Optimization of unbalanced power distribution networks via semidefinite relaxation

The papers considers an economic dispatch problem for unbalanced three-phase power distribution networks with distributed generation (DG) units. The objective is to minimize the overall active power supplied by the DG units and drawn from the substation, subject to constraints on the voltage magnitudes at the nodes, and on the power factor (PF) at the substation. The latter constraint is also applied to nodes equipped with capacitor banks. Similar to its optimal power flow counterparts for balanced systems, the formulated optimization problem is nonconvex. Nevertheless, a semidefinite relaxation technique is advocated to obtain a relaxed convex problem solvable in polynomial-time complexity. Numerical tests on the IEEE 13-node test feeder demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex problem.