Privacy masking distributed saddle-point algorithm for dynamic economic dispatch

In smart grids, the goal of the dynamic economic dispatch problem (DEDP) is to obtain the optimal dispatch schedule for each generating unit in a set of periods under certain constraints. A major challenge is that privacy disclosures possibly occur during the exchange and updating of communications. To address the issue, we propose a fully distributed saddle point algorithm while preserving the privacy of participants by injecting the decaying Laplace noise. Based on the properties of the multi-Lyapunov function, we prove that the algorithm has an asymptotic convergence in the sense of expectation. Using the mechanism of differential privacy, we prove that the algorithm can guarantee e-differential privacy. In addition, we characterize the trade-off between levels of differential privacy and algorithmic accuracy. Finally, numerical simulations on IEEE 30-bus and IEEE 118-bus are used to validate the theoretical results.