A Distributed Sub-Gradient Optimal Scheduling Method Based on Primal Decomposition with Application to Multi-Area Interconnected Power Systems

In order to overcome the shortcoming that the dual distributed sub-gradient optimization methods need to construct a feasible solution, a novel distributed sub-gradient optimization method based on primal decomposition is proposed in this paper and used to solve the joint dynamic economic dispatch (JDED) problem of multi-area interconnected power systems (MAIPSs). Firstly, the centralized optimization model is established and decomposed into multiple independent local areas' optimization and a global coordinator's optimization by splitting area power grids and cross-area tie-lines. Moreover, the slack variables and corresponding penalties are introduced into the local optimization to ensure feasibility and optimality. Secondly, a distributed sub-gradient optimization method is proposed to solve the decomposed model, in which the sub-gradient is calculated by using the dual multipliers from local optimization. Furthermore, in order to get better convergence, the heuristic updating rules for step size and penalty factor are designed. Finally, the numerical tests are carried out on two interconnected systems of different scales, and results show that the proposed method can obtain a good feasible solution directly and has high computational efficiency.