Statistical methodology for taking into account multi-mode in the problems of electrical system functioning

Abstract

The problem of optimal compensation of reactive loads by the criterion of the minimum loss of electric energy is considered. To solve the problem, it is necessary to analyze the parameters of the whole set of steady-state modes of the electrical system and summarize the economic estimates of the whole variety of its modes (multi-mode). The direct use of the characteristics of each mode separately leads to a sharp increase in the volume of source data and the complexity of solving the corresponding problem. Since electrical loads are random variables, it is advisable to use a statistical approach and special methods of mathematical statistics, allowing to take into account the statistical nature of a significant part of the initial information. Moreover, multimode models using the moment correlation matrix of loads were widely recognized. A compact, concise presentation of load curves and high-dimensional MCMs seems to be the most effective on the basis of factor (component) analysis. The optimization process itself is based on the reduced gradient method as the most adapted one to solving electric power problems.