*Article* **Accounting for Slot Harmonics and Nonsinusoidal Unbalanced Voltage Supply in High-Speed Solid-Rotor Induction Motor Using Complex Multi-Harmonic Finite Element Analysis**

**Tomasz Garbiec \* and Mariusz Jagiela**

Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, ul. Proszkowska 76, 45-758 Opole, Poland; m.jagiela@po.edu.pl

**\*** Correspondence: t.garbiec@po.edu.pl

**Abstract:** Solid rotor induction machines are still used in high-speed systems. A two-dimensional field-circuit model based on the finite element method and the complex magnetic vector potential has been shown as a very time-effective tool in the analysis of their steady states compared to timedomain models. This continuation work presents a validated computational algorithm that enables the inclusion of the nonsinusoidal and/or asymmetrical voltage supply in the multi-harmonic field-circuit model of these machines that was presented in the previous works by the authors. The extended model accounts for both spatial harmonics due to slotting and/or winding distribution and the time-harmonics due to voltage waveform. The applicability range of the model therefore increases to cases when the machine is supplied with a nonsinusoidal three-phase system of voltages with symmetry or asymmetry that can be decomposed into three symmetrical components. Its short execution time characteristic allows for much more insightful design studies of the contribution of voltage supply- and slotting-related harmonics to the overall efficiency of the machine than is possible with the time-consuming time-domain models. The proposed computational framework has never been presented in the literature. The model is verified positively by the comprehensive time-domain model. It is especially useful in design studies on solid rotor induction motors related to the optimisation of the efficiency of induction motor-based drive systems.

**Keywords:** induction motor; solid rotor; effective parameters; finite element method
