In a constantly and rapidly changing global environment, one of the main priority tasks for every country is preserving, maintaining, and operating an independent and individually robust and stable energy system. This paper aims at researching electrical power systems’ (EPSs) behavior during desynchronization from a synchronous area, its stability in islanded mode, and its synchronization. The analysis of EPS behavior was accomplished utilizing numerical simulations in a widely used programming/simulation package. The sudden tripping of the EPS into an isolated island mode with known generation and load values was simulated, analyzed, and discussed. We investigated the behavior of an isolated EPS in the case of the loss of a certain amount of active power, and determined the maximum power that must be available to ensure the reliable operation of the isolated EPS and the power reserve that must be maintained to prevent the EPS from triggering UFLS. The simulation of the synchronization of an isolated EPS with a synchronous area was accomplished and analyzed. The obtained results were applied to reveal the sequence of actions that will help an EPS to ensure and maintain the stable and reliable operation of electrical installations during desynchronization.