In this article, in conditions where environmental deterioration and energy shortages are observed throughout the world, a mathematical model for improving and developing new types of synchronous generators for low-speed wind power plants and micro-hydroelectric power plants is developed free of charge extraction of running water and simulation processes. As a result of mathematical and simulation modeling of a synchronous generator, it is based on the analysis of electromagnetic processes and the study of improvement issues to ensure its efficient operation at low speeds. In mathematical modeling, the electromagnetic processes of a low-speed synchronous generator were analyzed using mathematical equations. For this purpose, mathematical and simulation models of an improved generator designed for low speed were developed and research was carried out. The article creates a mathematical model based on the Park-Gorev equations of asymmetric modes of a synchronous generator designed to generate electricity from low-speed wind and freely flowing water. The mathematical model of the generator was expressed in the Simulink package and a simulation model was built, research was carried out and characteristics were obtained.