*2.9. Hysteresis Losses*

Referring to [18], the hysteresis losses can be calculated for various sectors of SRM using the following equations:

$$P\_h = P\_{sph} + P\_{rph} + P\_{sph} + P\_{rph} \tag{19}$$

$$P\_{sph} = \frac{\omega}{2\pi t} P\_s P\_r \mathcal{W}\_{sp} E\_h(0, B\_{spm}) \tag{20}$$

$$P\_{rph} = \frac{\omega}{2\pi} P\_r P\_s \mathcal{W}\_{rp} \left[ \frac{h\_{rph}}{2} E\_h (-B\_{rpm}, B\_{rpm}) + (1 - h\_{rph}) E\_h (0, B\_{rpm}) \right] \tag{21}$$

$$P\_{\rm sym} = \frac{\omega}{2\pi t} P\_{\rm s} P\_{\rm r} N\_{\rm ph} \mathcal{W}\_{\rm sy} \left[ \frac{h\_{\rm syl}}{2} E\_{\rm h} (-B\_{\rm sym}, B\_{\rm sym}) + (1 - h\_{\rm syl}) E\_{\rm h} (B\_{\rm sy0}, B\_{\rm sym}) \right] \tag{22}$$

$$P\_{rph} = \frac{\omega}{2\pi} P\_r^2 N\_{ph} \mathcal{W}\_{ry} \left[ \frac{h\_{rph}}{2} E\_h (-B\_{rym} B\_{rym}) + (1 - h\_{rph}) E\_h (B\_{ry0}, B\_{rym}) \right],\tag{23}$$

where :

$$E\_h(-B\_{\max}, B\_{\max}) = \mathcal{C}\_h f B\_{\max}^{\left(a+bB\_{\max}\right)} \tag{24}$$

$$Or\ E\_h(-B\_{\max}, B\_{\max}) = aB\_{\max} + bB\_{\max}^2. \tag{25}$$

Referring to [14], the second formula is used and the constants *a*, *b* are −4.6445 × <sup>10</sup>−3, 0.01652 respectively. The rest of symbols are shown in Table 3.

The flux density waveforms depend on the phase current waveform and the speed of the motor. Flux density waveforms calculated in this paper rated the speed of 1000 rpm and control is by a single pulse voltage. Hence, it is expected that the resulted designs will have maximum efficiency at 1000 rpm and rated torque average. Note that phase current has the peak of 6 ampere for all SRMs candidates.


**Table 3.** Symbols in Equations (19)–(25).

#### **3. SRM Design Optimization Techniques**

The optimization is a search problem that seeks better objectives. One of the most popular techniques is the genetic algorithm. Wherein, better generations are produced by crossover between the best individuals of the previous generation. To make a decision which is the best, the objective of the optimization problem is needed to be defined. There are two types of optimization, single objective and multi-objective optimization. The decision making criteria is then different, in single objective optimization the criteria is to choose the greater value in the maximization problem to be the best (the smaller for minimization problem). At the end, the best value is considered as the optimal solution .

In the optimization of SRM ,the dimensions in Table 1 represent one possible solution (individual). All individuals information are stored in a vector in suitable data structure.
