Distributed Economic Dispatch with Dynamic Power Demand: An Implicit Dual Gradient Tracking Algorithm under Random-Triggered Transmission Protocol

This paper investigates the distributed economic dispatch problem (EDP) under dynamic power demand in power systems. The dynamic power demand implies that the optimal solution to the EDP changes continuously over time, requiring the algorithm to find and track the optimal solution trajectory rapidly. To address this challenge, an implicit dual gradient tracking algorithm (IDGT) is developed based on the distributed gradient tracking algorithm. The IDGT utilizes state and direction information at historical time intervals to track the optimal solution without the requirement for generator units (GUs) to share the estimation of the average gradient. Furthermore, the paper also analyzes the limitations of the conventional event-triggered scheme under dynamic power demand and proposes a novel random-triggered transmission protocol (RTTP). The communication state of each GU is modeled as a Markov chain, including successful communication, packet loss (unknown but bounded), and no communication. This modeling allows the communication frequency between GUs and neighbors to be adjusted and eliminates the requirement to calculate the complex triggering function. Finally, the effectiveness of the proposed IDGT and RTTP is verified through case studies.