Principles of measuring power components in a three-phase three-wire unbalanced circuit in light of the CPC theory

Abstract

The article presents an analysis of a three-phase electric circuit in terms of describing the power components measured and determined on a three-wire line connecting an unbalanced power source with periodic, non-sinusoidal waveforms with an unbalanced receiver. In this study, the case was considered when the load admittance changes its value when the direction of rotation of the symmetrical voltage and current components is changed. This is a typical situation where three-phase power must be measured on a three-wire line connecting a real source to a load that contains three-phase rotating machines. In real systems, such machines often change their current/voltage relationship when the direction of rotation changes. This paper presents a modification of the currents’ physical components (CPC) power theory to decompose currents and powers into symmetrical components. This constitutes the theoretical framework of this study. Using the determined dependencies, it is possible to develop a new measurement algorithm. As a result of these measurements, it is possible to determine the electromechanical efficiency of the rotating machine, i.e., the efficiency that does not take into account the influence of higher harmonics and power source asymmetry. This is important information needed to optimise the active power consumption of electromechanical machines. Measurement of active power using classical methods does not allow one to observe the influence of supply voltage asymmetry on the power that affects active conversion to mechanical power. Thanks to such measurements, it is possible to select optimal parameters of the electric motor in order to improve the efficiency of converting electrical energy into mechanical energy. In this approach, the asymmetry of the power supply and the introduction of higher voltage harmonics are perceived as external interferences in the optimisation process. This fragment of the article constitutes the practical side, i.e. the application of the theoretical considerations derived. In the presented calculation example, it was shown that the efficiency of the machine strongly depends on the asymmetry of the voltage source, and less on the harmonics.