensitive information. However, adversaries may exploit synthetic data to calibrate cyberattacks on the source grids. To control these risks, we propose new DP algorithms for synthesizing data that provide the source grids with both cyber resilience and privacy guarantees. The algorithms incorporate both normal operation and attack optimization models to balance the fidelity of synthesized data and cyber resilience. The resulting post-processing optimization is reformulated as a robust optimization problem, which is compatible with the exponential mechanism of DP to moderate its computational burden.

Synthesizing Grid Data with Cyber Resilience and Privacy Guarantees

TL;DR

This work tackles the dual challenge of privacy and cyber resilience in releasing synthetic OPF data. It introduces Cyber Resilient Obfuscation (CRO) and an exponential-mechanism variant (CRO-Exp) that embed attack-optimization into post-processing, recasting the difficult tri-level problem as a tractable robust optimization framework. The methods maintain DP guarantees while explicitly penalizing attack damage under load-redistribution scenarios, using a robust optimization (RO) surrogate to bound adversarial effects. Experimental results on standard testbeds demonstrate that CRO can preserve data fidelity while dramatically reducing vulnerability to attacks, and CRO-Exp significantly lowers computational burden without compromising resilience. The approach offers a practical pathway for sharing realistic yet secure grid models for analysis and validation.

Abstract

Differential privacy (DP) provides a principled approach to synthesizing data (e.g., loads) from real-world power systems while limiting the exposure of sensitive information. However, adversaries may exploit synthetic data to calibrate cyberattacks on the source grids. To control these risks, we propose new DP algorithms for synthesizing data that provide the source grids with both cyber resilience and privacy guarantees. The algorithms incorporate both normal operation and attack optimization models to balance the fidelity of synthesized data and cyber resilience. The resulting post-processing optimization is reformulated as a robust optimization problem, which is compatible with the exponential mechanism of DP to moderate its computational burden.

Paper Structure

This paper contains 18 sections, 3 theorems, 18 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. DC Optimal Power Flow (OPF) Problem
  4. Differential Privacy for Synthetic OPF Datasets
  5. Cyber Resilience Risks in Releasing Differentially Private OPF Datasets
  6. Cyber Resilience and Privacy Guarantees for Synthetic OPF Datasets
  7. Computational Tractability via Robust Optimization (RO)
  8. Differentially Private CRO
  9. Exponential Mechanism to Ease Computational Burden
  10. Experiment Results
  11. Substantiating Attacks Calibrated on DP Data
  12. Insights from the Small PJM 5-Bus Testbed
  13. Large-Scale Applications with CRO-Exp
  14. Conclusion
  15. Proof of Proposition 3
  16. ...and 3 more sections

Key Result

Proposition 3

For any feasible load vector $\mathbf{d}$, relation $C_{\text{att}}^{\text{RO}}(\mathbf{d}) \geqslant C_{\text{att}}^\text{BO}(\mathbf{d})$ holds. $\triangleleft$

Figures (3)

  • Figure 1: Histograms of normal and post-attack OPF costs in the PJM 5-bus systems. Blue and red dotted lines represent the average OPF costs on synthetic load parameters in normal and post-attack scenarios, respectively. Top row: histograms resulting from the standard post-processing based on \ref{['eq:blpp']}. Bottom row: histograms resulting from the CRO algorithm.
  • Figure 2: Num. of variables and complementarity constraints in CRO, CRO-Exp ($\tau$=5) and standard post-processing \ref{['eq:blpp']} across four testbeds (log-scale).
  • Figure 3: Outcomes of the BO load redistribution attack calibrated on synthetic CRO-Exp loads for varying number of the worst-case constraints $\tau$. The damage in percentage is computed as $(C_\text{att}^\text{BO}(\tilde{\mathbf{d}})-C_\text{opf}(\tilde{\mathbf{d}}))/C_\text{opf}(\tilde{\mathbf{d}})\times 100$. $\tau=0$ means the synthetic dataset generated by the standard post-processing in \ref{['eq:blpp']}. Adjacency $\alpha$ are determined in percentages of the average load in the testbed. Attack magnitudes are $\eta=15\%$ in IEEE 14-bus system and $\eta=5\%$ in IEEE 24-bus and 118-bus systems. Red lines represent the mean value, the blue area represents the 80% confidence interval.

Theorems & Definitions (5)

  • Definition 1: Adjacency
  • Definition 2: $\varepsilon-$DP
  • Proposition 3: Conservative attack approximation
  • Theorem 4: DP of CRO
  • Theorem 5: DP of CRO-Exp