Coupled Finite Element and Extended-QD Circuit Induction Machine Model, Part I: Formulation

The design of squirrel-cage induction motors (IMs) entails the capability to predict the motor efficiency map with high accuracy over an operating range. In particular, modeling harmonic rotor bar currents becomes important for loss analysis. In theory, it is possible to analyze an induction motor using time-stepping finite element analysis (TS-FEA); however, this is not viable due to computational limitations. To bridge this gap, we set forth a computationally efficient method that couples magnetostatic FEA with a qd-circuit model of the cage. The proposed IM model includes the effects of saturation, winding and slot harmonics, as well as nonuniform current density distribution in the rotor bars. The model is presented in two parts. Part I focuses on the formulation of a qd cage circuit model with segmented bars. Part II is a companion paper that proposes an FEA-based parameter estimation and a solution method.