An Application of Interior Point Quadratic Programming Algorithm to Power System Optimization Problems

Abstract

This paper presents a new algorithm of the interior point quadratic programming which can solve power system optimization problems with profoundly less computational efforts. The proposed algorithm has the following two special features. First, it is based on the path-following interior point algorithm, the search direction of which is taken as Newton direction, thus having quadratic convergence. In the second place, it solves directly a symmetric indefinite system instead of reducing it to the usual system with a positive-definite matrix. Under this artifice, the algorithm avoids the formation of [ADA^T] and generates fewer fill-ins than the case of factorizing the positive definite system matrix for large scale systems, realizing its impressive speed-up. Since the formula of the interior point method have been deduced more generally, the proposed algorithm can start from either a feasible (interior point) or an infeasible point (non-interior point).
Numerical results on the IEEE test systems and a Japanese 344 bus system (2100 variables, 2088 equality constraints and 1400 inequality constraints) have verified that the proposed algorithm possesses enough robustness and needs significantly less solution time compared with already reported applications of the interior point method.