Privacy-Preserving Economic Dispatch in Microgrids via Robust Gradient-Tracking Over Directed Networks

Existing differentially private optimization algorithms for the distributed economic dispatch problem (EDP) often involve a trade-off between privacy performance and optimization accuracy. This paper presents a robust gradient-tracking based differentially private distributed algorithm to enhance both privacy performance and optimization accuracy for EDP. In particular, we employ solely row stochastic weight matrices to enable each agent to locally allocate weights to received messages. Moreover, unlike most existing approaches that rely on decaying noise, our algorithm integrates persistent noise into the exchanged information to enhance privacy performance. To mitigate the impact of persistent noise, we incorporate robust gradient-tracking techniques and introduce noise attenuation factors. By carefully selecting the step size and noise attenuation factors, we demonstrate that our algorithm achieves almost sure convergence while simultaneously ensuring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-differential privacy. Finally, simulation experiments conducted on the modified IEEE 14-bus microgrid system and IEEE 118-bus power system validate the effectiveness of our algorithm in terms of both convergence and privacy performance.