Favorable properties of Interior Point Method and Generalized Correntropy in power system State Estimation

Abstract

The paper provides the theoretical proof of earlier published experimental evidence of the favorable properties of a new method for State Estimation – the Generalized Correntropy Interior Point method (GCIP). The model uses a kernel estimate of the Generalized Correntropy of the error distribution as objective function, adopting Generalized Gaussian kernels. The problem is addressed by solving a constrained non-linear optimization program to maximize the similarity between states and estimated values. Solution space is searched through a special setting of a primal-dual Interior Point Method. This paper offers mathematical proof of key issues: first, that there is a theoretical shape parameter value for the kernel functions such that the feasible solution region is strictly convex, thus guaranteeing that any local solution is global or uniquely defined. Second, that a transformed system of measurement equations assures an even distribution of leverage points in the factor space of multiple regression, allowing the treatment of leverage points in a natural way. In addition, the estimated residual of GCIP model is not necessarily zero for critical (non-redundant) measurements. Finally, that the normalized residuals of critical sets are not necessarily equal in the new model, making the identification of bad data possible in these cases.