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Article

Multiobjective Optimization for a Li-Ion Battery and Supercapacitor Hybrid Energy Storage Electric Vehicle

1
School of Automation, Wuhan University of Technology, Wuhan 430070, China
2
Wuhan Digital Engineering Institute, Wuhan 430074, China
*
Author to whom correspondence should be addressed.
Energies 2022, 15(8), 2821; https://doi.org/10.3390/en15082821
Submission received: 4 March 2022 / Revised: 2 April 2022 / Accepted: 10 April 2022 / Published: 12 April 2022
(This article belongs to the Special Issue Integrated Energy Networks and Microgrids)

Abstract

:
The acceptance of hybrid energy storage system (HESS) Electric vehicles (EVs) is increasing rapidly because they produce zero emissions and have a higher energy efficiency. Due to the nonlinear and strong coupling relationships between the sizing parameters of the HESS components and the control strategy parameters and EV’s performances, energy consumption rate, running range and HESS cost, how to design the HESS EVs for different preferences is a key problem. How to get the real time performances from the HESS EV is a difficulty. The multiobjective optimization for the HESS EV considering the real time performances and the HESS cost is a solution. A Li-ion battery (BT) semi-active HESS and optimal energy control strategy were proposed for an EV. The multiobjectives include energy consumption over 100 km, acceleration time from 0–100 km per hour, maximum speed, running range and HESS cost of the EV. According to the degrees of impact on the multiobjectives, the scaled factors of BT capacity, the series number of Li-ion BTs, the series number of super-capacitors (SCs), the parallel number of SCs, and charge power of the SCs were chosen as the optimization variables. Two sets of different weights were used to simulate the multiobjective optimization problem in the ADVISOR software linked with MATLAB software. The simulation results show that some of the multiobjectives are sensitive to their weights. HESS EVs meeting different preferences can be designed through the weights of different objectives. Compared with the direct optimization algorithm, the genetic algorithm (GA) has a stronger optimization ability, and the single objective is more sensitive to its corresponding weight. The proposed optimization method is practical for a Li-ion BT and SC HESS EV design.

1. Introduction

Due to advantages such as energy conservation, environmental protection, and low charging cost, EVs have been gradually accepted by the market [1,2]. EVs have been considered as a good approach to reduce carbon dioxide emissions, for EVs can overcome the shortcomings of traditional fuel vehicle exhaust pollution. At the same time, EVs can save energy because they can be charged when the power consumption of the power grid is low [3]. The BT is one of the most expensive components of the EV and has a decisive impact on EV’s price and some of their performance [4]. In current EVs, the BTs are always oversized in order to improve power performance and acceleration capability. Such challenges as power performance, running range, lifetime of the BT, and cost of the EV with a sole energy storage system limit the EV’s wider use.
The SC has the advantages of high-power density, short charge and discharge time, and long service life and is less affected by the temperature, but the energy density is small [5]. The Li-ion BT and SC HESS can make up for the advantages of both sides while avoiding their disadvantages [6].
The BT and SC HESS is widely used in different objects and occasions. The BT and SC HESS in smart phones extends the service life of Li-ion BTs [7]. The lead-acid BT and SC HESS in trucks reduces carbon dioxide emissions [8,9,10]. The BT and SC HESS reduces the power fluctuation of fuel cell and wind energy in the HESS with fuel cell and wind energy [11,12,13,14,15,16].
The performance of BT and SC HESS depends on an appropriate energy management strategy. The wavelet analysis method is used to identify the road conditions; then, the neural network is used to learn the conditions data, and the fuzzy energy management strategy is used to distribute the power of the HESS, which improves vehicle performance [17]. The HESS real-time energy management strategy based on SC voltage detection has achieved good results. By improving the topology of HESS, flexible control of lithium BT current is realized, and the effect of energy management is improved. The power performance of HESS is improved by the fuzzy predictive control method [18]. A HESS energy management strategy based on dynamic programming considering lithium BT degradation is proposed [19].
Compared with the BT, the HESS not only improves the performance but also leads to the increase of system complexity and cost. Therefore, the evaluation and optimization of HESS should be carried out with multiple objectives. The purpose of HESS EV is to improve the performances of the EV while taking into account the economy of the EV.
The GA algorithm is widely used in the field of EV optimization [20,21,22,23,24]. The GA algorithm is used to optimize the multi objectives of fuel cell current, lithium BT current, lithium BT’s SOC change, SC’s SOC change, and hydrogen consumption cost by the control of the powers of the BT and SC and the load in the fuel cell, BT, and SC hybrid EV [20]. The multi-objective GA algorithm is used to optimize the automotive electric transmission [21]. The GA algorithm is used to optimize the location and power of EV charging stations [22,23]. The multi-objective GA algorithm is used to optimize the driving paths and powers of multi depot vehicle [24].
The above studies focus on comparing HESS performance with BT or SC performance or, for specific HESS, using an intelligent control method to optimize the energy management strategy and improve the HESS performance, with less consideration of the influence of the sizing parameters of components in HESS and less consideration of the optimal design based on the EV’s specific performance indicators in the optimization. At the same time, how to get the real time performances of the HESS EV is a difficulty. In this paper, a multiobjective optimization on a BT and SC HESS EV using both GA algorithm and ADVISOR software will be studied. The real time performances of the HESS EV are obtained by the ADVISOR software. The EV’s energy consumption over 100 km, acceleration time from 0–100 km per hour, maximum speed, HESS cost, and running range are considered in the objective function. The structure of the paper is as follows: The fundamentals of a BT semi-active HESS EV, the scheme of the multiobjective optimization and an optimal energy management strategy are designed in Section 2. Section 3 focuses on the multiobjective problem analysis. In Section 4 the GA algorithm optimization based on ADVISOR software and MATLAB software is carried out. The study discussion is also presented in Section 4. The conclusions are presented in Section 5.

2. Fundamentals of a BT Semi-Active HESS

2.1. HESS Components

ADVISOR software is a popular advanced vehicle simulation software, which is especially suitable for vehicle performance evaluation, testing, and optimization. A variety of vehicle structures such as traditional fuel vehicles, pure EVs, and fuel cell and Li-ion BT hybrid vehicles are available in the ADVISOR software, but there is no BT and SC HESS EV model available [25]. The new BT’s semi-active HESS EV model is specially developed in the ADVISOR software. The semi-active HESS architecture is reasonable for EVs considering the HESS cost, efficiency, and reliability. The BT’s semi-active HESS structure is easy to lead to unstable motor voltage, but it is still within a range of voltage fluctuation that the motor can withstand. The Li-ion BT pack is connected to the input of the motor controller through a DC/DC converter, and the SC pack is directly connected to the input of the motor controller. The BT semi-active HESS scheme in the ADVISOR software is shown in Figure 1.
The SC pack consists of Nsc,p strings in parallel and Nsc,s SCs in series. The BT pack consists of Nbt,s BTs in series. Phess,r is the required power of the HESS. Phess,a is the available output power of the HESS. Pbt,r is the required power of the Li-ion BT pack. Pbt,a is the available output power of the Li-ion BT pack. Psc,r is the power required of the SC pack. Psc,a is the available output power of the SC pack.
A midsize EV’s parameters are listed in Table 1. A Saft VL45E LiFePO4 BT is used, whose parameters are listed in Table 2 [25]. A Maxwell BACP3000 SC is chosen for the HESS, whose parameters are listed in Table 3 [25]. A Westinghouse AC75 motor model is used with the parameters listedin Table 4 [26].

2.2. The Scheme of the Multiobjective Optimization for the HESS EV

The scheme of the multiobjective optimization for the HESS EV is as in Figure 2. The optimal energy control strategy of the HESS will be designed in the HESS EV in the ADVISOR software by secondary development at first. Then, the relationships between the sizing parameters of the HESS components and the control strategy parameters and EV’s real time performances, energy consumption rate, running range and HESS cost, etc., can be obtained by the HESS EV performance simulation in the ADVISOR software. According to the degrees of impacts between them, the optimization variables and multiobjects are selected. Then, a multiobjective optimization in the ADVISOR software linked with the MATLAB software can be carried out with two sets of weights. The conclusion and discussion will be presented at the end.

2.3. The Optimal Energy Control Strategy of the HESS

An optimal energy control strategy is proposed for the BT semi-active HESS. The optimal energy control strategy distributes the output powers of BT and SC according to the required power of the HESS and the SOC of the SC pack. The available output power of the Li-ion BT pack is limited within the rated value of high efficiency to extend the life of the BT, but the available output power of the SC pack can fluctuate greatly for the good performance of the SC pack. The power fluctuation of the EV is large and frequent, and therefore, the SC pack is used as an energy buffer. The SC pack adopts the charge sustaining energy management strategy to meet the power demand of the HESS and maintain the state of charge (SOC) of the SC pack near the target value as far as possible. The optimal control strategy is shown in Figure 3.
SOCsc is the SOC of the SC pack. SOCsc,cs,hi is the high SOC of the SC pack. SOCsc,cs,lo is the low SOC of the SC pack. SOCsc,goal is the goal value of SOCsc. The optimal control strategy works on the following rules:
(a)
In normal cases, in order to improve the efficiency and service life of lithium BT,Pbt,r is limited by the minimum control power Pbt,cs,min and the maximum control power Pbt,cs,max.
(b)
When Phess,r∈[0,Pbt,cs,max] and SOCsc∈[0,SOCsc,goal], as the mode 1 in Figure 3, the SC pack is charged by the BT pack, and SOCsc approaches SOCsc,goal.
(c)
When Phess,rPbt,cs,max, as the mode 4 in Figure 3, both the BT pack and SC pack provide power to the EV.
(d)
When Phess, r∈ [0,Pbt,cs,max] and SOCsc∈[SOCsc,goal, 1], as the mode 2 in Figure 3, the SC pack discharges, and SOCsc approaches SOCsc,goal.
(e)
When Phess,r ≤ 0, as the mode 3 in Figure 3, the SC pack recovers all regenerative braking power.
When Phess,r ≤ 0, Pbt,r is shown in Equation (1).
Pbt,r =Pbt,cs,min
When Phess,r > 0, Pbt,r is shown in Equation (2).
Pbt,r = Phess,r + Padditional
Esc,cs,hi is the energy of the SC pack when SOCsc is SOCsc,cs,hi. Esc,cs,lo is the energy of the SC pack when SOCsc is SOCsc,cs,lo. Esc,goal is the energy of the SC pack when SOCsc is SOCsc,goal. Esc,goal is the average value of Esc,cs,hi and Esc,cs,lo, as in Equation (3).
Esc,goal = 0.5×(Esc,cs,hi + Esc,cs,lo)
According to the SC’s energy formula, Esc,goal and Esc,cs,hi, Esc,cs,lo are as in Equations (4)–(6), respectively.
Esc,goal = 0.5×C×V2sc,goal = 0.5×C×V2×SOC2sc,goal
Esc,cs,hi = 0.5×C×V2sc,cs,hi = 0.5×C×V2×SOC2sc,cs,hi
Esc,cs,lo = 0.5×C×V2sc,cs,lo = 0.5×C×V2×SOC2sc,cs,lo
C is the SC’s capacitance; V is the SC’s voltage. SOCsc,goal is obtained from Equations (3)–(6), which is shown in Equation (7).
S O C sc , goal = S O C 2 sc , cs , hi + S O C 2 sc , cs , lo 2
Padditional is the additional power needed to maintain SOCsc near SOCsc,goal. Padditional is shown in Equation (8).
P additional = S O C sc , goal S O C sc 0.5 × ( S O C s c , c s , h i S O C sc , cs , lo ) P charge
Pcharge is the charge power of the SC pack.
Psc,r is as shown in Equation (9).
P sc , r = P hess , r P bt , a η DC / DC
ƞDC/DC is energy conversion efficiency of the DC/DC converter.
The parameters of the optimal energy control strategy are in Table 5.

3. Multiobjective Optimization Analysis

The HESS EV performance simulation results [26] of the HESS EV in the ADVISOR software show that both the sizing parameters of the HESS components and the control strategy parameters have a certain impact on EV’s performances, energy consumption rate, running range, and HESS cost. When kbt increases, t100, Q100, l, and Chess increases, and Vveh,max decreases. When Nbt,s increases, Vveh,max, t100, l, and Chess increase, and Q100 increases or decreases. When Nsc,s increases, Vveh,max, Q100, and Chess increase, and t100 and l decrease. When Nsc,p increases, Vveh,max, l, and Chess increase, and Q100 and t100 decrease. When Pcharge increases, Vveh,max and Q100 increase, and t100, l and Chess decrease. Therefore, the relationships between the sizing parameters of the HESS components and the control strategy parameters and EV’s performances, energy consumption rate, running range, and the HESS cost are nonlinear and strong coupling.
The HESS EV performance simulation results show that, among the sizing parameters of HESS’s components and the control strategy parameters, the scaled factors of BT capacity kbt, Nbt,s, Nsc,s, Nsc,p, and Pcharge have a greater impact on the five objectives, while other parameters have less impact on the five objectives. Therefore, kbt, Nbt,s, Nsc,s, Nsc,p, and Pcharge are selected as the optimization variables.
The semi-active HESS EV evaluation focuses on the energy consumption over 100 km Q100, the acceleration time from 0–100 km per hour t100, the maximum speed Vveh,max, the running range l, and the HESS cost Chess, which are essentially contradictory. The variables of the multiobjective optimization problem for the HESS EV contain kbt, Nbt,s, Nsc,s, Nsc,p, and Pcharge, as shown in Equation (10).
f ( x ) = [ k b t , N b t , s , N s c , p , N sc , s , P charge ]
The HESS EV performance simulation results and the HESS EV performance constraints reduce the amount of calculations during the optimization. The varied ranges of the variables are described in Equation (11).
x 1 1 , 4 , x 2 50 ,   150 , x 3 1 4 , x 4 75 ,   135 , x 5 6000 ,   9000
The multiobjective function is given by Equation (12). The optimization objective is to maximize the value of F(x).
F ( x ) = w 1 · ( 1 t 100 · norm ) + w 2 · V v e h , m a x , norm + w 3 · l norm + w 4 · ( 1 - Q 100 · norm ) + w 5 ( 1 C hess , norm )
t100,norm,Vveh,max,norm, lnorm, Q100,norm, and Chess,norm are the normalization value of t100, Vveh,max, l, Q100, and Chess, between zero and one, based on the maximum and minimum values obtained.
t100,norm is shown in Equation (13).
t 100 , n o r m = t 100 - t 100 , m i n t 100 , m a x - t 100 , m i n
t100,min is the reference minimum value of t100, and t100,max is the reference maximum value of t100.
Vveh,max,norm is shown in Equation (14).
V veh , max , n o r m = V veh , max - V v e h , m a x , m i n V veh , max , m a x - V v e h , m a x , m i n
Vveh,max,min is the reference minimum value of Vveh,max, and Vveh,max,max is the maximum value of Vveh,max.
lnorm is shown in Equation (15).
l norm = l l min l max l min
lmin is the reference minimum value of l, and lmax is the reference maximum value of l.
Q100,norm is shown in Equation (16).
Q 100 , norm = Q 100 Q 100 , min Q 100 , max Q 100 , min
Q100,min is the reference minimum value of Q100, and Q100,max is the reference maximum value of Q100.
Chess,norm is shown in Equation (17).
C hess , norm = C hess C hess , min C hess , max C hess , min  
Chess,min is the reference minimum value of Chess. Chess,max is the reference maximum value of Chess.
The optimization constraints parameters are shown in Table 6. mveh is the weight of the HESS EV.
The weights w1, w2, w3, w4, and w5 are chosen to indicate the importance of the five objectives. The sum of w1, w2, w3, w4, and w5 is 1.

4. Optimization Results

The GA algorithm has been shown to be an effective strategy to solve complex and non-linear engineering optimization problems. The GA algorithm is written in the ADVISOR software in the MATLAB environment. The GA algorithm parameters are as in Table 7.
The HESS optimization flowchart diagram based on the ADVISOR software and GA algorithm is as in Figure 4. The optimized variables kbt, Nbt,s, Nsc,s, Nsc,p, and Pcharge are encoded by binary method. w1, w2, w3, w4, and w5 are 0.2, 0.2, 0.2, 0.2, and 0.2, respectively. The equivalent fuel economy of the HESS EV under UDDS driving condition is good. Therefore, two consecutive UDDS (Urban Dynamometer Driving Schedule) drive cycles are used in the simulation.
The HESS cost is evaluated by considering a BACP3000 super-capacitor cost as USD 50 and a SAFT VL45E Li-ion BT cost as USD 40. The Li-ion BT packs are replaced once in the cycle lifetime, so the cost of a BT is USD 80. Chess is presented as Equation (18).
C hess = 80 k bt N bts + 50 k sc N scs N scp
The objection function F(x) convergence process is as in Figure 5, basically stable after nearly 15 generations.
The t100 convergence process is as in Figure 6, basically stable after near 20 generations.
The Vveh,max convergence process is as in Figure 7, basically stable after near 25 generations.
The Q100 convergence process is as in Figure 8, basically stable after near 25 generations.
The Chess convergence process is as in Figure 9, basically stable after near 30 generations.
The l convergence process is as in Figure 10, basically stable after near 30 generations.
The simulation results are as in Table 8. It is clear that the optimization results meet the constraints of the optimization. The GA algorithm can find the optimal value. The optimization results are reasonable taking into account the five objectives, such as t100, Vveh,max, l, Q100, and Chess.
Two sets of weights are used to study their influences on the results of multiobjective optimization. The two sets of weights are as in Table 9. The five weights of the five objectives are the same in the first set of weights. This means that these five objectives are equally important. In the second set of weights, w1, w2, and w5 change, but w3 and w4 remain unchanged comparing the first set of weights. The results are shown in Table 10. It can be seen from Table 9 and Table 10 that when w1 decreases from 0.2 to 0.15, the corresponding objective t100 increases from 8.2 to 9.5. When w2 decreases from 0.2 to 0.15, the corresponding objective Vveh,max decreases from 133.28 to 108.85. When w5 increases from 0.2 to 0.3, the corresponding objective Chess decreases from 30,800 to 19,800. Some of the multi objectives are sensitive to their weights. The weight of each objective can be selected according to the importance of each objective.
The optimization of HESS EV in ADVISOR software is realized by the direct optimization algorithm, which directly uses a large number of simulations and compares the results, so as to obtain the optimal solution or approximate optimal solutions. Compared with GA algorithm optimization, the direct optimization algorithm of the HESS EV takes longer time, but the optimization effect is poor, and it is difficult to find a better solution. Compared with direct optimization algorithm, the GA algorithm has a stronger optimization ability, and the single objective is more sensitive to its corresponding weight.

5. Conclusions

Due to the nonlinear and strong coupling relationship between BT and SC HESS EV sizing parameters and control strategy parameters and the EV’s performances, driving range, and price, as well as the different preferences of different consumers, the GA algorithm is used to study the multiobjective optimization of an HESS EV. A Li-ion semi-active HESS and optimal energy control strategy were presented for the EVs. A multiobjective optimization problem is analyzed based on the ADVISOR software in the MATLAB environment. The multi objectives include energy consumption over 100 km, acceleration time from 0–100 km per hour, maximum speed, running range, and HESS cost of an EV, and the ADVISOR software is used to obtain them. The scaled factors of BT capacity, the series number of Li-ion BTs, the series number of SCs, the parallel number of SCs, and charge power of the SCs are chosen as optimization variables. The optimization results show that the weights are sensitive to their objectives. The proposed optimization method is practical for a Li-ion BT and SC HESS EV.

Author Contributions

Conceptualization, G.X., Q.C., P.X., L.Z. and Q.R.; methodology, G.X. and P.X.; software, G.X., Q.C. and P.X.; validation, L.Z. and Q.R.; formal analysis, G.X. and P.X.; investigation, G.X. and Q.C.; resources, P.X.; data curation, G.X. and P.X.; writing—original draft preparation, G.X., Q.C. and P.X.; writing—review and editing, P.X.; visualization, G.X.; supervision, Q.R.; project administration, G.X.; funding acquisition, P.X. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities grant number WUT:2020IVA031 and the APC was funded by the Fundamental Research Funds for the Central Universities grant number WUT:2020IVA031.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. A BT semi-active HESS scheme in the ADVISOR software.
Figure 1. A BT semi-active HESS scheme in the ADVISOR software.
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Figure 2. The scheme of the multiobjective optimization for the HESS EV.
Figure 2. The scheme of the multiobjective optimization for the HESS EV.
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Figure 3. Optimal energy control strategy.
Figure 3. Optimal energy control strategy.
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Figure 4. The flowchart diagram of the HESS optimization.
Figure 4. The flowchart diagram of the HESS optimization.
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Figure 5. Objective function F(x) convergence process.
Figure 5. Objective function F(x) convergence process.
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Figure 6. t100 convergence process.
Figure 6. t100 convergence process.
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Figure 7. Vveh,max convergence process.
Figure 7. Vveh,max convergence process.
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Figure 8. Q100 convergence process.
Figure 8. Q100 convergence process.
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Figure 9. Chess convergence process.
Figure 9. Chess convergence process.
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Figure 10. l convergence process.
Figure 10. l convergence process.
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Table 1. EV’s model parameters.
Table 1. EV’s model parameters.
ParametersValue
Cargo mass/kg200
Glider mass/kg680
Wheelbase/m2.7
Frontal area/m22.6
Table 2. SAFT VL45E Li-ion BT parameters.
Table 2. SAFT VL45E Li-ion BT parameters.
ParametersValue
Capacity/Ah44
Internal resistance/mΩ3.6
Stored energy/Wh140
Mass/kg0.91
Table 3. BACP3000 SC parameters.
Table 3. BACP3000 SC parameters.
ParametersValue
Rated capacitance/F3000
Internal resistance/mΩ0.29
Stored energy/Wh3.04
Mass/kg0.51
Usable power/W·kg−15900
Table 4. Motor parameters.
Table 4. Motor parameters.
ParametersValue
Max. power/kW75
Max. voltage/V375
Min. voltage/V120
Table 5. The optimal energy control strategy parameters.
Table 5. The optimal energy control strategy parameters.
ParametersValue
Pbt,cs,min/kW1.5
Pbt,cs,max/kW12
ηDC/DC0.95
SOCsc,init0.9
SOCsc,goal0.74
SOCsc,cs,hi0.95
SOCsc,cs,lo0.45
SOCsc,init is the initial value of SOCsc.
Table 6. The optimization constraints parameters.
Table 6. The optimization constraints parameters.
ParametersValue
t100(s)<10
Vveh,max/(kmph)>100
l/(km)>100
mveh/(kg)<1600
Table 7. GA algorithm parameters.
Table 7. GA algorithm parameters.
ParametersValue
Number of termination evolution generations40
Crossover probability0.95
Mutation probability0.08
Table 8. Simulation results.
Table 8. Simulation results.
Generation
Number
kbtNbt,sNsc,sNsc,pPcharge/Wt100/sVveh,maxl/kmChess (USD)Q100/(L/100 km)
11.5991104150159.4108.3210216,4001.9391
51.6893130165009109.76110.223,4001.9265
201.94109114476008.4125.6150.432,1001.8566
402.01111.2109481008.2137.5155.130,8001.7695
Table 9. Two sets of weights.
Table 9. Two sets of weights.
No.W1W2W3W4W5
10.20.20.20.20.2
20.150.150.20.20.3
Table 10. The results with two sets of weights.
Table 10. The results with two sets of weights.
No.kbtNbt,sNsc,s N sc,p P charge (W) t 100(8) V veh,max (km/h) L (km) C hess ($) Q 100 (L)
12.01111.2109481008.2155.1151.8308001.7695
22110.9109.1280619.5108.85154.9198001.7708
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Xiao, G.; Chen, Q.; Xiao, P.; Zhang, L.; Rong, Q. Multiobjective Optimization for a Li-Ion Battery and Supercapacitor Hybrid Energy Storage Electric Vehicle. Energies 2022, 15, 2821. https://doi.org/10.3390/en15082821

AMA Style

Xiao G, Chen Q, Xiao P, Zhang L, Rong Q. Multiobjective Optimization for a Li-Ion Battery and Supercapacitor Hybrid Energy Storage Electric Vehicle. Energies. 2022; 15(8):2821. https://doi.org/10.3390/en15082821

Chicago/Turabian Style

Xiao, Gang, Qihong Chen, Peng Xiao, Liyan Zhang, and Quansen Rong. 2022. "Multiobjective Optimization for a Li-Ion Battery and Supercapacitor Hybrid Energy Storage Electric Vehicle" Energies 15, no. 8: 2821. https://doi.org/10.3390/en15082821

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