Instantaneous single-phase system power demonstration using virtual two phase theory

Abstract

The paper deals with the virtual approach and application of orthogonal transform theory, used for ordinary single-phase system to its transformation into equivalent two-axes system. It is well known that the analysis of multiphase systems can be more simple using the Park/Clarke transform into two-axis stationary (alpha, beta) or rotary (d, q) reference frame. The above transform can be used for electrical machines as well as for power electronic systems. The projection of time state-space vector for any quantity of symmetrical three-phase system in Gauss complex plane (alpha + jbeta) shows out six-side symmetry of vector quantity trajectory. Then, analysis of such system can be focused on the interval equal to 1/6 of the time period only. It is clear that when using similar transform of single-phase quantity into equivalent two-axes orthogonal system it will be possible to use all advantages as in three-phase transformed system with respect of 4-side symmetry instead of 6-side of previous case. Analysis in such orthogonal coordinates system will then be identical to the three-phase one under Park/Clarke transform, including determination of instantaneous reactive power. The presented method creates a virtual two-phase system from the original singlephase system by adding a new fictitious phase. The new thought is based on the idea that ordinary singlephase quantity can be complemented by virtual fictitious phase so that both of them will together create orthogonal system, as is usual in three-phase systems. Application of above-mentioned theory makes it possible to use complex methods of analysis as instantaneous reactive power method. Both, the active and reactive powers can be determined by this way. Practical application of the method is outlined for the case of active and reactive power determination for single-phase power active filter, unified power flow controller, and dynamic voltage restorer, Fig.1 [14], [15], [17] - [19].