Statistical multimode accounting in the problem of optimal reactive load compensation when constructing smart grids

The article deals with the development prospects for smart grids. An approach to optimizing the modes of electric power systems in terms of reactive power is presented in detail. The solution of this problem considers the multimodality, determination of the integral characteristics of the modes, etc. Analytical modeling of load changes by means of the method of factor analysis allows to reduce the amount of information drastically without a significant loss of the accuracy of the obtained solutions. For this purpose, the actually correlated electrical loads of various nodes of electric power systems are represented in the form of a linear combination of independent random variables, namely, generalized load graphs. It is shown that the inclusion of multimode by orthogonal graphs results in a significant simplification of the solution of multimode problems. The choice of the dependent and independent variables composition when solving the optimization problem with the power consumption modes has a fundamental effect both on the modeling of constraints, the formation of the reduced gradient and the main calculation expressions, and on the speed of the optimization search as a whole.