Application of Vyshnegradky's diagrams for transient analysis in electric discharge installations with stochasticload

Abstract

Purpose. To analyze the transient processes in the discharge circuit of reservoir capacitor of electric discharge installationsat a change in the circuit configuration duringthe discharge as well as to determine the appropriate circuit parameters for which the discharge process described by the third-order differential equation remains a dampedoscillatory process. Methodology. We have applied the concepts of theoretical electrical engineering, the principles of theory of electrical circuits, theory of automatic control systems and mathematical simulation in the software package MathCAD 12. Results. We have obtained the analytical expressions and graphical dependenciesthat allow us to determine a relationship between the value of the element parameters of the discharge circuit of installations with anadditional active-inductive chain and the character ofthe transient discharge process without solving a third-order differential equation. Originality. Using Vyshnegradsky's criteria and their graphical representations in the form of diagrams,we have proposed the procedure for determining the inductance value in additional chain shunting the capacitor of electric discharge installation in order to avoid the undesirable aperiodic discharge transient process in the stochastic load. Practical value. The use of this approach makes it possible to determine the ranges of the expedient change in the additional inductance at different load resistances for the realization of transient process required by the technology – the oscillatory discharge of the reservoir capacitor trough the load.