## 3 Results
* If, according to the N-1 criterion, a cascading failure process for a given power flow and network topology occurs in the first step with the disconnection of different generators, \(G_{i}\), loads, \(P_{i\text{ load}}\), and network components, \(L_{n}\), i.e., for several options, and the check according to point 2.3 shows the feasibility of the obtained power flows in terms of static aperiodic stability, then, according to the N-1 criterion, the cascading process can develop along several trajectories. Consequently, it is essential to continue checking for the possibility of cascading failure process development in the second step along all the identified trajectories. * To prepare for the second step of the algorithm, if the conditions of point 2.5 are met, identify components for which Inequality (1) is satisfied in the first step from the list of generators, \(G_{i}\), loads, \(P_{i\text{ load}}\), and network components, \(L_{n}\). If the cascading process develops in accordance with point 2.6 along several trajectories, then for each trajectory, determine its list of network components. * The network components, \(L_{n}\), for which Inequality (1) is satisfied are considered disconnected in the next step of the algorithm. * In each subsequent step of the algorithm, perform all actions following the recommendations of points 2.1-2.7. * In each \(i\)-th step of the algorithm, if, during the implementation of points 2.4 and 2.5, the calculations indicate that power flow is inadmissible in terms of the static aperiodic stability, then, following the N-1 criterion, the cascading failure process for the given power flow and network topology exists up to the \(i\)-th step. Starting with the \(i\)-th step, however, the power flow does not exist according to the conditions of static aperiodic stability. Therefore, there is no need to further check for the possibility of cascading failure process development in step \(i+1\). This is because along this trajectory, the cascading failure process ends with a loss of stability, and hence, it is inadmissible. * If point 5 is fulfilled in the first step of the algorithm or Inequality (1) is not satisfied for each of the network components \(L_{n}\) in the first step of the algorithm, then, following the N-1 criterion, there are no conditions for the occurrence of a cascading failure process for the given power flow and network topology. * If in the \(i\)-th step of the algorithm, during the implementation of points 2.4 and 2.5, the power flow is admissible in terms of the static aperiodic stability, then, according to the N-1 criterion, the cascading failure process for the given power flow and topology exist before the \(i\)-th step. If, at the same time, in step \(i\), no network components \(L_{n}\) for which Inequality (1) is satisfied are identified, then it is not necessary to check for the possibility of cascading failure process development according to the N-1 criterion for the given power flow and network topology along this trajectory in step \(i+1\). Thisis because the cascading failure process ends with an admissible post-contingency power flow. Based on the experience of analyzing steady-state calculations, an algorithm was designed to identify the trajectories of the cascading failure process development for the N-X criterion. For a cascading failure process to develop, the EPS at hand must have the following characteristics:  
* The EPS operation must continue in more than one step after an emergency disturbance from the limit power flow in terms of static aperiodic stability;
* The non-homogeneity of the network parameters must be such that in the event of an emergency disturbance (disconnection of generating equipment, network component), a surge in the current \(\Delta I_{ij}\) occurs in the next component, resulting in the current exceeding the limit admissible for emergency and causing its disconnection.