الفهرس 
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Abstract
The development of electricity generation technologies, which are based on the renewable energy sources (RES), significantly change the framework and principles of management of electric power systems (EPS). The low cost of energy for RES contributes to their widespread implementation in generating electric power from several kW to hundreds of MW. At the same time, uncontrolled renewable energy sources of relatively low power create the effect of pseudo-reduction in the power consumption of a separate territory. RES introduces significant uncertainty into the system of both generating and consumed (hidden RES) capacities. The uncertainty caused by the stochasticity of energy resources (solar, wind) affects the reliability indices (RI) of the EPS, and, consequently, the value of the required centralized power reserve. As a rule, reliability assessment plays a crucial role in the decision-making process when planning the future development of EPS. However, when solving the problems of adequacy, the characteristics of RES shifts the calculations direction towards the assessment of the current state of the EPS. At the same time, the performance of EPS in providing adequate electric services within accepted standards to all points of consumption can be judged acceptable or unacceptable by reliability criteria. The RI evaluation approaches range from relatively simple deterministic calculations (criterion N-1) to rigorous probabilistic reliability indices considering the stochastic nature of the EPS factors. The reliability analysis incorporates the probabilistic modelling of power system uncertainties and then reflects their impact on the customers service through the probabilistic evaluation of reliability indices. The probabilistic reliability index does not only consider the probability or likelihood of occurrence of uncertain events but also quantifies the consequence of the occurrence of that event. Based on the measure of severity, the reliability indices are named. The severity can be measured in power system operation by the frequency or magnitude or duration of loss of load faced by the customers of the network. The most significant among probabilistic reliability indices are LOLP (Loss of Load Probability), LOLE (Loss of Load Expectation), expected power not supplied (EPNS), and expected energy not supplied (EENS). In North America, a LOLE of no more than 1 day in 10 years is widely used. While in Western European countries, the standard LOLE value is set at a slightly different level (3 hours per year). In Russia, the list and calculation of RI is regulated by the national standard of the Russian Federation: “304-2018: Balance reliability of EPS. Part 1. General requirements ”. In 2019, the Unified Energy System (UES) Operator introduced technical report 59012820.27.010.005-2018, which regulates methodological guidelines for carrying out RI calculations. The most significant RI are recognized as the probability and mathematical expectation of the power deficit of consumers. The appearance of these guidelines indicates the relevance of the problem of calculating the RI of an EPS in Russia. Over the past several decades, tremendous amount of research has been done on developing probabilistic methods for power system reliability evaluation. However, a trade-off between detailed modeling and computational cost is still an important issue, especially with the growing complexity, uncertainty, and dimensionality of a power system. A widely used method both in Russia and abroad for the RI calculation is the Monte Carlo simulation (MCS) which is insensitive to the form of individual distribution functions of random variables and the dimension of the electrical network. However, MCS requires a great computational effort to guarantee the accuracy of the reliability indices results. Moreover, the high reliable property of EPSs and the enlarged sample space with the probabilistic modeling of renewable energy resources increase more and more the MCS computational burden. The analytical methods such as convolution method, cumulants method, and point estimate method (PEM) can act as alternatives to the MCS method. The analytical method in contrast to simulation method (MCS), give the same solution when recalculated. The convolution method gives highly accurate solution. However, it involves complicated mathematics which further hampers its application. The use of analytical methods, such as the cumulant method and PEM, is limited by the requirements for the accuracy of the resulting values, since, as a rule, these methods are not adaptive to rare events. As a result, to obtain an acceptable solution, additional calculation procedures are required, considering the specifics of the EPS. Such procedures are proposed in this dissertation work. On the other hand, to increase the MCS computational efficiency, two research tracks are adopted: improvement of the state evaluation efficiency and the improvement of the sampling efficiency. The first group includes approaches to improving computational procedures that make it possible to reduce the duration of the analysis of individual states of the EPS. The second direction is to develop more efficient methods for forming a sample of EPS states, with an emphasis on significant states. Since the failure events interpreted in the RI EPS problem associated with the power deficit, in modern EPS are becoming increasingly rare, the second direction is currently more relevant. The relevance of identifying significant rare events is increasing for EPS with a large share of intensively aging equipment. Here, multiple failures with a low probability of their occurrence become significant events. In the direction of identifying rare events, research and development have been presented in the dissertation work.