Thesis (M.Eng., Electrical and Computer Engineering) -- University of Idaho, December 2014 | This thesis developed a topology-based model for two-winding, shell-type, single-phase transformer inter-turn faults. The principle of duality between the electric and magnetic equivalent circuits is concisely explained. The magnetic equivalent circuit of a two-winding, shell-type, single-phase transformer is extended to the magnetic circuit with an inter-turn fault. The model is implemented into the Alternative Transients Program (ATP/EMTP) using ATP components. While the developed model is for single-phase transformers, extending it to topology-based, three-phase, three-legged and five-legged transformers are straight forward. Based on basic electric theory, the thesis also derived equations for direct solution of the transformer inter-turn fault. This may find its important usage in transformer relay protection. The thesis discussed using PSPICE for the solution of transformer inter-turn fault as well.