## 1 Introduction
This stems from the complication of EPS topology; the use of various types of generating equipment at power plants, which have different features and limitations; a decline in the qualifications of repair and maintenance personnel in EPSs; and an increase in the energy availability of consumers [33; 34; 35]. A cascading failure is defined as a sequence of dependent failures of individual components that gradually weaken an EPS [36]. The study [37] proposes dividing cascading processes into a slow stage (the speed of action of protection devices prevents the development of accidents) and a fast stage (the sequential shutdowns of EPS components with the disruption of power supply to consumers and subsequent operation of emergency control systems to maintain stability in the EPS). The reliability of power supply to consumers could be improved by dividing large power systems into segments using direct current transmission lines [38]. To minimize consumer outages, the approach presented in the study focused on changing the power flows along DC transmission lines connecting different segments. In this case, the electrical network within individual segments became more independent, which reduced the likelihood of a cascading blackout. A spectral clustering algorithm was designed to identify EPS components whose disconnection would result in the least damage to electricity consumers in the asynchronous mode [39]. The algorithm relied on assumptions about the coherence of generators in certain clusters. The results of simulation demonstrated that this method could prevent power supply disruptions by islanding EPS parts. However, an analysis of emergency shutdowns revealed that it is extremely difficult to ensure stable operation of generating equipment and consumer power receivers during cascading failures [40]. The paper [41] presented the findings of a reliability assessment for a network when it was transformed into a set of several simple networks. Modeling the cascading failures in the network relied on the developed algorithm consisting of six steps. Changes in the operating conditions were recorded, depending on the disturbance, and a cascading failure was demonstrated in the form of a state transition graph. The presented approach could not provide an analysis of all variations in changes in the states and power flows in the EPS network. In [42], the results of a study on cascading outages were exemplified by two models of the electric network: ORNL-PSerc-Alaska and Crucitti-Latora-Marchiori. The findings indicated that an increase in the size of the network enhanced its stability under identical emergency disturbances. Calculations proved the influence of network non-homogeneity (differences in the transfer capability of components) on the development of cascading failure processes. At the same time, there was no clear definition and mathematical description of what exactly was meant by non-homogeneity and how the relations for the non-homogeneity factor were obtained. In [43], reliability is understood as the property of an object of performing specified functions within a specified scope under certain operating conditions. The reliability of an object and its components are complex properties that, depending on the purpose and operating conditions, may include the following (separately or in a certain combination): failure-free operation, recoverability, survivability, (technical) safety, controllability, storability, and stability. In the concept of \"reliability\", it is crucial to separately distinguish \"survivability\", which is the ability to withstand special disturbances, preventing their development into a chain and cascading process, ending with the complete loss of the functionality of a part or the entire object. In this case, cascading processes are viewed as a sequence of events that culminate in a triggering disturbance, resulting in the sequential disconnection of several components within an EPS.