**2. Machine Modeling**

Due to the double saliency of SRMs, the flux-linkage *λ*(*i*,*θ*), inductance *L*(*i*,*θ*), and torque *T*(*i*,*θ*) have nonlinear relations with current (*i*) and position (*θ*). Equation (1) shows the voltage equation. The electromagnetic torque of *kth* phase ( *Tk*) and the total electromagnetic torque ( *Te*) with *q*-phases can be represented by Equation (2). The mechanical dynamics is shown by Equation (3) [25].

$$\upsilon\_{k} = R i\_{k} + \frac{\partial \lambda\_{k}(i\_{k}, \theta)}{\partial t}; \quad \lambda\_{k}(i\_{k}, \theta) = \int (\upsilon\_{k} - R i\_{k}) \, dt \tag{1}$$

$$T\_k = \frac{1}{2} \frac{\partial L\_k}{\partial \theta} i\_k^2; \quad T\_c = \sum\_{k=1}^q T\_k \tag{2}$$

$$T\_c - T\_L = B\omega + J\frac{d\omega}{dt} \tag{3}$$

where *J* is the inertia, *B* is the frictional coefficient, *ω* is the rotor speed, and *TL* is the load torque.

The finite element method (FEM) is employed to generate the magnetic characteristics of the studied 8/6 SRM. The FEM data are used in form of look-up tables to build the machine model in MATLAB/Simulink [25]. The studied motor is 4 kW, 1500 r/min, 600 V, 8/6 poles, 4 phases SRM. The flux linkage and torque characteristics are shown in Figure 1a,b, respectively. These figures show only a few curves for simplification, while the complete flux and torque characteristics are calculated for current [0:1:50]A and position of [0:0.5:30]◦. The unaligned and aligned positions are defined by angle *θ*= 0◦ and angle *θ* = 30◦, respectively. As seen, both the flux and torque have highly nonlinear characteristics.

**Figure 1.** The finite element method (FEM)-calculated characteristics—(**a**) flux linkage and (**b**) torque.
