*2.8. Copper Losses*

Copper losses value depends on phase current, which is determined by the control technique. When considering that *Nph* is number of phases, *Rj* is phase dc resistance, and *Ij* is phase current, the total copper loss instantaneous value may be calculated by the equation:

$$P\_{cu}(t) = \sum\_{j=1}^{j-N\_{ph}} I\_j^2(t) R\_j \tag{7}$$

The average copper losses can be calculated by equation:

$$P\_{\rm cu} = \frac{1}{T} \int\_0^T P\_{\rm cu}(t)dt,\tag{8}$$

where *T* is the period of time for *Ps*/2 strokes. For sake of simplification, we assume no overlap between phases. Because the current of phase is not pure dc. The peak value of it (*Ip*) is considered for copper losses calculation as a pessimistic prediction. Copper loss is then calculated straight forwardly by the equation:

$$P\_{\rm cu} = I\_p^2 R\_{ph} \tag{9}$$

## *2.9. Eddy Currents Losses*

Referring to [35], the eddy current losses in SRM can be calculated by the equation:

$$P\_t = \frac{c^2}{4k\_{cir}\rho\_{fc}\delta} \frac{1}{T} \int (\frac{\partial B}{\partial t})^2 dt \,, \qquad w/kg \tag{10}$$

where *e*: sheet thickness in meter, *kcir*: constant (1 < *kcir* < 3) introduced to account for the fact that paths in the interior of the lamination will have smaller emfs than those that are near the surface; *ρf e*: the electrical resistivity of the ferromagnetic material (in Ω*m*); *δ*: density of the ferromagnetic material (in kg/m3).

From Equation (10), the waveform of flux density (*B*) for all SRM sectors must be known. Once they are available, *Pe* is calculated by numerical integration and differentiation. There are a lot of methods to obtain these wave-forms and many of them are time consuming. In [34], a mathematical method using matrices is introduced in order to obtain the wave-forms of all the SRM sectors in a systematic manner. The calculation of *B* wave-forms for all sectors is achieved by the modulation of triangular pulses. The stator poles wave-forms only consist of unipolar triangular pulses, while those of the rotor poles contain both positive and negative pulses. The stator and rotor yoke wave-forms have a

more complicated relationship with the triangular pulses. This method is demonstrated in details in [34] and then used here for 8/6 and 6/4 SRMs.
