Distributed DC Optimal Power Flow Based on Primal-Dual Gradient Dynamics

This paper presents a primal-dual gradient dynam-ics (PDGD)-based algorithm for solving the DC optimal power flow (DC-OPF) problem in a distributed manner. Since PDGD-based algorithms usually have simple structures and are scalable to large-scale problems, they have been widely applied in various fields. However, they require the optimization problems to have strictly convex objective functions and thus cannot be used directly for a DC-OPF problem that typically has only a convex objective function. To address this issue, the original DC-OPF problem is first transformed into an equivalent version featuring a strictly convex objective function and reduced decision variables by eliminating equality constraints. The PDGD-based algorithm is then employed to solve the reformulated problem. Theoretical analyses are conducted to prove the equivalence between the original and reformulated problems, and the optimality and convergence of the proposed algorithm. Finally, case studies on several IEEE standard test systems illustrate the effectiveness of the proposed algorithm and its superior performance compared to the existing methods.