**4. Results and Discussion**

The results of the simulations are first presented graphically for the reference and the two-speed gearbox case to illustrate optimal gear shift scheduling and efficiency improvement by motor and inverter operation point shifting. Then, differences in energy consumption between the reference and the two-speed gearbox and CVT alternatives are presented numerically to address the first research question. In the final section, a comparison of lifecycle costs of the powertrain alternatives shows that the two-speed gearbox is the cost optimal solution on the standard Braunschweig driving cycle.

Figure 8 shows the two-speed gearbox induced efficiency improvement in terms of motor operating points on the E11-MT cycle, which had the highest energy consumption on the Espoo 11 route. The most notable effect of the two-speed gearbox is that the operating points were shifted towards lower motor speeds and higher torques in the positive torque region. In the negative torque region during regenerative braking the full speed range of the motor was utilized. More generally, the operating point pattern variation between propulsion and braking is larger for the two-speed gearbox compared to the reference.

**Figure 8.** Comparison of operating points of the motor (E11-MT).

The Espoo 11 reference cycle is characterized by a high number of stops and subsequently a high number of acceleration and braking events. With the two-speed gearbox, regenerative braking is frequently executed with the first gear (high gear ratio) resulting in lower torque and higher speed of the motor compared to the second gear. This is evident from the negative torque region in Figure 8. Additionally, Figure 9 shows clearly that high gear ratios are favored for decelerations with both multispeed gearbox options.

Tables 4 and 5 show numerical values of energy consumption for each of the five studied routes, comparing the reference two-speed gearbox and CVT alternatives. The gear shift time limit parameter was set to one second in all the simulations that are reported in the tables.

**Figure 9.** Illustration of optimal gear ratio selection policy for the CVT (**a**) and the two-speed gearbox with five second minimum gap between changes (**b**). The speed profile is a 200 second section from the E11-LT driving cycle.

**Table 4.** Energy consumption advantage achieved with the two-speed gearbox in five driving cycles. All energy consumption related numerical values are reported in units of Wh/km.


**Table 5.** Energy consumption comparison between the CVT and the reference powertrains. Positive Δ*E* value represents consumption disadvantage with CVT.


With the two-speed gearbox the results show increased combined efficiency of the motor, inverter and the gearbox in all the E11 cycles, resulting in lower energy consumption. On the contrary, the CVT results in increased consumption in all the cases. Although the CVT reaches higher efficiency operating points of the motor and the inverter due to continuous gear ratio adjustment, this advantage is undone by the losses in the belt system.

Overall, the two-speed gearbox could improve energy efficiency by 2.0 to 3.2%, depending on the driving cycle and the powertrain characteristics. Energy consumption decreased most on the E11-HT cycle with the two-speed gearbox and inversely increased least with the CVT. This cycle has higher speed variation than the other E11 cycles. The Braunschweig cycle is also characterized by high speed variation and shows a significant 2.5% consumption decrease. On all the cycles the CVT performed worse than the two-speed option.

The difference in optimal gear ratios across all the cycles is small, with the optimal ratios found on the higher ends of the ranges for both the low and high gears on all the E11 cycles. Due to the optimal ratios located at the end of their ranges, the gap between the ratios is wide. Subsequently, the motor control needs to respond to large changes in the reference speed.

The relationship between the two-speed gearbox shifting time delay (gap) parameter *M* and the energy consumption is presented in Figure 10 for the E11-LT, E11-HT and Braunschweig cycles. The pattern is similar in E11-LT and E11-HT, showing consumption increasing roughly linearly with the shift gap values between 1 and 20 s. For the E11-LT cycle, all of the consumption advantage of the two-speed gearbox is lost when the shift gap value reaches 20 s. On the other hand, increasing the shift gap from one to ten seconds has only a marginal influence on the consumption with the Braunschweig cycle.

**Figure 10.** Energy consumption as a function of the minimum shift gap parameter value. The dashed horizontal lines represent the reference consumptions.

Table 6 shows the tradeoff between capital, operation and technology replacement costs. Only comparison between the reference single-speed and the two-speed option are shown, as the CVT didn't show any efficiency improvement. Importantly, the savings in charging cost and battery investment and replacement costs achieved with two-speed gearbox option exceed the increased investment cost of the transmission. The savings are distributed rather evenly between battery cost and charging cost.

**Table 6.** Comparison of lifecycle costs between the reference and two-speed gearbox vehicles for the Braunschweig cycle. Energy consumption advantage of the two-speed gearbox is translated proportionally to battery capacity and cost.


### **5. Conclusions**

The results of this work point towards a marginal potential of a two-speed gearbox utilization to improve ECB energy efficiency. The developed gearbox gear ratio and shifting policy two-level optimization model was found to be a practical and useful tool for vehicle powertrain design. The computational of the two-level optimization time was only a few seconds with a standard desktop computer for a typical 30 min driving cycle with one second time step duration.

The motor and inverter losses were found to depend on the driving cycle characteristics, and the simulation results suggest that powertrain efficiency was increased at higher power, which correlates with higher speeds and frequency of acceleration and deceleration events. On the other hand, utilization of motor and inverter operation point shifting along a power contour brings larger benefits on above average vehicle speeds when power demand is low instead of high. This is most evident in Figure 5, where the slope of the 20 kW power line is the steepest. The energy efficiency of an ECB can be improved with a two-speed gearbox, but the best utilization requires the consideration of the optimal motor-inverter-gearbox combination.

The PMSM motor in the case study vehicle was originally selected because it has high efficiency on a wide speed and torque range, which is useful when the power is transmitted through a single speed gearbox. However, a multispeed gearbox can favor other motor types, such as an induction motor, that have narrow high efficiency region, but lower capital cost than PMSM. Although the focus of the present work was energy efficiency, a two-speed gearbox also improves acceleration and top speed performance. A smaller motor could then be installed to the bus while retaining acceleration and top speed performance with the help of the two-speed gearbox. Further work is needed on the question of how the motor and gearbox interact in terms of selecting the motor design and power rating.

Innovations in gearbox technology, with respect to lower losses, would increase the attractiveness of the multispeed gearbox options for battery electric busses. This is evident from the large increase in motor and inverter efficiency with the CVT, which is then more than canceled out by the losses of the gearbox components. On the other hand, technology improvements in electric machines may lead to a more even efficiency throughout the motor operating region and thus reduce the potential to improve powertrain efficiency by operating point shifting. For instance, a prototype direct liquid cooled PMSM shows variation in efficiency that is at most only five percentage points between the extremes [27].

In translating the reported energy consumption advantages to real vehicles, the limitations of the modeling approach need to be considered. Lower efficiency of the multispeed gearbox options, both during continuous operation and shifting, compared to the single speed reference, influence the attractiveness of the gearbox alternative. Experimental tests, considerations on the increased complexity, and extending the scope of the analysis to reliability, serviceability, and compatibility are advised before final design decisions are made. In the end, the design decision comes down to the relative economic value of the alternatives. The increased efficiency with the multispeed gearbox options translate to lower electricity charging cost and battery investment cost but these advantages may be partially canceled by higher investment and maintenance costs.

Compared to light duty electric vehicles, ECBs have more consistent driving cycles, and the powertrains are dimensioned according to the nominal operation with only a small margin for excess performance. This results in higher overall powertrain efficiency because operating points are close to the motor and inverter maximum power rating, which provides the highest efficiency. Assuming similar main component selection, such as PMSM motor, it can be assumed that the results of the present work can be generalized to ECBs that operate in different, but similar urban routes.

Previous work on light-duty EV multispeed gearbox feasibility has found that the typical power demand in these vehicles is only around 10% of the maximum rating [28]. Optimal gear ratio selection and shifting of operation points in these low-power contours are different from the higher power region, which explains the results in the present work differ from similar work for light-duty vehicles, such as Nissan Leaf. This suggests that a separate analysis for different vehicle types and operating environments is required.

**Author Contributions:** Conceptualization, A.R., J.V., K.K., H.L. and K.T.; methodology, A.R., H.L. and K.T.; investigation, A.R.; writing—original draft preparation, A.R. and H.L.; writing—review and editing, A.R., J.V., K.K. and K.T.; supervision, K.T.; project administration, K.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors thank Linkker Ltd. for providing data for this study.

**Conflicts of Interest:** The authors declare no conflict of interest.
