Load Flow optimization of Meshed Networks: A Convex Relaxation and An Illustrative Example

Load flow optimization focuses on the optimal operation and control of power system, which is a nonlinear and nonconvex optimization problem. And the optimal problems in meshed networks are common but hard to solve because of the angle constraints. In order to solve this optimization problem, a convex optimal model in meshed networks is proposed in this paper. The load flow optimization model is relaxed to be convex by two steps. In the first step, new variables are taken in to reformulate the optimal problem. In the second step, the nonlinear equality constraints are relaxed into convex second-order cone constraints. With the relaxed optimal load flow model, the exact solutions of optimal load flow can be obtained for meshed networks and the global optimum can be guaranteed. Especially, the phase angle of the voltage can be obtained directly. The exactness of the relaxation is tested by an illustrative example.