abc model of induction motor

The abc model expresses an induction motor in its original three-phase variables using phase voltage–flux equations with a rotor-angle-depen

The abc model of an induction motor describes the machine directly in the three-phase a ⁣− ⁣b ⁣− ⁣ca\!-\!b\!-\!ca−b−c variables by writing phase-domain stator and rotor voltage equations vabc=R iabc+dλabcdtv_{abc}=R\,i_{abc}+\frac{d\lambda_{abc}}{dt}vabc​=Riabc​+dtdλabc​​ (with rotor terms including speed-dependent coupling), where the flux linkages λabc\lambda_{abc}λabc​ come from a self/mutual inductance matrix that varies with rotor electrical position, capturing the rotating magnetic coupling without transforming to dq. The electromagnetic torque is computed from the energy/co-energy viewpoint, commonly using Te=12iT∂L(θ)∂θiT_e=\tfrac{1}{2}i^T\frac{\partial L(\theta)}{\partial \theta}iTe​=21​iT∂θ∂L(θ)​i. This model is especially good for transients and unbalanced or fault conditions, but it is computationally heavier than dq models because inductances depend on rotor angle.