## 1 Introduction
A necessary and sufficient condition for the development of a cascading process is the excess of the admissible current during emergencies in the component being disconnected. In [44; 45], the survivability of technical systems is understood as their ability to maintain their basic functions, even with an acceptable loss in the quality of their performance, under the influence of external factors of an urgent nature, as well as unfavorable operating conditions. With regard to EPSs, the reliability of parallel operation is associated with the ability to maintain stability, which is characterized by the presence/absence of damages and losses for consumers due to the undersupply of electricity for a certain period of time. Power supply disruptions to consumers can result from large-scale emergency shutdowns that occur in a cascading manner, triggered by a sequence of events that lead to an initiating disturbance [46; 47]. In this case, there is no possibility of localizing the initiating disturbance at the place of its origin, which causes it to spread to adjacent fragments of the EPS, leading to failures of other equipment, as well as serious disruptions in the EPS operational conditions. The cascading development of accidents is caused by the successive tripping of generating and/or power grid equipment by the action of protection devices and/or emergency control systems. It can also be a result of operating conditions that are unacceptable for the specified equipment [48; 49]. This definition is of a fairly general nature, since it does not specify the conditions and parameters that influence the development of a cascading failure process. Cascading failures normally occur due to off-design disturbances and overload failures in electrical grid equipment, followed by its shutdown that leads to power outages affecting vast areas [50; 51]. In [52], a systemic failure is understood as a disruption in the stability of the parallel operation of power plants, an unacceptable deviation in frequency in the EPS and voltage at its nodes, current overloads of power grid equipment leading to its cascading shutdown, the emergence of the asynchronous mode, and the division of the EPS into unbalanced parts with a mass shutdown or restriction of electricity consumers across a large area. A cascading process should be understood as a sequence of quasi-steady states (QSSs) with a transition from one to another as a result of the step-by-step disconnection of EPS components overloaded by current. This process continues until it reaches the region of admissible or inadmissible power flows. In the event that the cascading process terminates in the region of inadmissible power flows, it turns into a cascading system failure. Evidence indicates that the development of a cascading process with the disconnection of electric grid equipment unfolds over a certain period of time, from several minutes to several days. In this case, there can be no loss of stability in an EPS. Consequently, dispatching personnel can proactively make topological adjustments and implement operational measures to prevent an unfolding failure and its transition to a systemic one. In recent years, energy storage systems have been increasingly used to enhance the survivability of EPSs. This facilitates preventing unnecessary shutdowns of generating and power grid equipment due to overload [53; 54; 55]. Energy storage systems have yet to see widespread implementation in EPSs, which is due to their high specific cost relative to the required power and energy capacity [56; 57]. The causes of a cascading blackout and its development in the Moscow power system on 25 May 2005 were addressed in [58; 59]. During the development of the failure, resulting from overloads, seven 220 kV overhead PTLs were successively disconnected from 09:23 (short circuit in the 220 kV Ochakovo-Choboty overhead PTL) to 10:45 (short circuit in the 220 kV Kedrovo-Ochakovo overhead PTL).