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The possibility of using the method of state variables for mathematical description of the dynamics of an autonomous power supply system is considered. The main advantages of using this approach are noted. The specifics of object construction presented in the form of discrete circuits and elements is taken into account. A system of state equations for the studied element of the system is presented having the form of a linear combination of state variables, input variables, and parameters of the element. The issue of controllability and observability of calculations is taken into account. An iterative calculation algorithm of transient voltage deviations is developed. [ABSTRACT FROM AUTHOR]