*2.2. Reference Time-Stepping Model*

All the results of the calculations presented in this work using the proposed approach were compared with the results of calculations using the complete model formulated in the time domain. The equations for such a model after discretisation via the Galerkin procedure and the implicit Euler method take the form of [31]:

$$
\begin{bmatrix}
\mathbf{S}(\mu\_{\rm DC}) + \mathbf{G}\Delta t^{-1} & -\mathbf{D}^{\rm T}\mathbf{K}^{\rm T} \\
 l\_{z}\mathbf{K}\mathbf{D}\Delta t^{-1} & \mathbf{K}(\mathbf{R} + \mathbf{L}\Delta t^{-1})\mathbf{K}^{\rm T}
\end{bmatrix}^{n}
\begin{bmatrix}
\boldsymbol{\Psi} \\
\dot{\mathbf{s}}\_{\rm S}
\end{bmatrix}^{n} = \begin{bmatrix}
\mathbf{G}\Delta t^{-1} & \mathbf{0} \\
l\_{z}\mathbf{K}\mathbf{D}\Delta t^{-1} & \mathbf{K}\Delta t^{-1}\mathbf{K}^{\rm T}
\end{bmatrix}^{n-1} \begin{bmatrix}
\boldsymbol{\Psi} \\
\dot{\mathbf{s}}\_{\rm S}
\end{bmatrix}^{n-1} + \\
+
\begin{bmatrix}
\mathbf{0} \\
\mathbf{K}\mathbf{e}\_{\rm S}
\end{bmatrix}^{n-1},
\end{bmatrix}
\tag{2}
$$

where: **S**—reluctivity matrix, **G**—conductivity matrix, **D**—matrix describing the winding, **K**—matrix describing the winding connection method, **R**—winding resistance matrix, **L**—winding leakage inductivity matrix, Δ*t*—time-integration step, ϕ—vector of nodal values of the vector magnetic potential, **iS**—vector of instantaneous values of the stator loop currents, **eS**—vector of the instantaneous supply voltages in the stator winding, *μDC*—DC magnetic permeability. The rotational movement was modelled using a simple and reliable moving band technique which is presented in detail in [32,33].
