A three-phase comprehensive methodology to analyze short circuits, open circuits and internal faults of transformers based on the compensation theorem

Three-phase bus impedance matrix reveals some good potential in fault analysis in phase coordinates. In this paper, a comprehensive methodology is proposed to analyze a large variety of faults including short circuits in buses and lines, open circuits, open circuits with falling conductors and internal faults of transformer, separately or simultaneously, in unbalanced networks. Load effect is also considered. The methodology is based on the compensation theorem and Thevenin equivalent circuit which derives a fault side equation for each fault case. By combining the fault side and the network side equations, it replaces the fault side with equivalent injected current sources and calculates the voltage mismatch in every bus by using three-phase bus impedance matrix. A modified transformer model is also proposed to account for internal faults of transformer windings. The formulation is derived based on the initial three-phase bus impedance matrix and except for internal faults, there is no need to modify the impedance matrix during fault analysis which eliminates the demand for new factorization or inversion of a huge matrix. Moreover, a correction factor matrix is proposed which improves the results of a previous sequence component method in literature. The methodology is tested on IEEE 13-node and IEEE 34-node test feeders which are inherently unbalanced networks and it is implemented in MATLAB software.