On the periodic steady-state analysis of induction machines interfaced through VSCs using the Poincaré map method and a Voltage-Behind-Reactance model

•The most efficient method to date to determine periodic solutions of three-phase induction machines is presented.•It consists on the amalgamation of the Poincaré map method and a Voltage-Behind-Reactance representation.•A per-unit VBR model, tailored to the Poincaré map method, is developed.•Harmonic analyses for the operation of a PWM inverter and an unbalanced supply condition are presented.•Speed up gain of 100% compared to the classical phase coordinates model is reported.

This paper presents the most efficient method to date to determine the periodic steady-state solution of three-phase induction machines based on the amalgamation of the Poincaré map method and the so-called Voltage-Behind-Reactance (VBR) representation. An acceleration procedure based on the discretization of the dynamic equations with the Poincaré map and the application of Newton’s method allows locating periodic solutions. A per-unit VBR formulation, suitable for the Newton-based acceleration procedure, is used in this paper to ensure highly efficient solutions. To test further the robustness and versatility of the per-unit VBR model, it is interfaced to a voltage source converter (VSC) and the results show that the high efficiency of the new model remains unabated – this applies to both small and large induction machines. The method is particularly useful to carry out harmonic-oriented analyses where the computational effort reduces dramatically compared to cases when more traditional induction machine models and solution approaches are employed.