Closed-Loop Modeling to Evaluate the Performance of a Scaled-Up Lithium–Sulfur Battery in Electric Vehicle Applications

: A closed-loop modeling method was established here to evaluate the performance of new battery technology from lab research to scaled-up developed electric vehicle (EV) applications. As an emerging energy-storage device, the lithium–sulfur battery (LSB) is a very promising candidate for the next generation of rechargeable batteries. However, it has been difﬁcult to commercialize the LSB up to now. In this work, we designed and built a battery, EV, and driver system loop model to study the key performance parameters of LSB operation in EVs, in which the tested data from the lab were introduced into the model followed by simulating driving cycles and fast charging. A comparison with the lithium-ion batteries used in real vehicles veriﬁed the high reliability of the model. Mean-while, the simulation results showed that the LSB needs more improvements for EV application; in particular, developments are still highly needed to overcome the high power and energy loss and sharp voltage vibration for practical applications. The novelty of this work relies on the created closed-loop modeling method to simulate lab research results for evaluating new battery technology in scaled-up EV applications in order to not only vividly predict EV operation performance and commercialization feasibility, but also thoughtfully guide researchers and developers for further optimization and problem solutions. Therefore, this method holds great promise as a powerful tool for both lab research and the industrial development of new batteries for EV applications.


Introduction
Air pollution has resulted in severe environmental problems [1]. In particular, exposure to traffic-related air pollution can cause potentially fatal human health concerns such as asthma, cancer, and cardiovascular disease [2]. It has been reported that about 1.3 billion vehicles including trucks, buses, and cars are registered and running worldwide [2]. The replacement of conventional gasoline vehicles with electrified power-train vehicles is an efficient approach to significantly reduce the emissions of contaminants such as PM 2.5, CO 2 , NOx, and CO. Therefore, governments worldwide have formulated policies to accelerate the development of EVs, which is being treated as an important strategy in economic development. For example, the USA has initiated the national "Zero Emission Vehicle Program", and the UK and China started financial incentive programs such as the Plug-in Car and Van Grant Eligibility and New Energy Vehicle Credit Program in 2016 and 2017, respectively [3].
Currently, most electric vehicles are powered by lithium-ion batteries (LIBs) [4], and a "should cost" model was reported by BloombergNEF in that the price of a car battery (Li2Sx, x = 1-8) possess poor ionic and electronic conductivities, which increase the internal resistance of the battery very much [27]. Consistently, based on our configuration and testing, the internal resistance of the LSB pack is extremely higher than that of the LIB, thereby, the former has more obvious output voltage oscillation and more power and energy loss for automotive applications. Accordingly, the LSB takes a much longer time for a full charge than the LIB. This work vividly demonstrates the power of model simulation with uses of lab research data for the scaled-up development of applications while guiding further research and development directions.

Simulation Method
This work presents a closed-loop modeling system using lab research results to simulate the LSB in scaled-up electric vehicle applications for the first time. The LSB-based loop model was built with a battery model, driver model, and vehicle dynamic model through the equivalent circuit principle, vehicle driving force balance principle, and speed feedback mechanism. The system is schematically illustrated in Figure 1.
Accordingly, the LSB takes a much longer time for a f vividly demonstrates the power of model simulation w scaled-up development of applications while guiding directions.

Simulation Method
This work presents a closed-loop modeling sys simulate the LSB in scaled-up electric vehicle applicatio loop model was built with a battery model, driver m through the equivalent circuit principle, vehicle driving feedback mechanism. The system is schematically illus

Battery Modeling
Electrical equivalent circuit networks [15,17,18] model as depicted in Supplementary Figure S1, in whi the cell, r0 represents the internal resistance, and uout cell is connected to the system. A widespread coulom and the SOC can be estimated by integrating the lo capacity (cap) and that remaining can be monitored on The key parameters for the battery management s where SOC0 is the initial SOC, and uout can be figured o

Battery Modeling
Electrical equivalent circuit networks [15,17,18] were used to establish the battery model as depicted in Supplementary Figure S1, in which u ocv is the open-circuit voltage of the cell, r 0 represents the internal resistance, and u out reflects the output voltage when a cell is connected to the system. A widespread coulomb-counting method was selected, and the SOC can be estimated by integrating the load current (I); thereby, the used capacity (cap) and that remaining can be monitored online [17].
The key parameters for the battery management system (BMS) can be defined as where SOC 0 is the initial SOC, and u out can be figured out from Supplementary Figure S1: where u ocv is a function of SOC: and r 0 is a function of temperature (T) and SOC:

Vehicle Modeling
Vehicle modeling and simulation can be carried out to efficiently analyze the performance of electric vehicles and their subsystems in various driving conditions, and they have been widely used in the automotive industry. Herein, a vehicle model with a sub battery model was built to investigate the battery's attributes in the electric vehicle application scenario and to distinguish the LSB and LIB through comparison. For the electric vehicle, the force analyses are shown in Supplementary Figure S2; the force condition of an electric vehicle can be described by the equation below: where F t is the driving force and F f , F w , F i , and F j are the rolling, air, gravity, and acceleration resistances, respectively. These can be expressed as: where f r is the rolling friction coefficient: where 21.15 is a conversion factor of m/s to km/h, thus resulting in an air density of 1.209 kg/m 3 . The force of gravity along the ramp as a grade resistance can be written as Acceleration resistance, a force used for overcoming the inertia of its mass during vehicle acceleration, is in the form of Driving force (F t ) is actually the sum of various vehicle driving resistances that can also be expressed as Rotating mass conversion factor δ is used for converting the inertial resistance of rotating mass into translational inertial resistance, which can be defined as For a middle-sized EV, the conversion factor can be simplified as The rolling resistance, air resistance, grade resistance, and the driving force modeled in the software are shown in Supplementary Figure S3.
Furthermore, a driver model was built to control the acceleration and brake pedals to simulate the instantaneous driving and braking forces that are required to overcome the aerodynamic, rolling, grade and inertia resistances, in order to adjust the actual vehicle speed to follow the target speed defined by the driving cycles, NEDC (New European Driving Cycle), WLTC (World-wide harmonized Light duty Test Cycle) and HWFT (Highway Fuel Economy Test) as depicted in Supplementary Materials Figure S4.

Battery Configuration
For scaled-up modeling of the LSB applications along with NCM (Ni, Co, Mn) LIB, both types of battery packs were configured with a similar energy of 60 kWh. The cells for the two types of packs were 50 Ah and 3.3 Ah, respectively, similar to the technical specifications used in industry and published studies [19,20]. The active material weight, sulfur loading, and lithium excess to active material in the LSBs were 15.7356 g, 48.64 g/m 2 , and 0.5 g, respectively, while the ratio of the electrolyte-to-sulfur loading was 3.997. Since LSBs have not been industrialized, their real battery packs have not been constructed. In the modeling work, they were designed and configured based on the lab results of cells. The designed configurations are presented in Figure 2a,b, in which both the LIB and LSB packs are a combination of single cells in mixed series and parallel. The pack output power is decided by u bus , which is the sum of the u outt of all cells. Table 1 summarizes the technical information of the two battery packs.
the two types of packs were 50 Ah and 3.3 Ah, respectively, similar to the technical spe ifications used in industry and published studies [19,20]. The active material weight, su fur loading, and lithium excess to active material in the LSBs were 15.7356 g, 48.64 g/m and 0.5 g, respectively, while the ratio of the electrolyte-to-sulfur loading was 3.997. Sin LSBs have not been industrialized, their real battery packs have not been constructed. the modeling work, they were designed and configured based on the lab results of cell The designed configurations are presented in Figure 2a,b, in which both the LIB and LS packs are a combination of single cells in mixed series and parallel. The pack output pow is decided by ubus, which is the sum of the uoutt of all cells. Table 1 summarizes the technic information of the two battery packs.

Vehicle Configuration
The EV (electric vehicle) in which the LIB and LSB packs were configured to pow was mid-sized, and the vehicle's basic parameters are displayed in Table 2.

Vehicle Configuration
The EV (electric vehicle) in which the LIB and LSB packs were configured to power was mid-sized, and the vehicle's basic parameters are displayed in Table 2.

Test and Parameter Identification
A PEBC05-500 tester connected with both the LSB and LIB for the experiments is depicted in Supplementary Figure S5. The experiment started at a full-charge state and was carried out by applying various discharge currents to measure the voltage until the terminal voltage dropped below the cutoff voltage. The NCM LIB and LSB voltage platforms were 2.5-4.5 V and 1.5-2.6 V, respectively. Accordingly, the parameters of the cells including OCV and r 0 at room temperature were recorded at different SOC levels. The test results are shown in Figure 3. It is noted that Figure 3d exhibits a sudden increase in resistance from 40 to 70% SOC for LSB. Theoretically, a battery internal resistance is the sum of the liquid phase (electrolyte) and solid phase (electrode) resistance. The sudden increase in resistance is very likely to result from the poor conductivity of the sharply increased various charge products including intermediates (Li 2 S x , x = 1-8) [27]. However, when SOC becomes deeper, the high order Li 2 S x forms with better conductivity, decreasing the resistance. Similar resistance-vibration phenomena have been reported in previous reported works [18]. Furthermore, Figure 3b,d shows that the internal resistance of LSB was much higher than that of LIB, which apparently can be ascribed to the same reason as discussed above. Nevertheless, it is noteworthy that the testing was conducted on a 3 Ah LSB battery cell and 50 Ah LIB cell, so an accurate resistance difference between two kinds of batteries should be obtained after configuring the cells to battery packs with comparable energy.

Test and Parameter Identification
A PEBC05-500 tester connected with both the LSB and LIB for the experiments is d picted in Supplementary Figure S5. The experiment started at a full-charge state and w carried out by applying various discharge currents to measure the voltage until the term nal voltage dropped below the cutoff voltage. The NCM LIB and LSB voltage platform were 2.5-4.5 V and 1.5-2.6 V, respectively. Accordingly, the parameters of the cells inclu ing OCV and r0 at room temperature were recorded at different SOC levels. The test r sults are shown in Figure 3. It is noted that Figure 3d exhibits a sudden increase in r sistance from 40 to 70% SOC for LSB. Theoretically, a battery internal resistance is the su of the liquid phase (electrolyte) and solid phase (electrode) resistance. The sudden i crease in resistance is very likely to result from the poor conductivity of the sharply i creased various charge products including intermediates (Li2Sx, x = 1-8) [27]. Howeve when SOC becomes deeper, the high order Li2Sx forms with better conductivity, decrea ing the resistance. Similar resistance-vibration phenomena have been reported in prev ous reported works [18]. Furthermore, Figure 3b, d shows that the internal resistance LSB was much higher than that of LIB, which apparently can be ascribed to the same re son as discussed above. Nevertheless, it is noteworthy that the testing was conducted o a 3 Ah LSB battery cell and 50 Ah LIB cell, so an accurate resistance difference betwee two kinds of batteries should be obtained after configuring the cells to battery packs wi comparable energy.

Pack Parameter Identification
The cell parameters' OCV and r0 at different SOCs were measured, which were ide tical to that of the previously reported LSB pouch cells [17][18][19]. The test results for bo the LSB and LIB cells are illustrated in Figure 3. The voltages of the LSB pack configuratio in Figure 2 can be presented as (1

Pack Parameter Identification
The cell parameters' OCV and r 0 at different SOCs were measured, which were identical to that of the previously reported LSB pouch cells [17][18][19]. The test results for both the LSB and LIB cells are illustrated in Figure 3. The voltages of the LSB pack configuration in Figure 2 can be presented as (13) and the LIB pack voltage as From Equations (13) and (14), the voltage platforms for the LIB and LSB packs were 268-384 V and 290-470 V, respectively. However, the internal resistance, r 0 , of the former was 100 times higher than that of the latter. The pack levels of the LSB with a mixed configuration of 196 in serial and 44 in parallel was still 10 times higher than that of the LIB pack with the same configuration. The data obtained above were employed in the closed-loop model to simulate and compare the performance of the two battery systems for three driving cycles and a fast-charge feature.

Model Accuracy Verification
Before the application of a model, its accuracy should be verified to confirm the closeness to a real vehicle. A comparison testing was executed separately with the real prototype vehicle and the simulation model. We used the same driving and charging cycles for both the real prototype vehicle and the simulation model to characterize the battery performance and parameters changed during charging and discharging, and then we analyzed the variations between the real vehicle and the simulation model for evaluating the model reliability. A vehicle dynamometer was used for the real vehicle testing (Supplementary Figure S6). The driving condition and charging condition were set up for the comparison testing. Battery voltage, SOC, and current were recorded and analyzed to evaluate the matching degree between the model and reality, as shown in Supplementary Figure S7.
The difference ratio between the model and reality is defined as Using Equation (15), the difference ratio between the simulation model and the real vehicle is summarized in Supplementary Table S1. It clearly shows that the simulation model has high accuracy with the real tested pack, thus proving that this model can be used to reliably predict the battery performance in real vehicle application to provide valuable research, optimization, and scaled-up fabrication information for LSBs.

Results and Discussion
Based on the battery lab tests and simulated parameters, the internal resistance level of the LSB pack was around 10 times higher than that of the LIB. The internal resistance has a great influence on LSB applications in an electric vehicle. In an electric vehicle operation, the electric load of the battery pack contains the electric power-train system and other electric auxiliaries such as DCDC, air compressors, etc. The battery output voltage is the actual voltage, u out , applied on the electric load. For certain vehicle drive cycles, the electric load usage was determined; however, the u out applied on the electric load is affected by the difference in internal resistance. Equation (2) can be used to explain the internal-resistance-effect mechanism, in which the deviation of u out from u ocv is directly related to the internal resistance, r 0 , and a large internal resistance will increase the voltage variance between u ocv and u out , resulting in an unstable output voltage on the vehicle's electric load, which would shorten the service life of the auxiliaries.
Considering the efficiency from the electric vehicle system level, the power and energy usage on the electric load (power-train and auxiliaries) is battery-effective work. The effective work power, P out , and the effective energy, E out , can be determined by Equations (16) and (17), respectively: Meanwhile, the internal-resistance-generated heat is useless work for the electric vehicle, and the battery power loss, P loss , and useless heat energy, E loss , are expressed in Equations (18) and (19), respectively: For certain drive conditions, P out is determined by the power demand of the vehicle, which is affected directly by the battery internal resistance. It has been found that a larger internal resistance causes larger battery power loss and battery energy loss. Simulations were conducted to analyze the operation performance of the LSB and the LIB in an electric vehicle application for three typical driving conditions. In all driving cycles, namely the NEDC, WLTC and HWFT, the gradient was 0.
The NEDC was chosen as the first simulation condition. As shown in Supplementary Figure S8a [28,29], the entire driving cycle (total time, 1180 s) included urban driving cycles (UDCs) and extra-urban driving cycles (EUDCs). The first 780 s was the UDC (maximum speed 50 km/h), and the next 400 s was the EUDC (maximum speed 120 km/h). This driving cycle has been widely used to test vehicle energy consumption, emissions, and driving range [30][31][32]. Figure 4a,b exhibits the voltage variation curve under the NEDC for the LSB and the LIB, respectively, indicating that the charge and discharge voltage output of an EV battery increases and decreases, respectively, due to internal resistance. A large battery internal resistance causes a sharp voltage vibration. Since the LSB has a larger internal resistance, it experienced a more severe voltage vibration (from 359.9 to 441.5 V) in comparison to the LIB (344.9-357.5 V). It can be concluded that the high LSB internal resistance, and resulting unstable output voltage, is one of the main obstacles for the LSB's electric vehicle application. which is affected directly by the battery internal resistance. It has been found that a internal resistance causes larger battery power loss and battery energy loss. Simu were conducted to analyze the operation performance of the LSB and the LIB in an vehicle application for three typical driving conditions. In all driving cycles, nam NEDC, WLTC and HWFT, the gradient was 0.
The NEDC was chosen as the first simulation condition. As shown in Supplem Figure S8a [28,29], the entire driving cycle (total time, 1180 s) included urban driv cles (UDCs) and extra-urban driving cycles (EUDCs). The first 780 s was the UDC mum speed 50 km/h), and the next 400 s was the EUDC (maximum speed 120 km/h driving cycle has been widely used to test vehicle energy consumption, emission driving range [30][31][32]. Figure 4a,b exhibits the voltage variation curve under the NEDC for the LSB a LIB, respectively, indicating that the charge and discharge voltage output of an EV increases and decreases, respectively, due to internal resistance. A large battery i resistance causes a sharp voltage vibration. Since the LSB has a larger internal resi it experienced a more severe voltage vibration (from 359.9 to 441.5 V) in compar the LIB (344.9-357.5 V). It can be concluded that the high LSB internal resistance, sulting unstable output voltage, is one of the main obstacles for the LSB's electric application. During the driving-cycle simulation, the battery power and energy to overco the mechanical drag force were defined as driving power/energy, while the inter sistance-resulting power and energy loss was ascribed to battery power/energy l reality, the usage of battery power and energy contains driving power/energ During the driving-cycle simulation, the battery power and energy to overcome all the mechanical drag force were defined as driving power/energy, while the internal-resistanceresulting power and energy loss was ascribed to battery power/energy loss. In reality, the usage of battery power and energy contains driving power/energy and power/energy loss. Hence the gap between the driving power and the battery power at certain time points is the battery power loss, and a cumulative energy loss indicated by the gap between driving energy consumption and battery energy consumption can vividly indicate the battery performance in EV applications.
NEDC simulation results for the power consumption of the LSB and LIB in Figure 4c,d, respectively, indicate that the LSB had an obvious larger power loss during vehicle driving, and the peak loss of the LSB during the NEDC cycle was 9.2 kW at 1120 s, while that of the LIB was 1.2 kW at 1121 s. The simulation energy consumption by the end of the NEDC driving cycle at 1200 s is shown in Figure 4e,f for the LSB and LIB, respectively, revealing that the driving energy consumption and battery energy consumption for the LSB were 1.526 kWh and 1.646 kWh, respectively, in other words, a battery energy loss of 0.12 kWh, while for the LIB, they were 1.542 kWh and 1.558 kWh, respectively, a battery energy loss of 0.016 kWh. This simulation clearly indicated that the LSB had a very notable battery energy loss, which was much higher than that of the LIB.
The WLTC was the second driving cycle for the simulation analysis. The WLTC adds real road emissions requirements and significantly strengthens evaporative emissions control, which is closer to the realistic vehicle driving condition, and thus is a very important driving condition to evaluate the power-train system and is referred to by many vehicle test standards [33][34][35]. The WLTC speed curve is shown in Supplementary Figure S8b, and the simulation voltage curves under the WLTC for the LSB and LIB in Figure 5 reveal that the LSB underwent an extremely more severe output voltage vibration (288.2-440.9 V) than the LIB (324.5-357.1 V), and was also worse than that under the NEDC, as the WLTC has more frequent driving and braking demand change [36]. The results showed that the LSB's unstable voltage caused by a large internal resistance becomes worse in more aggressive driving conditions. driving, and the peak loss of the LSB during the NEDC cycle was 9.2 kW at 1120 that of the LIB was 1.2 kW at 1121 s. The simulation energy consumption by the en NEDC driving cycle at 1200 s is shown in Figure 4e,f for the LSB and LIB, respe revealing that the driving energy consumption and battery energy consumption LSB were 1.526 kWh and 1.646 kWh, respectively, in other words, a battery energy 0.12 kWh, while for the LIB, they were 1.542 kWh and 1.558 kWh, respectively, a energy loss of 0.016 kWh. This simulation clearly indicated that the LSB had a very battery energy loss, which was much higher than that of the LIB.
The WLTC was the second driving cycle for the simulation analysis. The WLT real road emissions requirements and significantly strengthens evaporative em control, which is closer to the realistic vehicle driving condition, and thus is a v portant driving condition to evaluate the power-train system and is referred to b vehicle test standards [33][34][35]. The WLTC speed curve is shown in Supplementary  S8b, and the simulation voltage curves under the WLTC for the LSB and LIB in F reveal that the LSB underwent an extremely more severe output voltage vibration 440.9 V) than the LIB (324.5-357.1 V), and was also worse than that under the NE the WLTC has more frequent driving and braking demand change [36]. The showed that the LSB's unstable voltage caused by a large internal resistance b worse in more aggressive driving conditions.     Figure 5c,d indicates that the LSB had an obvious power loss during vehicle driving; the peak power loss during the WLTC was 19.4 kW at 1648 s, while the peak power loss of the LIB battery was 3.8 kW at 1652 s. The energy consumption during the WLTC is shown in Figure 5e,f; by the end of the WLTC, the driving energy consumption was 9.521 kWh, the battery energy consumption for the LSB was 11.98 kWh, with a battery energy loss of 2.459 kWh, while the energy consumption for the LIB was 9.277 kWh, with a battery energy loss of 0.056 kWh. Under the aggressive acceleration/deceleration defined by the WLTC, the large LSB internal resistance created more significant power loss and energy loss, significantly reducing the electric vehicle energy efficiency. Finally, the HWFT cycle was used for this simulation to observe the battery performance under a continuous high-speed driving condition. The HWFT cycle is a chassis dynamometer driving schedule developed by the US EPA for light-duty vehicles. The speed curve of the HWFT cycle is shown in Supplementary Figure S8c.
The LSB and LIB were further simulated using the HWFT cycle with an aggressive acceleration operation, thereby consuming a large current to result in an extremely severe output voltage vibration for the LSB (310.1-441.3 V), a much larger value than that of the LIB (339.7-357.6 V) in Figure 6a,b. Figure 6c,d discloses that the LSB had an obvious power loss during highway driving, and the peak power loss during the HWFT was 28.1 kW at 10.3 s, while the power loss for the LIB battery was only 6.2 kW at 10.1 s during the fast acceleration of the vehicle. The driving and battery energy consumptions by the end of the HWFT cycle, shown in Figure 6e,f, were 2.098 kWh and 2.334 kWh, respectively, for the LSB, there was a battery energy loss of 0.236 kWh, while they were 2.136 kWh and 2.174 kWh, respectively, while for the LIB, there was a battery energy loss of 0.038 kWh, clearly symbolizing that the LSB had a very notable battery energy loss in the HWFT cycle, further confirming its notable internal resistance. kWh, with a battery energy loss of 0.056 kWh. Under the aggressive accelerat ation defined by the WLTC, the large LSB internal resistance created more power loss and energy loss, significantly reducing the electric vehicle energy Finally, the HWFT cycle was used for this simulation to observe the battery p under a continuous high-speed driving condition. The HWFT cycle is a chassis eter driving schedule developed by the US EPA for light-duty vehicles. The s of the HWFT cycle is shown in Supplementary Figure S8c.
The LSB and LIB were further simulated using the HWFT cycle with an acceleration operation, thereby consuming a large current to result in an extre output voltage vibration for the LSB (310.1-441.3 V), a much larger value than LIB (339.7-357.6 V) in Figure 6a,b. Figure 6c,d discloses that the LSB had an obv loss during highway driving, and the peak power loss during the HWFT was 10.3 s, while the power loss for the LIB battery was only 6.2 kW at 10.1 s dur acceleration of the vehicle. The driving and battery energy consumptions by the HWFT cycle, shown in Figure 6e,f, were 2.098 kWh and 2.334 kWh, resp the LSB, there was a battery energy loss of 0.236 kWh, while they were 2.13 2.174 kWh, respectively, while for the LIB, there was a battery energy loss of clearly symbolizing that the LSB had a very notable battery energy loss in the H further confirming its notable internal resistance. Supplementary Figure S9 summarizes the voltage oscillation, peak pow total energy loss comparison between the LSB and the LIB. Due to its large sistance, the output voltage of the LSB is affected sensitively by unstable out and more power loss, worse than that of the LIB.
To evaluate the LSB performance during fast charge, a charging simulat up to observe the potential charge capability for EV. A fast-charge simulation s designed as in the following List: 1. Charge start: start the charge when the battery SOC is 20%. Supplementary Figure S9 summarizes the voltage oscillation, peak power loss, and total energy loss comparison between the LSB and the LIB. Due to its large internal resistance, the output voltage of the LSB is affected sensitively by unstable output voltage and more power loss, worse than that of the LIB.
To evaluate the LSB performance during fast charge, a charging simulation was set up to observe the potential charge capability for EV. A fast-charge simulation strategy was designed as in the following List:

1.
Charge start: start the charge when the battery SOC is 20%.

2.
Charge current ramp: ramp the charge current 1 A per second, until the charge current reaches the configured constant-charge current value.

3.
Constant current charge: continuously charge with the configured current and decrease the charge current accordingly to avoid the battery output voltage reaching the voltage limit. 4.
The fast-charge simulation results for the LSB are shown in Figure 7a-e. In a previous analysis, it can be noted from Equation (1) that the large internal resistance will raise the output voltage variance. Under certain fast-charge currents, the output voltage of the LSB increases more easily to reach the voltage limit because of its 10 times higher internal resistance compared to the LIB, and its charge current has to be limited to avoid the output voltage exceeding its limit threshold. To avoid exceeding the battery voltage limit (470 V), the charge current was set to 131 A for a constant current charge after the SOC reached 70%, at which point the OCV platform began to rise and the charge current had to be reduced for the voltage below the battery limit. Using this fast-charge strategy, it took 2681 s to charge the LSB from SOC 20% to SOC 80%. The fast-charge simulation results for the LIB battery are shown in Figure 7b-f. The charge current could be set to 255 A for a constant current charge, the LIB battery could be charged to 80% SOC with a 255 A constant voltage, and the battery voltage never exceeded the voltage limit (384 V) during the entire charging process. It took 508 s to charge the LSB from SOC 20% to SOC 80% by using the fast-charge simulation strategy. The charging simulation results are summarized in Table 3. From the simulation results, we found that the LSB's performance was good and that the LSB could adapt to the application of an electric vehicle under mild driving conditions; however, the high internal resistance of the LSB resulted in a sharp output voltage vibration, significant loss of peak power, and energy in the aggressive driving condition, which could affect the life and safety of the electrical systems, reduce the dynamic performance, and shorten the driving range of the EV. The charging time was five times longer than for the LIB, so the LSB could not meet the fast-charging requirement.
crease the charge current accordingly to avoid the battery output voltage the voltage limit. 4. Charge stop: when battery SOC reaches 80%, stop charging.
The fast-charge simulation results for the LSB are shown in Figure 7a-e. In a analysis, it can be noted from Equation (1) that the large internal resistance wil output voltage variance. Under certain fast-charge currents, the output voltage increases more easily to reach the voltage limit because of its 10 times higher in sistance compared to the LIB, and its charge current has to be limited to avoid t voltage exceeding its limit threshold. To avoid exceeding the battery voltage lim the charge current was set to 131 A for a constant current charge after the SOC 70%, at which point the OCV platform began to rise and the charge current reduced for the voltage below the battery limit. Using this fast-charge strateg 2681 s to charge the LSB from SOC 20% to SOC 80%. The fast-charge simulati for the LIB battery are shown in Figure 7b-f. The charge current could be set to a constant current charge, the LIB battery could be charged to 80% SOC wit constant voltage, and the battery voltage never exceeded the voltage limit (384 the entire charging process. It took 508 s to charge the LSB from SOC 20% to SO using the fast-charge simulation strategy. The charging simulation results ar rized in Table 3. From the simulation results, we found that the LSB's perform good and that the LSB could adapt to the application of an electric vehicle u driving conditions; however, the high internal resistance of the LSB resulted i output voltage vibration, significant loss of peak power, and energy in the a driving condition, which could affect the life and safety of the electrical system the dynamic performance, and shorten the driving range of the EV. The char was five times longer than for the LIB, so the LSB could not meet the fast-ch quirement.

Conclusions
In summary, a closed-loop modeling method was established here to bridge a new battery technology from lab research to scaled-up development for its development in EV applications. The results exhibit a small variation (2.8/2.6% voltage difference ratio, 2.9/0.6% current difference ratio, and 1.2/2.6% SOC difference ratio) in comparison to a real vehicle, indicating its high accuracy. Based on the model systems, the performed simulations under the NEDC, WLTC, and HWFT and fast-charge schedule clearly indicates that the LSB holds great promise and confidence for its applications in electric vehicles. However, the LSB has a much larger internal resistance than that of LIB, thereby generating more obvious output voltage oscillation as well as higher power and energy loss than that of the LIB, highlighting some difficulties in automotive applications. In particular, the fast charging of the LSB takes nearly five times longer than that of the LIB, impeding the LSB's EV commercialization.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/app11209593/s1, Figure S1: Electrical equivalent circuit model. Figure S2: Vehicle force analysis. Figure S3: (a) Rolling resistance in driving model; (b) air resistance model; (c) grade resistance model; (d) driving force model. Figure S4: Driver model with driving-cycle targets. Figure S5: (a) PEBC05-500 tester; (b) LSB and LIB cells are fixed and tested in the box next to the tester. Figure S6: Vehicle testing with dynamometer. Figure