An analysis of delay-constrained consensus-based optimal algorithms in virtual power plants

In virtual power plants (VPPs), consensus-based distributed optimal dispatch algorithms aim to collectively minimize the operating cost. As ubiquitous latency on communication networks may lead to divergence, convergence to a nonoptimal solution, or a longer convergence time, mitigating the impacts of arbitrarily large but bounded time-varying delays is significant both in theory and in practice. To modify a typical consensus-based optimal dispatch algorithm under time-varying delays, this paper designs new update rules and introduces a reduction approach to evaluate the performance of the algorithm. The results reveal that the modified algorithm can always converge to the optimal solution with a tactical initial setup in a distributed manner if the undirected interaction topology is connected and the gain parameter is sufficiently small. The analytical expression of the gain is also given. Furthermore, we show that the convergence time is determined by the maximum time delays, the number of generators, and the convergence accuracy. Several numerical simulation studies validate our theory.