A Mathematical Description of Dynamic Modes of Operation of the Autonomous Power Supply System in the Presence of Nonlinear Elements in Its Composition

Methodological provisions for studying transient processes in the systems of autonomous power supply with a chemical current source are considered in the presence of nonlinear elements in the voltage control system. The method of statistical linearization has been used to study the dynamics of this system. The equivalent circuit of the system and the mathematical apparatus that allows one to determine the statistical amplification coefficients have been suggested. The stationary random process to change power consumption from the power supply is represented as a mathematical expectation and a decreasing correlation function, and the electrochemical cell in the transition mode at the section a slow change in the output coordinate is considered as an aperiodic link of the first order. Two methods to solve the obtained system of equations, which describes a change in the voltage at output of an electrochemical cell, have been suggested: the method of successive approximations and the graphical method. An example of calculation of the transient process of an autonomous power supply system with an electrochemical cell has been considered.