**Contents**


## **About the Editors**

**Dirk S ¨offker** Professor—Chair of Dynamics and Control (SRS), University of Duisburg-Essen, Duisburg campus, Germany. Dirk Soeffker received a Dr.-Ing. degree in mechanical engineering and a Habilitation degree in automatic control/safety engineering from University of Wuppertal, Wuppertal, Germany, in 1995 and 2001, respectively. Since 2001, he has led the Chair of Dynamics and Control with the Engineering Faculty, University of Duisburg-Essen, Germany. His current research interests include elastic mechanical structures, modern methods of control theory, human interaction with safety systems, safety and reliability control engineering of technical systems, and cognitive technical systems.

**Bedatri Moulik** Assistant Professor—Department of Electrical and Electronics Engineering, ASET, Amity University, Noida, India. Bedatri Moulik received her Bachelors degree in Electrical Engineering and Masters degree in Control and Instrumentation Engineering from West Bengal University of Technology, Kolkata, India. She received her Dr.-Ing. degree from the Chair of Dynamics and Control, University of Duisburg-Essen, Germany. She is now an Assistant Professor at Amity University, Noida, India in the department of Electrical and Electronics Engineering. Her current research interests include battery parameter estimation methods, battery and power management in electric/hybrid vehicles, drive pattern recognition and intelligent control in the context of electric/hybrid vehicles.

## *Editorial* **Battery Management System for Future Electric Vehicles**

#### **Bedatri Moulik 1,\* and Dirk Sö**ff**ker <sup>2</sup>**


Received: 7 July 2020; Accepted: 21 July 2020; Published: 24 July 2020

**Abstract:** The future of electric vehicles relies nearly entirely on the design, monitoring, and control of the vehicle battery and its associated systems. Along with an initial optimal design of the cell/pack-level structure, the runtime performance of the battery needs to be continuously monitored and optimized for a safe and reliable operation and prolonged life. Improved charging techniques need to be developed to protect and preserve the battery. The scope of this Special Issue is to address all the above issues by promoting innovative design concepts, modeling and state estimation techniques, charging/discharging management, and hybridization with other storage components.

**Keywords:** battery electric vehicles; battery management; hybrid energy storage

#### **1. Introduction**

Recent advancements in battery technology have pushed the sales of electric (EVs) and hybrid electric vehicles (HEVs) further. The improvements in the EV/HEV range, energy/charging efficiency, safety, reliability, and lifetime are entirely dependent on the design and chemistry of the battery pack and its associated systems. Most of the safety concerns regarding the battery's unexpected temperature rise and predictions of the internal reactions leading to fluctuations in internal temperature also need to be addressed.

#### **2. Battery Management System for Future Electric Vehicles**

The aim of the Special Issue "Battery Management System for Future Electric Vehicles" is to investigate advanced battery management technologies for the estimation, monitoring, and control of battery states, associated modeling techniques, thermal and charging/discharging management for optimized life, performance, and range. Optimal sizing, the hybridization of storage systems, and innovative battery test-benches were also encouraged. There are a total of seven accepted and published papers, which are summarized as follows:

The first paper, authored by Hakeem and Solyali [1], presents a battery thermal management system (BTMS) with improved performance in terms of battery cooling. An improved pack structure is proposed, which is experimentally investigated with different air flow rates and current rates of charge–discharge profiles. Finally, based on the obtained data, an artificial neural network is trained to obtain the thermal model of the battery pack.

The second paper, authored by Tseng and Yang [2], presents a torque and battery distribution strategy (TBD) that takes into account the torque–speed characteristics, as well as the battery state of charge to obtain optimized range and efficiency. Based on the State of Charge (SoC) gaps and ratios between the front and the rear battery packs, three torque distribution modes are then proposed. First simulation, then hardware-in-the-loop experimentation, followed by actual road tests, are performed to validate the effectiveness of the TBD in the extension of the electric vehicle range.

The third paper, authored by Kuo [3], presents a battery model based on a modified Thévenin circuit, Butler–Volmer kinetics, Arrhenius equation, Peukert's law, and a back propagation neural network (BPNN). The model can estimate the coulombic efficiency and the remaining capacity of the battery, as analyzed experimentally under various environmental conditions. Based on experimental results and curve fitting techniques, a comprehensive model is developed. A correction factor is introduced and the prediction of remaining capacity is done using a BPNN.

The fourth paper, authored by Cao [4], presents a wireless distributed and enabled battery energy storage system (WEDES) for electric vehicles (EVs) derived using a small signal modeling technique. The WEDES controller is designed to address SoC balancing, bus voltage regulation, and battery module current/voltage regulation at the same time. Finally, simulation and hardware experiments are carried out to evaluate and validate the accuracy and effectiveness of the derived model and controller.

The fifth paper, authored by Guo, et al. [5], presents an online SoC estimation method by using an equivalent circuit model, followed by model parameter identification. An optimization method is proposed to improve the accuracy of the SoC estimation. Then, an online estimation based on the adaptive unscented Kalman filter (AUKF), and with optimized model parameters, is performed. The estimation accuracy of the AUKF with the UKF is compared. The convergence of the initial error of the AUKF before and after parameter optimization is also compared.

The sixth paper, authored by Chen, Chen, and Duan [6], presents an optimization method to cooperatively optimize the economic dispatching and capacity allocation of both renewable energy sources (RESs) and electric vehicles (EVs). Both the installation capacity of RESs and the number of EV charging/discharging infrastructures (EVCDIs) are optimized. This optimization method is based on the EVs' across-time-and-space energy transmission. The main optimization objective is to improve the economics of the system allocation and decrease the cost of the microgrid operator. A two-loop optimization is considered using an improved particle swarm optimization (IPSO). The inner loop comprises the optimization of system dispatching, while in the outer loop, the allocation of EVs and RESs is optimized.

The seventh paper, authored by Hou, et al. [7], presents a variational Bayesian approximation-based adaptive dual extended Kalman filter (VB-ADEKF) to improve the accuracy of SoC estimation. First, the variational Bayesian results are used along with the extended Kalman filter to jointly estimate the states. Next, both variational Bayesian and variational Bayesian approximation-based adaptive dual extended Kalman filters are alternatively used. Additionally, measurement noise variances are considered to compensate for uncertainties in measurement. With the help of experiments, the proposed VB-ADEKF algorithm is compared with the traditional DEKF algorithm in terms of SoC estimation accuracy, convergence rate, and robustness.

Thus, summarizing all the seven papers brings us to the conclusion that this Special Issue has been successful in bringing together novel contributions considering multiple aspects of energy storage management and optimized charging/discharging schedules.

#### **3. Future Battery Management Systems**

Although this Special Issue is finished, immense work still remains in the field of innovative battery state estimation algorithms and optimization approaches to improve their accuracy and reliability in terms of online and real-time application in EVs.

**Author Contributions:** Both authors contributed equal parts to the paper, whereby the corresponding author was mainly responsible for initial writing, the second author for structuring and organizing, reviewing, and summarizing the entire contribution. All authors have read and agreed to the published version of the manuscript.

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

**Acknowledgments:** This Special Issue would not have been a success without the constant efforts of the authors—including those whose papers could not be selected. We can only hope that this Special Issue is able to provide them with a platform to learn and improve their existing works based on the valuable comments of the reviewers and editors. We would also like to thank the reviewers for dedicating their time and energy to the submitted manuscripts and motivating the authors to improve their work. Last, but not least, we would like to extend our heartiest congratulations to the entire editorial team of *Applied Sciences* for their sincere efforts and constant dedication in making this Special Issue a success.

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

#### **References**


© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Empirical Thermal Performance Investigation of a Compact Lithium Ion Battery Module under Forced Convection Cooling**

#### **Akinlabi A. A. Hakeem <sup>1</sup> and Davut Solyali 2,\***


Received: 10 April 2020; Accepted: 16 May 2020; Published: 28 May 2020

**Abstract:** Lithium ion batteries (LiBs) are considered one of the most suitable power options for electric vehicle (EV) drivetrains, known for having low self-discharging properties which hence provide a long life-cycle operation. To obtain maximum power output from LiBs, it is necessary to critically monitor operating conditions which affect their performance and life span. This paper investigates the thermal performance of a battery thermal management system (BTMS) for a battery pack housing 100 NCR18650 lithium ion cells. Maximum cell temperature (Tmax) and maximum temperature difference (ΔTmax) between cells were the performance criteria for the battery pack. The battery pack is investigated for three levels of air flow rate combined with two current rate using a full factorial Design of Experiment (DoE) method. A worst case scenario of cell Tmax averaged at 36.1 ◦C was recorded during a 0.75 C charge experiment and 37.5 ◦C during a 0.75 C discharge under a 1.4 m/s flow rate. While a 54.28% reduction in ΔTmax between the cells was achieved by increasing the air flow rate in the 0.75 C charge experiment from 1.4 m/s to 3.4 m/s. Conclusively, increasing BTMS performance with increasing air flow rate was a common trend observed in the experimental data after analyzing various experiment results.

**Keywords:** air-cooled BTMS; electric vehicle; compact lithium ion battery module; ANN

#### **1. Introduction**

There is a growing global concern of the causes and effects of climate change which has led to stricter environmental regulations on carbon-based machines [1,2] coupled with huge advancements in portable battery technology—specifically, lithium ion electric vehicles (EVs) and hybrid electric vehicles, which are starting to disrupt the automobile industry markets by presenting themselves as the vehicle choice of the future [3,4]. Some major hindrances to electric vehicle mass adaptation are the range anxiety of EVs, the lack of super-fast charging and the lack of performance driving, etc. [1,5]. The performance driving and fast charging problems of EVs are due to the limitation of the lithium ion batteries in performing outside tight operating temperature ranges [6]. The range anxiety problem of electric vehicles is also attributed to the gravimetric density of lithium ion batteries (LiBs). When compared to traditional gasoline-powered vehicles, the average energy-to-weight ratio of lithium ion batteries is 0.3 MJ/kg and it is over 30 MJ/kg for gasoline-powered vehicles [7].

While the current gravimetric property limitation of LiBs may be a design constraint on EV performance, EV manufacturers have the freedom to design robust battery thermal management systems (BTMS) for EV battery packs (BP) to efficiently limit the amount of heat generated by the LiBs during their operating cycles (charge/discharge). One technique; a sub-classification (see Figure 1) of air-cooled BTMS employed by various researchers used in improving the cooling performance of a BTMS, is reviewed and investigated in this paper.

**Figure 1.** Classification of air-cooled battery thermal management systems (BTMS) and optimization parameters adapted from [1,4,8].

#### *1.1. Literature Review*

In recent years there have been many studies performed with the aim of improving the cooling performance of air-cooled BTMS by employing optimizing techniques as illustrated in Figure 1. The research studies conducted regarding the performance improvement of BTMS which deal primarily with design variables pertaining to manners of arranging cells inside a BP and the placement of cooling-air intake and exhaust vents to obtain the best performance are discussed in the following paragraphs.

Chen et al. (2017) performed a configuration optimization on prismatic lithium ion cells for a parallel air-cooled system. In this model, the BTMS is optimized through arranging the spacing among the battery cells to obtain the best cooling performance. The optimization strategy is applied several times on a developed flow resistance model and a heat transfer model until the appropriate cell spacing is obtained. Their results exhibited a 42% reduction in the maximum cell temperature over the design variable optimization iterations on the developed model [9].

By comparing an aligned versus staggered cylindrical cell arrangement for a BTMS (see Figure 2A,B), N. Yang et al. (2015) in [10] investigated the effects of transverse and longitudinal spacing between cylindrical cells in a BP with a forced-air cooling system. N. Yang et al. (2015) developed a numerical and thermal model for this BP, which was used to simulate the effects of various design variables on their BP model. The model with the best performance results was validated by physical experiment. N. Yang et al. (2018) reported that under a specific cooling-air flow rate, the maximum cell temperature rise in a BP is proportional to the longitudinal interval for staggered arrays, whereas the inverse holds for aligned cell arrays. Finally, they obtained a better performing BTMS model, by optimizing the longitudinal and transverse space between the cells, coupled with optimizing an air inlet duct width for a BP with aligned arrangements [10].

**Figure 2.** Schematic of aligned (**A**) and staggered (**B**) cell layout optimization adapted from [4,10].

Lu (2018) provided a parametric study of forced-air cooling for lithium ion batteries with staggered arrangements. They designed a three-dimensional simulation model (Gambit 2.4.6 CFD) of the BP that investigated the effects of cooling channel size and air supply strategy for the model. The CFD model was solved using the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. They deduced that a cooling channel size of 1 mm was appropriate for BPs with Panasonic 18,650 cells. Upon further investigation, they reported the best cooling performance was achieved when placing the cooling-air flow inlet and outlet on the top of the BP. Finally, they reported that the efficiency factor of a BTMS deceases with the number of cells in the horizontal direction; hence, they recommended a maximum of 10 cylindrical cells along the air flow direction for a BP [11].

In a more recent study, Chen et al. (2020) in their paper numerically studied five (5) BTMS battery pack configurations and verified simulation results by conducting physical experiments. They developed a simple method to achieve symmetrical air flow inside each of the five battery packs by repositioning inlet and outlet vents on each original battery pack design (I, II, III, IV and V) to get newly optimized BPs; (I1, II1, III1, IV1 and V1) as depicted in Figure 3 below. Further parametric optimization of cell spacing revealed that uneven cell spacing in the improved battery packs resulted in better BTMS cooling performance just as BPs with a symmetrical air flow path did over their original counterparts [12]

**Figure 3.** Asymmetrical vs. symmetrical BTMS battery packs adapted from [4,12].

#### *1.2. Current Study*

This paper investigates the performance of a battery thermal management system (BTMS) for a proposed battery pack model with "H" symmetrical air vents housing 100 NCR18650 lithium ion cells. The battery module is built in a 10P10S configuration with aligned cells. Maximum cell temperature (Tmax) and maximum temperature difference (ΔTmax) between cells were the performance criteria for the BTMS. The battery pack is investigated for three levels (1.4 m/s, 2.4 m/s and 3.4 m/s) of air flow rate combined using a full factorial experiment design method with two current rates (0.5 C and 0.75 C) under charging and discharging power cycles.

#### **2. Investigated Battery Module**

The cells in the battery module (Figure 4 above) are connected in a 10S10P configuration to provide a minimum rated power of 1.024 KWh minimum and 1.344 KWh maximum. Nominal data specification value of a single NCR18650 cell used in the battery module being tested are presented in Table 1 below.

**Figure 4.** Battery module investigated.



An experimental setup up was designed to test the battery module for real-life scenarios while varying optimizing parameters—cooling-air velocity and current flow rate of the battery pack.

The experimental setup in Figure 5 consists of a battery pack with four switch-mode power supply (SMPS) cooling fans, a 3D-printed part connecting a flexible vent pipe to connect the fans to the atmosphere, a CPX400D (Aim TTi, Huntingdon, United Kingdom) power supply, a 16-channel temperature data acquisition device (Applent, China), a 4000 W EA-EL 9200 electronic load (Electro Automatik, San Diego, CA, USA) and a 200 V EA-PSI 9200 (Electro Automatic, San Diego, CA, USA) power supply.

**Figure 5.** Experimental setup.

#### *2.1. Experimental Setup*

#### 2.1.1. Battery Pack

The battery pack in the experimental setup was designed and built from medium fiberboard (MDF) of 18 cm thickness with four vent holes of 0.07 m diameter (Figure 6a). The pack had dimensions (30 × 25 × 10 cm) and was built slightly larger than the exact volume of the battery module (24 × 24 × 10 cm). This extra volume in the MDF box was designed to create a partition that would accommodate the excess length of the thermocouple sensor wires attached to the cells in the battery module (see Figure 6b). Glass fiber, (a nonconductive and nonflammable material) was placed between the battery module top cover of the MDF board as a protective measure to prevent possible electrical and fire hazards present during the experiment and most importantly prevent a low-resistance path for air flowing into the battery pack (Figure 6c).

**Figure 6.** (**a**) Built battery pack from fiberboard, (**b**) Placement of thermocouples to the cells. (**c**) Protective wool placed on top of the battery cells.

#### 2.1.2. Temperature Data Acquisitions Device

In order to monitor and record the temperature of cells in the battery module during testing, a 16-channel Applent temperature data acquisition device in Figure 7 was employed.

**Figure 7.** Temperature data acquisition device (T-DAQ).

The T-DAQ used in the experimental setup was powered by an ARM microprocessor capable of measuring temperatures from a variety of thermocouple types (T, J, K, E, etc.) at three sampling rates (fast, medium and slow) and had a resolution of 0.1 ◦C. It allowed for multiple recording of temperature values from 16 channels simultaneously which it stored onto a USB stick or directly onto a computer via a USB-serial connection.

K-Type thermocouples sensors with lower and upper limits of 0 ◦C and 200 ◦C temperature ranges well within the limits of the expected temperature rise of the cells in the battery module to be tested were employed during the experiment to measure temperature profiles of selected cells.

The positions of cells to be monitored was systematically selected based on the assumption that the temperature of each selected cell would represent the local temperature of other cells in its surrounding. Factors such as the number of channels the T-DAQ is limited to impacted the decision to monitor only 16 cells out of 100 cells in the battery module, as well as the preexisting compact nature of the battery module (see Figure 8 below).

**Figure 8.** Thermocouple position selection and attachment.

The following measurements were taken to ensure proper contact between the sensor and the cells:


• Finally, the majority of the sensor wire length was kept folded in a separate partitioned section inside the MDF box to prevent accidental tension that might threaten or sever the connection between the sensor-cell attachment.

**Figure 9.** Sensor attachment measures.

#### 2.1.3. CPX400D Power Supply

To achieve cooling on the battery module in the battery pack, four (4) SMPS fans attached to the vents of the MDF box were connected in parallel and routed via two connecting cables on the MDF box to be powered simultaneously using the CPX400D power supply Figure 10 below. This method of connection ensured all the cooling fans operated at the same speed at any preset voltage.

Operating the SMPS fans in constant current mode, controlling the voltage input to the fans via the power supply allowed for the adjustment of power delivered to the fans hence controlling air flow into the battery pack.

**Figure 10.** Controlling fan speed with the CPX400D power supply.

Figure 11 shows the base air-flow configuration of the battery pack investigated in this thesis.

**Figure 11.** Battery vent configuration, inlet Fans I and II, outlet fans III and IV.

#### 2.1.4. Electronic Power Supply/Load

The electronic load and power supply used in this study were the Electro-Automatik (EA) heavy duty laboratory Direct Current (DC) load and power supply. The versions used in conducting the experiments—the EA-EL 9200 electronic load capable of an output of 4000 W and the EA-PSI 9200—operated at efficiency of up to 95.5% (see Figure 12).

To test the battery pack module for charge and discharge cycles during the experiments, 50 Amps-rated cables were used in connection between the battery pack, the electronic load and power supply.

**Figure 12.** EA electronic power supply and load.

As testing for two current ratings on the battery pack module (0.5 C and 0.75 C) were to be investigated, the load and power supply were programmed to a constant current rating of 0.5 C, and the maximum and minimum voltages set to fit the specification of the battery pack maximum and minimum cut off voltages (see Table 2). The Graphic User Interface (GUI) of the load/supply provided real-time voltage and current readings of the battery pack for monitoring purposes during the charge/discharge cycles.



#### *2.2. Designing of Experiments*

This study aimed to investigate the thermal performance of a hundred (100) NCR18650 lithium cells battery modules in a battery pack with four vents. The test process used in this study aimed to simulate as closely as possible near real-time application scenarios, hence the ambient conditions such as room temperature are considered an uncontrollable parameter so that little or no action is taken to control or alter ambient conditions during the test period.

After defining factors and their levels to be tested for experiment in this study, various design of experiment (DOE) methods such as Plackett–Burman, Taguchi, latin square and full factorial posed as viable methods to be used in planning and designing the experiments to be carried out. After assessing various strength and features of each method, the "full factorial experiment design" was settled for as it allowed for a study of the main and interacting factor (air and current flow rate) effects on the battery module and also allowed for the development of a response surface of the design space tested. The full factorial method employed also provided the maximum number of experiments be performed for selected factors and levels. A total number of thirty-six (36) experiments were carried out (due to repetition) and twelve (12) unique experiments analyzed after the results of experiments with similar combinations of factors were averaged.

Table 3 below shows the various factors and levels tested during the experiment and the experiment design development code using MATLAB (R2016B, Mathworks, Inc., Natick, MA, USA, 2016).



DOE= 1 1 2 1 1 2 2 2

1 3 2 3


**Table 3.** *Cont*.

#### *2.3. Experiment Procedure*

The charge/discharge method employed while testing the battery pack performance followed the constant current–constant voltage (CC–CV) or Galvanostatic method. Employing this method of charging, the battery module is initially charged at a specified current rate of 0.5 C (16 Amps) from its minimum cutoff voltage of 32 V until it barely reaches its maximum cutoff voltage—typically 41.99 V. At this stage in the charging process, the voltage is held at constant until the current flow rate reaches 0.3 − 0.2 Amps.

Before each cycle of the experiment, the cooling fans were inspected and set to the required level of air flow rate and measured with an anemometer. As the battery pack design employs two inlet cooling fans, the area of the vents calculated in Table 4, was doubled to determine the total volume of air being pushed into the battery pack at every set cooling fan speed.

After each charge/discharge cycle was completed, time was allowed for the cells in the battery module to rest in order to ensure electrochemical stability [14] before a new cycle commenced. This waiting period also allowed for the entire battery module to reach a uniform cooled temperature. Figure 13 illustrates the systematic steps carried out to perform each experiment cycle.


**Table 4.** Battery Pack Parameters.

**Figure 13.** Experiment cycle procedures. CC-CV: constant current–constant voltage.

#### *2.4. Objective Functions Investigated*

Temperature profiles of sixteen (16) cells from the battery module were monitored and recorded by the K-type thermocouples and the temperature DAQ as the output variables of the experiment. An average of 172 temperature data points (corresponds to 172 min) were generally recorded during the 0.5 C level charge experiment and 150 data points during the charging experiment with 0.75 C current rate. Generally, lower times of discharging period were observed for the 0.5 C and 0.75 C experiments.

The temperature values recorded during each charge/discharge cycle experiment were stored in a generic created file by the T-DAQ which was retrieved for data processing for data analysis.

For results analysis of the measured temperature profile of selected cells in the battery module, the nomenclature depicted in Figure 14 was adopted to address various individual cells (e.g., Cell#01, Cell#07, etc.), or a group of cells in a row as Row 1, Row 2, Row 3 and Row 4.

**Figure 14.** Sensor position nomenclature.

#### 2.4.1. Maximum Temperature (TMAX)

The performance and longevity of a cell operating under any given charge or discharge cycle greatly relies on its operating temperature not exceeding 40 ◦C [13,15,16]. The maximum temperature (TMAX) of any individual cell in a battery pack cooled under any battery thermal management system is therefore indicative of the overall performance of the BTMS system.

#### 2.4.2. Temperature Increase (TINC)

The Temperature increase (TINC) represents the temperature difference between the initial temperature (TI) and the highest temperature (TH) of each measured cell in the battery pack. This measure, similar to the maximum temperature of a cell in the battery pack, is indicative of the performance of a BTMS but takes into consideration the temperature profile of each measured cell in relation to its neighboring cells. It also allows for the measure of temperature uniformity between cells in similar rows—one (1) through four (4)—or submodules. For a better BTMS performance, temperature uniformity between cells improves charging uniformity.

#### 2.4.3. Temperature Difference (ΔTMAX)

The maximum allowable temperature between cells in a BP of 5 ◦C has been reported in several studies including [16–19], to promote battery balancing and uniform charging and discharging during the LiB's operating cycle. The average temperature of cells in each row was determined to determine the temperature difference among cells in the battery module for each experiment performed.

Typically, an experiment with a combination of design levels which yields a temperature difference among various cells in a battery pack above 5 ◦C would be considered to have performed poorly.

#### **3. Results and Discussion**

This section provides a concise and precise description of the experimental results, their interpretation as well as how they are interpreted within the perspective of previous studies.

#### *3.1. Thermal Performance of BTMS*

The maximum temperature experienced by monitored cells in the battery pack during the experiment performed in this study were obtained by averaging the temperature values of experiments performed under similar combinations of design parameters after repetition. Figure 15 presents a capture of the results of all the tests performed in this study.

The data points are plotted based on the arrangements of cells in the battery pack with respect to the cooling-air flow channel; so that maximum temperature (TMAX) of cells in Row 1 (Cells: #01, #05, #9, #13) which are closest to the inlet vents are plotted first following the systematic pattern through to cells in Row 4 based on the illustration presented in Figure 14, page 11 above.

From the graph of results presented in Figure 15 a common trend in the thermal behavior of cells in Row 1, irrespective of the current rate, charging cycle or the cooling-air speed, is that they recorded the least maximum temperature. This can be associated to the fact that they naturally experience the effects of cooling air pumped into the battery pack at its ambient state in terms of temperature and speed. Another factor that plays greatly to this observed trend is the absence of accumulated heat generated by collective cells in the battery pack at the inlet vent area.

Another common trend observed in the results across all the graphs in Figure 15 is the relatively similar maximum temperatures in the battery packs during the discharge cycle and the charge cycle experiments. Quantitatively, the absolute peak temperature obtained by the cell in channel 12 during the 0.5 C charge cycle is 30.7 ◦C, and 29.3 ◦C during the discharge cycle under a 1.4 m/s cooling rate. Table 5 presents further comparisons during the charge and discharge cycle for cell #06 observed during tests carried out in this study.

**Figure 15.** Thermal characteristics of the battery pack.

**Table 5.** Disparities in Maximum Temperature of Cell 12 during Charge/Discharge Cycle.


In the data presented in Figure 15 there is a relatively bigger difference in the thermal behavior of the battery pack during its operation under a cooling-air flow rate of 1.4 m/s as compared to the performance between the air flow rates of 2.4 m/s and 3.4 m/s. The closeness in performance of the battery pack for air flow rate 2.4 m/s and 3.4 m/s is observed for charging and discharging under 0.5 C and for discharging under 0.75 C while the trend does not hold true for charging under 0.75 C. This break in trend can be associated with the tendency of lithium ion cells to generate significantly heat at a higher current rate.

The general increase in the trend of the maximum temperature registered in the cells as they move further away from the inlet vents is observed for cells 1 through 16 in the entire test performed and can be associated with the effects of heat accumulation and increase in resistance of the flow of the cooling-air path. Similar effects have been reported in [18,20] and measurements such as bidirectional air flow have been proposed and investigated for battery packs minimizing cell maximum temperature and inter cell temperature difference hence improving temperature uniformity in the cells of a battery pack [18,20,21].

A critical study of the thermal result of the battery module presented in Figure 15, cellmonitored by channel 12 of the T-DAQ is noticed to always record slightly lower temperatures than cells in its locality (Row 4). Upon investigating this behavior, it was observed that Cell 12 happens to be directly in front of an exhaust vent hence it is hypothesized that Cell 12 experienced slightly better cooling as

the heated air in the battery pack was constantly vented from its position. This phenomenon would also prevent heat accumulation at that locality.

Finally, comparing results obtained for the battery pack performance presented in this study, an averaged maximum temperature of 36.1 ◦C was obtained for the 0.75 C charge experiment at a 1.4 m/s flow rate and a temperature value of 37.5 ◦C after three repetitions of discharging at 0.75 C and 1.4 m/s. In a real-life application, charging under such conditions (0.75 C & 1.4 m/s) would not be recommended as the optimal temperature for operating lithium ion cells is 40 ◦C [13,22]: a value which the worst-obtained results in this study (4 to 5 ◦C) is just shy of.

#### 3.1.1. Effects of Air Flow Rate on Maximum Temperature

From previous research conducted in the literature review stage of this study, the general trend observed in many published research under BTMS studies is that a higher cooling-air flow rate yields better BTMS performance in terms of the objective functions: minimization of maximum cell temperature, increases temperature uniformity amongst cells and minimizes temperature differences between cells.

A similar trend has been observed for the battery pack model presented and tested in this study. As shown in Figure 16. The test results presented in Figure 16 just as in Figure 15 are obtained after averaging the temperature data recorded for the unique experiments after repetition.

**Figure 16.** Effects of air increasing air flow rate on maximum temperature.

#### 3.1.2. Effects of Air Flow Rate on Temperature Difference

Investigating the performance of the battery pack for temperature difference between cells, the average temperature of cells in each row (one through four) is determined for all the individual unique experiments. This measure taken reduces the measured temperature output from sixteen cells to four cells classified by their positions in the battery pack (see Figure 14, page 11 above). After classification of all sixteen cells into four rows, the maximum temperature in each row is determined. Lastly, the absolute difference in TMAX between all the combinations of rows is presented in Figures 17 and 18.

In Figure 17, it is observed that for the lower current rate of 0.5 C tested, the majority of temperature differences between rows measured in the battery pack is below 5 ◦C. The maximum temperature difference measured during experiments conducted under the 0.5 C current rate was recorded to be 8 ◦C during a charge cycle under 1.4 m/s and 6.37 ◦C for a discharge cycle under the same flow rate which occurred between cells in Row 1 and Row 4.

For flow rates of 2.4 and 3.4 m/s tests under 0.5 C, the temperature difference between all interacting rows in the BP was kept well below 5 ◦C.

**Figure 17.** Effects of air flow rate on temperature differences (0.5 C).

In Figure 18, which plots the cell temperature difference for experiments conducted under a 0.75 C current rate, the temperature differences between Row 1 and Row 2, Row 1 and Row 3, Row 1 and Row 4 and Row 2 and Row 4 were observed to be above the 5 ◦C threshold of under air flow rate of 1.4 m/s during the charge and discharge experiments.

As the air flow rate increases to 2.4 m/s, the temperature difference which occurred under the charge cycle is reduced from three to two interactions (Rows 1 and 3, Rows 1 and 4) similar to results obtained for the 0.5 C charge experiment under 1.4 m/s.

The maximum temperature differences between Rows 1 and 4 during the charge and discharge cycle under 0.75 C were 13.81 ◦C and 12.42 ◦C respectively for 1.4 m/s flow rate. These values reduced to 6.0 ◦C and 5.25 ◦C under an air flow rate of 3.4 m/s.

#### *3.2. Battery Pack Model Development*

In this section, two model development techniques are applied to the data set applied and obtained from the experiments in this study. Raw input data as described in Table 6 and maximum temperature data obtained from the 16 monitored cells are used as input and output training data for an artificial neural network (ANN) algorithm to develop a model for the battery pack investigated in this study. All 12 unique current rate and air flow rate combination experiments developed by the full factorial DOE method are used as input data (X,Y) with the averaged absolute maximum temperature of each unique experiment used as an output (Z) to develop a surface regression model.


**Table 6.** Artificial Neural Network (ANN) Input Training Data Sample.

#### 3.2.1. Artificial Neural Network

An artificial neural network (ANN) is a set of interconnected neurons that mimic information processing, similar to humans. It provides a function for creating, training, visualizing and simulating neural networks capable of performing classification, regression, clustering time-series forecasting and dynamic modeling [23,24]. A neural network consists of a two layer feed-forward network with sigmoid hidden neuron and linear output neurons that can fit multidimensional mapping problems arbitrarily well, given consistent data and enough neurons.

Several types of neural network and how they are applied to solve the specific problems they are suited for have been demonstrated in literature. Peculiar to research on lithium ion batteries, X. Qian, et al. in [25] applied neural networks in optimization of his design parameters for a proposed battery pack model and H. Sassi et al. applied ANN to an empirical data set to develop a model to predict the State of Charge (SOC) level of lithium ion cells studied in their work [23].

In this study, an ANN architecture model (Figure 19) is trained offline with the input data set from all experiments conducted in this study. Input data included the charge cycle (represented as 1), discharge cycle (represented as 0), the ambient temperature during the experiment, the current rate and the air flow rate (Table 6) while the maximum temperature of all monitored cells were fed as output data to the neural network.

**Figure 19.** ANN architecture.

In total, a matrix of 4 by 37 and 16 by 37 data size were used as input and output data sets respectively. Seventy percent of input data was allocated for the neural network for model training while 15% each was allocated for the testing and validation phase of the ANN model development.

After several iterations of training, a model obtained with an R value (correlation value) of 0.99139 was obtained between the fitted model and the given training data, 0.9812 correlation R value between the fitted model and the given data for testing and an R value of 0.98869 for an overall correlation between the actual outputs and the targets was obtained (see Figure 20). In Figure 21, the error histogram is plotted showing the difference between the target and actual output of the ANN training, which revealed that among the total samples considered, the majority of the error lies in the range 0.1034 to 2.08.

**Figure 21.** Error histogram.

The training algorithm selected for training the ANN module in this thesis study was the 'Bayesian Regularization' algorithm for its performance with difficult, small and noisy data sets [24]—a critical feature of the data output obtained during the conducted experiments in this study.

#### 3.2.2. ANN Model Validation/Error Analysis

After the ANN model was developed and trained with experimental data, a simulink model illustrated in Figure 22 and a MATLAB function code was generated as a representation of the model. In this chapter, the accuracy of the model developed was tested in a closed loop fashion by comparing the model output value to a set of experimentally obtained output values and finding the absolute percentage error between the two values for a given set of input data. A lower percentage error value between a predicted and measured value is desired for a good model and implies such a model will be good for studying the physical model applying optimization if need be.

Figure 23 shows the maximum temperature comparison between empirically obtained data for a discharge cycle experiment conducted with a 0.75 C current rate and 2.4 m/s air flow rate versus the obtained maximum temperature values predicted by the trained model. Figure 23 shows a close relation between the experiment and predicted model output with an absolute maximum percentage error of 1.84%. As Figure 23 compares and presents the relative error between the outputs of the trained ANN model and actual experimental output values for a given input data set, Figure 24 illustrates the error percentage graph between the predicted and actual maximum temperature values for the entire experiment input data. The data in Figure 24 showed that 93% of the entire input-data-predicted output by the ANN model when compared to their counterpart experimentally obtained output had an absolute percentage error of less than 4%. A maximum percentage error of 10.38% between a predicted and an actual output for a given set of input was measured.

**Figure 22.** ANN simulink model.

**Figure 23.** Predicted maximum cell temperature (Tmax) versus actual value.

**Figure 24.** Percentage error between real output and predicted output values for the entire experiments.

#### 3.2.3. Response Surface Model (RSM) Development

An RSM comprises regression surface fitting over a bounded design space to predict approximated responses for input variable combinations not accounted for during a physical or simulation experiment [26]. Usually, a design of experiment method is used to obtain the minimum number of experiments needed to develop an RSM. In the RSM method implemented in this study, the approximation function used in developing the response surface illustrated in Figure 25 is a second degree polynomial. Most response surfaces functions are generated with polynomials depending on the number of data points provided from an experiment.

**Figure 25.** Response surface model (RSM) developed for charge and discharge experiment.

The RSM developed for the battery model was done using a MATLAB curve fitting tool box. Fitting parameters R2 adjusted were used to determine the goodness of fit, and sum of square error (SSE) and mean square error are used to determine the predictability of the model. The R2 adjusted values lie between 0 and 1 for which a good response surface has a value closest to 1 [26,27]. On the contrary, an SSE and Mean Square Error (MSE) value closer to zero is desired for a good response surface. An SSE value closer to zero indicates a model has smaller random error components hence higher prediction accuracy [27]. Just as for SSE, an MSE value closest to zero is desired for a good response model.

After various variations of the fit method applied on the variables were tested to obtain the best adjusted R<sup>2</sup> and SSE values, the model was developed with the polynomial function with robustness "off" as this trail produced the most suitable fitness parameters results. Table 7 provides a comparison of various selection criteria values obtained during the iterative training process.


**Table 7.** Comparison of Various Fitness Parameters for the Developed Regression Model.

\* Root Mean Square Error. \*\* poly21: A second degree polynomial fit with two degrees of X and one degree of Y. SSE: sum of square error.

The model equation of the RSM developed for the charge and discharge experiments performed for the battery pack and module in this study is presented as:

$$f(\mathbf{x}, \mathbf{y}) = P\_0 + P\_1 \mathbf{x} + P\_2 \mathbf{y} + P\_3 \mathbf{x}^2 + P\_4 \mathbf{x} \mathbf{y} \tag{1}$$

where *x* and *y* are designed variables air flow rate and current rate respectively, *P*<sup>0</sup> − *P*<sup>4</sup> are coefficient constants and *f*(*x*, *y*) is the design objective function. Table 8 presents coefficient values for the developed model equations.


**Table 8.** Model Equation Coefficients.

#### 3.2.4. RSM Model Validation/Error Analysis

In an attempt to validate the regression model developed in this study, equations of the developed RSM's were tested for experimental inputs to compare the output results. Figure 26 plots and compares the predicted absolute maximum temperatures against the actual maximum temperatures for the charge experiment at 0.5 C and the discharge experiment at 0.75 C.

**Figure 26.** Regression model predicted output vs. actual output for a sample input.

Table 9 below shows the absolute relative error calculations between the predicted model and the actual outputs for absolute maximum temperature in a battery pack for all twelve of the unique experiments performed. The results showed the developed model predicts accurately with an absolute maximum error of approximately 3.00%.


**Table 9.** Absolute Relative Error between Regression Model and Actual Experiment.

#### **4. Conclusions**

In this study, a battery thermal management system (BTMS) for a battery pack housing a battery module consisting of a hundred NCR18650 lithium ion cells was designed and tested in relatively cold ambient conditions.

The BTMS performance was tested for two major objective function criteria which are:


The temperature limit threshold for operating LiBs was optimally obtained from various literature and battery data specification documents.

Design variables—three levels of cooling-air flow rate and two levels of current rate were combined using a full factorial experiment design method to develop a full array of experiments performed on the BTMS for the battery pack after experimentation. General BTMS performance trends were observed in the obtained results such as higher current rate experiments produced relatively higher maximum temperature amongst the cells and significant changes in maximum cell temperature and temperature difference are observed as air flow rate is increased.

Upon investigating the effects of increasing air flow rate on maximum cell temperature, a 15.09% reduction in maximum temperature recorded by a cell was achieved during a charging experiment with a 0.5 C current rate by increasing the air flow rate from 1.4 m/s to 2.4 m/s. For the same charge experiment, there was no significant improvement in the maximum temperature recorded at a higher air flow rate of 3.4 m/s. On the contrary, at a higher current rate of 0.75 C charging, a 13.20% reduction in the maximum temperature of a cell was achieved by increasing the air flow rate from 1.4 m/s to 2.4 m/s. Further increment of the air flow rate to 3.4 m/s produced a 22.81% reduction in the maximum cell temperature.

The results summarized above aids in drawing a hypothesis that for the investigated battery pack design, for each current rate, there exists an optimal cooling-air flow rate that if exceeded, will yield little or no improvement in an operating BTMS performance at a specific range of ambient conditions. This hypothesis will prove vital in scenarios where power consumption of an operating BTMS is a critical objective function to be minimized. This will be applicable and vital to the development of an intelligent/dynamic BTMS where cooling operation of a BTMS will operate in a dynamic mode depending on the current profile the battery module.

When assessing the BTMS performance based on temperature difference between cells, for a cooling-air flow rate of 1.4 m/s for every cycle experiment, there was always an instant where the maximum temperature difference between monitored cells exceeded 5 ◦C, reducing the performance of the BTMS. However, at higher speeds of 2.4 m/s and 3.4 m/s, in experiments under 0.5 C, the temperature difference among cells in the battery pack was found to be always below the 5 ◦C threshold.

Lastly, for 0.75 C experiments under 1.4 m/s, 100% of the interactions between cells in Rows 2, 3 and 4 with Row 1 exceeded 5 ◦C. However, after increasing the air flow rate temperature difference between cells in Rows 2, 3 and 4 with Row 1 which exceeded 5 ◦C, is reduced by 33.33%. The highest temperature recorded under 0.75 C with 2.4 m/s was found to be 7.71 ◦C (a 44.14% reduction from operation under 1.4/s) and 6.3 ◦C (a 54.38% reduction from operation under 1.4/s) for 3.4 m/s between cells in Row 4 and Row 1.

The observations made aides in affirming the conclusion based on literature that a higher cooling-air flow rate reduces maximum cell temperature and temperature difference between cells in a battery pack due to the increased convective heat transfer coefficient of air at higher velocities. However, the gradient in temperature difference amongst cells remains the same with at least a single case of interaction between cells at different positions in the battery module exceeding 5 ◦C for the investigated battery module.

To fully obtain an air-cooled BTMS performance with the possibility of no interacting cells in the battery module having ΔTmax exceeding 5 ◦C, a bidirectional cooling flow path scheme must be implemented.

**Author Contributions:** The work carried out and presented in this manuscript was carried out as part of A.A.A.H. Master's program completion requirement under the close supervision of D.S. as his thesis project supervisor. All authors have read and agreed to the published version of the manuscript.

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

**Acknowledgments:** The authors would like to acknowledge the entire EMU EVDC [28] and the director Davut Solyali for the support provided in the successful completion of this project in terms of experimental equipment setup and a conducive laboratory working environment.

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

#### **References**

1. Kim, J.; Oh, J.; Lee, H. Review on battery thermal management system for electric vehicles. *Appl. Therm. Eng.* **2019**, *149*, 192–212. [CrossRef]


© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Torque and Battery Distribution Strategy for Saving Energy of an Electric Vehicle with Three Traction Motors**

#### **Yi-Hsiang Tseng <sup>1</sup> and Yee-Pien Yang 1,2,\***


Received: 12 March 2020; Accepted: 8 April 2020; Published: 11 April 2020

**Abstract:** A torque and battery distribution (TBD) strategy is proposed for saving energy for an electric vehicle (EV) that is driven by three traction motors. Each traction motor is driven by an independent inverter and a battery pack. When the vehicle is accelerating or cruising, its vehicle control unit determines the optimal torque distribution of the three motors by particle swarm optimization (PSO) theory to minimize energy consumption on the basis of their torque–speed–efficiency maps. Simultaneously, the states of charge (SOC) of the three battery packs are controlled in balance for improving the driving range and for avoiding unexpected battery depletion. The proposed TBD strategy can increase 7.7% driving range in the circular New European Driving Cycle (NEDC) of radius 100 m and 28% in the straight-line NEDC. All the battery energy can be effectively distributed and utilized for extending the driving range with an improved energy consumption efficiency.

**Keywords:** torque and battery distribution; particle swarm optimization; electric vehicle

#### **1. Introduction**

Hybrid and pure electric vehicles (EVs) have been commercially available for many years. A lot of research that focused on multiple propulsion and energy storage systems and the related power split and energy economy strategies has become imperative issue in EVs. For EVs with only one battery pack, it is important to balance the capacity of battery cells for improving its lifetime. Li et al. [1] presented a real-time state-of-charge (SOC) calculation method for a pure EV, where the lithium battery was simulated with a second-order resistance–capacitance (RC) model and the remaining capacity in battery cells was balanced by fuzzy control through a set of bi-directional fly-back direct current-direct current (DC–DC) converters. Gallardo-Lozano et al. [2] introduced a shunting transistor method to balance battery cells during the recharging and driving modes. Huang and Abu Qahouq [3] proposed an energy sharing control scheme to regulate the DC bus voltage, and simultaneously, to balance the SOC of battery cells with micro DC–DC converters. Pham et al. [4] addressed a fast-balancing topology for lithium-ion batteries in an EV by transferring the power in high-voltage cells directly to low-voltage cells through DC–DC converters. During battery charging, Dung et al. [5] eliminated the racing phenomenon by a pulse width modulation (PWM) based equalization process among battery packs so that the charging time was reduced by 48%.

For EVs with hybrid energy storage systems (HESSs), Jin et al. [6] and Akar et al. [7], respectively, proposed for their HESS of batteries and ultracapacitors a fuzzy control-based power management strategy to reduce battery degradation. A PWM technique was introduced by Menon et al. [8] for balancing the SOC of independent battery packs by continuously regulating the power flow from

two inverters on the basis of the driving demands. Tanaka et al. [9] used two batteries in a hybrid EV for investigating a high-efficiency energy conversion system to improve the driving range. The main battery provided fundamental power that did not need to be passed through a DC–DC converter, while additional power was supplied by a sub-battery through the DC–DC converter.

Lately, pure EVs with multiple traction motors have been commercially available. Examples are the Porsche Mission E Cross Turismo with two permanent magnet synchronous motors (PMSMs) and the Audi e-tron quattro with three traction motors. Rossi et al. [10] introduced a two-motor, two-axle, two-battery pack powertrain configuration for a compact EV and proposed an optimal front-rear motor transmission combination for the best driving performance. Several advantages of multiple motors and battery packs were addressed: the increased fault tolerance; the reduction of power rating in electric drive with possible simplification and cost reduction; the reduction of insulation level and electromagnetic emission of low-voltage power modules; and the additional degrees of freedom in torque vectoring for stable vehicle maneuverability.

Some studies have focused on the driving and braking torque distributions on motors for vehicle stability and handling performance. Yin at al. [11] used a hierarchical electronic stability controller (ESC) to distribute direct torque to four in-wheel motors of an EV for improving the vehicle stability and handling performance. Zhai et al. [12] proposed a similar ESC algorithm to improve vehicle stability by distributing the driving and regenerative braking torque for an EV with four independent in-wheel motors. Other studies have focused on the energy economy of EVs that use torque split strategies to arrange multiple traction motors. Dizqah et al. [13] formulated a parametric energy-efficient torque distribution optimization problem depending on the speed of an EV driven by four identical drivetrains, resulting in an energy consumption reduction of 0.1%–0.5% under various European driving cycles. An EV with four in-wheel motors was introduced by Fujimoto and Harada [14] where the slip ratio and motor loss were optimized on the basis of the vehicle speed and acceleration over the Japanese JC08 cycle. Sun et al. [15] proposed an online braking torque allocation scheme for a four-wheel-drive EV that minimized tire and electromechanical losses. Simulations showed that the driving efficiency was increased 4.3% in high speed driving cycles and 1.5% in normal speed driving cycles.

Yang et al. [16] proposed a real-time torque distribution strategy for a pure EV with three motors and three battery packs. The front wheels were driven indirectly by a traction motor through reduction gears, while two rear wheels were driven directly by two in-wheel motors. Torque distribution was determined by the particle swarm optimization (PSO) theory for minimizing energy consumption on the basis of the torque–speed–efficiency (TNE) maps of all the traction motors. Subsequently, Yang and Chen [17] introduced a coupled parallel energy saving and safety strategy that minimized energy consumption by torque distribution according to the PSO theory. The stabilizing direct yaw moment was also minimized on the basis of the stability region on the phase plane of sideslip angle and yaw rate.

Most of the above research focused either on the battery energy distribution to keep the battery cells in balance, or on the torque distribution for vehicle stability, handling, or energy economy. This paper extends the authors' previous study [18] that proposed a coupled parallel energy balancing and energy saving strategy by keeping the SOC of three independent battery packs in balance and distributing the driving torque of three traction motors during vehicle motion. Section 2 introduces vehicle configuration, longitudinal and lateral vehicle dynamics models, tire and transmission models, and battery SOC model. Section 3 elaborates the proposed torque and battery distribution strategy, and Section 4 provides experiments of model-in-the-loop (MIL) and hardware-in-the-loop (HIL) simulations, and road tests. Section 5 presents concluding remarks.

#### **2. Vehicle Configuration**

The EV was fitted with a 15-kW radial-flux PMSM that drove the two front wheels indirectly through a gearbox reducer and two identical 7-kW axial-flux PMSMs to drive the left and right rear wheels directly through the hubs (Figure 1a). The control strategy was validated by CarSim simulation

software with 15 mechanical degrees of freedom (DOF) for the four-wheeled vehicle. The steering system had one DOF, each wheel had one spin DOF, each suspension had two DOF, and the sprung mass was simplified as a rigid body with six DOF. The vehicle variables for the longitudinal and lateral dynamics models are defined in Figure 1b,c.

**Figure 1.** Electric vehicle configuration and variable definitions (**a**) propulsion system of multiple motors, and (**b**) the longitudinal and (**c**) lateral vehicle dynamics models.

Figure 2a,b provide the TNE maps from the experiments for the driving modes of the three traction motors. The braking modes were estimated from the mirror image of 75% efficiency of the driving mode. The maximum torque was 150 Nm and the maximum speed was 2400 rpm for the 15-kW front motor, and they were 122 Nm and 1200 rpm for the 7-kW rear motors. Three motor control units were responsible for driving the three motors, and three lithium-ion batteries were deployed for providing the power: one pack of 144 V, 72 Ah, and 10.45 kWh for the front drive and two packs of 72 V, 72 Ah, and 5.2 kWh for the two rear drives.

**Figure 2.** Torque-speed-efficiency maps: (**a**) the driving mode of the 15-kW front motor, (**b**) the driving modes of the two 7-kW rear motors.

#### *2.1. Longitudinal Vehicle Dynamics Model*

When the vehicle travels in a straight line, the longitudinal traction forces are usually simplified as *Fxr* = *Fxr*<sup>1</sup> = *Fxr*<sup>2</sup> and *Fx f* = *Fx f* <sup>1</sup> = *Fx f* 2. The force with subscript 1 is the force exerted on the left tire, while 2 on the right tire. The tractive force *Fx* and the normal forces *Nf* and *Nr* of the front and rear wheels were obtained by the following equations:

$$F\_x = M\dot{V}\_x + Mg\sin\theta + \frac{1}{2}\rho \mathbf{C}\_d A\_f V\_x^2 + 2\mathbf{C}\_t \left(\mathbf{N}\_f + \mathbf{N}\_r\right) \tag{1}$$

$$N\_f = \frac{M\_\mathcal{V} g L\_r \cos \theta - \frac{1}{2} \rho \mathcal{C}\_d A\_f V\_x^2 h\_a - \left[M\_\mathcal{V} h\_{\text{in}} + 2\left(m\_{\text{wf}} + m\_{\text{wr}}\right) r\_l\right] \dot{V}\_x}{2\left(L\_f + L\_f\right)} + m\_{\text{wf}} \mathcal{g} \cos \theta} \tag{2}$$

$$N\_{\rm r} = \frac{M\_{\rm vg}L\_{f}\cos\theta + \frac{1}{2}\rho C\_{d}A\_{f}V\_{\rm x}^{2}h\_{\rm u} + \left[M\_{\rm v}h\_{\rm u} + 2\left(m\_{\rm uv} + m\_{\rm uv}\right)r\_{\rm t}\right]\dot{V}\_{\rm x}}{2\left(L\_{f} + L\_{\rm r}\right)} + m\_{\rm uvg}\cos\theta\tag{3}$$

$$F\_X = 2\left(F\_{xf} + F\_{xr}\right) \tag{4}$$

$$M = M\_{\upsilon} + 2\left(m\_{wf} + m\_{wr}\right) \tag{5}$$

where *M* is the total vehicle mass; *Mv* is the vehicle mass excluding tire and wheel mass; *mw f* is the front tire and wheel mass; *mwr* is the rear tire and wheel mass; *g* is the gravity acceleration; θ is the slope angle in degrees; ρ is the air density; *Vx* is the longitudinal velocity of vehicle; *Fx f* and *Fxr* are the traction forces exerted on the front and rear tires; *Lf* is the distance from mass center to front tire; *Lr* is the distance from mass center to rear tire; and *rt* is the tire radius. Other vehicle specifications used in this paper are described in Table 1.

#### *2.2. Lateral Vehicle Dynamics Model*

As shown in Figure 1b, the lateral vehicle dynamics are described by a four-wheel model when the vehicle is cornering. The longitudinal, lateral, and yaw vehicle dynamic equations are expressed as:

$$\left[ (F\_{xf1} + F\_{xf2}) \cos \delta - (F\_{yf1} + F\_{yf2}) \sin \delta + F\_{xr1} + F\_{xr2} = M \left| \dot{V}\_x - \left( \gamma + \frac{d\beta\_\mathcal{V}}{dt} \right) V\_y \right| \tag{6}$$

$$(F\_{xf1} + F\_{xf2})\sin\delta + (F\_{yf1} + F\_{yf2})\cos\delta + F\_{yr1} + F\_{yr2} = M\left[\dot{V}\_y + \left(\gamma + \frac{d\beta\_v}{dt}\right)V\_x\right] \tag{7}$$

$$L\_f(F\_{yf1} + F\_{yf2})\cos\delta - L\_r(F\_{yr1} + F\_{yr2}) + \frac{L\_w}{2}(F\_{yf1} - F\_{yf2})\sin\delta + M\_z = I\_z\frac{d}{dt}\Big(\gamma + \frac{d\beta\_\upsilon}{dt}\Big) \tag{8}$$

$$M\_{\overline{x}} = L\_f (F\_{xf1} + F\_{xf2}) \sin \delta + \frac{L\_w}{2} (-F\_{xf1} + F\_{xf2}) \cos \delta + \frac{L\_w}{2} (-F\_{x1} + F\_{x2}) \tag{9}$$

where δ is the steer angle; *Fx f* <sup>1</sup> and *Fx f* <sup>2</sup> are longitudinal traction forces on the left and right front tires and these forces are assumed equal for δ = 0; *Fy f* <sup>1</sup> and *Fy f* <sup>2</sup> are lateral traction forces on the left and right front tires; *Fxr*<sup>1</sup> and *Fxr*<sup>2</sup> are longitudinal traction forces on the left and right rear tires; *Fyr*<sup>1</sup> and *Fyr*<sup>2</sup> are lateral traction forces on the left and right rear tires; γ is the yaw velocity; β*<sup>v</sup>* is the vehicle sideslip angle; *Iz* is the mass moment of inertia in the yaw direction; and *Mz* is the yaw moment for cornering. These equations were used to determine torque distributions when the vehicle is cornering.


**Table 1.** Vehicle Specifications.

For simplicity, the hill climbing resistance, aerodynamic drag, and rolling resistance of the last terms in (1) are omitted, and the roll and pitch motions are neglected. However, the vehicle in CarSim for the real-time HIL simulation was modelled with self-contained yaw, roll, and pitch dynamics.

#### *2.3. Tire Model*

The CarSim tire lookup table that was obtained directly from the laboratory measurements was used to model the tire characteristics. The friction coefficient between the tire and road surface was chosen at 0.85, the longitudinal and lateral traction (or friction) forces on the tire were expressed as a function of normal force and tire slip ratio. Once the vehicle velocity, acceleration or deceleration, the normal forces *Nf* and *Nr* are known, the slip ratio of each wheel can be obtained. The front and rear wheel speeds ω*<sup>f</sup>* and ω*<sup>r</sup>* are therefore determined by the definition of tire slip ratio, as follows:

$$\text{Acceleration}: \ \omega = \frac{V\_{\text{x}}}{r\_{\text{f}}(1-\lambda)}, r\_{\text{f}}\omega > V\_{\text{x}} \tag{10}$$

$$\text{Deceleration} : \omega = \frac{V\_x (1 + \lambda)}{r\_t}, r\_t \omega < V\_x \tag{11}$$

where the tire slip ratio λ represents λ*<sup>f</sup>* and λ*<sup>r</sup>* that correspond to the speeds ω*<sup>f</sup>* and ω*<sup>r</sup>* of the front and rear wheels.

#### *2.4. Transmission Model*

After the wheel speeds and accelerations are obtained, the output torque *Tm f* of the front traction motor, the output torque *Tmr* provided by the right rear in-wheel motor, and the output torque *Tml* provided by the left rear in-wheel motor can be calculated under the following assumptions:


Therefore, when the vehicle accelerates:

$$Front\;\text{ubech}\;s:\;T\_{mf}n\_{\mathcal{S}} = \frac{2I\_{\text{w}}\dot{\omega}\_f}{n\_{\mathcal{S}}} + 2F\_{xf}r\_t\tag{12}$$

$$\text{Rear\;wheels}: T\_{mi} = I\_{\text{uv}} \dot{\omega}\_{\text{i}} + F\_{\text{xr}} r\_{\text{t}} \quad \text{i} = r, \text{ l} \tag{13}$$

where *ng* is the reduction ratio of gearbox; *Iw* is the wheel inertia; ω*<sup>f</sup>* is the speed of the front traction motor; ω*<sup>r</sup>* and ω*<sup>l</sup>* represent, respectively, the speed of the right and left rear in-wheel motors. In the steady state for a small steer angle and by neglecting frictions on wheel motors, the yaw moment Equation (9) can be simplified as

$$T\_{mr} = T\_{ml} + 2r\_t \mathcal{M}\_z / L\_w \tag{14}$$

where *Lw* is the distance between two rear wheels. This equation will be used for determining the real-time torque distribution in the PSO process when the vehicle is cornering. For a straight-line driving, *Mz* = 0 and *Tmr* = *Tml*.

#### *2.5. Battery State of Charge Model*

The SOC of each battery pack on the EV is estimated by the following equation:

$$\text{SOC} = \text{SOC}\_i - \frac{\int\_0^t I\_b dt}{Q\_b} \tag{15}$$

where *SOCi* is the initial state of SOC, *Ib* is the battery current, and *Qb* is the battery maximum capacity. By a simple internal resistance model, the output power of battery is estimated by:

$$P\_{\rm b} = V\_{\rm ac} I\_{\rm b} - I\_{\rm b}^2 \mathcal{R}\_{\rm b} \tag{16}$$

where *Rb* is the internal resistance of the battery and was set at 0.17 Ω for all the battery packs in the MIL simulations in Section 4. The open circuit voltage (OCV) *Voc* is a function of SOC and is obtained from experiments for each battery pack. Figure 3 illustrates the OCV curve of the front battery pack. Accordingly, the battery current *Ib* is easily calculated from (16).

**Figure 3.** The open circuit voltage and state of charge curve of the front battery pack.

#### **3. Torque and Battery Distribution Strategy**

#### *3.1. Torque Distribution Strategy: Particle Swarm Optimization*

The total torque, *Tt*, used to accelerate the vehicle was

$$T\_t = (\mathbf{F}\_\mathbf{x}/r\_t) = T\_{mf}\mathbf{n}\_\mathcal{\mathcal{S}} + T\_{mr} + T\_{ml} \tag{17}$$

From (14), the corresponding yaw moment, *Mz*, in the steady state of a small steer angle was provided by the differential torque of the left and right in-wheel motors. The maximum and minimum torque ranges of the three traction motors were first determined on the basis of the TNE maps of the three traction motors, wheel angular speeds, SOC of the batteries, and current limits. PSO was then used to determine the best torque distribution for the three traction motors under the constraints of their operation ranges and Equations (14) and (17).

The PSO theory originated by observing the hunting behavior of a swarm of birds or fish. In the process of torque distribution, a particle is a point on a search space of TNE map. As shown in Figure 2a,b, three swarms of particles were initially distributed at random on the three TNE maps of the traction motors, and each swarm had N particles. Each particle had a position state, which was defined as the torque where the particle was located. The pedal command given by the EV driver was their common target at a specific vehicle speed.

Each particle at its initial position in the search space determined its best direction, and all the particles approached their common target with the minimal global effort.

$$\eta = \frac{T\_{mf}\omega\_{mf}}{\eta\_{mf}\Big(T\_{mf}, \omega\_{mf}\Big)} + \frac{T\_{ml}\omega\_{ml}}{\eta\_{ml}\big(T\_{ml}, \omega\_{ml}\big)} + \frac{T\_{mr}\omega\_{mr}}{\eta\_{mr}\big(T\_{mr}, \omega\_{mr}\big)} \tag{18}$$

During the PSO process, the N particles were renewed through J generations and reached the target of minimal energy consumption in the end. After the least energy consumption converged in each generation, the particles were updated according to their own best and swarm best solutions as

$$
\Delta T\_{mf,i}^{j+1} = wT\_{mf,i}^{j+1} + rand\_1 \times c\_{L1} \left( P\_i^j - T\_{mf,i}^j \right) + rand\_2 \times c\_{L2} \left( G^j - T\_{mf,i}^j \right) \tag{19}
$$

$$T\_{mf,i}^{j+1} = T\_{mf,i}^j + \Delta T\_{mf,i}^{j+1} \tag{20}$$

where the sub-index i stands for the ith particle; j stands for the generation number; *cL*<sup>1</sup> and *cL*<sup>2</sup> are learning factors; *G* represents the swarm's best known solution of all the particles; *Pi* represents its own best known solution of the ith particle; *rand*<sup>1</sup> and *rand*<sup>2</sup> are random values between 0 and 1; and *w* is the inertia weight. At the final generation, the output torques of the rear left and right motors were calculated:

$$T\_{ml} = \frac{T\_t - T\_{mf}}{2} - \frac{r\_t M\_z}{L\_w} \tag{21}$$

$$T\_{mr} = \frac{T\_t - T\_{mf}}{2} + \frac{r\_t M\_z}{L\_{av}} \tag{22}$$

Details of the original work of the real-time torque-distribution strategy by PSO for a pure EV with three traction motors were described in [16].

#### *3.2. Torque Distribution Strategy: Priority Torque Ratio in Front and Rear Motors*

For comparison, a priority torque ratio (PTR), *Pr*, can be assigned from 0 to 1 to the front motor with respect to the rear motors. For example, *Pr* = 1 means that the front motor takes the first priority for delivering the torque within its feasible range for driving the EV, while *Pr* = 0 expresses that the

rear motors have the top priority for delivering the torque over the front motor. Therefore, the torque given by the front motor is calculated as

$$T\_{mf} = \left(T\_{mf,\text{max}} - T\_{mf,\text{min}}\right) P\_r + T\_{mf,\text{min}} \tag{23}$$

where *Tm f*,*max* and *Tm f*,*min* are, respectively, the upper and lower limits of the front motor at a certain speed. If *Tm f* is calculated higher than or equal to the total torque *Tt* required for acceleration, the front motor will provide *Tt* as demanded. If *Tm f* is calculated lower than *Tt* even though *Pr* = 1, the rear motors must be responsible for delivering the rest portion of torque according to (21) and (22).

#### *3.3. Battery Energy Consumption*

The energy consumption and balance of the three battery packs were investigated when the torque distribution was executed by the PSO or PTR strategy. In this study, the urban driving cycle (UDC) of the New European driving cycle (NEDC) was used because of the limited motor speeds and battery voltage. Table 2 presents two simulation results for the energy consumption for the three battery packs after the EV drove (1) on a straight road and (2) clockwise on a circular path with a 100 m radius using the proposed PSO and PTR torque distribution strategies. For the cases of *Pr* = 1 and 0.75, the front traction motor had the highest priority by delivering power over the rear motors, and the rear battery restored more power from regenerative braking than that consumed for driving. This was an example of negative battery energy consumption.


**Table 2.** Energy consumption of battery packs.

For the three battery packs, energy consumption was found to be unbalanced, thereby causing an unbalanced SOC. If any of the three battery packs was depleted, the torque distribution strategy would fail. This could cause a serious deterioration in vehicle maneuverability and stability.

#### *3.4. Torque and Battery Distribution (TBD) Strategy*

Figure 4 shows the flowchart for the torque and battery distribution (TBD) strategy. Before the EV started from rest, the SOC of the front, rear right, and rear left battery packs was respectively measured as *SOCF*, *SOCL*, and *SOCR*. The SOC gap and SOC ratio were calculated:

1. SOC gap *(SOCg):* The SOC gap was defined as the difference between the SOC of the front battery pack and the lower SOC of the two rear battery packs. It was negative when the front battery had less power remaining than the rear batteries, and it was positive when the front battery had more

power than the rear batteries. In applications, a default value *SOCg* < −κ% (0 <κ< 2) can be assigned to determine the torque distribution mode (Figure 4).

2. SOC ratio (*SOCr*): The SOC ratio was defined as the ratio of energy consumption in terms of the SOC between the front battery pack and the two rear battery packs. On the basis of the simulation of straight road driving under the PSO strategy, as indicated in Table 2, the *SOCr* converged to 2.94 for the long-term operation of the UDCs. In applications, a default value, ρ (< 2.94), was assigned to determine the torque distribution mode under the TBD strategy.

**Figure 4.** Flowchart of the torque and battery distribution strategy.

Through the use of *SOCg*, the state of balance (SOB) of the three battery packs was investigated. The three states of battery balance are described:


Three torque distribution modes were then determined by the SOC gap (*SOCg*):

1. Mode 1: *Pr* = 1 was proposed when the front motor had the first priority for delivering the torque under the condition of *SOCg* > 0 and *SOCr* ≥ ρ.

At Mode 1, the SOC of the front battery pack was much higher than that of the rear battery packs. When the *SOCr* was larger than 2.94, the *SOCg* could increase continuously, and the battery balance could worsen even though the PSO strategy was executed. It was better for the front battery pack to reach a balance between the front and rear batteries.

2. Mode 2: The PSO strategy was prescribed when there was not much difference in the SOC of the three battery packs under the following conditions: *SOCg* = 0 or (*SOCg* > 0 and *SOCr* < ρ) or (0 > *SOCg* ≥ −κ% and |*SOCg*| was increasing).

Because the PSO strategy is superior to the PTR strategy for distributing the torque among the traction motors, it should be used whenever the difference in the SOC of the battery packs is negligible. For example, *SOCg* = 0 is an ideal case in which all of the batteries are in balance, and the PSO strategy

can save more energy than the other PTR strategies when distributing the torque. With *SOCg* > 0 and *SOCr* < ρ, the amount of power stored by the front and rear batteries was similar and sufficient. It was also an appropriate situation for torque distribution under the PSO strategy.

When 0 >*SOCg* ≥ −κ%, there was not much difference in the energy storage of the battery packs, and it was still safe to execute PSO even though the SOC gap was increasing.

3. Mode 3: *Pr* = 0 was proposed when the rear motors took top priority for delivering more the torque than the front motor under the following conditions: *SOCg* < −κ% or (0 >*SOCg* > −κ% and |*SOCg*| was decreasing).

At Mode 3, the SOC of the rear battery packs was much higher than that of the front battery. The consumption in the rear batteries had top priority so that the balance in the batteries could be restored. After the SOCg was restored within [0, −κ%], Mode 3 remained in operation because the SOC gap continued to decrease until the best balance state 2 was achieved. This avoided frequent shifts between Modes 2 and 3.

#### **4. Experiments**

#### *4.1. Model-in-the-Loop Simulations*

In Figure 5, the TBD strategy was simulated on a model-in-the-loop (MIL) platform. MATLAB Simulink was applied to model the TBD strategy, battery model, driver model, slip ratio control (SRC), and direct yaw moment control (DYC), while CarSim provided the vehicle dynamics. The driver model simulated human driver behavior by a proportional-integral (PI) controller. The SRC was responsible for stabilizing vehicle motion through the tractive control system (TCS) during acceleration and the anti-lock brake system (ABS) during deceleration. The TBD strategy was performed after vehicle safety was confirmed. Because of the limited motor speeds and battery voltages, only the UDC part of NEDC was used for MIL simulations.

**Figure 5.** Simulation block diagram of torque and battery distribution strategy.

Both the straight and circular road tests were simulated. Figure 6a shows the SOC records of the three battery packs during the TBD process for the EV driving a clockwise cornering on a circular path of radius 100 m for 3.5 UDCs of the NEDC. The indices ρ and κ were assigned at 1.0056 and 1, respectively.

At the beginning, the SOC of the front battery (91%) was higher than that of both rear batteries (90%). In addition, *SOCr* > 1.0056, the torque distribution of Mode 1, was executed until the *SOCr* reduced to 1.0056 at approximately 170 s, where the PSO of Mode 2 was executed for torque distribution.

The torque distribution mode shifted from Mode 2 to Mode 3 when the *SOCg* was less than −1% at approximately 1375 s. The torque distribution mode shifted back to Mode 2 about 1575 s when the SOC gap was reduced. The SOC of the front and rear batteries remained within a SOB by shifting

the torque distribution mode during the driving cycle. The torque distribution histories from three traction motors are presented in Figure 6b.

(b)

**Figure 6.** (**a**) The state of charge records for the three battery packs and (**b**) torque distribution from the front, rear left, and rear right traction motors during the torque and battery distribution process for the electric vehicle driving on a circular path of radius 100 m and using the urban driving cycle of the New European Driving Cycle.

It was also interesting to compare the differences of the energy economy of the proposed TBD strategy by having the battery energy storage in balance and using other torque distribution strategies without balancing the batteries. In these simulations, the initial SOC of each of the three battery packs was 90%, and their corresponding amounts of energy are 10.45, 5.2, and 5.2 kWh for the front, rear right, and rear left battery packs, respectively. The EV stopped when any of the batteries was depleted. It was found that both the rear batteries were exhausted soon for *Pr* = 0, 0.25, and 0.5 when the rear motors took higher priority for delivering more torque than the front motor; while the front battery was depleted soon for *Pr* = 0.75 and 1 when the front motor had the first priority for delivering the torque to the EV.

Energy consumption efficiency was defined as the ratio between the total energy consumption and the initial battery energy. The energy consumption rate was defined as the total energy consumption per travel distance.

Table 3 shows the energy consumption results for both the circular and straight road simulations. For clockwise cornering on a circular path of radius 100 m during the UDCs, the proposed TBD strategy had a travel distance: 142.6 km, which was 7.7% higher than the PSO strategy without the balancing of the SOC of the battery packs. The torque distribution strategy under PSO without battery balancing had a better energy consumption rate at 104.5 Wh/km than the TBD strategy, but the front battery was delpeted after 132.4 km, and the energy consumption efficiency was 73.6%. The rear battery packs had 26.4% energy remaining when the EV stopped.


**Table 3.** Torque and battery distribution strategy results.

On the straight road, the torque distribution strategy under PSO without battery balancing exhibited the best energy consumption rate: 75.21 Wh/km. However, the front battery was depleted after 167.6 km, and energy consumption efficiency was 67.5%. Thus, the rear battery packs had only 32.5% energy remaining when the EV stopped. The proposed TBD strategy of partly using torque distribution by PSO had the highest driving range: 214.4 km, i.e., approximately 248 UDCs. This was attributed to the SOC of the three battery packs being kept in balance to avoid unexpected battery depletion. Therefore, approximately 28% more driving range was extended by the TBD strategy than by the PSO strategy without battery balancing.

It was also found in the simulation that the battery energy was fully utilized by the TBD strategy for the EV on a straight road of UDC. The 99.9% energy consumption efficiency for the TBD strategy was calculated in Table 4. The energy of three battery packs can be effectively distributed and utilized to extend the driving range, when the SOC gap of the three battery packs remains within a prescribed limit during vehicle operation.

**Table 4.** Energy consumption efficiency for the EV on a straight road of UDC by the TBD strategy.


Other strategies with a PTR, *Pr* from 0 to 1, presented lower travel distances and less energy consumption efficiency than observed for the proposed TBD strategy.

#### *4.2. Hardware-in-the-Loop Simulations*

Figure 7 presents the architecture of hardware-in-the-loop experiment. A Mitsubishi Colt-Plus was retrofitted with a 15-kW radial-flux PMSM and a 144-V battery pack for front wheels and two 7-kW axial-flux PMSMs and two 72-V battery packs for rear wheels. This EV was set up on a Horiba MAHA-AIP ECDM-48 emission chassis dynamometer. The maximum test speed was 200 km/h, the maximum power absorbing was 150 kW at 100 km/h, the maximum tractive force was 5400 N for light duty and 6750 N for heavy duty, and the maximum vehicle inertia simulation was 4540 kg for 4-wheel drives.

**Figure 7.** Architecture of the hardware-in-the-loop experiment.

In experiments, the battery SOC information and throttle command were received by a real-time rapid control prototyping unit dSPACE MicroAutoBox II, in which the TBD strategy was built to determine the torque command for each motor. This MicroAutoBox took a role of vehicle control unit with an 800-MHz processor, 18-MB main memory, 16-MB flash memory, and dual CAN interfaces.

In the HIL experiment, the vehicle followed the complete NEDC but the maximum speed at EUDC was restricted at 40 km/h in the HIL experiment. The initial SOCs of the front, rear left, and rear right batteries were 94.8%, 93.6%, and 95.5%, respectively. In order to make the experiment efficient, driving modes were shifted at *SOCg*= −κ% = −1% and *SOCr*= ρ = 1.006, according to the flowchart of the TBD strategy in Figure 4.

Figure 8 illustrates the time history of mode, state, *SOCr*, and *SOCg* and the corresponding torque distribution histories of the front, rear left, and rear right motors during the TBD process in the hardware-in-the-loop experiment. During the first 95 s, the SOC of the front battery pack was higher than the SOC of anyone of the rear battery packs. Therefore, State 1 (*SOCg*> 0) was identified and *SOCr* was larger than 1.006, the front motor took the first priority of delivering torque and Mode 1 (*Pr* = 1) was executed. Between 95 and 200 s, it was still at State 1 (*SOCg*> 0) but *SOCr* was less than 1.006, Mode 2 was executed with the PSO strategy.

Between 200 and 300 s, State 2 (*SOCg*= 0) was identified, i.e., the SOC of the front battery pack was equal to any one of the two rear battery packs. Mode 2 with the PSO strategy was working. Between 300 and 485 s, the SOC of the front battery pack was lower than the SOC of the rear battery packs, and State 3 (*SOCg*< 0) was identified. Because 0 > *SOCg* ≥ −1% and |*SOCg*| was increasing, Mode 2 remained.

When *SOCg* was less than −1% at State 3 between 485 and 585 s, the rear battery packs and motors started to take their top priority for delivering more power than the front battery and motor, and Mode 3 (*Pr* = 0) was executed. Between 585 and 680 s, the SOC gap was between −1% and 0%, but |*SOCg*| was decreasing, Mode 3 remained.

**Figure 8.** Histories of the mode (solid line), state (dashed line), state of charge (SOC) ratio, SOC gap and the torque distributions of the front, rear left, and rear right motors during torque and battery distribution process for the electric vehicle in the hardware-in-the-loop experiment.

The corresponding SOCs of the three battery packs is shown in Figure 9. In the first 500 s, the front battery provided all power to the vehicle. After 500 s, the rear and front batteries powered the vehicle alternatively, so that the SOC gap would always remain in 1% as expected.

**Figure 9.** Histories of mode and the states of charge of the front, rear left, and rear right battery packs during torque and battery distribution process for the electric vehicle in the hardware-in-the-loop experiment.

#### *4.3. Road Tests*

The road test was executed on the Industrial Technology Research Institute (ITRI) campus. The total driving distance was about 5.4 km, during which the road slope varied and the maximum speed was 30 km/h. The driving curve is shown in Figure 10. The initial SOCs of the front, rear left, and rear right batteries were 72.8%, 70%, and 71.2%, respectively. Driving modes were shifted at *SOCg* = −κ% = −1% and *SOCr* = ρ = 1.02, according to the flowchart of the TBD strategy in Figure 4. Figure 11 illustrates the time history of mode, state, *SOCr*, *SOCg*, and the corresponding torque distributions.

**Figure 10.** Driving speed curve for the torque and battery distribution strategy in the road test on the campus of Industrial Technology Research Institute.

**Figure 11.** Histories of the mode (solid line), state (dashed line), state of charge (SOC) ratio, SOC gap and the torque distributions of the front, rear left, and rear right motors during torque and battery distribution process for the electric vehicle in the road test.

Similar to the result of HIL test, the front battery pack took the first priority to supply power to drive the EV at Mode 1 (*Pr* = 1) during the first 180 s. Because the EV moved upslope approximately at 150 s, two rear motors delivered extra torque. Between 180 and 480 s, Mode 2 with the PSO strategy worked when the SOC of the front battery was lower than that of the rear battery packs. The front motor still provided the major torque until the SOC gap was less than −1% (*SOCg* < −1%) while Mode 3 (*Pr* = 0) was executed. Then, Modes 2 and 3 shifted alternatively. The SOC difference of the three battery packs was finally kept within 1%, as shown in Figure 12.

**Figure 12.** The variation of SOC of the three battery packs in the road test.

The two strategies with a PTR, *Pr* = 0 and *Pr* = 1, were also executed in the road test. The total energy consumption and the consumption of each battery pack are given in Table 5. It shows that the energy consumption rate of the TBD strategy was lower than those of *Pr* = 0 and *Pr* = 1. It means that with the same battery energy, the EV has a longer driving range by the proposed TBD strategy than that by other PTR strategies. For example, the TBD strategy extended 11% more driving range than the PTR strategy when *Pr* = 0, and the TBD strategy extended 23.5% more driving range than the PTR strategy when *Pr* = 1.


**Table 5.** Battery energy consumption in road tests.

F: Front battery, RL: Rear left battery, RR: Rear right battery.

#### **5. Conclusions**

A novel TBD strategy has been proposed for the EV with three independent traction motors and battery packs. Upon acceleration of the EV, the demanded torque was provided by all three traction motors together at their highest efficiency under the PSO strategy for saving battery energy. Simultaneously, the SOC of the three battery packs had to be kept in balance to avoid any unexpected battery depletion and to improve the EV's driving range. Thus, a combination of PSO and the PTR for torque distribution strategy was applied to compromise between energy saving and energy balance. On the basis of the model-in-the-loop simulations, the proposed TBD strategy shows better travel distance and the higher energy consumption efficiency than a pure PSO method or PTR strategies. Similar results were also proved on a real vehicle for hardware-in-the-loop experiments on dynamometer and road tests. The road test proved that the TBD strategy extended 11% and 23.5%

more driving range than other PTR strategies, when *Pr* = 0 and *Pr* = 1, respectively. The proposed TBD strategy is promising for extending the driving range of an EV with multiple traction motors and battery packs with an improved energy consumption efficiency.

**Author Contributions:** Y.-H.T. and Y.-P.Y. conceived and design the experiments; Y.-H.T. performed the experiments and analyzed the data; Y.-P.Y. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Ministry of Science and Technology of Taiwan, Republic of China under contract MOST 106-2221-E-002-064.

**Acknowledgments:** The authors acknowledge the financial support of the Ministry of Science and Technology of Taiwan, Republic of China under contract MOST 106-2221-E-002-064.

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

#### **References**


© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

#### *Article*
