Characteristics of Battery SOC According to Drive Output and Battery Capacity of Parallel Hybrid Electric Vehicle

: To mitigate global warming caused by vehicles, emission regulations have been implemented for all automobiles. Hybrid electric vehicles (HEVs) are being designed to meet consumer demand for eco-friendly vehicles that o ﬀ er increased power and improved fuel e ﬃ ciency. HEVs are powered by an internal combustion engine (ICE) in combination with one or more electric motors that use electrical energy stored in a secondary battery, which is typically a lithium-based battery. With the use of such a hybrid drivetrain system, the fuel e ﬃ ciency can be improved over that of conventional ICE vehicles. In this study, we conducted a vehicle-driving experiment to evaluate a transmission-mounted electric device (TMED) type parallel HEV using a chassis dynamometer and on-board diagnostics (OBD) signal-measuring equipment. In addition, we performed a numerical analysis using the CRUISE vehicle simulation code with experimental data. In our analysis, the engine output, which a ﬀ ects the torque of the drive motor, and the capacity (energy density) of the lithium-ion polymer battery were set as variables that a ﬀ ect the fuel-economy performance. As a result of this numerical analysis, a hybrid power-drivetrain model based on CRUISE was developed, and the current balance was evaluated according to the change in the battery capacity. We found that the battery state of charge (SOC) dropped because of a decrease in battery capacity. Thus, we predicted that the lithium-ion battery capacity would be reduced. (eddy-current dynamometer, Jastec, Sungnam, Korea) and hybrid electric vehicle (2011 YF Sonata HEV, Hyundai Motors) used in the vehicle driving experiment. A PicoScope oscilloscope (Pico Technology, Cambridgeshire, UK) and an on-board diagnostics (OBD)-II monitoring system (Cantalker, D & K Information Communication Technology, Sungnam, Korea) were used to measure the charge and discharge current. Table 1 lists the speciﬁcations of the HEV used in the present study.


Introduction
Countries worldwide have begun to impose stringent environmental regulations to mitigate global warming due to greenhouse gases (GHG) such as CO 2 . In the industrial sector, emissions of pollutants due to road traffic are significant contributors to global warming [1]. Therefore, reducing the fossil fuels consumed by cars is a fundamental solution to overcome the problem of air pollution.
According to a comprehensive assessment report by the Intergovernmental Panel on Climate Change (IPCC), the rate of climate change is expected to accelerate. Studies have indicated that the complete stoppage of fossil-fuel consumption by 2100 is necessary to ensure that the rise in global temperature does not exceed 2 • C [2].
However, despite the imposition of stricter environmental regulations, the control of air pollution in large cities (e.g., Seoul, Beijing, Shanghai, Delhi, Paris, and London) has been inadequate, and governments worldwide have proposed several countermeasures to address this challenge [3].
After the 2015 Paris Agreement, several countries established regulations for average vehicle fuel consumption and CO 2 emissions, which are expected to be stringently applied by 2021. Several nations

Related Previous Research
Among studies on HEV rechargeable batteries and their SOC, Cheng et al. [11] investigated a nonlinear-model based on predictive control of the power-management system of a power-split type HEV to improve the fuel efficiency. Zhou et al. [12] studied the effects of lithium-ion battery (LIB) aging on various driving cycles. Moreover, Pilley et al. [13] designed a small, lightweight, and inexpensive battery pack using the design-for-assembly approach. Uddin and Ku [14] proposed a design for an air-cooled battery thermal-management system to predict the temperature distribution in the battery module of mild hybrid vehicles. Zhang and Filipi [15] developed an electrochemical aging model of lithium iron phosphate/graphite (LiFePO 4 ) graphite batteries based on a single particle model. Xu et al. [16] studied charging strategies to evaluate the charging time, effective full-charge capacity, and charging-energy efficiency of LiFePO 4 batteries based on the battery internal mechanisms and operating conditions. Feng et al. [17] researched the application of model predictive-control algorithms to improve the fuel economy of power split-type hybrid vehicles. Zhou et al. [18] investigated the effect of SOC limitation on the aging and fuel economy of LIBs. Khan et al. [19] proposed a method for estimating the SOC and state of health (SOH) of LIBs by integrating the current, voltage conversion, and ampere-hour throughput. Sriniwas et al. [20] conducted an experimental study on the development of a state-estimation algorithm for a lead-acid battery. Sharma et al. [21] studied the high-voltage battery-charge state of parallel hybrids using an intelligent predictive-control strategy with path topography. Minarcin and Rask [22] investigated the problems and potential of energy-state estimation, which is directly related to vehicle energy efficiency.

Experimental Apparatus and Setup
The HEV driving test was conducted in the IM240 mode. From Figure 1, we note that the IM240 mode was set as the default mode in the experiment. Figure 2 shows the chassis dynamometer (eddy-current dynamometer, Jastec, Sungnam, Korea) and hybrid electric vehicle (2011 YF Sonata HEV, Hyundai Motors) used in the vehicle driving experiment. A PicoScope oscilloscope (Pico Technology, Cambridgeshire, UK) and an on-board diagnostics (OBD)-II monitoring system (Cantalker, D & K Information Communication Technology, Sungnam, Korea) were used to measure the charge and discharge current. Table 1 lists the specifications of the HEV used in the present study.

Related previous research
Among studies on HEV rechargeable batteries and their SOC, Cheng et al. [11] investigated a nonlinear-model based on predictive control of the power-management system of a power-split type HEV to improve the fuel efficiency. Zhou et al. [12] studied the effects of lithium-ion battery (LIB) aging on various driving cycles. Moreover, Pilley et al. [13] designed a small, lightweight, and inexpensive battery pack using the design-for-assembly approach. Uddin and Ku [14] proposed a design for an air-cooled battery thermal-management system to predict the temperature distribution in the battery module of mild hybrid vehicles. Zhang and Filipi [15] developed an electrochemical aging model of lithium iron phosphate/graphite (LiFePO4) graphite batteries based on a single particle model. Xu et al. [16] studied charging strategies to evaluate the charging time, effective fullcharge capacity, and charging-energy efficiency of LiFePO4 batteries based on the battery internal mechanisms and operating conditions. Feng et al. [17] researched the application of model predictivecontrol algorithms to improve the fuel economy of power split-type hybrid vehicles. Zhou et al. [18] investigated the effect of SOC limitation on the aging and fuel economy of LIBs. Khan et al. [19] proposed a method for estimating the SOC and state of health (SOH) of LIBs by integrating the current, voltage conversion, and ampere-hour throughput. Sriniwas et al. [20] conducted an experimental study on the development of a state-estimation algorithm for a lead-acid battery. Sharma et al. [21] studied the high-voltage battery-charge state of parallel hybrids using an intelligent predictive-control strategy with path topography. Minarcin and Rask [22] investigated the problems and potential of energy-state estimation, which is directly related to vehicle energy efficiency.

Experimental Apparatus and Setup
The HEV driving test was conducted in the IM240 mode. From Figure 1, we note that the IM240 mode was set as the default mode in the experiment. Figure 2 shows the chassis dynamometer (eddycurrent dynamometer, Jastec, Sungnam, Korea) and hybrid electric vehicle (2011 YF Sonata HEV, Hyundai Motors) used in the vehicle driving experiment. A PicoScope oscilloscope (Pico Technology, Cambridgeshire, UK) and an on-board diagnostics (OBD)-II monitoring system (Cantalker, D & K Information Communication Technology, Sungnam, Korea) were used to measure the charge and discharge current. Table 1 lists the specifications of the HEV used in the present study.   To measure the current in the LIB available for the hybrid drive motor in real-time, we performed current measurements using high-power battery ammeter clamps (9287 Universal Clampon CT, Hioki Co., Japan), as shown in Figure 3a. The ammeter clamps were installed on the wires that connect the high-voltage battery and drive motor. The measured current data were stored in the PicoScope (Pico Technology), shown in Figure 3b, and the charge and discharge statuses were analyzed using the measured data. The OBD signals (engine torque, motor torque, current, gear stage, SOC, and engine speed) were acquired using the Cantalker, which is shown in Figure 3c. Figure 4 shows the overall schematic of the experimental setup employed in this study.   To measure the current in the LIB available for the hybrid drive motor in real-time, we performed current measurements using high-power battery ammeter clamps (9287 Universal Clamp-on CT, Hioki Co., Japan), as shown in Figure 3a. The ammeter clamps were installed on the wires that connect the high-voltage battery and drive motor. The measured current data were stored in the PicoScope (Pico Technology), shown in Figure 3b, and the charge and discharge statuses were analyzed using the measured data. The OBD signals (engine torque, motor torque, current, gear stage, SOC, and engine speed) were acquired using the Cantalker, which is shown in Figure 3c. Figure 4 shows the overall schematic of the experimental setup employed in this study.  To measure the current in the LIB available for the hybrid drive motor in real-time, we performed current measurements using high-power battery ammeter clamps (9287 Universal Clampon CT, Hioki Co., Japan), as shown in Figure 3a. The ammeter clamps were installed on the wires that connect the high-voltage battery and drive motor. The measured current data were stored in the PicoScope (Pico Technology), shown in Figure 3b, and the charge and discharge statuses were analyzed using the measured data. The OBD signals (engine torque, motor torque, current, gear stage, SOC, and engine speed) were acquired using the Cantalker, which is shown in Figure 3c. Figure 4 shows the overall schematic of the experimental setup employed in this study.

Numerical modeling and verification
The numerical model for the vehicle in CRUISE software (AVL) used the specifications of a TMED-type HEV, and the reliability of the model was verified by detailed calibration based on the experimental data. Figure 5 shows the numerical model of the TMED-type hybrid vehicle developed for this study. The main components include the lithium-ion battery, gasoline engine, electric motor, and auto transmission module. The voltage of the Li-ion battery was 270V, and its capacity was 1.431 kW•h. The initial SOC value was set to 50% upon considering the control target value of the battery of the TMED-type HEV. The gasoline engine was considered to operate based on the Miller cycle, and the maximum torque was approximately 180 N•m. The drive motor and hybrid starter and generator (HSG) were each operated at 270 V, and the maximum torque values of the motor and HSG were 205 N•m and 43.2 N•m, respectively. The rotational speed of the HSG was 2.4 times the gasoline engine speed. Table 2 shows the main elements of the HEV model used for the numerical analysis. The curb weight and gross weight of the actual vehicle were entered into the hybrid vehicle model. The elements of the hybrid system controller were from the basic model provided by the CRUISE program. In the data bus, the signals of the driving motor and the generator were modified to be suitable for a TMED-type hybrid vehicle, as shown in Table 3. The specifications of the engine were applied as the actual vehicle values. The engine torque and drive motor elements were applied with correction diagrams, considering the experimental values measured by the dynamometer. The torque values for the engine and the motor were corrected by considering the experimental values.
The torque of the engine and the motor was corrected in consideration of the torque and the rotation speed of the actual experiment obtained in the engine-only mode, EV mode, and hybridmixed mode. The gear ratio was adjusted based on the engine torque and RPM data collected in the experiment after entering the specifications of the vehicle.

Numerical Modeling and Verification
The numerical model for the vehicle in CRUISE software (AVL) used the specifications of a TMED-type HEV, and the reliability of the model was verified by detailed calibration based on the experimental data. Figure 5 shows the numerical model of the TMED-type hybrid vehicle developed for this study. The main components include the lithium-ion battery, gasoline engine, electric motor, and auto transmission module. The voltage of the Li-ion battery was 270V, and its capacity was 1.431 kW·h. The initial SOC value was set to 50% upon considering the control target value of the battery of the TMED-type HEV. The gasoline engine was considered to operate based on the Miller cycle, and the maximum torque was approximately 180 N·m. The drive motor and hybrid starter and generator (HSG) were each operated at 270 V, and the maximum torque values of the motor and HSG were 205 N·m and 43.2 N·m, respectively. The rotational speed of the HSG was 2.4 times the gasoline engine speed.    Table 2 shows the main elements of the HEV model used for the numerical analysis. The curb weight and gross weight of the actual vehicle were entered into the hybrid vehicle model. The elements of the hybrid system controller were from the basic model provided by the CRUISE program. In the data bus, the signals of the driving motor and the generator were modified to be suitable for a TMED-type hybrid vehicle, as shown in Table 3. The specifications of the engine were applied as the actual vehicle values. The engine torque and drive motor elements were applied with correction diagrams, considering the experimental values measured by the dynamometer. The torque values for the engine and the motor were corrected by considering the experimental values.
The torque of the engine and the motor was corrected in consideration of the torque and the rotation speed of the actual experiment obtained in the engine-only mode, EV mode, and hybrid-mixed mode. The gear ratio was adjusted based on the engine torque and RPM data collected in the experiment after entering the specifications of the vehicle.        Figure 6a shows a comparison of the results of the vehicle test in IM240 mode and the numerical simulation in terms of the engine torque. A higher torque was observed in the medium-and high-speed regimes. In addition, the analysis indicates that the torque increases when the engine operation enters the idling stage. We note here that even when the engine clutch disconnected the transmission of power between the engine and motor, the experimental data was collected by disconnection of the signal in the OBD system. Figure 6b compares the experimental and simulation results in terms of the drive-motor torque. A torque error is observed in specific modes, such as the engine mode. However, a similar pattern is seen in the experiment and simulation throughout the driving process in the IM240 mode. Figure 6c shows the battery SOC throughout the vehicle test in the IM240-mode, and the simulation results are consistent with the experimental results for up to 100 seconds. Subsequently, an error is observed, but the overall SOC charging and discharging trends are similar. Figure 7 shows a comparison of engine torque and the duration of fuel-injection as functions of engine speed between simulation and experimental results. Torques below 10 Nm near 1600 rpm did not occur due to the setting of the analytical model. By comparing the patterns of the main output required for vehicle driving, the most frequent output was seen at 1600 rpm, and the torque distribution was similar over the range of 800 to 3200 rpm. This comparison indicated that the analysis model was reliable because the engine in the vehicle and the analysis model performed similarly.
Based on the difference in the torque between the 2000-cc and 1600-cc engines, engine outputs that were reduced by 10% and 20% were used as variables in the numerical model. A comparison between the torques of the 1600-cc and 2000-cc engines and the driving-test vehicle torque from the same manufacturer revealed a difference of approximately 20%. The lithium-ion battery capacity is another analysis variable that affects fuel efficiency, and was also reduced by 10% and 20%. These driving torque and battery capacity variables were applied to the numerical analysis, and the scenarios are listed in Tables 4 and 5  Based on the difference in the torque between the 2000-cc and 1600-cc engines, engine outputs that were reduced by 10% and 20% were used as variables in the numerical model. A comparison between the torques of the 1600-cc and 2000-cc engines and the driving-test vehicle torque from the same manufacturer revealed a difference of approximately 20%. The lithium-ion battery capacity is another analysis variable that affects fuel efficiency, and was also reduced by 10% and 20%. These driving torque and battery capacity variables were applied to the numerical analysis, and the scenarios are listed in Tables 4 and 5

Experiment Results of Power Distribution with Two Driving Modes for TMED-Type Hybrid Vehicle
To understand the driving characteristics of the TMED hybrid vehicle, a driving experiment was performed in the chassis dynamometer with three driving modes, and the results of engine torque, motor torque, and SOC changes are shown in Figure 8. The FTP-75 mode has a longer travel time than the HWFET mode and has various characteristics ranging from low speed to high speed as shown in Figure 8a. The power source of the vehicle is generated by the motor at low speed, and by engine operation or mixed operation of the engine and motor at high speed driving. In this driving condition, the charging of the battery is active due to the harmonious operation of the engine and the motor, thus providing the characteristics of the universally expected full-type hybrid vehicle.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 17 In Phase 2, the proportion of high-speed driving is higher than in Phase 1, and the engineoperating period is longer. The SOC difference is large at the end of the driving mode due to the increased amount of charging current under the high-torque condition of the engine. The driving force is generated by the motor at speeds up to 30 km/h, but at higher speeds, the engine is also used as a power source. In Case 1, the torque of the engine is relatively high, so the amount of electric energy charged by the engine is higher than in other conditions. The lower the engine torque, the lower the amount of power generated, the lower the charging, and the SOC drop gradually decreases.  Figure 9b shows the SOC drop for the three cases of battery-capacity listed in Table 5 for Phase 1 and Phase 2 in the IM240 mode. As the battery capacity decreases, the SOC drop gradually increases. In particular, Phase 2 consists of a high proportion of high-speed driving, and the increase in SOC drop is larger than in Phase 1. As the engine torque decreases, the SOC drop increase compared to Case 1. As a result, the difference in SOC drop gradually increases due to the reduction The HWFET mode shown in Figure 8 simulates highway driving. At the beginning of driving, the driving motor operates only up to about 50 s, which is an acceleration section, and when entering the high-speed section, the output of the internal combustion engine plays a major role in driving the vehicle. Since the driving force is supplied to the vehicle by the output of the engine throughout the driving, the extra output to be charged by the regenerative braking of the motor during driving is insignificant, and only the surplus energy due to deceleration during coasting driving is recovered. After all, when driving at a medium speed or higher with a full-type hybrid vehicle, the capacity of the battery and the electric motor are only elements of resistance that hinder the driving of the vehicle.

Numerical Analysis of Characteristic of SOC and Current Balance with IM240 Mode
Driving torque and battery capacity were applied as variables to the CRUISE model developed in this study. The numerical analysis under the IM240 driving mode yielded the following results for SOC characteristics and current balance. Figure 9a shows the SOC drop between Phase 1 and Phase 2 for the three engine-torque cases listed in Table 4. This figure illustrates the difference in the battery SOC values between Phase 1 and Phase 2 in the IM240 mode. We note that during Phase 1, the SOC drop is lower than that during Phase 2. During Phase 1, the maximum speed does not reach 60 km/h, and speeds between 30 and 40 km/h account for approximately half of Phase 1. Therefore, the influence of motor driving is dominant, and the effect of reduced engine power is considered to be insignificant compared to that during Phase 2. At low speeds, engine operation is negligible, and the motor operates primarily. The difference in SOC drop was not significantly caused by the energy recovered by the regenerative braking of the drive motor and the advantage of the motor, which is more efficient than the engine.
In Phase 2, the proportion of high-speed driving is higher than in Phase 1, and the engine-operating period is longer. The SOC difference is large at the end of the driving mode due to the increased amount of charging current under the high-torque condition of the engine. The driving force is generated by the motor at speeds up to 30 km/h, but at higher speeds, the engine is also used as a power source. In Case 1, the torque of the engine is relatively high, so the amount of electric energy charged by the engine is higher than in other conditions. The lower the engine torque, the lower the amount of power generated, the lower the charging, and the SOC drop gradually decreases. Figure 9b shows the SOC drop for the three cases of battery-capacity listed in Table 5 for Phase 1 and Phase 2 in the IM240 mode. As the battery capacity decreases, the SOC drop gradually increases. In particular, Phase 2 consists of a high proportion of high-speed driving, and the increase in SOC drop is larger than in Phase 1. As the engine torque decreases, the SOC drop increase compared to Case 1. As a result, the difference in SOC drop gradually increases due to the reduction in engine torque during Phase 2, which is greatly affected by engine torque. When the capacity of the battery is high, the electrical energy generated by the engine can be smoothly charged to 50% SOC. For efficient battery use, the SOC is charged to near 50%. Therefore, if the battery capacity is small, it is charged to 50% quickly, and the extra electricity cannot be charged. For this reason, the difference in SOC drop during Phase 2 occurs because the change in torque is more significant than the change in battery capacity.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 17 in engine torque during Phase 2, which is greatly affected by engine torque. When the capacity of the battery is high, the electrical energy generated by the engine can be smoothly charged to 50% SOC. For efficient battery use, the SOC is charged to near 50%. Therefore, if the battery capacity is small, it is charged to 50% quickly, and the extra electricity cannot be charged. For this reason, the difference in SOC drop during Phase 2 occurs because the change in torque is more significant than the change in battery capacity.  Figure 10a shows the SOC drop after completing of the entire driving cycle in the IM240 and FTP-75 modes. The FTP-75 mode has a longer driving time (approximately eight times longer) and a higher proportion of high-speed driving than the IM240 mode. Consequently, the load of the drive motor increases as engine power decreases, which increases the consumption of electrical energy. Therefore, the SOC drop is very sharp during the FTP-75 mode. The amount of electrical energy charged with lower levels of engine torque is predicted to decrease, and the SOC drop is more likely to occur as mileage increases. To maintain a constant SOC under conditions when the engine torque is decreasing, the fuel efficiency can be improved by applying a strategy of artificially operating the engine at optimum efficiency. The SOC drop due to a reduction in engine torque is expected to  Figure 10a shows the SOC drop after completing of the entire driving cycle in the IM240 and FTP-75 modes. The FTP-75 mode has a longer driving time (approximately eight times longer) and a higher proportion of high-speed driving than the IM240 mode. Consequently, the load of the drive motor increases as engine power decreases, which increases the consumption of electrical energy. Therefore, the SOC drop is very sharp during the FTP-75 mode. The amount of electrical energy charged with lower levels of engine torque is predicted to decrease, and the SOC drop is more likely to occur as mileage increases. To maintain a constant SOC under conditions when the engine torque is decreasing, the fuel efficiency can be improved by applying a strategy of artificially operating the engine at optimum efficiency. The SOC drop due to a reduction in engine torque is expected to increase as mileage increases. To maintain the battery SOC constant, the length of time when the engine operates as a generator must be increased. Figure 10b shows the SOC drop due to a reduction in the lithium-ion battery capacity during the IM240 and FTP-75 modes. The observed differences in SOC drop between the two modes were less than those observed when engine torque was reduced. When the battery capacity decreases by 20%, the difference in the SOC drop between the IM240 and FTP-75 modes is approximately 2.66%. In other words, because the test modes correspond to shorter distances than would be driven in practice, this difference in SOC drop may be remarkable. The differences in SOC drop converge with reduced battery capacity, which suggests the capacity of the LIBs mounted in the test vehicle could be reduced. Additionally, by considering the battery life, if the battery SOC can be higher than 50%, then performance equal to that achieved currently can be realized with lower battery capacity.
increase as mileage increases. To maintain the battery SOC constant, the length of time when the engine operates as a generator must be increased. Figure 10b shows the SOC drop due to a reduction in the lithium-ion battery capacity during the IM240 and FTP-75 modes. The observed differences in SOC drop between the two modes were less than those observed when engine torque was reduced. When the battery capacity decreases by 20%, the difference in the SOC drop between the IM240 and FTP-75 modes is approximately 2.66%. In other words, because the test modes correspond to shorter distances than would be driven in practice, this difference in SOC drop may be remarkable. The differences in SOC drop converge with reduced battery capacity, which suggests the capacity of the LIBs mounted in the test vehicle could be reduced. Additionally, by considering the battery life, if the battery SOC can be higher than 50%, then performance equal to that achieved currently can be realized with lower battery capacity.  Figure 11 shows the relationship between the current balance and SOC according to the change in engine torque between the IM240 and FTP-75 modes. In the IM240 mode, which corresponds to a relatively short driving period, the results are located in the first quadrant and gradually move closer  Figure 11 shows the relationship between the current balance and SOC according to the change in engine torque between the IM240 and FTP-75 modes. In the IM240 mode, which corresponds to a relatively short driving period, the results are located in the first quadrant and gradually move closer to the origin as the engine torque decreases. The electrical energy consumption tends to increase gradually.
In the FTP-75 mode, the motor torque rapidly decreases and locates in the third quadrant. The maximum decrease in SOC is approximately −11% relative to the initial SOC because the driving time is relatively long and the frequency of motor use at medium and low speeds increases. Also, because the engine torque decreases as the drive-motor ratio increases, the amount of charge during power generation is reduced, which tends to move in three quarters compared with the IM240 mode significantly. As mentioned above, an intermittent operation is required at the optimum efficiency of the internal combustion engine to maintain a constant SOC. gradually.
In the FTP-75 mode, the motor torque rapidly decreases and locates in the third quadrant. The maximum decrease in SOC is approximately -11% relative to the initial SOC because the driving time is relatively long and the frequency of motor use at medium and low speeds increases. Also, because the engine torque decreases as the drive-motor ratio increases, the amount of charge during power generation is reduced, which tends to move in three quarters compared with the IM240 mode significantly. As mentioned above, an intermittent operation is required at the optimum efficiency of the internal combustion engine to maintain a constant SOC. Figure 11. Current balance during IM240 and FTP-75 modes under conditions of reduced enginetorque. Figure 12 shows the relationship between the current balance and SOC according to changes in the battery capacity during IM240 and FTP-75 modes. For both driving modes, the SOC values are located in the first quadrant, but the trend in current-balance values as the battery capacity changes shows that that the IM240 mode affords a more gradual change in both SOC and current balance. However, we observe that the SOC values are no relatively big difference between modes when the battery capacity is reduced by 20%, and the difference is less than 3%, which corresponds to a relatively low sensitivity to battery capacity. By using a variety of strategies (e.g., downsizing, engine operation mode, limiting, SOC increase) to compensate for the SOC drop, HEVs can be designed to operate at lower battery capacities.  Figure 12 shows the relationship between the current balance and SOC according to changes in the battery capacity during IM240 and FTP-75 modes. For both driving modes, the SOC values are located in the first quadrant, but the trend in current-balance values as the battery capacity changes shows that that the IM240 mode affords a more gradual change in both SOC and current balance. However, we observe that the SOC values are no relatively big difference between modes when the battery capacity is reduced by 20%, and the difference is less than 3%, which corresponds to a relatively low sensitivity to battery capacity. By using a variety of strategies (e.g., downsizing, engine operation mode, limiting, SOC increase) to compensate for the SOC drop, HEVs can be designed to operate at lower battery capacities.

Conclusions
The aim of this study was to analyze SOC characteristics by setting the driving output and capacity of the lithium-ion battery as parameters of the TMED-type parallel HEV. We first conducted