Three-phase distribution transformer connections modeling based on matrix operation method by phase-coordinates

This paper proposes a matrix operation method for modeling the three-phase transformer by phase-coordinates. Based on decoupling theory, the 12 x 12 dimension primitive admittance matrix is obtained at first employing the coupling configuration of the windings. Under the condition of asymmetric magnetic circuits, according to the boundary conditions for transformer connections, the transformers in different connections enable to be modeling by the matrix operation method from the primitive admittance matrix. Another purpose of this paper is to explain the differences of the phase-coordinates and the positive sequence parameters in the impedances of the transformers. The numerical testing results in IEEE-4 system show that the proposed method is valid and efficient.