**1. Introduction**

Due to their high energy density and convenience, fossil fuels have been exploited for vehicles for a long time. However, this exploitation has been accompanied by global problems of air pollution in the form of fine particulates resulting from vehicle exhausts, including NO*x*, as well as global warming, which is attributable to carbon dioxide emissions.

Therefore, countries worldwide have strengthened regulations on the fuel efficiency and emissions of vehicles. Additionally, some countries and cities have even prohibited the driving and sale of vehicles equipped with internal combustion engines [1]. To cope with these regulations, the global automobile industry has developed and released various kinds of eco-friendly vehicles, denoted as 'xEV'. Among them, electric vehicles have been spotlighted as alternatives that can help reducing air pollution due to their zero emission. There has also been a rapid increase in the number of electric vehicle models that have been released into the market, as well as the sales [2]. The market outlooks estimate that the share of electric vehicles could reach approximately 28% of all motor vehicles in the motor vehicle industry by 2030 [3].

**Citation:** Jang, I.-G.; Lee, C.-S.; Hwang, S.-H. Energy Optimization of Electric Vehicles by Distributing Driving Power Considering System State Changes. *Energies* **2021**, *14*, 594. https://doi.org/10.3390/en14030594

Academic Editor: Islam Safak Bayram Received: 21 December 2020 Accepted: 22 January 2021 Published: 25 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The charging time and driving distance per battery charge still remain as issues that can be further improved. In case of the charging time issue, the charging time for 400 km driving range of electric vehicle equipped with 400 V system is 29 min, but, the charging time can be reduced to less than 15 min for the same driving range by changing the voltage level from 400 V to 800 V [4]. In case of driving distance, the driving distance between 80 km and 200 km for a battery-powered electric shuttle bus equipped with 30.7 kWh and 33 kWh, respectively, has been presented [5,6]. To extend the driving distance provided by a single charge of an electric vehicle battery, various methods have been introduced, including one that developed a high-power-density battery (solid state battery) to increase the energy capacity [7], as well as another study that installed two different driving systems on the front and rear wheels and optimized the power distribution of the front and rear wheels [8]. Furthermore, Xibo et al. proposed the traction force distribution method to minimize power losses for permanent magnet (PM)-type traction motors for a front and rear wheel driven electric vehicle [9]. Studies on independent four-wheel driving systems intending to increase the performance efficiency of electric vehicles have also shown promising results. For example, Park et al. conducted a study on the optimization of the driving energy and systematic stability of an electric vehicle equipped with a four-wheel drive system by employing fuzzy logic [10]. The efficiency of the driving system of an electric vehicle depends substantially on the temperature and input voltage of the driving system [11], and the input voltage is also dependent on the voltage level at the terminal of the battery because of the wire connection between the terminal of the battery and the input terminal of the driving system. The voltage level at the terminal and capacity of the battery vary according to the elapsed driving hours, and changes in the input voltage affect the output of the driving system. However, the studies mentioned above [8–10] did not account for changes in the system state.

This paper presents methods to increase the energy efficiency of a battery-powered electric shuttle bus equipped with a decentralized four-wheel drive system. First, the specification of a battery-powered electric shuttle bus will be derived. Then, the analysis of the input voltage effects on the driving system efficiency will be conducted, and an algorithm to obtain the optimal distribution of driving torque to the front and rear wheels by accounting for the varying input voltages will be proposed. The effects and gain of the algorithm on the driving efficiency of a battery-powered electric shuttle bus will be verified by Matlab/Simulink simulation.

This paper is organized as follows: The specifications for a driving system and requirements for a battery-powered electric shuttle bus are defined in Section 2, in Section 3, design results for the drive system are described. The efficiency changes are also examined with the input voltage changes in Section 3. The algorithm used to allocate the driving torque to the front and rear wheels while securing optimal system efficiency is explained in Section 4. In Section 5, the simulation model for a battery-powered electric shuttle bus is built and the effects on the system efficiency in low voltage condition is analyzed by comparing with uniform distribution method and also with a fixed voltage optimization method through simulation according to 'Manhattan Bus cycle'. Finally, an effectiveness of proposed algorithm is analyzed for a battery-powered electric shuttle bus.

### **2. Electric Vehicle System Design**

In this section, the requirement of the target vehicle is defined and then, the requirement for propulsion system is specified by using longitudinal dynamics.

#### *2.1. Vehicle Requirements*

The target vehicle selected for the simulation is a battery-powered electric shuttle bus. This bus drives according to a predetermined interval to connect key places to respective final destinations as a means of last-mile transportation. The driving route for the target vehicle has a one-way interval of 3.7 km, wherein the simulation design included an average

driving speed of 15 km/h, a driving time of approximately 15 min, a daily operation of 8 h, and up to 15 passengers. The specifications of the target vehicle are summarized in Table 1.


**Table 1.** Specifications of the target vehicle.

Table 2 presents the performance requirements of the target vehicle. By considering the fact that the vehicle drives at a low speed along the last-mile interval in the downtown regions of cities, the following performance requirements were set for the vehicle: a maximum driving speed of 45 km/h [5,6], an autonomous driving speed of 25 km/h [5,6], a maximum climbing capacity enabling propulsion on a road with a maximum gradient of 28%, continuous driving at 5 km/h on a road with an identical gradient, and a maximum acceleration or deceleration capability of 3 m/s2.

**Table 2.** Performance requirements of the target vehicle.


The electric shuttle bus has an independent four-wheel drive system with the following power transmission architecture. Figure 1 shows the configuration of the power system of the target autonomous electric vehicle.

**Figure 1.** System architecture of the target electric shuttle bus. VCU: Vehicle Control Unit; M1 to M4: In-wheel Motor; I1 to I4: Inverter; PRA: Power Relay Assembly; DCDC: DCDC Converter; HV: High Voltage.

#### *2.2. Propulsion System Sizing*

To fulfill the power requirements for the desired performance of the target vehicle, it is necessary to set the design objectives of the power system. Thus, according to the power performance requirements of the target vehicle, the correlation thereof with the attributes of the power system needs to be identified. As shown in Figure 2, the correlations between the indicators of the power performance of the target vehicle and the attributes of the power system are defined.

**Figure 2.** Assignment of vehicle performance requirements to propulsion system requirements.

The maximum speed signifies the maximum continuous driving speed of the target vehicle on a flat road (gradient 0%) corresponding to the continuous output of its power system. As an attribute of a vehicle that corresponds to the continuous output of its power system, the performance of that vehicle continuously driving along a gradient road (gradeability) could be taken into account. In addition, the performance in terms of the maximum acceleration and deceleration, along with the maximum gradeability (gradient), correspond to the instantaneous output of the power system.

The forces (*Fx*) acting on the driving vehicle can be differentiated as the driving force of the vehicle (*Ft*) and the forces of air resistance (*Faero*), rolling resistance (*Frolling*), and climbing resistance (*Fgrade*). These are illustrated in Equations (1)–(5). The balance relationship between forces, corresponding to the power performance objectives of the vehicle in question, can be represented in terms of longitudinal vehicle dynamics (illustrated in Equation (1)), from which the forces required for each wheel can be determined [12]:

$$
\sum F\_x = \, M\ddot{x} \tag{1}
$$

$$F\_{\text{x}} = F\_{\text{t}} - F\_{\text{acro}} - F\_{\text{radiing}} - F\_{\text{grade}} \tag{2}$$

$$F\_{\text{aro}} = \frac{1}{2} \rho \mathbf{C}\_d A\_f \dot{\mathbf{x}}^2 \tag{3}$$

$$F\_{rolling} = \mathcal{C}\_r M \mathfrak{g} \cos \mathcal{Q} \tag{4}$$

$$F\_{\text{grade}} = M \mathfrak{g} \sin \mathfrak{Q} \tag{5}$$

Here, *ρ* represents the air density of 1.293 kg/m3; *Cd* is a coefficient of air resistance; *Af* and . *x* represent the front area and velocity of the vehicle, respectively; *Cr* denotes the coefficient of rolling resistance, which is 0.01; and *M*, *g*, and ∅ represent the mass of a vehicle, gravitational acceleration, and longitudinal gradient of the road, respectively. The other specifications were borrowed from the vehicle specifications presented in Table 1.

Table 3 and Figure 3 present the results of the power output and torque required for the vehicle, which were obtained using Equations (1)–(5) and Equations (6) and (7), respectively. By accounting for changes in the loading condition, air pressure, and tire diameter of the vehicle, a speed of 2 km/h and a 1% margin for the gradient angle were added:

$$T\_l \;=\; F\_l R\_l \tag{6}$$

$$P = T\_t \omega\_t = F\_t \dot{\mathbf{x}} \tag{7}$$

Here, *Tt* and *Rt* represent the wheel torque and tire radius, respectively.

**Table 3.** Propulsion system requirements corresponding to vehicle performance.


<sup>1</sup> C: Continuous; <sup>2</sup> P: P signifies the 'Peak'.

**Figure 3.** Sizing results of (**a**) power-gradient-speed and (**b**) torque-speed chart with the requirement point.

An operating speed of 25 km/h was selected to satisfy the requirement that the maximum speed remain below 45 km. Based on the above results, the largest value among the values corresponding to the continuous output was selected by using Equations (8) and (9), by which the continuous maximum torque of 2971 Nm and the continuous maximum output of 33.5 kW were derived. Additionally, a base speed of 108 rpm was determined by Equation (7), which is the TN characteristic expression of the driving system. Here, the instantaneous maximum torque and instantaneous maximum output are dependent upon the cooling mechanism of the motor. For example, in the case of water cooling, these are approximately 1.8 to 2 times the continuous peak torque and continuous output, respectively. In this paper, the value of 1.8 was used, resulting in a maximum torque of 5348 N and an instantaneous maximum output of 60.4 kW:

$$T\_t \;=\; F\_t \mathcal{R}\_t \tag{8}$$

$$T\_{\text{max}} = \max(T\_{\text{max}\\_s \text{pred}\\_\prime}, T\_{\text{sync\\_25\%}}, T\_{\text{grndc\\_12\%}}) \tag{9}$$

As shown in Figure 1, four driving motors are mounted on the vehicle. Furthermore, the required performance of each driving motor in the single driving system was derived by dividing the entire torque and output of the vehicle into four shares, as presented in Table 4.


**Table 4.** Unit propulsion system requirements.

#### *2.3. Propulsion System Design*

This section describes the specifications of the driving motor that is capable of satisfying the requirements of the output characteristics in the drive system derived from Section 2.2. The correlation between the *Vdclink* value and the efficiency map of the motor is analyzed.

Table 5 lists the specifications of the motor used in this study. Figure 4 illustrates the dimensions and shapes for the cross-sectional view of the motor. Figure 5 shows the efficiency map of the motor corresponding to *Vdclink* values of 105 V and 75 V, respectively. To develop the efficiency map of the motor, the finite element method (FEM) was used to obtain the inductance *Ld* and *Lq* on the *dq*-axis, as well as the magnetic flux *ψ<sup>a</sup>* for a permanent magnet.


**Table 5.** Design specifications of the in-wheel motor.

Based on the FEM results, the information needed for the efficiency map of the motor is derived through the following Equation of torque (10) and Equations of voltage (11)–(13) [13], by using the equivalent circuit (Figure 6) on the *dq*-axis of the motor [14]:

$$T = \frac{3}{4} \mathcal{N}\_{\mathbb{P}} \left\{ \psi\_{\mathbb{d}} \, i\_{\mathbb{dq}} + \left( L\_{\mathbb{d}} - L\_{\mathbb{q}} \right) i\_{\mathbb{d}d} \, i\_{\mathbb{d}q} \right\} \\ = \frac{3}{4} \mathcal{N}\_{\mathbb{p}} \left\{ \psi\_{\mathbb{d}} \, i\_{\mathbb{d}d} \cos \beta + \frac{1}{2} \left( L\_{\mathbb{d}q} - L\_{\mathbb{d}d} \right) i\_{\mathbb{d}d}^2 \sin 2\beta \right\} \tag{10}$$

$$
\omega\_{\rm od} = -\omega\_{\rm \varepsilon} L\_{\rm q} l\_{\rm q}, \quad \upsilon\_{\rm \alpha \eta} = \omega\_{\rm \varepsilon} L\_{\rm d} l\_{\rm od} + \omega\_{\rm \varepsilon} \psi\_{\rm \mu}, \quad \upsilon\_{\rm o} = \sqrt{\upsilon\_{\rm od}^2 + \upsilon\_{\rm o}^2} \tag{11}
$$

$$v\_d = R\_d I\_{od} + \left(1 + \frac{R\_d}{R\_c}\right) v\_{od}, \quad v\_q = R\_d I\_{oq} + \left(1 + \frac{R\_d}{R\_c}\right) V\_{oq} \tag{12}$$

$$V\_{limit} = V\_{dclink} \times \eta\_{inv} \ge \sqrt{v\_d^2 + v\_q^2} \tag{13}$$

**Figure 4.** In-wheel motor model.

**Figure 5.** Efficiency map according to *Vdclink*: (**a**) *Vdclink* = 105 V and (**b**) *Vdclink* = 75 V.

**Figure 6.** Equivalent circuit: (**a**) *d-axis* and (**b**) *q-axis* [14].

The meanings of the symbols expressed in Equations (10)–(13) are as follows: *Np*: Number of poles; *ψa*: Magnetic flux of a permanent magnet; *Ld* and *Lq*: Inductance on the *dq*-axis;

*iod* and *ioq*: Current on the *dq*-axis; *icd* and *icq*: Current for the core resistance *Rc* on the *dq*-axis;

*id* and *iq*: Input current on the *dq*-axis; *ia*: Input current; *β*: Current angle;

*ωe*: Electric angular velocity; *ωm*: Mechanical angular velocity; *vod* and *voq*: Voltage on the *dq*-axis;

*Ra*: Phase resistance for the winding; *Rc*: Core loss resistance; and *ηinv*: Inverter efficiency.

Equation (10) for torque T can be derived using Faraday's law [15]. In order to meet the voltage limit by considering the maximum speed of the vehicle, the given voltage limit *Vlimit* is required to satisfy equation (13). In Equation (13), *Vdclink* denotes the peak voltage in the terminal of the inverter input for the battery. The inverter efficiency is assumed as *ηinv* = 0.95 to derive *Vlimit* [13]

The motor efficiency *η<sup>m</sup>* is derived by the maximum torque per ampere (MTPA) control methodology to generate the maximized efficiency. The efficiency of the motor is reduced by the losses generated from the motor. These losses can be distinguished into the copper loss, iron loss, and mechanical loss. The copper loss *Pcu* is due to the input current of the stator coil. The iron loss for the electrical core of the stator and rotor *Piron* results from the eddy current of the core, which is proportional to the rotating speed of the motor. *Pcu* is calculated using Equation (14), and *Piron* is calculated using Equation (15) by deriving the iron loss resistance *Rc* after conducting finite element analysis by using the loss information of the electrical core (15). The mechanical loss is excluded in this study due to the fact that the measurements are indispensable. Therefore, the efficiency of the motor can be expressed as shown in Equation (16) [13]:

$$P\_{cu} = i\_a^2 R\_a \tag{14}$$

$$P\_{iron} = \frac{v\_o^2}{R\_c} \tag{15}$$

$$\eta\_m = \frac{P}{P + P\_{loss}} = \frac{T\omega\_m}{T\omega\_m + P\_{cu} + P\_{iron}} \tag{16}$$

#### **3. Analysis of the Propulsion System Efficiency**

As illustrated in Figure 5, an analysis of the efficiency and output for a torque of 25 Nm over the entire speed interval for the whole efficiency map was conducted to identify changes in the efficiency for the two *Vdclink* models. By using Equations (10)–(16), the causes of the changes in efficiency according to *Vdclink* were analyzed. Figure 7 shows the analyzed results. The efficiency of the *Vdclink* = 75 V model decreased compared to that of the *Vdclink* = 105 V model, in accordance with the increase of speed after exceeding the base speed. In the drive region for the torque of 25 Nm as shown in Figure 5, the mechanical output at each speed was identical.

**Figure 7.** Efficiency and power according to *Vdclink*: (**a**) efficiency, (**b**) power, and (**c**) voltage.

The difference in the loss characteristics, which caused the difference in the efficiency of the two *Vdclink* models, is described by using Figure 8. The phase resistance *Ra* of the two *Vdclink* models is identical, since the two models use the same motor. However, the phase currents used to generate the torque of 25 Nm are different for different *Vdclink* values, as shown in Figure 8a. The requirement of the two models is to meet the identical power condition, as shown in Figure 7b. In the case of *Vdclink* = 105 V, the voltage limit is reached at the base speed of 1450 rpm. However, in the case of *Vdclink* = 75 V, the voltage limit is reached at the base speed of 1000 rpm. Considering the voltage limit condition after reaching the base speed of the two models, the *Vdclink* = 75 V model requires more current *Ia* than the *Vdclink* = 105 V model in order to satisfy the identical power output condition *P=Vdclink Ia*.

**Figure 8.** Current and loss according to *Vdclink*: (**a**) current, (**b**) copper loss, and (**c**) iron loss.

In this paper, the power factor was assumed to be 1. Therefore, in the case of *Vdclink* = 75 V, a higher input current is required than in *Vdclink* = 105 V, as shown in Figure 8a. For this reason, the copper loss increased significantly compared to that of *Vdclink* = 105 V, as shown Figure 8b. In terms of the iron loss, the magnitude is significantly smaller than that of the copper loss, as shown in Figure 8c. Therefore, in the case of *Vdclink* = 75 V, the main cause of the reduced efficiency is that the increased copper loss due to the phase current is dominant.

#### **4. Control Strategy**

As illustrated in Figure 9, the real-time optimization algorithm for the power distribution to the front and rear wheels, which showed the lowest energy consumption to create the required driving torque under a given speed, is presented. The 'Virtual Driver' creates the required driving torque (*Td*) in order to follow the given speed (*Vr*), and the 'Energy Optimization' creates the 'set-point' of the driving torque of each system divided into four wheels with minimum energy consumption while satisfying the required driving torque. Here, *Vr*, *Td*, *Tm*1–*Tm*4, *Ttot*, *<sup>γ</sup>opt*, *PM*, *Pdcdc*, *Pbatt*, *Vm*, *Vdclink*, and . *SOC* signify the required speed, required torque by the driver, target torque of the driving system, total driving torque, ratio of the optimal energy distribution for the front and rear driving torques, required electric driving torque of the driving system, electric power consumption of the 12 V power system, total power consumption of the battery, vehicle speed, input voltage of the driving system, and rate of change in the electric energy of the battery, respectively.

The real-time optimization method presented in this paper is explained concretely below, and the effects of changing *Vdclink* were verified by comparing two cases of power consumption, where the changes in *Vdclink* were taken into account or not taken into account for the specified point (speed, required torque).

**Figure 9.** Energy optimization concept diagram.

#### *4.1. Optimal Front/Rear Torque Distribution Concept*

The real-time optimization of the driving energy can be modeled using Equations (17)–(23), shown below. The system state variable SOC and the controlled input of the ratio *γ* of the driving torques to the front and rear wheels are used for modeling. Here, the required torque (*Td*, *<sup>f</sup>*) for the front and rear wheel drive of the system varies according to the distribution ratio to the front and rear wheels.

Thus, the operating point varies accordingly, resulting in changes in the efficiencies (*η<sup>f</sup>* , *ηr*) of the front and rear wheel drive systems. Additionally, the electric power (*PM*) used by the drive system varies in accordance with the changing distribution ratio of the driving torque. Here, as examined in Section 3, the efficiency (*η*) of drive system as a map can be modeled with speed and torque. In this study, the efficiency (*η*) map of the drive system is modeled with Equation (22) by taking the change of the input voltage (*Vdclink*) into account. The input voltage (*Vdclink*) modeled by internal resistance circuit of the battery is as a function of SOC and the rate of SOC (23) [16]; in this way, the input voltage (*Vdclink*) of the given state is considered. In addition, the braking stability based on the ideal braking torque distribution was designed. Then, the regenerative braking torques distributed to the front and rear axles were limited by the maximum generated torque of the corresponding traction system.

By employing Equation (18), which represents the cost function, the total consumption of energy can be minimized by minimizing the consumption of electric power ( . *E*) required at each moment by the driving system in every time interval 10 ms, as expressed in Equation (19): .

$$\text{SOC} = f(\text{SOC}(t), P\_d(t), \gamma(t)) \tag{17}$$

$$J^\* = \min\_{\gamma(t), \ t\_0 \le t \le t\_f} \int\_{t\_0}^{t\_f} \dot{E}(P\_d(t), \gamma(t), t)dt \tag{18}$$

$$\dot{E}(P\_d(t), \gamma(t), t) = \left. \begin{array}{c} P\_{\mathcal{M}}(t) + P\_{\text{dcdc}}(t) \\ \end{array} \right| \tag{19}$$

$$P\_M(t) \;=\; P\_{M,f}(t) + \; P\_{M,r}(t) \tag{20}$$

$$P\_{M,f}(t) = \frac{P\_d(t)\gamma(t)}{\eta\_f(t)}, \quad P\_{M,r}(t) = \frac{P\_d(t)(1-\gamma(t))}{\eta\_r(t)}\tag{21}$$

(Front:Rear

(Front:Rear=0:1)

$$\eta\_f(\mathbf{t}) = \ \ \ \mathbf{g}\left(T\_{d,f}(\mathbf{t}), \omega\_f(\mathbf{t}), V\_{\text{dclink}}(\mathbf{t})\right), \quad \eta\_r(\mathbf{t}) = \ \ \mathbf{g}\left(T\_{d,r}(\mathbf{t}), \omega\_r(\mathbf{t}), V\_{\text{dclink}}(\mathbf{t})\right) \tag{22}$$

$$V\_{dclink}(t) = h\left(\text{SOC}(t), \, \text{S\dot{O}C}\right) \tag{23}$$

subject to:

$$\text{SOC}(t) \in \{\text{SOC}\_{\text{min}}, \text{SOC}\_{\text{max}}\}$$

$$\gamma(t) \in \{\gamma\_{\text{min}}, \gamma\_{\text{max}}\}$$

$$P\_{M,f} \in \{0, P\_{\text{max}}\}, \; P\_{M,r} \in \{0, P\_{\text{max}}\}$$

$$P\_{dcdc}(t) = \text{Constant}$$

Figure 10 illustrates the method of distribution of the driving torque to optimize the real-time energy consumption. When the torque (*Td*) required by a driver is given at a certain speed (*Vm*), then the combination of the available driving torques of *Td*, *<sup>f</sup>* and *Td*,*<sup>r</sup>* are created by the array (*γ*) of the driving torque distribution ratio. By exploiting the efficiency map reflecting the voltage of the input terminal, the efficiency vectors of the front and rear wheel corresponding to each created combination of the driving torque can be generated. Consequently, the energy consumption *PM* at each element in the array of the distribution ratio of the driving torque can be calculated. Additionally, as expressed in Equation (24), the array of the minimum consumption of energy ( . *E*) can be extracted to derive the distribution ratio (*γopt*) of the distribution driving torque to the front and rear wheels with minimized energy consumption:

$$\gamma\_{opt}(t) = \operatorname\*{argmin} \left\{ \dot{E}(P\_{batt}(t), \gamma(t), t) \right\} \tag{24}$$

**Figure 10.** Concept of energy optimization.
