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 ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}-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.