Simulation Study on Factors Affecting the Output Voltage of Extended-Range Electric Vehicle Power Batteries

Abstract

The power battery configuration of an extended-range electric vehicle directly affects the overall performance of the vehicle. Optimization of the output voltage of the power battery can improve the overall power and economy of the vehicle to ensure its safe operation. Factors affecting the output voltage of power batteries under different operating conditions, such as nominal voltage and the number of series and parallel connections of the battery cells, have been studied. This study uses AVL Cruise to establish an overall model of an extended-range electric vehicle to simulate the output voltage characteristics under the different operating conditions of the NEDC (New European Driving Cycle), WLTC (World Light Vehicle Test Cycle) and CLTC (China Light Duty Vehicle Test Cycle). The influence of the output voltage of the power battery under different operating conditions is studied to ensure that the power battery can output energy with high efficiency. The operating conditions have an impact on the output voltage with an idle voltage fluctuation of the operating conditions. The nominal voltage variation and the number of series and parallel connections of the battery cells affect the frequency and time of breakdown.

1. Introduction

Extended-range electric vehicles (EREVs) automatically start and provide power to the battery when the onboard battery reaches the minimum critical limit set by the state of charge (SOC). EREVs have numerous advantages, such as high charging flexibility [1,2], a long battery life [3,4] and superior environmental performance [5,6]. The power battery directly affects the economy, power and safety of EREVs [7,8]. Previous battery research has focused on thermal runaway and the heat dissipation treatment of battery packs or individual cells [9,10]. When the power battery is matched to the entire vehicle, the performance will be affected by various factors [11,12].

Previous research has focused on energy management strategies and control improvements for EREVs and power batteries. Zhang et al. used the hierarchical reinforcement learning-based energy management strategy for plug-in hybrid electric vehicles to improve performance during the ecological car-following process [13]. The proposed strategy avoided the additional energy consumption caused by speed fluctuations, which improved the efficiency of the engine operating points. Huang et al. applied the deep reinforcement learning-based energy management strategy for the range-extended fuel cell hybrid electric vehicle [14]. The final SOC of the battery increased by 2.54%, 2.24% and 1.92%. The operating power generation cost decreased by 36.3%, 41.4% and 40.1%. Xu et al. optimized the energy management strategy for EREVs with the multi-island genetic algorithm [15]. When EREVs adopted the optimized operating mode of the multi-island genetic algorithm as an equivalent fuel consumption minimization strategy, the fuel economy under WLTP conditions was improved by 4.49% and the cumulative ampere hours through the power battery were reduced by 11.37%.

Xiao et al. improved energy management via maximum entropy reinforcement learning for an extended-range electric vehicle [16]. They efficiently controlled the auxiliary power unit (APU) to charge the battery and increased the SOC in the WLTC and CLTC from 20% to 70% and 60% with a diesel consumption of 5.26 L and 4.37 L within half an hour. Parkar et al. modified particle swarm optimization-based powertrain energy management for EREVs [17]. The balance weight deviation between the two objectives resulted in a fuel consumption of 22.15 L and nitrogen oxide emissions of 1025.27 g, with a simultaneous reduction of 9.4% in fuel consumption and 7.9% in nitrogen oxide emissions. Yang et al. carried out research on an energy management strategy for EREVs based on a hybrid energy storage system [18]. Zhang et al. took the trajectory optimization-based APU strategy to improve EREV performance [19]. The trajectory optimization resulted in a 70.2% reduction in computational complexity with a 21.1% increase in convergence speed. Zhang et al. estimated the capacity of each battery for a series-connected battery pack based on partial charging voltage curve segments using a partial charging voltage curve at 30% SOC for EREVs [20]. The estimation error of the battery cells was less than 2%. Gong et al. compared the discharge characteristics of the lithium iron phosphate (LFP) battery and nickel–cobalt–manganese (NCM) ternary lithium battery in three different operating conditions of the NEDC, WLTP and CLTC-P [21]. LFP batteries have a higher maximum voltage and lower minimum voltage under the same initial voltage conditions, with a maximum voltage difference variation of 11 V.

The factors affecting the output voltage of EREV power batteries have rarely been studied [22]. This study used AVL Cruise to establish an overall model of an EREV to simulate the output voltage characteristics under different nominal cell voltages under the operating conditions of the NEDC, WLTC and CLTC. The influence of the output voltage of the power battery under different operating conditions was studied to ensure the power battery can output energy with high efficiency.

2. Simulation Model Establishment

Based on the structure and working principle of the EREV, AVL Cruise 2018 software (AVL List GmbH, Graz, Austria) was used to establish the EREV model. The parameters, indicators of the EREVs and the overall configuration of the vehicle were determined. The drive motor module, engine module and power battery module were established for the entire vehicle model.

2.1. Power Battery Model

2.1.1. SOC Calculation

The SOC of a battery refers to the change in the state of charge parameters involved in the reaction inside the battery [23,24], which reflects the remaining capacity of the battery. SOC is defined in Equation (1).

$$\mathrm{SOC}=1-{\displaystyle \frac{\mathrm{Q}}{{\mathrm{C}}_1}}$$

(1)

where Q is the amount of electricity already discharged, C, and C₁ is the actual capacity corresponding to the constant current discharge, A∙h.

The ampere-hour integration method is one of the most used algorithms in SOC calculation [23,24]. Its algorithm accumulates the battery current based on the initial SOC and ultimately obtains the required SOC value. Its mathematical expression can be expressed as Equation (2).

$$\mathrm{SOC}(\mathrm{t})=\mathrm{SOC}(0)-{\displaystyle \frac{1}{{\mathrm{C}}_N}}{\displaystyle \underset{0}{\overset{\mathrm{t}}{\int }}\eta \times }i\times dt$$

(2)

where SOC(0) is the rated capacity of the battery, C. i is the charging and discharging current of the battery, A. η is the charging and discharging efficiency of the battery.

In calculations, the battery is treated as a power system, and the SOC state of the battery is considered the internal state of the system. The mathematical equation of the battery model can be expressed as Equation (3).

$$\left\{\begin{array}{l}{x}_{k+1}=A_K{x}_k+B_k{u}_k+w_k\\ y_k=C_k{x}_k+v_k\end{array}\right.$$

(3)

where u_k is the system input, which generally includes variables such as battery current, temperature and state of charge. The uncertainty is caused by the process noise w_k when the system moves from state x_k to x_k+1.y_k is the system output and the operating voltage of the battery. w_k is the process noise of the system. v_k is the measurement noise of the system.

The estimation equation for SOC can be expressed as Equation (4).

$${\mathrm{SOC}}_{k+1}={\mathrm{SOC}}_k-{\displaystyle \frac{{\displaystyle {\int }_0^{\mathrm{t}}\eta (i_k)i_{k}dt}}{Q_m}}$$

(4)

where SOC_k+1 is the SOC value at time k + 1, C. η_(ik) is the charging and discharging efficiency. i_k is the charging and discharging current, A. Q_m is the battery capacity, A∙h.

2.1.2. No-Load Battery Voltage

In AVL Cruise, the operating voltage of the battery under no-load conditions will depend on the temperature and the SOC. The no-load voltage will be determined based on the corresponding input values (charge/discharge) and a smoothing factor, which can be calculated by Equation (5).

$$U_{QH,\mathit{idle}}(T_{QH},{\mathrm{SOC}}_{QH})=U_{QH,idle,\mathit{charge}}(0.5-F_{smooth})+U_{QH,idle,\mathit{discharge}}(0.5+F_{smooth})$$

(5)

where U_QH,idle is the no-load voltage of the battery, V. U_{QH,idle,charge} is the open-circuit voltage measured in charging mode, V. U_{QH,idle,discharge} is the open-circuit voltage measured in discharging mode, V. F_smooth is a smoothing factor commonly used to reduce the step effect between the charge and discharge.

2.2. EREV Model

2.2.1. Peak Power Calculation

The maximum power that the driving motor can achieve is called the peak power of the motor, which affects the acceleration and climbing performance of the vehicle. The required power P₁ and P₂ of the motor can be calculated from the maximum speed $v_{\max }$ and maximum climbing slope $i_{\max }$ of the vehicle. P₁ can be calculated by Equation (6).

$$P_1={\displaystyle \frac{v_{\max }}{3600{\eta }_T}}(mgf+{\displaystyle \frac{C_{D}A{v}_{\max }^2}{21.15}})$$

(6)

where P₁ is the motor power, kW; η_T is the mechanical efficiency; m is the mass of the car, kg; g is the acceleration due to gravity, m/s²; f is the adhesion rate; C_D is the coefficient of air resistance; and A is the windward area, m².

The maximum power P₂ is determined by the maximum climbing slope.

$$P_2={\displaystyle \frac{v_i}{3600{\eta }_T}}(mgf\cos {\alpha }_{\max }+mg\sin {\alpha }_{\max }+{\displaystyle \frac{C_{D}A{v}_i^2}{21.15}})$$

(7)

where v_i is the stable vehicle speed at maximum climbing slope, v_i = 20 km/h. α_max is the maximum climbing angle ${\alpha }_{\max }=\arctan i_{\max }$.

The rated power of the drive motor is often based on the power demand generated by 90% of the maximum designed vehicle speed.

$$P_{\mathrm{me}}={\displaystyle \frac{v}{3600{\eta }_T}}(mgf+{\displaystyle \frac{C_{D}A{v}^2}{21.15}})$$

(8)

where P_me is the rated power of the driving motor, kW. $v$ = 0.9·$v_{\max }$.

2.2.2. Calculation of Peak Speed

The peak speed N_mmax of the driving motor is related to its own quality and voltage. Vehicles using permanent-magnet synchronous motors have peak speeds ranging from 6000 to 10,000 rpm. The relationship between motor speed and vehicle speed is given in Equation (9).

$$N_m={\displaystyle \frac{v{i}_0}{0.377r}}$$

(9)

where N_m is the motor speed, rpm. v is the vehicle speed, km/h. i₀ is the motor current, A. The peak speed of the driving motor can be obtained.

2.2.3. Calculation of Peak Torque

The peak torque N_mmax can be calculated from the peak power and base speed of the motor. The base speed and peak speed of the motor have the following relationship.

$$N_{me}={\displaystyle \frac{N_{m\max }}{\beta }}$$

(10)

where β is the coefficient of the motor expansion constant power range. N_me is the base speed of the driving motor, rpm.

After obtaining the base speed of the motor, the peak torque T_mmax and rated torque T_me formula of the motor can be calculated with Equation (11).

$$\left\{\begin{array}{l}{T}_{me}={\displaystyle \frac{P_{me}\cdot 9550}{N_{me}}}\\ T_{m\max }={\displaystyle \frac{P_{m\max }\cdot 9550}{N_{me}}}\end{array}\right.$$

(11)

2.3. EREV Modeling of Cruise

The EREV requires a vehicle module, motor module, engine module, battery module, driving module, differential module, brake module, main reducer module, wheel module, electronic system module and control strategy module in the software. After all modules were placed on the main interface, they were connected separately. The red line represents the electrical connection, and the blue line represents the mechanical connection. The green pentagon on the left side of the module is the signal input and the red pentagon is the signal output. The vehicle model is depicted in Figure 1.

2.3.1. Vehicle and Engine Module

The vehicle- and engine-related parameters of the simulation study are listed in

Table 1. Key parameters of EREVs.

Parameter	Value
Empty weight m0/kg	2450
Full load mass m/kg	3080
Wheelbase L/mm	3005
Length × Width × Height/mm	5050 × 1995 × 1750
Tire radius/mm	354
Windward area A/m2	3.04
Number of cylinders	4

.

2.3.2. Drive Motor Module

The speed torque characteristic curve (Figure 2) and the drive motor efficiency map (Figure 3) are shown below.

2.3.3. Power Battery Module

The second-order Thevenin model has an RC loop based on the Thevenin model to characterize the differences in battery concentration, which presents the internal resistance characteristics of the battery. Figure 4 is the second-order Thevenin equivalent circuit model.

According to the selected vehicle model, the power battery of this car is a 40.9 kW·h ternary lithium battery, and the battery parameters are given in

Table 2. Battery parameters.

Parameter	Value
Nominal voltage/V	3.7
Energy density/W·h/kg	120~200
Specific power/W/kg	1500~2000
Charge temperature/°C	0~45
Discharge temperature/°C	−20~60
Internal resistance/mΩ	<30
Charging cycles	>1500

.

In the power battery module, the battery type is determined by inputting the characteristic parameters of the battery with the battery capacity, initial SOC, rated voltage, maximum and minimum voltage, number of series and parallel connections and the initial temperature of the battery. The SOC initial voltage characteristic curve of the battery under charge and discharge is shown in Figure 5.

3. Simulation Settings

After building the vehicle model and the parameters of each component, three cyclic operating simulations of the NEDC, WLTC and CLTC can be set up.

3.1. Cycle Condition Task Setting

The speed profile diagram is used to set each cycle task, which simulates the speed changes in the vehicle in the actual operation when facing corresponding working conditions. Figure 6 shows the speed profile diagrams for the three working conditions.

3.2. Simulation Initial Condition Setting

In the control module, this study set the power battery SOC to start the range extender after reaching 45% through the code [25,26]. The engine drove the electric motor to work and then the range extender began to supply power to the drive motor to charge the battery. When the battery SOC reached 65%, the range extender was turned off and the drive motor returned to being driven by the power battery. The vehicle operated in pure electric mode again.

4. Results Analysis and Discussion

4.1. Impact of Working Conditions

The output voltage of the power battery has a direct impact on the energy output stability and power performance of the vehicle’s power system. A stable voltage output can provide enough power to the vehicle. The output voltage is also related to the driving range of the vehicle. A higher output voltage is beneficial for extending the driving range of the vehicle. The voltage output curve is also closely related to the lifespan of the power battery. In the initial setup, the power battery parameters are set to an initial SOC of 46%, a battery capacity of 40.9 Ah and a nominal voltage of 7.2 V, with 40 batteries in series and 2 batteries in parallel. The cycle simulation task sets up and runs the simulation separately. After completing the simulation, the output curves of the power battery voltage under three different operating conditions are obtained as given in Figure 7.

A power battery that is in an unstable voltage state for a long time will damage the internal structure of the battery, which will affect the activity of chemicals in the battery cell and thus affect the battery’s lifespan. The relevant numerical comparisons of the output voltage curves of the power battery are listed in

Table 3. Voltage values for three operating conditions.

Operating Conditions	Idle Voltage/V	Maximum Voltage/V	Minimum Voltage/V	Standard Deviation
NEDC	306.44	353.06	186.78	30.02
WLTC	308.65	357.14	194.81	22.5
CLTC	308.59	375.67	191.53	24.52

.

From the NEDC operating condition curve in Figure 7a, the battery voltage was around 306 V at idle. There was a significant voltage fluctuation at the end of the curve, with a voltage fluctuation amplitude of 119.66 V compared to the idle voltage. The low number of parallel connections resulted in a smaller capacity of the power battery, which led to a large change in the SOC value of the power battery. It was not conducive to the stable output of the battery and consumed its service life. The working condition curve of the WLTC is given in Figure 7b. Due to the complexity of the curve of the WLTC working condition compared to the NEDC working condition, the voltage output was more unstable than in the NEDC working condition. The peaks and valleys of the curve were obvious, and the voltage amplitude fluctuated too much. The voltage fluctuation amplitude reached 113.84 V compared with the idle voltage. The working voltage of the battery changed more significantly when faced with the more complex working condition of the WLTC. The speed variation in the CLTC operating conditions was more complex, with speed ranges of low, medium and high. The CLTC output voltage curve, shown in Figure 7c, exhibited more abrupt changes and four instances of voltage breakdown. The references of [27,28,29,30,31] give the definition and influence factor for the breakdown. The reference [30] clearly states that nominal and acceleration conditions can change the voltage static shifts. The voltage fluctuation amplitude reached 117.06 V compared with the voltage at idle. The low battery capacity and output voltage of the battery cannot enable the vehicle to cope with more complex working conditions. Low voltage affected the power output of the vehicle. The frequent charge and discharge of the battery caused by low battery capacity will have an impact on the battery life. Frequent charge and discharge of the battery cycles can accelerate battery degradation. The chemical reactions during the charge and discharge process can produce other products which will accumulate and affect battery performance. This will accelerate the battery’s decay process when the battery is in a low battery capacity state, which is used to a point close to depletion. Keeping the battery in a low battery state for a long time will increase the natural decay rate of the battery. The chemical reactions inside the battery are more active in low battery states, resulting in faster natural charge loss.

4.2. Impact of Nominal Voltage on Battery Cells

The nominal voltage of the battery cell was changed without changing the other parameters. The effect of the nominal voltage of the battery cell on the output voltage of the power battery was obtained. The initial SOC, battery capacity, number of batteries in series and number of parallel connections remained unchanged. The nominal voltage changed from 7.2 V to 4.2 V. The output voltage curve in Figure 8 shows the nominal voltage change in the battery cell of the power battery under the NEDC, WLTC and CLTC operating conditions. The nominal voltage of the battery cells did not significantly improve the voltage output of the power battery in the NEDC, WLTC and CLTC operating conditions. The breakdown phenomenon still existed, but the breakdown time changed. Electric breakdown occurs when a solid medium is subjected to a strong electric field. A small amount of freely moving charge carriers inside moved violently, colliding with atoms on the lattice, which caused them to dissociate and rapidly expand, leading to breakdown. Its characteristic is that the voltage action time is short with high voltage. Rapid changes in the CLTC operating conditions can lead to excessive transient voltage in a short period of time, resulting in breakdown.

4.3. Series Parallel Connection of Battery Cells

The initial SOC, battery capacity, nominal voltage and operating temperature remained unchanged. The number of batteries connected in series was set to 100, and the number of batteries connected in parallel was set to 4 (the initial operating condition required 40 batteries connected in series and 2 batteries connected in parallel). The output curves of the power battery voltage under three different operating conditions obtained after simulation completion are shown in Figure 9. The number of battery cells changed in series and parallel can have a certain improvement effect on the output voltage of the power battery, as seen in Figure 9a. The voltage fluctuation at the end of the curve was reduced, which can significantly improve the energy output of the power battery and impact the stability of the vehicle’s electronic control system. The number of battery cells changed in series and parallel under the WLTC conditions significantly improved the voltage output of the power battery, as shown in Figure 9b. It reduced voltage fluctuations and the amplitude of voltage fluctuations, which had a positive effect on protecting the service life of the power battery. In Figure 9c, the voltage output of the power battery increased under the CLTC conditions and eliminated the breakdown phenomenon, which had a significant improvement effect on the voltage output, battery life and battery protection.

The relevant values of the output voltage curve of the power battery are shown in

Table 4. The voltage value after changing the number of battery cells in series and parallel.

Operating Conditions	Idle Voltage/V	Maximum Voltage/V	Minimum Voltage/V	Standard Deviation
NEDC	766.82	798.0	741.24	7.86
WLTC	766.9	797.52	746.6	10.56
CLTC	766.62	803.92	731.24	8.27

.

The standard deviation of the NEDC condition had changed from 30.02 to 7.86 compared with the initial voltage curve, which indicated that the voltage curve had become more stable under the NEDC condition. The maximum fluctuation amplitude decreased from 119.66 V to 31.18 V compared to the idle voltage, with a decrease of 73.9%. Compared with the initial voltage curve, the fluctuation amplitude and quantity of the power battery voltage curve under the WLTC condition were significantly reduced, with a standard deviation change from 22.5 to 10.56 and a maximum fluctuation amplitude reduction from 113.84 V to 30.62 V, with a decrease of 73.1%.

There was no further breakdown of the power battery under CLTC conditions. The voltage curve gradually stabilized with a standard deviation change of 24.52 to 8.27. There are still many small fluctuations in the voltage curve, with the maximum fluctuation amplitude decreasing from 117.06 V to 37.3 V, with a reduction of 68.1%. This effectively reduced the battery’s usage loss, protected the power battery kit, improved battery power output and protected the battery’s service life.

5. Conclusions

This study applied the AVL Cruise software to establish an EREV model, which conducted simulation research on the factors affecting the output voltage of the EREV power battery. The following conclusions can be drawn:

• The output voltage can be affected by operating conditions with the same battery configuration parameters. The idle voltage (308.59 V), maximum voltage (375.67 V) and minimum voltage (191.53 V) of the CLTC operating conditions are higher than those of the NEDC and WLTC operating conditions.
• The nominal voltage of the battery cell change did not significantly improve the voltage output of the power battery. The breakdown phenomenon still exists, but the breakdown time will change.
• The number of series and parallel connections of battery cells directly affects the output voltage which can avoid breakdown phenomena. The maximum fluctuation amplitude of the NEDC decreased from 119.66 V to 31.18 V compared to the idle voltage, with a reduction of 73.9%. The maximum fluctuation amplitude of the WLTC operating condition decreased from 113.84 V to 30.62 V, with a reduction of 73.1%. The maximum fluctuation amplitude of the WLTC operating condition decreased from 117.06 V to 37.3 V, with a reduction of 68.1%.