Application of phase portraits for estimation of reactive power of electric circuits

Abstract

In this paper we consider the principal possibility of using the estimation of the reactive power of electric circuits by phase portraits of electric current oscillations. The shift of the phase angle of current and AC voltage oscillations relative to each other is displayed on the phase portrait of oscillations by bifurcation of the phase trajectory. The region described by the phase trajectory corresponds to the reactive power. Reactive power must be kept to a minimum to produce an energy efficient power supply. As an optimization criterion it is proposed to use the size of the phase portrait area of stationary oscillations of alternating current. Simulation of the optimization process was carried out on the basis of numerical solution of the system of differential equations using dynamic programming methods. Typical functions of numerical solution of systems of differential equations and optimization of the target function, available in mathematical packages, were used.