Research on Coordinate Transformation of the Three- phase Circuit

Abstract The different three-phase circuit coordinate transformation matrixes were given in relevant literatures, which might cause some difficulties to understand and apply the coordinate transformation. The paper presented a general expression of the coordinate transformation matrixes in three-phase circuit and pointed 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 were 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 pointed 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 showed that the three-phase circuit coordinate transformation matrixes are essentially uniformed, though their forms and practical applications are different, which was helpful to further understanding and correctly using the coordinate transformation theory of three-phase circuit.