## 3 Results
A block diagram of the algorithm built to identify the possibilities of cascading failure processes and their development trajectories in the EPS for the N-X criterion is shown in Figure 1.  
We will present the findings from our analysis of the causes behind cascading failure processes and their development in several test schemes and one real-world EPS scheme. Figure 1: A block diagram of the algorithm for identifying the possibility of cascading failure processes and their development trajectories in the EPS for the N–X criterion. The test scheme (N nodes) was understood as a scheme that facilitated establishing the patterns of influence of the topology and parameters of network components on the cascading failure process development. The EPS schemes considered in the study were as follows:  
* The first test scheme contained a 110 kV distribution network (25 nodes), which is shown in Figure 2;
* The second test scheme contained a distribution network with voltage levels of 10, 35, and 110 kV with DG facilities (40 nodes, 67 branches), which is presented in Figure 3;
* The third test scheme contained a backbone 500 kV network (36 nodes, 60 branches). * The fourth scheme represented a real-world EPS scheme and described the sequence of disconnections for the network components during the cascading failure process development. Figure 2: The 110 kV distribution network (25 nodes): (**a**) the test scheme; (**b**) a graph of changes in currents in network branches during the cascading failure process development. The obtained patterns could be employed to analyze the schemes of various EPSs and their operating conditions. At the EPS nodes, one could set the required values of the generated powers (\(P_{i\text{ gen}}\) and \(Q_{i\text{ gen}}\)) and loads (\(P_{i\text{ load}}\), \(Q_{i\text{ load}}\)), as well as branch parameters (\(R\), \(X\), \(B\)) to change the network topology and adapt it to the required topology and operational conditions. The decentralization of energy is leading to a surge in the use of distributed generation facilities relying on both renewable energy sources (RESs), such as wind and solar power plants, and non-renewable energy sources, including gas reciprocating units, gas turbines, and diesel power plants [74; 75; 76]. This study performed a series of steady-state calculations for various topologies and operating conditions, in which the use of DG facilities was justified by the need to increase the survivability of the EPS. The first stage of the study involved modeling a cascading failure process for the scheme presented in Figure 2a, which consisted of seven steps, by making changes to the parameters of the network scheme. Figure 2b demonstrates histograms of currents for the EPS components: \(I_{\text{initial}}\) is the current in the network components in the initial conditions before the emergency disturbance, A; \(I_{\text{limit}}\) is the value of the current in the network component allowed in the event of emergency, A; and \(I_{\text{actual}}\) is the current in the network component under increased-load conditions, A. An initiating disturbance in the test scheme (Figure 2a) occurred in the form of a sharp increase in the load at node 23 from 52 + \(j\)26 MVA to 72 + \(j\)36 MVA, which caused overload in branch 18-23 (load 102.2%) and its disconnection. The parameters of branch 18-23 were set for the AC-70/11 steel-aluminum wire: \(R\) = 10.7 Ohm; \(X\) = 10.13 Ohm; and \(V\) = \(-\)255\(\cdot\)10\({}^{-6}\) Cm. The second stage of this study examined the feasibility of using DG facilities to increase the EPS survivability in the test scheme of the distribution network with voltage levels of 10, 35, and 110 kV (Figure 3). During the modeling, the power generation from the DG facilities (nodes 26 and 38--20 MW each; nodes 39, 40--10 MW each) enabled the prevention of a cascading failure process development in the EPS. These results proved the efficiency of using DG facilities.