Distributed Penalty Dual Decomposition Algorithm for Optimal Power Flow in Radial Networks

Optimal power flow (OPF) is a fundamental problem in power system operating and planning. The need for distributed solutions is rapidly growing in distribution systems with radial networks, discrete equipments and many distributed generation units. Typically the model is difficult to solve due to the highly non-convexity and even non-continuity of the arising OPF problem. In this paper, we address these challenges by developing a penalty dual decomposition (PDD) based algorithm to obtain distributed solutions. The proposed PDD based algorithm mainly consists of two loops: in the outer loop we update the dual variables and the penalty parameter according to the constraint violation, while in the inner loop we divide the primal variables into several blocks and employ the block successive upper-bound minimization (BSUM) method to iteratively optimize each block variables with fixed penalty parameter and dual variables. Each subproblem in the proposed PDD based algorithm can be solved either in closed-form or by the bisection method and every limit point generated by the proposed algorithm is guaranteed to be a stationary point of the OPF problem. Simulation results, and comparison with centralized PDD and concave-convex procedure (CCCP) based algorithms are presented to validate the effectiveness of the proposed algorithm.