Complex vector model of the squirrel-cage induction machine including instantaneous rotor bar currents

In this paper, a new detailed mathematical derivation of the squirrel-cage induction machine d-q model is introduced, The model is based on coupled ma gnetic circuit theory and complex space-vector notation and takes into acco unt the actual nonsinusoidal rotor bar distribution, It is shown for the fi rst time that, given the structural symmetry of the induction machine, both stator and rotor circuits can be modeled by the simple set of only four co upled differential equations, i.e., the d-q model. More importantly, the nu mber of equations does not depend on the number of rotor bars, and the mode l is valid even if the number of bars per pole is not an integer number, Th is enormous simplification is achieved without loss of generality nor loss of any information contained in the full set of equations, and it is valid for any operating condition. The actual n rotor bars and end-ring currents are fully included in the model, and they are obtained directly by using a simple vector transformation, In addition, the three-ph rotor equivalent pa rameters are obtained. Second-order effects; such as Skin effect in the rot or bars, can be taken into account by simply modifying the bar and end-ring resistance values. An equivalent circuit based on the model is also derive d.