Differentially Private Synthetic Voltage Phasor Release for Distribution Grids

Abstract

Training machine learning models, including Grid Foundation Models (GFMs), requires large volumes of realistic grid data, yet substantial privacy concerns discourage utilities and data providers from sharing load profiles and network parameters. We study the release of synthetic voltage phasor trajectories for distribution grids under differential privacy (DP). We first fit a DP generative model to historical customer loads, then propagate synthetic load trajectories through the AC power flow equations on the true admittance matrix to produce voltage phasors. The central question is whether the randomness already present in the DP synthetic loads is sufficient to protect not only the loads, but also the network topology encoded by the bus admittance matrix. We show that it is. The implication is that a corpus of voltage trajectories can be constructed from DP synthetic loads while preserving the statistics of AC power flow, which is critical for training GFMs. This preservation of the power flow statistics stands in contrast to approaches that perturb the admittance matrix directly or inject noise into the voltage outputs, both of which distort the underlying physics. Concretely, we derive $(\varepsilon,δ)$-DP guarantees for the released voltage trajectories with respect to the admittance matrix, meaning privacy of the network parameters is obtained without any additional noise mechanism. Our bound depends on the adjacency assumption, the Jacobian of the AC power flow, and the covariance of the synthetic DP-loads. Finally, we present a synthetic voltage generation procedure and an empirical evaluation against Gaussian output-perturbation baselines, demonstrating that our approach provides a clear advantage for enabling GFM training.