Research on coordinate transformation of the three-phase circuit

Abstract

The different three-phase circuit coordinate transformation matrixes are given in relevant literatures , which may cause some difficulties to understand and apply the coordinate transformation. The paper presents a general expression of the coordinate transformation matrixes in three-phase circuit and points out that the coordinate transformation matrixes having different specific expressions are due to existing the parameters which can be selected in the general expression. On this basis, the three often used expressions of coordinate transformation matrixes rotating at arbitrary speed are obtained through selecting these different parameters, which are Park transformation, orthogonal transformation and the coordinate transformation in the theory of instantaneous power. The paper further points out that, through particularly choosing coordinate rotation speed ,it can get commonly used special coordinate transformation matrixes between the three-phase stationary coordinate systems, and between the stationary coordinate system and synchronous rotating coordinate system by matrix general expression. The work of this paper shows that the three-phase circuit coordinate transformation matrixes are essentially uniformed, though their forms and practical applications are different, which is helpful to further understanding and correctly using the coordinate transformation theory of three-phase circuit. DOI: http://dx.doi.org/10.11591/telkomnika.v11i8.2268