## 3 Results  
This study proposes a cyclic algorithm designed to search for the development trajectories of cascading failure processes following the \(N\)-\(X\) criterion for given EPS power flows. This algorithm can also be used in planning and maintaining EPS power flows. The \(N\)-\(X\) criterion is widely used in the analysis of EPS operating modes, as it allows making a decision on the admissibility of a particular mode with the simultaneous disconnection of \(X\) elements of the electric grid, when in a normal scheme their number is equal to \(N\). In the calculations of the modes, the results of which are presented in this article, the \(N\)-\(1\) criterion was used, while the consequences of an emergency disconnection of one grid element were analyzed. If necessary, analysis could be carried out for the \(N\)-\(X\) criterion, when the simultaneous emergency disconnection of several grid elements at once was considered. Here is a detailed step-by-step description of the proposed algorithm, as well as the key features of its utilization:  
1. Before Step 1 of the algorithm, select a set of components of the studied EPS fragment: generators, \(G_{i}\), loads, \(P_{i\text{ load}}\), and network components, \(L_{n}\). Calculate the steady state for the studied fragment of the EPS to determine the possibility of its existence. 2. Step 1 of the algorithm implementation: 1. Identify the initiating emergency (single) disturbance, leading to the fulfillment of Inequality (1) for one or several network components by alternately disconnecting each generator, \(G_{i}\), load, \(P_{i\text{ load}}\), and network relative to the conditions of aperiodic static stability. 2.2. If, during the successive disconnection of each generator, \(G_{i}\), load, \(P_{i\text{ load}}\), and network component, \(L_{n}\), all steady-state calculations are performed and Inequality (1) is not satisfied, then, according to the N-\(1\) criterion, a cascading failure process for the given EPS power flows and network topology is impossible. The check according to the N-\(1\) criterion is completed. The second step of the algorithm is not required. 2.3. If, during the successive disconnection of each generator, \(G_{i}\), load, \(P_{i\text{ load}}\), and network component, \(L_{n}\), the check shows that at least one power flow is infeasible in terms of the conditions of static aperiodic stability, then, according to the N-\(1\) criterion, the power flow does not exist and it is not necessary to check for the possibility of a cascading failure process for a given EPS power flow and network topology in the second step. 2.4. If, with the disconnection of one of the generators, \(G_{i}\), loads, \(P_{i\text{ load}}\), and network components, \(L_{n}\), Inequality (1) is satisfied for one or several network components, \(L_{n}\), but the check according to p. 2.3 shows that the obtainedpower flow is infeasible in terms of static aperiodic stability, then, according to the N-1 criterion, a cascading process for a given power flow and network topology occurs in the first step. Since no power flow meets the conditions of static aperiodic stability, there is no need to check for the possibility of cascading failure process according to the N-1 criterion for a given power flow and network topology in the second step. * If, with the disconnection of one of the generators, \(G_{i}\), the loads, \(P_{i\text{ load}}\), and the network components, \(L_{n}\), Inequality (1) is satisfied for one or several network components, \(L_{n}\), and the check according to point 2.3 shows the feasibility of the obtained power flow according to the static aperiodic stability, then, according to the N-1 criterion, the cascading failure process is possible. Therefore, the check in the second step of the algorithm needs to be continued.