In this paper, it was proposed to carry out a preliminary normalization of diagnostic parameters using the Johnson distribution, which with three basic distribution groups (SL, SB, SU), covers a wide class of empirical distributions. The mathematical description of the family allows us to find the approximating probability density function in an explicit form, to determine the distribution parameters for obtaining the corresponding function (curve), as well as the inverse function for finding the quantiles of the specified levels. To assess the accuracy of the obtained normalized data, they were compared with the data obtained by replacing the resulting law with a Gaussian one. Percentages of values were compared in the implementation under study, which concentrated in the limits of estimated quantiles. Implementations were obtained using the simulation method. By the same method, the correctness (relative systematic error) of determining the quantile values of the specified levels was evaluated. The error value δ was estimated between the conditionally true quantile value calculated from the generated pseudo-general complex and the value estimated using the methods considered in the paper. Obtained data show that the relative error in the calculation of quantiles using the Johnson distribution does not exceed 0.07% and decreases in two orders of magnitude than the currently accepted procedure for replacing sample laws with Gaussian.

During the operation of solar and wind power plants, it is necessary to solve issues related to the guaranteed capacity of these plants, as well as the frequency stabilisation in the power system where they operate, and maintain an operating mode of self-sufficiency conditions. One of the solutions to these problems is the use of energy storage systems. This article proposes a mathematical model for the study of frequency and power regulation processes in power systems with distributed generation, which includes renewable energy resources and energy storage systems. The novelty of the model lies in the possibility of determining energy cost indicators based on instantaneous energy power data. The model allows us to estimate the conditions under which distributed generation becomes self-sufficient. The results of the model calculations of two variants of power system operation, which includes wind generators with a capacity of 1500 MW, demonstrate the ability of the proposed model to accurately reproduce the dynamics of the frequency stabilisation process. The calculation results of the energy-economic indicators of a real power system combined with a powerful subsystem of wind generation and a battery-type energy storage system prove the competitiveness of self-sufficient renewable energy power plants.