## 1 Introduction  
Despite the conventional structure of the Induction Motor (IM), the study of electromagnetic phenomena occurring in the machine is not immediate. For this reason, the most common way to obtain motor performance is using Time Domain (TD) Finite Element Analysis (FEA) [1]. The IM still plays an important role in the market, and accurate tools for its analysis and design are of great interest across industries [2, 3].  
To avoid a long computation time of time-stepping analysis, IM is often analyzed using the equivalent circuit [4, 5]. The FEA can improve the parameters estimation, considering the skin effect in the rotor bars, and the saturation of the magnetizing inductance [6].  
In this work, an accurate procedure is proposed: IM performance is derived by performing Magneto-Static (MS) FEA, in which both stator and rotor currents are imposed. In particular, the rotor current is computed connecting the FEA model with the inverse-\(\Gamma\) equivalent circuit, related to the Rotor Field-Oriented (RFO) model [7]. Basically, in the RFO analysis technique, stator and rotor \(d\) and \(q\) currents have to be imposed in order to verify the condition \(\lambda_{\eta}=0\), i.e., to reproduce the actual field distribution inside the machine and perform on-load MS simulations.  
These features are included in the method described in [8]; in this paper some improvements to the MS IM analysis are introduced together with practical application examples.  
In particular, the stray losses computation is not a trivial problem for the induction machine also supplied by a sinusoidal voltage source. In the classical FEA-augmented equivalent circuit, the iron losses resistance is derived by performing the no-load test in a single rotor position, taking the flux density peak value in the stator teeth and yoke.  
Furthermore, as far as the stray on-load losses are concerned, the classical methods neglect this effect or use an equivalent resistance based on measurements. The proposed technique also includes the computation of iron losses due to the stator and rotor slot harmonics, which occur both during no-load and on-load operations, by means of the element by element technique [9; 10]. Furthermore, the classical analysis does not consider the iron saturation due to the torque current, that can be serious during overload condition.  
The skewing effect is considered. The skewed motor is represented by a number of 2-D slices, each at a different axial position in the machine. The quantities (e.g., torque and fluxes) are computed for each slice independently and then summed [11; 12].  
In [11], a 2-D multi-slice model is presented for the skewing analysis, avoiding the whole 3-D problem. Each 2-D FEA problem is solved in the time domain, imposing that each rotor slot has the same current in the considered slices, leading to a very large FEA problem.  
In [12; 13], an alternative procedure is proposed, combining the analytical voltage equation of the considered machine with FEAs, used to upload, in each time instant, the inductive lumped parameters to the analytical model, considering the skewing.  
In this work, instead of TD analysis, MS problems are solved in each slice, since the rotor current has been already determined using the rotor field-oriented technique.