**Nomenclature**



### **Appendix A**

This section presents the motor/generator and the inverter efficiency functions that were applied to compute the maps featured in Figure 4. Modelling of the motor/generator efficiency is based on the work in [24], but with substantially different parameter values due to the different motor characteristics.

Motor/generator efficiency is defined by:

$$P\_{m,loss}(\tau\_m, \omega\_m) = \sum\_{i=1}^{I} a\_i \left(\frac{|\tau\_m|}{\tau\_{m,max}}\right)^{m\_i} \left(\frac{\omega\_m}{\omega\_{m,max}}\right)^{n\_i} (P\_{base\\_loss} - b\_i) \tag{A1}$$

$$\eta\_m(\omega\_{m\prime}, \tau\_m) = \max \left\{ \eta\_{m,min}, \frac{\omega\_m \tau\_m}{\omega\_m \tau\_m + P\_{m,loss}(\tau\_m, \omega\_m)} \right\} \tag{A2}$$

where *ai*, *bi*, *mi*, *ni*, and *Pbase\_loss* are parameters in the motor power loss function *Pm,loss*(ω*m,* τ*m*). The max function in (A2) gives a lower limit η*m,min* of the motor/generator efficiency. In the numerical case study, the parameter ω*m,max* is 314, τ*m,max* is 2000, *Pbase\_loss* is 11000 and η*m,min* is 0.5. The other parameters that are indexed over *i* = 1 ... 10 are given in Table A1.


**Table A1.** Numerical case study parameter values for the motor power loss function.

The inverter efficiency is computed similarly as the engine/generator, but with only three terms in the weighted sum. The formulation is:

$$P\_{m,loss} \left(\tau\_{m}, \omega\_{m}\right) = \sum\_{i=1}^{I} a\_{i} \left(\frac{|\tau\_{m}|}{\tau\_{m,max}}\right)^{m\_{i}} \left(\frac{\omega\_{m}}{\omega\_{m,max}}\right)^{n\_{i}} \left(P\_{base\\_loss} - b\_{i}\right) \tag{A.3}$$

$$\eta\_{\rm{m}}(\omega\_{\rm{m}}, \tau\_{\rm{m}}) = \max \left\{ \eta\_{\rm{m}, \rm{min}}, \frac{\omega\_{\rm{m}} \tau\_{\rm{m}}}{\omega\_{\rm{m}} \tau\_{\rm{m}} + P\_{\rm{m}, \rm{loss}}(\tau\_{\rm{m}}, \omega\_{\rm{m}})} \right\} \tag{A4}$$

where *c1, c2* and *c3* are parameters of the power loss function (A3) and receive values 5 <sup>×</sup> <sup>10</sup>−4, 0.5 and 2.0, respectively, in the numerical case study. Additionally, the lower threshold of the inverter efficiency η*inv,min* is set to 0.8.
