Abstract

Abstract

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. © 2019 Elsevier B.V.

Abstract

Abstract

Abstract
The penetration of distributed generation in medium (MV) and low (LV) voltage distribution grids has been steadily increasing every year in multiple countries, thus creating new technical challenges in grid operation and motivating developments in distributed optimization for flexibility management. The traditional centralized optimal power flow (OPF) algorithm can solve technical constraints violation. However, computational efficiency, new technologies (e.g., edge computing) and control architectures (e.g., web-of-cells) are demanding for distributed approaches. This work formulates a novel distributed multi-period OPF for three-phase unbalanced grids that is essential when integrating energy storage units in operational planning (e.g., day-ahead) of LV or local energy community grids. The decentralized constrained optimization problem is solved with the alternating direction method of multipliers (ADMM) adapted for unbalanced LV grids and multi-period optimization problems. A 33-bus LV distribution grid is used as a case-study in order to define optimal battery storage scheduling along a finite time horizon that minimizes overall grid operational costs, while complying with technical constraints of the grid (e.g., voltage and current limits) and battery state-of-charge constraints. © 2020