**1. Introduction**

In recent years, electric city buses (ECB) have experienced exponentially growing production rates and deployment to the public transportation systems of many cities around the world, as the lifecycle cost has decreased below traditional diesel bus levels in many routes and operating conditions [1]. In 2018, the global ECB fleet grew by 32% and reached 425,000 units worldwide [2]. The major advantage of ECBs is the higher energy conversion efficiency of the powertrain compared to diesel buses. ECBs are also locally emission-free, whereas diesel buses emit harmful particles that stay trapped between buildings, causing significant damage to human health in urban environments [3].

Although battery and charging technologies have developed at a fast pace in recent years, limited range is still a challenge with electric vehicles in general, because energy density of batteries is 25–100 times less than in liquid hydrocarbon fuels [4]. Increasing the battery capacity extends the range, but the size, weight, and cost set upper bound on the battery capacity. This limitation puts an emphasis on efficiency and optimal component selection in ECBs. Improved efficiency translates to an increasing rate at which ECBs displace diesel buses in cities' transportation systems, leading to reduced emissions and cleaner air.

The traction motor is the key component of an electric powertrain, and enabling the motor to operate at its highest efficiency region improves energy efficiency. Traction motors used in ECBs need to provide sufficient torque for acceleration and climbing inclined roads, while the maximum power output needs to be sufficient for high speed cruising. A motor with a wide speed range fulfills these requirements, and there is no absolute need for a multispeed gearbox as in ICE-powered vehicles [5]. However, in a traction application, a motor uses a wide speed range and thus is not operating at optimal efficiency [6]. ECB provides a promising application for a multispeed gearbox, because the vehicle operation consists of frequent braking and acceleration events that use a wide torque and speed range of the motor, which has been shown to result in reduced efficiency with a single gear drivetrain [7]. By contrast, electric vehicles that operate mostly at constant speed, such as long distance buses and trucks, can be equipped with a single speed reduction gear. The gear ratio is selected to operate the motor at the high-efficiency design point at nominal vehicle speed.

### *1.1. Previous Work*

The literature on the advantages of a multispeed gearbox in electric vehicles is extensive, although it is primarily focused on light-duty vehicles. To the knowledge of the authors, there are no studies that investigate multispeed gearbox options for electric city buses.

Wu et al. [8] developed a simulation model in Autonomie to study the impact of a two-speed gearbox (AMT) on the fuel economy of an electric car. Dynamic programming was applied to the optimization problem—A 4.2% reduction in energy consumption in city driving was observed.

Ren et al. [9] reported a simulation study using a backward modeling approach (wheels to motor) and a comparison of different gearbox options in terms of the energy consumption of EVs. The reference was the original single-speed transmission, which was compared to continuous variable transmission (CVT) and multispeed gearbox with two, three, and four speeds. The authors observed that the losses of the multispeed gearbox cancel the improvement in energy efficiency for the NEDC cycle. For the other five cycles studied, the improvement in efficiency varied from 5.3% to 12.4%. The authors also point out that in addition to a possible improvement in energy efficiency, the acceleration performance of the vehicle improves. Specifically, the acceleration time from zero to 100 km/h was reduced from 18.6 s to 12.4 s with a two-speed gearbox.

A similar study of powertrain efficiency comparison was completed by Bottiglione et al. [10]. The gearbox efficiency and increase in vehicle mass were taken into account. The compared gearbox options were infinitely variable transmission (IVT) and CVT with toroidal technology. Single and two-speed transmission were also considered. Both IVT and CVT had two different configurations. The planetary gear in the IVT was assumed to work with 100% efficiency. The simulations were run for the Urban driving cycle (UDC) and the Japanese 10–15 cycle (J10-15). For both cycles, the IVT and CVT were found superior to the two-speed gearbox, with the largest consumption improvement reaching 16.7%. The authors concluded that the energy efficiency of EVs could be significantly improved by optimizing the torque dependent efficiency of CVT and IVT.

Gao et al. [11] focused on the potential of a two-speed gearbox for EVs. The study included simulation and optimization of gear ratios and shift control. The gearbox efficiency was considered equal to the single-gear alternative, and the overall efficiency of the powertrain was assumed to be 96%. The reported results were in agreement with those discussed previously. One notable difference was that the largest energy savings were achieved in the NEDC cycle, which in [9] was found to produce the least savings potential. The authors also mentioned the improved performance of the EV with a two-speed gearbox, i.e., better acceleration and top speed. Their modeling efforts highlight the friction losses due to the clutch in the gear change and the effect of a gear change smoothness to the friction losses. Calm gear shift which is comfortable for the passengers with no torque interrupt generates substantial losses in comparison to more rough and rapid change.

In addition to simulation studies, Spanoudakis et al. [12] discussed a prototype for an experimental test of the potential of a two-speed gearbox for improving the efficiency of an ultralight vehicle for urban environment transportation. The power source in the test vehicle was a hydrogen fuel cell. The gear selection was manual, and the test drive was conducted on a simple oval test track. The results showed that energy savings of 3.4% were reached in comparison to the single-speed gearbox and most

of the energy savings were achieved during the acceleration phases of the test run. The energy savings potential is higher in city driving conditions with frequent accelerations and decelerations compared to highway driving.

In the realm of heavy-duty vehicles, Tan et al. [13] reported a study on an iron mine electric dump truck gear ratio optimization using particle swarm optimization algorithm. For a typical working cycle in a mine, energy consumption was found to be reduced by 6.1% with the gearbox and optimized ratios compared to the reference powertrain, which had only a single-speed reduction gear. The study is limited with respect to the conclusions that can be established for ECBs because the operation cycle of the electric dumb truck has significantly less variation than that of a city bus.
