Deriving the system equations of unbalanced two-phase induction motor

As there is no system driven especially for the two-phase induction motor fed from unbalanced two-phase supply yet, so we start for derivation the system equations for the said motor to be generally used even for the balanced or unbalanced two-phase supply. In this paper, we will derive a system equation starting from the sequence equivalent circuit for the forward and backwards equivalent circuits, then we will re-arrange the equations with some mathematical assumptions which will lead us to the new system equations. first for the voltage equations then for the current equations and finally for both power and torque equations. Moreover, we will put an example which will cover all cases with specific values and relations charts.