This paper presents a new method to model healthy and faulty wound-rotor induction machines (WRIMs) with and without inter-turn short circuit fault by a single set of equations. The model is presented for a machine with arbitrary pole, and rotor and stator slot numbers. A single set of equations, including both electric and magnetic parts, is solved to obtain full dynamic behavior of the machine. Therefore, the modified magnetic equivalent circuit with non-linear elements is used for modeling and a numerical technique is employed to solve the non-linear equations. The proposed modified method has a simple calculation procedure in comparison with the conventional magnetic equivalent circuit method. Solving the electric and magnetic equations by a single set of equations is the main advantage of the presented method, which is proposed for a WRIM machine, for the first time. In addition, to increase the accuracy, the saturation phenomenon is also considered in the model. Due to the saturation effect, there are some non-linear algebraic magnetic equations, which should be simultaneously solved with differential equations. A trapezoidal technique is used to convert differential equations to algebraic ones. To solve the non-linear equations, non-linear equations, Newton Newton–Raphson method is employed. Current signature analysis is used for rotor and stator inter-turn short circuit fault detection. Finally, the finite-element method is used to verify the effectiveness of the proposed modeling method. It is worth noting that the proposed method can model a healthy and faulty machine with different faults by a single model. [ABSTRACT FROM AUTHOR]