Obtaining probability distribution laws of power system steady-state mode parameters

Stable operation of electrical power systems is one of the crucial issues in the power industry. Current volumes of electricity consumption cause the need to constantly increase the generated capacity, repeatedly modifying and complicating the original circuit. In addition to this, given the current trend towards the use of digital power systems and renewable energy sources, more and more uncertainties difficult to predict by standard mathematical methods appear. Events in the power system are deterministic, i.e. random. Thus, it is difficult to fully assess the system stability, voltage levels, currents, or possible power losses. Finding the probability distribution laws can give us an understanding of all the possible states in which an object can exist. Obtaining them is complicated by the difficulty of accounting for all the correlations between the random arguments of the source data. These laws are necessary to determine the optimal operating modes, the possibility of solving the problem of determining the optimal renewable energy sources installation locations and the required amount of generated energy in a non-deterministic way. The purpose of this article is to test the developed SIBD method for obtaining the full probabilistic characteristics. This method, unlike the Monte Carlo methods, does not use a random sample of initial data, but completely covers the studied functional dependence. The problem was solved using the provisions of probability theory and mathematical statistics, numerical optimization methods in particular. The MATLAB Matpower application package was also used to solve technical computing problems.