Chordal Conversion Based Convex Iteration Algorithm for Three-Phase Optimal Power Flow Problems

The three-phase optimal power flow (OPF) problem has recently attracted a lot of research interests due to the need to coordinate the operations of large-scale and heterogeneous distributed energy resources in unbalanced electric power distribution systems. The nonconvexity of the three-phase OPF problem is much stronger than that of the single-phase OPF problem. Instead of applying the semidefinite programming relaxation technique, this paper advocates a convex iteration algorithm to solve the nonconvex three-phase OPF problem. To make the convex iteration algorithm computationally efficient for large-scale distribution networks, the chordal conversion based technique is embedded in the convex iteration framework. By synergistically combining the convex iteration method and the chordal based conversion technique, the proposed three-phase OPF algorithm is not only computationally efficient but also guarantees global optimality when the trace of the regularization term becomes zero. At last, to further improve the computational performance, a greedy grid partitioning algorithm is proposed to decompose a single large matrix representing a distribution network to many smaller matrices. The simulation results using standard IEEE test feeders show that the proposed algorithm is computationally efficient, scalable, and yields global optimal solutions while resolving the rank conundrum.