Symmetrization of asymmetrical three-phase systems with periodic nonsinusoidal voltage source taking their inner impedances into consideration

Abstract

The purpose of this paper is to present the principles of symmetrization of a system supplied from three-phase periodic nonsinusoidal voltage source with asymmetrical phase impedance. Symmetrization of the system is achieved by means of connection of the symmetrization system composed of LC two-terminal networks. Their structure will be determined as a result of proper synthesis process [1, 2, 4]. In the paper, the system including three-phase asymmetrical star connected load (Fig. 2) has been taken into account. It is assumed that voltage source has the inner asymmetry impedance, i.e.: ЛZaah ^ Zbbh Ф Zcch and asymmetrical load is described by non-singular full matrix of admittance Yh for the considered harmonics. If the system works without symmetrization its line currents ia,ib,ic are asymmetrical. With the proper symmetrization network currents become symmetrical and their RMS values and active power on source impedances become lower, but the source generates the active power P2 >P1. Deformation of currents of separate phases of the system is reduced, where as the generally understood source power factor is increased. The solution of presented problem may be obtained by means of solving the optimization problem determining the proper purpose function or by means of symmetrical components theory. In this paper the symmetrization problem has been solved by using the symmetrical components theory and compensation of reactive power for each of voltage harmonics under consideration.