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Mechanism and Communication Co-Design for Differentially Private Energy Sharing

Yingshuo Gu, Xi Weng, Yue Chen

Abstract

Integrating distributed energy resources (DERs) is a critical step toward addressing the global climate crisis. This transformation has driven the transition from traditional consumers to prosumers and given rise to new energy sharing business models. Existing works have extensively studied prosumer energy sharing mechanisms, yet little attention has been paid to privacy protection, particularly when communication constraints are taken into account. In this paper, we study an energy sharing mechanism where information is exchanged over wireless channels via over-the-air (OTA) multiple-input multiple-output (MIMO) aggregation to exploit spectral efficiency for scalable prosumer coordination. To characterize the privacy leakage risk during data transmission process, we introduce an adversarial attack model and demonstrate that, under certain conditions, the platform can extract and recover prosumers' private parameters from the base station observations. To safeguard the energy sharing mechanism against such attacks, we propose a differentially private equilibrium-seeking algorithm, analyze the achievable privacy level, and establish convergence guarantees that quantify the impact of privacy on the convergence accuracy. Numerical experiments demonstrate that our approach effectively protects prosumers' privacy while converging to near-optimal solutions.

Mechanism and Communication Co-Design for Differentially Private Energy Sharing

Abstract

Integrating distributed energy resources (DERs) is a critical step toward addressing the global climate crisis. This transformation has driven the transition from traditional consumers to prosumers and given rise to new energy sharing business models. Existing works have extensively studied prosumer energy sharing mechanisms, yet little attention has been paid to privacy protection, particularly when communication constraints are taken into account. In this paper, we study an energy sharing mechanism where information is exchanged over wireless channels via over-the-air (OTA) multiple-input multiple-output (MIMO) aggregation to exploit spectral efficiency for scalable prosumer coordination. To characterize the privacy leakage risk during data transmission process, we introduce an adversarial attack model and demonstrate that, under certain conditions, the platform can extract and recover prosumers' private parameters from the base station observations. To safeguard the energy sharing mechanism against such attacks, we propose a differentially private equilibrium-seeking algorithm, analyze the achievable privacy level, and establish convergence guarantees that quantify the impact of privacy on the convergence accuracy. Numerical experiments demonstrate that our approach effectively protects prosumers' privacy while converging to near-optimal solutions.

Paper Structure

This paper contains 29 sections, 1 theorem, 55 equations, 7 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Energy Sharing Mechanism Design
  4. Wireless Communication in Distributed Systems
  5. Privacy Protection
  6. Contributions and Organization
  7. Energy Sharing Game
  8. Communication-Aware Implementation
  9. Bid Encoding and Scaling
  10. Uplink Synchronization and OTA Aggregation
  11. Receive Combining and Normalization
  12. Potential Privacy Leakage at the Base Station
  13. Signal Isolation
  14. Bid Recovery via Gain Normalization
  15. Private-Parameter Inference
  16. ...and 14 more sections

Key Result

Theorem 1

Suppose Assumptions 1--2 hold. Let $\lambda^\star$ denote the equilibrium price of the energy sharing game $\mathcal{G}=(\mathcal{I},\mathcal{S},U)$. If the market sensitivity parameter satisfies then under Algorithm alg:alg1, the expected squared distance to equilibrium satisfies where $\rho = \left(1 - \frac{(I-1)\gamma}{a(I-1)+\gamma}\right)^2 \in (0,1)$ is the contraction factor with $\gamma

Figures (7)

  • Figure 1: System model of the OTA-based energy sharing framework, where prosumers submit bids over wireless MIMO channels to a platform that computes and broadcasts market-clearing prices.
  • Figure 2: Communication flow of the OTA-based bid aggregation.
  • Figure 3: Distribution of adversary's inferred private parameter $(d_i - p_i)$ for each prosumer under different noise-to-signal ratios ($\alpha = 0, 0.2, 0.4, 0.6, 0.8$). The dashed vertical lines indicate the true values. Higher $\alpha$ leads to more dispersed distributions, demonstrating the effectiveness of the DP mechanism.
  • Figure 4: Artificial noise-to-signal ratio $\alpha$ versus target privacy budget $\epsilon^{\text{target}}$, comparing a perfect channel (no channel noise) and wireless channels. The shaded area represents the artificial noise saving enabled by channel noise. Top: different SNR values with fixed $N_r = 8$. Bottom: different $N_r$ values with fixed SNR $= 10$ dB.
  • Figure 5: Convergence of production, demand, and clearing price under OTA aggregation with different noise-to-signal ratios ($\alpha = 0, 0.2, 0.4, 0.6, 0.8$). Shaded regions indicate 95% CI over 100 trials.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1: Generalized Nash Equilibrium
  • Definition 2: Per-prosumer $(\epsilon_i,\delta_i)$-DP
  • Theorem 1