The mathematical model of a synchronous machine developed by means of the authors' method of average voltages on an integration step is described. This model is formed in phase coordinates and takes into consideration non-linearity of a magnetization characteristic. The features of the mathematical model developed are high calculation performance and numerical stability that enables the developed model to be used for real-time modeling of complicated electrical power systems. The described mathematical model has been used as a part of the real-time mathematical model of the electric power generation system of South-Ukrainian Nuclear Power Plant. The computer simulation results are presented.

- O.G. Plakhtyna,
*Mathematical modeling of electrotechnical systems with semiconductor converters*. Lviv, Ukraine, 1986. (Russian) - А.S. Kutsyk, "The object-oriented mathematical model of a synchronous machine",
*Teoretychna elektrotekhnika*, no. 58, pp. 120 – 129, Lviv, Ukraine, 2005. (Ukrainian) - O.G. Plakhtyna, "The digital one-step method for simulation of electric circuits and its use in electromechanical tasks",
*Visnyk NTU "KhPI"*, nо. 30, pp. 223-225, Kharkiv, Ukraine. 2008. (Ukrainian) - O.Plakhtyna, A.Kutsyk, M.Malcev, and V.Chumak, “The analysis of dynamics of parallel operation of the South-Ukrainian Nuclear Power Station turbogenerators by using mathematical modelling method”,
*Elektromekhanichni i enerhozberihayuchi systemy*, vol. 19, no.3, pp. 342-344, Kremenchuk, Ukraine, 2012. (Ukrainian)