The Analytical Method of Calculating the Transient Process in the Circuit's with Distributed and Concentrated Parameters

In the paper is substantiates the methodology of calculation of the transitory process in the electrical circuit, which including of portions with distributed parameters and concentrated parameters. The purpose of this paper is to obtain and analyze the precise analytical solutions of the current and voltage wave propagation processes in the nonhomogeneous electrical circuits with the multiple reflections. The calculation of voltage and current in line and load is done using partial derivative equations. These equations are transformed into equations with the single variable by using of additional functions, which are Riemann invariants. The initial and limit conditions were formulated. The algorithm for calculating Riemann invariants has been proposed. These invariants are used to solve the Cauchy problem. Was the obtained of the general solution for calculating the current and voltage at the input and at the end of the line for different values of the active, inductive and capacitive components of the complex load. The solution elucidates the multiple reflections effect of the current and voltage waves in the examined circuit. Results of the calculation of the dynamic regime in the analyzed circuit are presented. The phenomenon of continuous energy accumulation in the inductance at the end of the line has been detected. This is possible in the wave propagation regime in the portion circuit with the distributed parameter's. This regime can be used to store energy in inductivitie with superconductivity. Analytical solutions can serve as standard solutions for verifying precision, for example, of the numerical solutions.