Distributed optimization method with weighted gradients for economic dispatch problem of multi-microgrid systems

After microgrids (MGs) are built in a near region, a good idea is interconnecting those neighboring MGs to form a multi-microgrid (MMG) system and support each other. Apparently, the economic dispatch problem (EDP) of an MMG system is much more complex than that of an MG. In this paper, the EDPs of an MMG system is formulated as a two-layer interdependent network, where the bottom layer is a network that energy flows (called energy network), while the top layer is a network that information exchanges (called information network). The information network consists of two types of subnetworks, within-MG subnetworks and between-MG subnetworks, in which on within-MG subnetworks, the optimal outputs of distributed generators (DGs) are achieved and the supply-demand balance is reached in an MG, while on between-MG subnetworks, the outputs of MGs are coordinated to support one another optimally in the MMG system. Further, a distributed optimization method with weighted gradients (DOWG) is proposed to solve the EDPs of the MMG system on the information network, where equality constraints in optimization problems are dealt with by the weighted matrix and dynamic step sizes are employed to achieve faster convergence rate. Furthermore, two propositions are proved, which ensure the supply-demand balance is not broken at an arbitrary iteration. Finally, Simulations are carried out on the MMG system built in MATLAB/Simulink. The results show that the convergence rate of the proposed method (DOWG) is faster and higher accuracies are obtained, compared to two other methods. Moreover, applying the proposed method, the optimal outputs of DGs are obtained in MGs and the MMG system is coordinated optimally, when both loads and environmental conditions fluctuate largely. More importantly, the proposed method still can run the MMG system well, even if the failures of agents occur.