Maximum Loadability of Meshed Networks: A Sequential Convex Optimization Approach

In power system static security analysis, it often requires to calculate continuous power flow from a certain load condition to a bifurcation point along a given direction, which is referred to as the maximum loadability problem. This paper proposes a convex optimization method for maximum loadability problem over meshed power grids based on the semidefinite relaxation approach. Because the objective is to maximize the load increasing distance, convex relaxation model is generally inexact, unlike the situation in cost-minimum optimal power flow problem. Inspired by the rank penalty method, this paper proposes an iterative procedure to retrieve the maximum loadability. The convex quadratic term representing the penalty on the rank of matrix variable is updated in each iteration based on the latest solution. In order to expedite convergence, generator reactive power is also included in the objective function, which has been reported in literature. Numeric tests on some small-scale systems validate its effectiveness. Any sparsity-exploration and acceleration techniques for semidefinite programming can improve the efficiency of the proposed approach.