This paper is devoted to the development of a model of an autonomous electric power system to study random processes of voltage, current and power changes in emergency and dynamic operation modes. A diagram for calculating short-circuit currents has been presented, which was focused on a typical wide range of autonomous power plants with three diesel generator units. A model of an autonomous power plant has been developed, allowing to solve the assignments of determining short-circuit currents and starting currents of electric power machines. The equivalent network of the studied power system for transient calculations has been presented. Thus, the voltage waveforms have been obtained. A comparative assessment of theoretical calculation methods and simulation analysis demonstrated a high degree of accuracy of the simulation results. The use of approach suggested in the article and the developed model allows to increase the accuracy of conclusions when testing the abruptly variable processes and to make the most reasonable choice of measures to improve the quality of electricity and the reliability of electrical equipment. In particular, simulation analysis and obtaining transient curves for starting powerful consumers allow more accurately choose the type of circuit breakers used and the related configuration parameters.