Powertrain Optimization for Electric Buses under Optimal Energy-Efficient Driving

State of the art powertrain optimization compares the energy consumption of different powertrain configurations based on simulations with fixed driving cycles. However, this approach might not be applicable to future vehicles, since speed advisory systems and automated driving functions offer the potential to adapt the speed profile to minimize energy consumption. This study aims to investigate the potential of powertrain optimization with respect to energy consumption under optimal energy-efficient driving for electric buses. The optimal powertrain configurations of the buses under energy-efficient driving and their respective energy consumptions are obtained using powertrain-specific optimized driving cycles and compared with those of human-driven unconnected buses and buses with non-powertrain-specific optimal speed profiles. Based on the results, new trends in the powertrain design of vehicles under energy-efficient driving are derived. The optimized driving cycles are calculated using a dynamic programming approach. The evaluations were based on the fact that the buses under energy-efficient driving operate in dedicated lanes with vehicle-to-infrastructure (V2I) communication while the unconnected buses operate in mixed traffic. The results indicate that deviating from the optimal powertrain configuration does not have a significant effect on energy consumption for optimized speed profiles; however, the energy savings from an optimized powertrain configuration can be significant when ride comfort is considered. The connected buses under energy-efficient driving operating in dedicated lanes may reduce energy consumption by up to 27% compared to human-driven unconnected buses.


Introduction
Current road-based transport systems are dominated by combustion vehicles, which have a major impact on energy consumption, air pollution and greenhouse gas emissions. In Singapore, transportation is responsible for 17.6% of the total energy consumption, of which around 90% is obtained from petroleum products [1]. Though 15% of all transportation carbon emissions in Singapore are produced by buses [2], they make up only 2% of all vehicles on the road [3]. This means that even small improvements in the energy efficiency of buses may have a significant impact on overall emissions. Technological improvements in the field of alternative power sources, driving assistance and intelligent control have the potential to reshape the environmental profile of the current transportation systems.

Vehicle Speed Optimization
The speed profile of the BEV is optimized for minimum energy consumption using a DP algorithm [35]. The problem is formulated as: where x k is the system state, which consists of the vehicle speed and time from the starting point; T k is the control input, which corresponds to the traction torque at the wheel; and the subscript k represents the discrete distance from the starting point. The problem is defined in the spatial domain, since the boundary conditions along the route, such as traffic lights and speed limits, are distance-based characteristics. The solution of the problem finds the torque control strategy that minimizes the total consumed energy E, while considering the boundary conditions for the state and control variables. The calculation of the energy consumption is based on a longitudinal vehicle simulation. First, the traction torque is discretized between two torque limits. The discretization at the traction torque level was used to achieve the same discretization for different gear ratios. Subsequently, for all torques, the resulting vehicle acceleration is calculated using Equation (2).
where a k corresponds to the acceleration, r tire is the tire radius, m is the vehicle weight and F drag , F roll and F slope correspond to the vehicle drag, roll and slope resistance, respectively. The resistance forces are calculated based on the equations given in [36] with constant drag coefficients. Based on the derived acceleration, the new state variables are calculated with Equations (3) and (4), where v corresponds to the vehicle speed, s is the distance from the start and t is the time from the starting point.
The motor torque T M and motor speed n are calculated based on the gear ratio i and its efficiency η G by Equations (5) and (6). Even though the efficiency of a gearbox is dependent on speed and torque, an assumption of a constant efficiency is reasonable [37]. Traction Finally, the energy consumption to move to the next state is calculated using Equation (7): where η is the motor efficiency derived from the motor map for the current load point. The optimal control strategy for the traction torque can then be found by implementing an optimal path search, which is evaluated backwards at discrete distances s k . The algorithm is implemented in MATLAB in a vectorized form to improve computation time. Its main sequence is similar to [38].

Ride Comfort Evaluation
Since lack of comfort is not penalized, the optimization algorithm may lead to uncomfortable speed profiles due to P&G. The optimal controlled vehicle may oscillate around a certain speed, which may result in a jagged speed profile. Ref. [11] showed this effect for light vehicles with combustion engines and smoothed the speed profile with an added term in the cost function. To gain more comfortable and thereby realistic speed profiles and determine the effects of comfort on the powertrain configuration and energy consumption, further optimizations are conducted with a modified cost function (Equation (8)). With the weighted sum method [39], multiple objectives can be reduced to one scalar value. Similar to [11], who used weighted penalty for acceleration, the new cost function, given in Equation (9), penalizes jerk, whereas j represents the jerk.
The weights and exponents of the cost function have been selected based on iterative simulations of speed profiles for all motor types and gear ratios to reduce P&G while leaving enough freedom to save energy due to gliding. The first term minimizes the jerk in general. The last term penalizes the jerk values over 1. Values were set to c 1 = 9 · 10 6 and c 2 = 10 10 . Other similar approaches using the weighted sum method can be seen in [40,41]. To find the global optimal solution, the DP algorithm would require acceleration as an additional state. As this would increase the computation time to a great extent, another approach was chosen. The acceleration of the optimal control at s k is saved. At s k−1 , the control vector is applied for all discrete points and the jerk is calculated by Equation (10).

Derivation of Boundary Conditions and Discretization
To find the optimal control strategy for the motor torque and the corresponding speed profile for a given route, the boundary conditions along the route need to be taken into account, i.e., speed limits, permitted cornering speed, traffic lights, stops and the total available time to complete the route.
The speed of the vehicle on straight segments of the road is capped at speed limits, while the maximum speed at the turns is calculated using Equation (11), with a lat,max describing the upper bound of comfortable lateral acceleration and r corner the cornering radius. Additionally, longitudinal acceleration is limited to 1 m/s 2 to ensure comfort. As an example, the resulting speed boundary profile is shown for a 3000 m stretch of a bus route with eight stops and eight turns in Figure 1a.
v corner = √ a lat,max r corner (11) The lower and upper time bounds are calculated by Equations (12) and (13), respectively, where t k,min is the lower time bound, t k,max is the upper time bound, v k,max refers to the upper speed bound based on the acceleration limit, t end is the maximum time to complete the route and t dwell is the dwelling time at the stops. The maximum time to complete the route and the dwelling time are based on actual bus operation data. Subsequently, the effect of traffic lights on the obtained upper and Energies 2020, 13, 6451 6 of 19 lower time bounds is incorporated. Traffic lights are modeled by a red phase and a green phase, where the duration of the green and red phases is fixed. When a red phase is encountered, the lower time bound is shifted up, while the upper time bound is shifted down. An example of the resulting upper and lower time bounds is shown in Figure 1b.    coordinates and speed was recorded for each route using a smart phone app [42]. [42] proposes the The optimization is conducted along distance s. The step size in s varies, depending on the upper bound of the speed. Thereby, the discretization is small where the vehicle is expected to be slow and wider where the vehicle is expected to be faster. The step size in s was set such that, corresponding to the upper bound speed, delta t is 0.3 s but not smaller than 0.2 m. The speed was discretized with 300 equally spaced points between the upper limit and zero. A stop was approximated with an upper value of 0.1 m/s. Time was discretized between the lower and upper bound with 350 equally distanced points and traction torque at the wheel was discretized in 15 Nm steps.

Assumptions
Various assumptions were made in the speed profile optimization. To see the effect of energy-efficient driving on the powertrain, it was assumed that the vehicle follows the optimal speed profile at all times, representing a best case scenario. With the V2I communication, the signal phase timings of all traffic lights are available before the start of the journey. Additionally, since the CEEDB drives in a dedicated lane, it was assumed that there are no vehicles or pedestrians that interfere with the bus operation. To see the effects of the powertrain isolated, the auxiliary power was set to zero.

Case Study
The powertrain optimization was implemented for the two bus routes in Singapore, routes 91 and 185, as they differ in their characteristics and represent two types of bus routes. Route 91 connects an MRT station to a business park and is characterized by frequent turns and a relatively short distance between stops. Route 185 connects a residential area to an industrial area via an expressway. The expressway section has a length of 4.2 km, with no stops or traffic lights, and a speed limit of 60 km/h instead of the standard 50 km/h speed limit. Route 185 is therefore characterized by longer straight segments and a higher average speed than Route 91. Measurement data in the form of geographic coordinates and speed were recorded for each route using a smartphone app [42]. Wittmann et al. [42] proposes the use of these data for the determination of energy consumption. Since the buses on Route 91 operate in a loop, the full operation was recorded, while for Route 185, which is bidirectional, only operation in the east-west direction was recorded. The obtained information was combined with the geographic location data of traffic lights and bus stops provided by the Singapore Land Transport Authority [43]. Figure 2 shows the measured route and the locations of stops and traffic lights. The measured route length, number of stops, average distance between stops, number of turns, number of traffic lights, speed limits, duration, total dwelling time and average speed of both routes are summarized in Table 1.    The longitudinal vehicle simulation was based on the vehicle characteristics of the 12 m battery electric BYD bus [44], hereinafter referred to as the reference vehicle. The mass, front area, drag coefficient, rolling resistance coefficient, tire radius and transmission efficiency are listed in Table 2. The bus is powered by a pair of motors connected to the rear drive axle, with a single gear stage at each wheel (see Figure A1). The torque is assumed to be split evenly between both motors. For the CEEDB and UCB, the same vehicle model and energy consumption simulation is used to see the effect of energy-efficient driving on powertrain design. The powertrain configuration is explored in terms of motor type and gear ratio. The motor types evaluated included IM and PMSM, which are modeled using motor efficiency maps. To enable a fair comparison, the efficiency maps were generated by a validated motor simulation tool using the same nominal voltage, maximal and nominal rotational speed, cooling type, number of pole pairs and nominal power, as listed in Table 3 [46]. The values are based on the motor used by the reference vehicle [47]. The simulation model used a squirrel-cage rotor for the IM and a rotor with internal permanent magnets for the PMSM. Data from the Singapore Land Transport Authority were used to derive the route infrastructure parameters. A turning radius of 12 m, which corresponds to the minimum corner radius specified by Singapore infrastructure guidelines, was used for all turns [48]. Combined with the suggested maximum lateral acceleration of 0.05 g [48], this results in a maximum cornering speed of 8.7 km/h. The signal phase durations of the traffic lights along the routes were provided by the Singapore Land Transport Authority. The start of each green phase was aligned with the data from the measured bus routes as follows. At the traffic lights where the bus had to stop, the time at which it resumed driving was used for the start of the green phase. At the traffic lights where the measured bus did not stop, it was assumed that it passed halfway through a green phase. Figure 3 illustrates optimal speed profiles for the CEEDB with a PMSM and an IM with their optimal gear ratio with and without the comfort factor (e.g., PMSM-Comfort indicates the CEEDB PMSM with controlled comfort) on a stretch of Route 91 along with the measured driving cycle of the UCB operating on that route. The bus stops and traffic lights are indicated in the figure with vertical lines. Without the comfort factor, the figure shows similar speed profiles for PMSM and IM, with primarily three phases of movement, including acceleration, coasting with no applied motor torque and deceleration. A P&G strategy can be seen. With the applied comfort factor, the speed profiles are smoother, but the three phases of movement can still be identified. The UCB has to stop more often as traffic lights, right turns with oncoming traffic, or traffic 241 congestion may force it to stop. These stop events are avoided by the CEEDB and therefore, the CEEDB

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As the speed profiles without the comfort factor seems uncomfortable due to the occurring P&G, 248 further discussion focuses on the speed profiles with the comfort factor.

Powertrain Optimization Analyses
As the speed profiles without the comfort factor seem uncomfortable due to the occurring P&G, further discussion focuses on the speed profiles with the comfort factor. Figures 5 and 6 show the optimal gear ratio for each motor type along with the change in energy consumption for different gear ratios for the CEEDB with the comfort factor and the UCB operating on Route 91 and Route 185, respectively.
As the speed profiles without the comfort factor seems uncomfortable due to the occurring P&G, 248 further discussion focuses on the speed profiles with the comfort factor. Figure 5 and 6 show the 249 optimal gear ratio for each motor type along with the change in energy consumption for different 250 gear ratios for the CEEDB with the comfort factor and the UCB operating on Route 91 and Route 185, 251 respectively. As can be seen from the figures, gear ratios range from 10 to 22 for the PMSM and 12 to 22 for the IM, as they correspond to a minimal gradeability of 12% and a minimal top speed of 60 km/h for the reference vehicle. For both routes, the PMSM performed best for the CEEDB and UCB. The IM required more energy than the PMSM for all cases. For the CEEDB, the optimal gear ratios are higher compared to the UCB for the IM but similar for the PMSM. As the region of best efficiency for the IM is at higher revolutions, the optimal gear ratio was higher compared to that of the PMSM, which moves the load points to higher motor revolutions, as can be seen in Figure 4. The sensitivity of the energy consumption over the gear ratio is lower for the CEEDB. On Route 91, for the CEEDB with the comfort factor, the optimal gear ratio may result in energy savings of up to 3.7% and 1.8% for the PMSM and IM, respectively, while for the UCB, energy savings of up to 9% and 6.2% can be achieved for the PMSM and IM, respectively. On Route 185, for the CEEDB with the comfort factor, optimal gear ratio may result in energy savings of up to 4.2% and 2.9% for the PMSM and IM, respectively, while for the UCB, energy savings of up to 10.1% and 9.9% can be achieved for the PMSM and IM, respectively.   Figure 7 illustrates the lowest achieved energy consumption of each motor for the CEEDB with and without the comfort factor and UCB. As expected, the energy consumption for the optimal controlled vehicle with a dedicated lane and V2I communication is significantly lower than the UCB for all motors and routes. Between the CEEDB and the UCB, savings of up to 27% can be achieved. With the comfort factor (indicated with C), the energy consumption is 6.8-10.8% and 6.5-8.9% higher compared to the CEEDB without the comfort factor for PMSM and IM, respectively. and without the comfort factor and UCB. As expected, the energy consumption for the optimal 267 controlled vehicle with a dedicated lane and V2I communication is significantly lower than the UCB 268 for all motors and routes. Between the CEEDB and the UCB, savings of up to 27% can be achieved.

269
With the comfort factor (indicated with C), the energy consumption is 6.8-10.8% and 6.5-8.9% higher 270 compared to the CEEDB without the comfort factor for PMSM and IM, respectively. The share of gear-ratio-specific operation on energy consumption is explored by evaluating one optimized speed profile for different gear ratios for the PMSM and IM. The speed profile of the smallest gear ratio was chosen for the fixed speed profile for each motor. Figure 8a,b show the energy consumption relative to the best configuration for the PMSM and IM, with the fixed and gear-ratio-specific optimized speed profiles for Route 91 with and without the comfort factor, respectively. The difference in the energy consumption can be explained by the gear-ratio-specific operation. It can be seen from the figure that for the CEEDB with IM, the effect of gear-ratio-specific operation is noticeable only at high gear ratios. However, with the PMSM, the effect of gear-ratio-specific operation becomes more pronounced, resulting in savings of up to 1% based on the minimal archived energy consumption. For the CEEDB with PMSM, it can be seen that the impact of gear ratio on energy consumption decreases even more if comfort is neglected.
can be seen from the figure that for the CEEDB with IM, the effect of gear ratio-specific operation is 278 noticeable only at high gear ratios. However, with the PMSM, the effect of gear ratio-specific operation 279 becomes more pronounced, resulting in savings up to 1% based on the minimal archived energy 280 consumption. For the CEEDB with PMSM it can be seen that the impact of gear ratio on energy 281 consumption decreased even more if comfort is neglected.

Sensitivity Analysis
A sensitivity analysis was conducted for the CEEDB without the comfort factor, varying the time and acceleration limit by 20%. The simulations were conducted for the first four bus stops of Route 91 without traffic lights to reduce computation time. As a reference, the maximum time was set to 224.1 s, which corresponds to an average speed of 20 km/h, and the reference acceleration was set to 1 m/s 2 . Figure 9a-c show the optimal gear ratio for each motor type along with the change in energy consumption for different gear ratios for the varying maximal arrival times.
The optimal gear ratio for each motor type along with the change in energy consumption for different gear ratios for the different acceleration limits of 0.8, 1 and 1.2 m/s 2 can be seen in a, b and c of Figure 10, respectively.

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The relative difference between PMSM and IM decreases with released boundary conditions. This

300
Literature has shown the effect of a P&G strategy to achieve maximal efficiency for combustion 301 engines [5], [11]. This work has shown, similar to [7], that P&G maximizes efficiency for electric 302 motors as well, which can be explained by load point shifting. As load points at low torques have 303 low efficiencies it may be more efficient with the implemented model to repeatedly accelerate in 304 short increments with a high torque followed by some coasting than to drive at a constant speed.

305
However, this results in an uncomfortable speed profile. Therefore, a comfort factor is required to 306 enable passenger comfort. The relative difference between PMSM and IM decreases with released boundary conditions. This can be explained by the efficiency maps. The PMSM has high efficiency over a broad range, while the IM's efficiency varies significantly with torque and RPM. Therefore, with the released boundary conditions, the IM has more potential to shift the load points to a higher efficiency area. Thus, the life cycle costs of the IM become more competitive, as the acquisition cost of the IM is lower than that of a PMSM.

Ride Comfort
The literature has shown the effect of a P&G strategy to achieve maximal efficiency for combustion engines [5,11]. This work has shown, similar to [7], that P&G maximizes efficiency for electric motors as well, which can be explained by load point shifting. As load points at low torques have low efficiencies, it may be more efficient with the implemented model to repeatedly accelerate in short increments with a high torque, followed by some coasting, than to drive at a constant speed. However, this results in an uncomfortable speed profile. Therefore, a comfort factor is required to enable passenger comfort.

Effect of Gear Ratios on Energy Consumption
For optimal speed profiles, the impact of gear ratio on energy consumption decreases compared to the UCB, as can be seen from Figures 5 and 6. The reduced change in energy consumption over gear ratios can be explained in two possible ways. One is that longer coasting but shorter acceleration and recuperation periods may reduce the effect of gear ratio. The energy consumption of the coasting phases is independent of the gear ratio in the implemented model. The short acceleration and recuperation phases are driven with high torque and hence result in load points at higher efficiency areas with small gradients for all gear ratios. Therefore, the gear ratios may not further improve the energy consumption of the optimized speed profiles with predominantly coasting phase and acceleration and recuperation phases that are already in high efficiency areas. Another explanation is that the effect of gear ratio on energy consumption may subside because of the gear-ratio-specific operation, as the speed profiles are optimized for each powertrain configuration.
For the CEEDB with PMSM, both effects are significant, as can be seen from Figure 8. Thus, the great share of coasting and the gear-ratio-specific operation reduce the sensitivity. However, for the CEEDB with IM, the effect of coasting is dominant, as can be seen in Figure 8. Due to the low acceleration limit combined with the slow speed and the desired high motor speed for best efficiency, the acceleration profiles for the considered gear ratios look almost identical. Thus, the effect of gear-ratio-specific control is smaller for the IM in this scenario.

Limitations
This study compared different powertrain configurations for vehicles operating under energy-efficient driving, which may apply to connected vehicles with speed advisory systems as well as to automated/autonomous vehicles. In the former, a human driver controls the vehicle and the optimal speed profile is only an advisory which may or may not be followed. Accordingly, the extent of the described effects on the powertrain design due to energy-efficient driving depend on the adoption rate of the human driver. The automation of vehicles takes the human out of the loop. Thus, autonomous vehicles are seen as enablers of energy-efficient driving. However, they require high maturity of autonomous driving functions. In this work, we assumed the vehicle parameters of a state-of-the art electric production bus. This allows an isolated examination of the energy-efficient operation's impact on the powertrain design. However, today's concepts of autonomous buses differ in design and their maximum speed is low [49,50]. Thus, the actual energy consumption for current autonomous buses may differ from our results.
As Singapore has no dedicated lanes for buses, it was not possible to obtain measured driving cycles and the necessary geo-data for a bus with a dedicated infrastructure to derive the benchmark for the optimization results. Thus, the measurements were conducted at off-peak hours with low traffic to obtain speed profiles that were close to those of a bus operating in a dedicated lane. Furthermore, the measured speed profiles were filtered to remove unrealistic accelerations. This may limit the accuracy of the absolute energy consumption of the UCB. Without the comfort factor, the results are globally optimal within the discretization of the model; however, inclusion of jerk requires a new state, which would increase calculation time. Therefore, the new state was not introduced and the speed profiles with the comfort factor are not a global minimum per se.
Only one motor of two different kinds was analyzed. The IM with its significant change in efficiency over torque and RPM becomes more competitive with the introduction of energy-efficient driving and released boundary conditions. Based on the design parameters, the efficiency map of different PMSM and IMs can focus on maximal efficiency or high overall efficiency. Subsequently, further research with multiple PMSMs and IMs is required to derive trends in motor design for vehicles under energy-efficient driving.
The analysis in this study is limited to single speed transmission systems. Previous studies have shown the potential reduction in the energy consumption of multi-gear or continuously variable transmissions for fixed driving cycles [23]. Further research is required to assess this potential for CEEDBs.
The achieved energy savings in this study were higher compared to those of the reviewed literature [8]. This may be explained by the fact that the energy savings in this study are achieved due to the combination of optimal control and V2I communication.
Finally, the study was limited to buses that drive in a dedicated lane and have traffic light information available. Although the work did not focus on the implementation of the driving strategies in real time, an implementation could be realized by communicating the desired speed to the vehicles based on its location, as shown in [51]. To extend the validity of the results, an analysis of a bus within dynamically changing boundary conditions, like mixed traffic, should be conducted. However, this would introduce additional constraints to the system, which would require advanced control strategies.

Conclusions
This study demonstrated optimal powertrain configurations for a connected, energy-efficient driven bus and a human-driven unconnected bus. The impact of powertrain configuration for the connected, energy-efficient driven bus was further evaluated for the cases of powertrain-specific optimal speed, non-powertrain-specific optimal speed and with and without consideration of ride comfort. It was shown that the connectivity and speed optimization may reduce the energy consumption of a bus by up to 27%.
The PMSM has lower energy consumption compared to the IM for all considered cases. However, with released boundary conditions, the difference in energy consumption decreases between PMSM and IM, making the cheaper IM more competitive.
The optimal gear ratio for PMSM is smaller than that of the IM. This is mainly due to the IM having higher efficiencies at higher speeds and therefore requiring higher gear ratios to shift the operating points to higher motor revolutions. However, the optimal gear ratio does not change significantly for the connected bus under energy-efficient driving when the comfort factor is considered compared to that of the human-driven unconnected bus.
The connected bus under optimal speed control predominantly operates at coasting, which is independent of the powertrain, and the remaining operating phases, acceleration and recuperation, already correspond to the high motor efficiencies for all regarded powertrain configurations. Hence, the change in energy consumption over different gear ratios subsides for the connected energy-efficient driven bus. Furthermore, due to the powertrain-specific optimization of the speed profiles, the change in energy consumption over different gear ratios subsides even more compared to the human-driven unconnected bus. The reduced sensitivities show that intelligent driving may help powertrain designers to achieve a good compromise between drivability and energy consumption.
Author Contributions: A.K. is the initiator of the research topic, developed the dynamic programming algorithm and revised the paper to its final status. O.T. defined the use cases for the analysis, drafted the structure of the paper and was intensively involved in the paper revisions. S.K. generated the motor efficiency maps and contributed to the discussion on different motor types. A.O. is the principal investigator of the research project and gave constructive comments on the paper. M.L. made an essential contribution to the conception of the research project. He revised the paper critically for important intellectual content. M.L. gave final approval of the version to be published and agrees to all aspects of the work. As a guarantor, he accepts responsibility for the overall integrity of the paper. Conceptualization

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

Abbreviations
The following abbreviations are used in this manuscript: