*3.1. Parameter Values*

The parameter values for the case study are presented in Table 1. All the values for the reference single speed transmission are from the work of Vepsäläinen et al. [23], who developed a dynamic simulation model for the case study vehicle. The model has been validated previously based on measurements from multiple electric city buses operating in Finland. In the present work auxiliary power was discarded since it would make no difference for powertrain comparisons.

The motor efficiency map model was based on the work of Mahmoudi et al. [24] for PMSM motors. The map that was modeled based on their work was modified by changing the loss coefficients to match the specifications of the case vehicle, which has 180 kW maximum rating motor with 2000 Nm and 314 rad/s limits for torque and speed. Figure 4a shows the motor efficiency map and Figure 4b shows the inverter map. Appendix A presents the equations and parameters values for drawing the maps.



**Figure 4.** (**a**) Motor efficiency map; (**b**) Inverter efficiency map.

The potential of a multispeed gearbox to increase energy efficiency originates from the option to convert between torque and speed, which moves the motor operating point along a power level contour. The instantaneous motor torque and speed are determined by power demand, gear ratios, and gear selection. The advantage that comes from shifting the point along the curve depends on the efficiency characteristics of the motor and the inverter as well as the power level. Figure 5 shows efficiencies on four power levels for the case vehicle motor and inverter combination.

**Figure 5.** Combined efficiency of the motor and the inverter at different power contours.

The transmission and the gearbox efficiencies were assumed to be constant throughout the study. Efficiency of the reference transmission that was comprised of a differential and a final drive only was 0.95. Efficiencies of 0.99 and 0.95 were used for the two-speed and CVT gearboxes, respectively. The total efficiency of the transmission for the multispeed gearbox configurations was computed by multiplying the gearbox and the differential efficiencies. Due to the lack of experimental data that authors are aware of, the value of the shifting loss parameter *S* was set to zero.

### *3.2. Driving Cycle Data Acquisition*

The studied vehicle, shown in Figure 6a, was equipped with an online data acquisition system. Speed and GPS coordinate measurements, and the corresponding timestamps, were acquired from this system. The speed signal was obtained from the anti-lock brake system (ABS) sensors with 1 Hz sampling rate.

The suburban bus route examined is line 11 in Espoo, Finland, shown in Figure 6b. This 10.4 km line is a typical suburban bus line consisting of commutes between local business and residential centers, featuring short urban sections and periods with higher speed limits. The route includes a multilevel stack interchange, which causes the route profile and total distance to vary according to the direction of driving. All the cycles in line 11 considered in this work start from Friisilä terminus and end at Tapiola, excluding the drive from the terminus to the fast-charging station nearby. As all the cycles have the same direction, the distances are the same as well.

Suburban bus routes are characterized by a large variation in speed profiles between cycles due to daily and hourly passenger and traffic level variation. To account for this, the speed profile of the bus was measured in three distinctly different traffic intensity levels from the line 11. These cycles in line 11 in Espoo are denoted by the abbreviation E11 and extensions LT, MT, and HT are applied, respectively, for the low, medium, and high traffic instances. Two additional cycles are included for comparison. First, the standard Braunschweig bus cycle is commonly used in academic research and in emission testing. Second, a combined cycle E11-C, which has the three E11 cycles in consecutive order, was constructed. Table 2 shows the cycle features and Figure 7 shows the speed profiles.

**Figure 6.** (**a**) The case study ECB operating in Espoo, Finland; (**b**) The bus route 11 in Espoo. Map data is by OpenStreetMaps.


**Table 2.** Braunschweig (BR) and three Espoo 11 (E11) cycle characteristics.

**Figure 7.** Three measured driving cycles from Espoo line 11 and the Braunschweig standard reference cycle.

The altitude profile of the route E11 included a variation of 14 m between the extreme points, and a road grade change of at most one degree per meter. However, in this work the altitude changes were discarded.
