Journal of Power Sources 494 (2021) 229727
Contents lists available at ScienceDirect
Journal of Power Sources
journal homepage: www.elsevier.com/locate/jpowsour
Performance analysis on liquid-cooled battery thermal management for
electric vehicles based on machine learning
Xingwang Tang a, b, Qin Guo c, Ming Li a, b, *, Changhua Wei d, Zhiyao Pan a, b, Yongqiang Wang d
a
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130025, China
College of Automotive Engineering, Jilin University, Changchun, 130025, China
c
College of Computer Science and Technology, Jilin University, Changchun, 130025, China
d
Jiangsu Chaoli Electric Co., Ltd., Dangyang, 212321, China
b
H I G H L I G H T S
• Comprehensive analysis from the perspective of air conditioning system.
• Automatic calibration model for battery thermal management system.
• The battery thermal performance estimation based on the SVR model.
• SVR model with RBF kernel exhibits better generalization ability.
A R T I C L E I N F O
A B S T R A C T
Keywords:
Battery electric vehicle
Battery thermal management
Liquid cooling
Support vector regression
Particle swarm optimization
In this paper, the coupling system of liquid-cooled battery thermal management system (BTMS) and heat pump
air conditioning system (HPACS) for battery electric vehicles (BEV) is designed and analyzed. The performances
of liquid-cooled BTMS are concerned and analyzed from the perspective of air conditioning based experimental
data. Besides, an automatic calibration model of the liquid-cooled BTMS based HPACS is established to predict
cooling capacity and system coefficient of performance (COP) of the BTMS by support vector regression (SVR).
To better obtain three hyper parameters (the penalty coefficient C, the RBF kernel function parameter γ, and the
insensitive loss coefficient ε) of SVR model, particle swarm optimization (PSO) algorithm is introduced to
optimize above three parameters. It is found that compared to SVR model, the correlation coefficient (R) of
cooling capacity and system COP for the proposed PSO-SVR model in this paper is improved 2.1% and 2.8%
respectively, the mean squared error (MSE) of and cooling capacity and system COP is reduced 87.8% and 82.9%
respectively, which indicated that PSO-SVR model can be used as a new method to fit the complex nonlinear
relationship among the system COP, cooling capacity and other influencing factors of the liquid-cooled BTMS
based HPACS.
1. Introduction
With the improvement of resource conservation and environmental
protection laws and standards, BEV is considered to be the future
development direction of transportation due to its high energy effi­
ciency, environmental protection, and noise-free advantages [1,2]. As
the core component of the BEV, the power battery needs to operate in
the suitable temperature range to ensure driving mileage of vehicles,
safety and life of battery. Based on the research on the thermal
characteristics of lithium-ion batteries, it is found that optimum oper­
ating temperature range for batteries is 20–30 ◦ C and its temperature
uniformity is less than 5 ◦ C [3,4]. Overheating of battery will lead to
thermal failure and overcooling also harms the charge/discharge effi­
ciency and reduce the available capacity [5–8]. Therefore, it is necessary
to design and develop an efficient integrated electric vehicle thermal
management system to improve the energy efficiency of BEV, increase
the driving mileage of vehicles, and extend reliability and cycle life of
batteries. Zhang et al. [9] proposed the main functions of the BTMS: (1)
Ensuring the power battery operates in the suitable temperature range to
* Corresponding author. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130025, China.
E-mail addresses: tangxw18@mails.jlu.edu.cn (X. Tang), guoqin16@mails.jlu.edu.cn (Q. Guo), limingtiger@jlu.edu.cn (M. Li), changhua.wei@chaoli-electric.com
(C. Wei), panzy1516@mails.jlu.edu.cn (Z. Pan).
https://doi.org/10.1016/j.jpowsour.2021.229727
Received 17 September 2020; Received in revised form 3 February 2021; Accepted 25 February 2021
Available online 18 March 2021
0378-7753/© 2021 Elsevier B.V. All rights reserved.
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Nomenclature
HPACS
BEV
BTMS
COP
SVR
LR
LAR
PSO
MSE
MAPE
PCM
TCS
R
RBF
C
T
P
Q
W
h
Heat Pump Air Conditioning System
Battery Electric Vehicles
Battery Thermal Management System
Coefficient of Performance
Support Vector Regression
Linear Regression
Least Angle Regression
Particle Swarm Optimization
Mean Squared Error
Mean Absolute Percentage Error
Phase Change Material
Thermal Conductive Structure
Correlation Coefficient
Radial Basic Function
Penalty Factor
Temperature
Pressure
Greek symbols
ε
loss coefficient
γ
kernel function parameter
η
Efficiency
Subscripts
comp
Compressor
air
Air
0
Ambient
in
Battery inlet
Com, in Compressor Inlet
Com, out Compressor Outlet
Chi, in
Battery Chiller Inlet
Chi, out Battery Chiller Outlet
which makes it popular in the field of BEV. Table 1 shows the BEV with
liquid-cooled BTMS.
Meanwhile, more and more experts and scholars focus on the study
of the liquid-cooled BTMS. Lai et al. designed a thermal conductive
structure (TCS) with three curved contact surfaces based liquid-cooled
BTMS and simulated the effect of different structural parameters and
mass flow rate of TCS on cooling performances. The results show that the
designed TCS can significantly improve the maximum temperature and
temperature difference of lithium-ion power battery pack and maximum
temperature can be controlled below 313 K and temperature difference
is controlled below 5 K when mass flow rate is 0.0001 kg/s [20]. Zhao
et al. designed a mini-channel liquid-cooled cylinder based cylindrical
batteries and investigated the influence of the mini-channel quantity on
cooling performance. The results showed that compared to natural
convection cooling, the cooling capacity is more advantageous when the
mini-channel quantity is greater than eight [21]. Sheng et al. developed
a novel serpentine-channel liquid cooling plate with double inlets and
outlets and investigated the effect of flow directions, flows rates and
channel widths of the cooling plate on cell temperature distribution
under different operating conditions. The results showed that when
channel width of the cooling plate is increased from 4 mm to 12 mm,
module maximum temperature is almost unchanged at 36.5 ◦ C, while,
the ratio of power consumption falls sharply. When flow rates of the
cooling plate are increased from 0.00025 to 0.002 L s− 1, the maximum
temperature rise decreased significantly, while the change range of
temperature difference is less than 4 ◦ C [22].
Nowadays, most research on liquid-cooled BTMS based HPACS is
limited to the structure optimization of the liquid cooling plate with the
purpose of minimizing the flow resistance and the best heat transfer
performance. However, little research pay attention to the impact of air
conditioning systems on BTMS. In addition, there are many factors that
affect the performance of the liquid-cooled BTMS, such as compressor
speed, ambient temperature and air flow rate of external heat
exchanger. To conduct a comprehensive analysis of liquid-cooled BTMS
based HPACS, a lot of experiments are required. Although experimental
studies are highly valuable, they are high-cost and time-consuming due
to the complexity of liquid-cooled BTMS based HPACS and a lot of
operation conditions. Alternatively, machine learning algorithms can be
applied to predict the performance by considering a set of operating
condition.
With the development of artificial intelligence technology, machine
learning methods have been widely used in the field of science and
engineering. Warey et al. predicted and evaluated the influence of air
Table 1
The BEV with liquid-cooled BTMS.
OEMs
Product
Thermal management methods
NIO
Mercedes-Benz
Tesla
XPeng
GM
ES8
EQR
Model S; Model X; Model3
G3; P7
Chevrolet Bolt
Liquid cooling
Liquid cooling
Liquid cooling
Liquid cooling
Liquid cooling
Cooling Capacity of Battery Chiller
Power Consumption of Compressor
Specific Enthalpy
avoid battery temperature distortion (2) The battery high temperature
and low temperature identification mode is established to identify the
critical point of overheating and overcooling, so as to preheat and cool
the battery in advance.
At present, BTMS can be summarized as air cooling, liquid cooling,
heat pipes cooling and phase change material (PCM) cooling from the
perspective of different heat transfer media [10]. The air-cooled BTMS
has the advantages of simple structure and low cost, so it is widely used
in lower energy density electric vehicles [11,12]. However, the cooling
performance of air-cooled battery modules is poor, and the cooling effect
of liquid-cooled battery modules is three times that of air-cooled battery
modules [13]. PCM can be another method to cool or heat battery pack
[14,15]. It can absorb or release large latent heat during phase change
from the solid to the liquid. Although PCM is widely used in BTMS due to
its high latent heat, there are still some significant challenges in this
technology: (1) weak structural strength and leakage of melted PCM; (2)
relatively low thermal conductivity; (3) low surface heat transfer coef­
ficient and run out of the available latent heat [16,17]. Heat pipe is a
heat exchange element that absorbs and releases heat according to the
phase change of the working medium in the pipe. Compared with other
cooling methods, heat pipe has the advantages of high thermal con­
ductivity and flexible geometry. However, at present, heat pipe cooling
technology is still in the research and development stage [18,19].
The liquid-cooled BTMS mainly decreases temperature of the battery
system through coolant. The air conditioning system exchanges heat
with the coolant in the battery chiller and lowers the temperature of the
coolant. After the low-temperature coolant flows through the liquid
cooling plate of battery system, the battery pack exchanges heat with the
low-temperature coolant and then coolant flows back to the battery
chiller to achieve the battery cooling cycle. Compared to other cooling
methods, the liquid cooling technology has become the mainstream of
BTMS due to its advantages in cooling speed and compact structure,
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X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Fig. 1. Overview of different research methods.
conditioning system on cabin thermal comfort based on the machine
learning method [23]. Krishnayatra investigated and predicated the
thermal performance of fins for a finned-tube heat exchanger by ma­
chine learning regression technique [24]. Generally, machine learning
models use some regressions such as linear regression (LR), least angle
regression (LAR) and SVR to characterize the relationship between input
and output variable [25]. In view of effective nonlinear expression
ability of SVR model, SVR algorithm model is applied in some compli­
cated nonlinear relationship. To find an optimum value of hyper pa­
rameters of SVR algorithm model, PSO algorithm is usually employed
[26–28].
To investigate the performances of liquid-cooled BTMS comprehen­
sively, this paper is organized in the following three points: (1) the
performances of liquid-cooled BTMS are verified under extreme condi­
tions; (2) The performances of liquid-cooled BTMS are investigated
under different ambient temperature, compressor speed and air flow
rate of external heat exchanger; (3) The automatic calibration model of
liquid-cooled BTMS based on PSO-SVR algorithm model is established
and on the basis of this automated calibration model, system perfor­
mance parameters such as cooling capacity and system COP can be
predicted, which makes it possible to get satisfactory performance
parameter of liquid-cooled BTMS based HPACS without the complicated
thermodynamics theory and equations, thereby avoiding a lot of highcost and long-term experiments. In view of above-mentioned organiza­
tional structure of this paper, the novelty of work consists in the per­
formances of liquid-cooled BTMS are concerned from the perspective of
air conditioning system and construction of automatic calibration model
for liquid-cooled BTMS based on machine learning method.
2. Research method
2.1. Methodology
Fig. 1 Shows the differences between the research method of this
paper and the traditional method. First of all, the traditional method is
mainly to investigate or improve the performance of the liquid-cooled
BTMS based HPACS through optimizing the structure of liquid cooling
plate, while, in this paper, the performances of the liquid-cooled BTMS
based HPACS are analyzed from the perspective of air conditioning.
Secondly, compared with traditional experimental methods, this paper
combines the experiment and machine learning methods to investigate
the performance of the liquid-cooled BTMS based HPACS and its
advantage is that the performance results are obtained by an “end-toend” idea. Namely, establishing a nonlinear relationship between the
input data and the output data about the parameters affecting the liquidcooled BTMS based HPACS. Through machine learning method, per­
formance results of the liquid-cooled BTMS based HPACS can be ob­
tained quickly without the complicated thermodynamics theory and
equations.
2.2. Model description and experiment of liquid-cooled BTMS based
HPACS
A model of liquid-cooled BTMS based HPACS for BEV is illustrated in
Fig. 2(a). After being compressed by the compressor, the refrigerant
R134a enters the internal condenser (the air door is closed to minimize
heat transfer), and then goes through the solenoid valve 02 and enters
the external heat exchanger. Because solenoid valve 04 is closed, the
refrigerant R134a from the external heat exchanger goes through the
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Journal of Power Sources 494 (2021) 229727
Fig. 2. Model diagram and test system bench of liquid-cooled BTMS based HPACS.
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Journal of Power Sources 494 (2021) 229727
2.3. Data preparation of SVR algorithm model
Table 2
Sensor type and precision.
Measurement parameter
Sensor type
Range
Precision
Temperature ( C)
Pressure (kPa)
Mass flow rate (kg h− 1)
Omega temperature sensor
Omega pressure sensor
Micromotion mass flow meter
− 50–200
0–4000
0–200
±0.1
±5
±0.5
◦
The input parameters for the SVR model of liquid-cooled BTMS based
HPACS are the compressor speed Vcomp , ambient temperatures T0 and air
flow rate Vair of the external heat exchanger. And the output parameters
predicted by the SVR model are the cooling capacity and system COP.
Table A.1 in appendices summarizes complete experiment data about
the input and output variables.
In order to improve the convergence rate and accuracy of the model,
the sample data is normalized according to the following formula:
Table 3
Operating conditions of liquid-cooled BTMS based HPACS.
Ambient
temperature (◦ C)
Compressor speed
(rpm)
Air flow rate of the external
condenser (m s− 1)
32
2000/3000/4000/
5000/6000
2000/3000/4000/
5000/6000
2000/3000/4000/
5000/6000
2000/3000/4000/
5000/6000
2000/3000/4000/
5000/6000
2000/3000/4000/
5000/6000
1.5/2.5/3.5/4.5/5.5
34
36
38
40
42
′
X =
(
)
qm hcom,out − hcom,in
COP =
ηmech
Q
W
1.5/2.5/3.5/4.5/5.5
1.5/2.5/3.5/4.5/5.5
2.4. SVR algorithm model
1.5/2.5/3.5/4.5/5.5
SVR is a powerful machine learning tool which is firmly grounded in
the framework of statistical learning theory [29–32]. The basic idea is to
map the training data in the input space to a high-dimensional linear
space through a nonlinear mapping Φ(x), thereby make the nonlinear
function in the input space transformed into a linear regression problem
in a high-dimensional linear space. If the training data {(x1 , y2 ), (x2 , y2 )
…, (xn ,yn )} are considered, where xi ⊆R, yi ⊆R, i = 1…n and n is the total
number of training samples, then the SVR function can be shown as
follows:
1.5/2.5/3.5/4.5/5.5
(6)
f (x) = w⋅Φ(x) + b
Where Φ(x) is the nonlinear function that maps the input data vector x
into a feature space where the training data exhibit linearity, b is a scalar
bias and w is a weight vector; x is the input variable of sample data.
To minimize the regression risk of the SVR algorithms, the objective
function of SVR algorithms can be expressed as Eq. (7).
(
)
n
∑
1
2
min ‖w‖ + C
(lε (f (xi ) − yi )
(7)
w,b
2
i=1
Where lε is ε-insensitive loss function and C is the penalty factor. The
larger the value of C, the greater the penalty for data exceeding lε ; y is
the output variable of sample data.
The ε-insensitive loss function lε can be expressed as:
{
0, if |z| ≤ ε
lε (z) =
(8)
|z| − ε, otherwise
(2)
(3)
Taking the ε-insensitive loss function as the structure minimization
risk estimation problem, introducing the slack variables δi , δi * , the
optimization objective can be expressed as:
(
)
n
∑
(
)
1
min
δi + δ*i
‖w‖2 + C
w,b,δ,δh* 2
i=1
Where Q and W are the cooling capacity of battery chiller and power
consumption of compressor, respectively; hchi,in and hchi,out are the spe­
cific enthalpy of battery chiller inlet and battery chiller outlet, respec­
tively; hcom,in and hcom,out are the specific enthalpy of compressor inlet
and compressor outlet; qm is the mass flow of system refrigerant; ηmech is
the mechanical efficiency.
The specific enthalpy at each operating point can be obtained based
on the REFPROP software through the pressure and temperature at this
point, as shown in Eq. (4).
h = h(P, T)
(5)
Where Xmin and Xmax are the minimum and maximum of sample data,
′
respectively; X is the sample data, X is the normalized data, which is
normalized to the range [0,1].
1.5/2.5/3.5/4.5/5.5
chiller. At this time, the refrigerant R134a exchanges heat with the
coolant (water and ethylene glycol solution) in the battery chiller,
thereby, the temperature of the coolant is dropped accordingly. After the
cooled coolant flows through the liquid cooling plate of BTMS, the
battery pack exchanges heat with the low-temperature coolant and then
coolant flows back to the battery chiller to achieve the battery cooling
cycle. In the liquid-cooled BTMS based HPACS designed in this paper, a
positive temperature coefficient (PTC) is used to simulate battery cool­
ing demand.
In this paper, a bench test system of liquid-cooled BTMS based
HPACS for BEV is established, as shown in Fig. 2(b). In order to better
characterize the refrigeration performance of the system, the evaluation
index cooling capacity and system COP are used. With respect to the
cooling capacity of battery chiller, as well as the power consumption of
compressor, the system COP are calculated by the following formula:
(
)
Q = qm hchi,out − hchi,in
(1)
W=
X − Xmin
Xmax − Xmin
⎧
⎪
⎪
⎪ f (xi ) − yi ⩽ε + δi
⎪
⎪
⎪
⎨
s.t. ​ yi − f (xi )⩽ε + δ*i
⎪
⎪
⎪
⎪
⎪
⎪
⎩ δi ⩾0, δ*i ⩾0
(4)
Where P and T are the pressure and temperature of the refrigerant
measured in the experiment, respectively.
And the type and precision information of the sensors used to mea­
sure the pressure, temperature and flow at each operating point in this
bench test system are listed in Table 2. Besides, the experiment system
provides reliable training data for the machine learning model. The
detailed operating conditions are illustrated in Table 3.
(9)
i = 1, 2, …n
In order to simplify the computation complexity, the Lagrange
function is introduced to transform the above formula into the dual
problem, which can be shown as follows:
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Journal of Power Sources 494 (2021) 229727
Fig. 3. System performance at an ambient temperature of 42 ◦ C.
[
]
n ∑
n
n
) (
2.5. PSO algorithm model
)
(
)(
) ∑
(
)
1∑
*
*
*
max
αi − α yi −
αi − αi αj − αj K xi , xj −
αi + αi ε
α,α*
2
i=1
i=1 j=1
i=1
The PSO algorithm is a population-based search optimization tech­
⎧∑
n
nique developed by Kennedy and Eberhart [33]. Compared with other
(
)
⎪
⎪
αi − α*i = 0
⎪
evolution algorithms, such as genetic algorithms, PSO algorithm has the
⎨
i=1
s.t.
advantages of easy implementation, fast convergence speed and strong
⎪
⎪
⎪
global search capability, so PSO algorithm is very suitable for SVR model
⎩
*
0⩽αi ⩽ C, 0⩽αi ⩽C
parameter optimization [34,35]. In this algorithm, a particle represents
(10)
an individual, corresponding to a group of solutions and each particle
has its own speed, location, and fitness value determined by the target
*
Where αi , αi are Lagrange multipliers and K(xi , xj ) is the kernel function
function. During initialization, particles are randomly generated. The
and common kernel functions include polynomial kernel function, linear
global best particles tracked in the iteration process are recorded as Gbest ,
kernel function, radial basis function (RBF) kernel function, and sigmoid
and the best particles in each generation are recorded as pbest . Each
kernel function. In the SVR model, the goal is to find a function f(x)
generation of particles will undergo adaptive random mutation after
makes possible to express the nonlinear relationship between input
updating. The particle update formulas are as follows:
parameters and output parameters. In order to improve the generaliza­
]
]
[
[
(15)
Vi j+1 = W⋅Vi j + a1 ⋅r1 ⋅ Xi pbest − Xi j + a2 ⋅r2 ⋅ Xi Gbest − Xi j
tion ability and regression performance of model, a kernel function is
introduced into SVR model.
Xi j+1 = Xi j + Vi j+1
(16)
The regression function f(x) can be obtained by solving Eq. (10)
based on Karush-Kuhn-Tucker (KKT) condition, which can be shown as
where V is the particle renewal speed; X is the particle solution; W is
follows:
inertia weight, j is the number of iterations; i is the number of particles;
⎧
αi (f (xi ) − yi − ε − δi ) = 0,
⎪
r1 and r2 are the random numbers at an interval (0, 1); a1 and a2 are the
⎪
⎨ *
αi (f (xi ) − yi − ε − δi * ) = 0,
learning factors.
(11)
*
*
⎪
⎪ αi αi = 0, δi δi = 0, * *
The specific steps for PSO to optimize SVR parameters can be sum­
⎩
(C − αi )δi = 0, (C − αi )δi = 0
marized as following steps:
n
∑
(
*
i
Step 1. Initialize three hyper parameters (C, ε, γ) of the SVR model.
And the coefficient w and b and the regression function f(x) can be
shown as follows:
w=
n
∑
(
)
αi − α Φ(xi )
Step 2. Determine fitness function of PSO algorithm and initialize PSO
algorithm parameters: Population number, initial search point position
and speed (X0 , Y0 ), maximum iteration number k, inertia weight W and
learning factors a1 and a2 .
(12)
*
i
i=1
{
b=
1
NnSV
∑
∑
[
yi −
0<αi <C
[
∑(
) (
xi ∈SV
∑(
) (
)
αj − α K xi , xj + ε
yj −
0<αj <C
)
]
Step 3. Calculate the fitness value of each particle and determine pbest
and Gbest .
αi − α*i K xi , xj − ε +
]}
(13)
Step 4. Update the particle speed and position according to equations
(15) and (16).
*
j
xj ∈SV
n
∑
(αi − αi * )K(xi , x) + b
f (x) =
Step 5. Check the termination rule. If the current iteration arrives at its
maximum value, turn to Step 6. Otherwise, execute Steps 3–4
(14)
Step 6. Input the optimal solution of the three parameters (C, ε, γ)
obtained by the PSO algorithm into the SVR model.
i=1
Where NnSV is the number of support vectors, SV is the support vector of
which some parameters (αi − αi * ) or (αj − αj * ) are unequal to zero.
Step 7. Train SVR model and output the prediction results.
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Journal of Power Sources 494 (2021) 229727
Fig. 4. Influence of external heat exchanger air velocity on system performance.
3. Results and discussion
3.1. System performance verification under extreme conditions
The proposed liquid-cooled BTMS based HPACS and its perfor­
mances are investigated under different compressor speed, ambient
temperature and air flow rate of external heat exchanger. The perfor­
mance characteristics are assessed through compressor power, cooling
capacity, system COP and the coolant temperature of the battery inlet.
Besides, for the liquid-cooled BTMS based HPACS designed in the paper,
the “end to end” automatic calibration model of the operating param­
eters and performances parameters are established based on the PSOSVR machine learning algorithm model and the prediction results are
compared with the experiment values.
For the liquid-cooled BTMS based HPACS designed in this article, in
order to test whether it can meet the cooling requirement of the battery
pack, it was found from Fig. 3 that the compressor speed has a greater
impact on the system COP and the coolant temperature of the battery
inlet. The coolant temperature of the battery inlet decreases with the
increasement of compressor speed or air flow rate of the external heat
exchanger. When the ambient temperature was 42 ◦ C, the coolant
temperature of the battery inlet could reach 19.8 ◦ C and the COP at this
time is 2.36 under the operating conditions of the liquid-cooled BTMS
based HPACS, which explains that the system has high energy efficiency.
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Journal of Power Sources 494 (2021) 229727
Fig. 5. Influence of external heat exchanger inlet air temperature on system performance.
exchanger on cooling performance is investigated by changing its air
flow rate. Fig. 4 shows that as the air flow of the external heat exchanger
increases from 1.5 m/s to 5.5 m/s, the compressor power consumption
decreases gradually. When the compressor speed is 6000 rpm, the power
consumption of the compressor decreased the most, which is dropped
from 2.53 kW to 2.13kw and the drop rate is 15.9%. In fact, the reason
why the power consumption of the compressor decreases is that with the
increment of the air flow rate of the external heat exchanger, the
condensing pressure and temperature will also decrease, at the same
time, the suction pressure of the compressor will also decrease, so the
evaporation pressure and temperature will decrease. In addition, the
drop of the suction pressure will cause the increase of the suction spe­
cific volume of the compressor and the decrease of the refrigerant mass
flow, so the power consumption of the compressor will be reduced.
Besides, as the compressor power decreases, the COP of the system will
Table 4
Kernel function of SVR model.
Kernel
Functions
Kernel parameter
Linear
K(xi , xj ) = xi T ⋅xj
_
Polynomial
K(xi , xj ) = (xi T xj + 1)γ
⃦2
⃦
K(xi , xj ) = exp( − γ⃦xi − xj ⃦ )
Radial basic function
Sigmoid
K(xi , xj ) = tanh(γxi T xj + 1)
γ
γ
γ
3.2. Effect of air flow rate of the external heat exchanger
As the core component of the liquid-cooled BTMS based HPACS, the
external heat exchanger plays an important role in the cooling perfor­
mance of the system. In this section, the influence of external heat
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Journal of Power Sources 494 (2021) 229727
Fig. 6. Comparative analysis of predictive COP and Cooling capacity of different kernel functions. (a) Sigmoid, (b) RBF, (c) Polynomial, (d) Linear.
increase with the increment of the air flow rate of the external heat
exchanger. When the air flow rate of the external heat exchanger reaches
2.5 m/s, the growth rate will obviously decrease. Although the cooling
capacity can not be increased by adjusting the air flow rate of the
external heat exchanger, the power consumption of the compressor can
be reduced. Furthermore, the evaporation temperature will decrease
with the increment of the air flow rate of the external heat exchanger,
which will lead to the decrease of the coolant temperature of the battery
inlet.
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Journal of Power Sources 494 (2021) 229727
Fig. 6. (continued).
3.3. Effect of ambient temperature
liquid-cooled BTMS based HPACS can have a good cooling performance
at any high temperature, effect of the ambient temperature on the per­
formance of liquid-cooled BTMS based HPACS is investigated. As can be
seen from Fig. 5, when the compressor speed was 6000 rpm, the
compressor power increased by 0.35kw and the growth rate was 15.2%
as the ambient temperature increased from 32 ◦ C to 42 ◦ C, while the
COP of the system decreased by 15.6%. In fact, when ambient
Nowadays, with the gradual increment of energy density of power
battery and the development of fast charging technology, the heat
generated by power battery increases rapidly in the charging and dis­
charging process, thus too high ambient temperature may aggravate the
thermal failure of the battery. In view of this, in order to ensure that the
10
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Table 5
PSO algorithm initialization parameters.
Population size
50
Maximum iterations
Learning factor
100
a1 = 1.5;a2 = 1.7;
(C, ε, γ)
the experiment value. y is average of predictive value; f is average of the
experiment value.
In the paper, in order to better express the generalization ability of
the model, four common kernel functions are considered for compara­
tive analysis and the specific information of the kernel function is shown
in Table 4.
It is known from Fig. 6 that the changing trend of predicted value for
system COP and cooling capacity based on the automatic calibration of
the SVR algorithm is basically the same as the experimental value. The
SVR model with the RBF kernel function has the smallest error in the
predicted value, and the worst is the linear kernel function. In addition,
the generalization ability of the automation calibration model to predict
the cooling capacity is not as good as the system COP prediction. In fact,
for system COP and cooling capacity, the R between the measured value
and the predicted value of the SVR model with RBF kernel function is at
least 2.7% and 2.2% higher than the model using the other three kernel
functions, and the MSE is at least 10.1% and 6.7% lower than the model
using the other three kernel functions, respectively, so the best kernel
function is the RBF kernel function for SVR model that predict cooling
performance of liquid-cooled BTMS based HPACS.
When RBF Gaussian function was selected as the kernel function of
the SVR model, the SVR model can be abstractly expressed as equation
(19),
C ∈ (0.01, 10); ε ∈ (0.001, 10); γ ∈ (0.1, 1)
y = f (x|(C, ε, γ))
According to the expression of the SVR abstract model (Eq. (19)), the
prediction effect of the SVR model is mainly determined by three hyper
parameters of the model: the penalty coefficient C, the RBF kernel
function parameter γ, and the insensitive loss coefficient ε. In order to
ensure good performance in all aspects of the SVR model, the above
three parameters need to be optimized. In the current SVR parameter
selection method, there are mainly experience determination and grid
search. However, the empirical determination method needs to have a
solid SVR theoretical foundation and the grid search method has a large
calculation amount, so the two methods can’t guarantee to find the
global optimal solution. Given the complexity of SVR model hyper pa­
rameters selection, in this paper, the PSO algorithm is introduced to
optimize three hyper parameters before predicting the sample data.
In the paper, PSO algorithm parameters are initialized as shown in
Table 5, and the mean absolute percentage error (MAPE) between the
experiment value and the prediction value is used to establish the fitness
function, as shown in Eq. (20).
⃒
n ⃒
⃒f (xi ) − yi ⃒
1∑
⃒
⃒
MAPE =
(20)
n i=1 ⃒ f (xi ) ⃒
Fig. 7. Fitness curve.
temperature is increased, condensing pressure, condensing temperature
and compressor suction pressure will increase, resulting in a decrease in
the suction specific volume of the compressor and an increase in the
refrigerant mass flow, which the power consumption of the compressor
will be increased. Moreover, as ambient temperature increased from 32
to 42 ◦ C, the coolant temperature of the battery inlet will increase
slightly at any compressor speed. The reason why the battery inlet
coolant temperature is increased is that with the increasement of the
ambient temperature, the evaporation temperature will decrease, which
will cause the coolant temperature of the battery inlet to increase
slightly. Meanwhile, when compressor speed exceeds 4000 rpm, the
coolant temperature of the battery inlet can drop to 25 ◦ C to meet the
cooling requirements of the battery even if the ambient temperature is
greater than 40 ◦ C.
Fig. 7 shows the change of the population fitness during the evolu­
tion process. After a certain number of iterations, the fitness values of
the system COP and cooling capacity optimization are 0.011 and 0.019
respectively, and remain unchanged, the optimization process will be
convergent. For the prediction of system COP and cooling capacity,
three optimal hyper parameters (C, ε, γ)of the SVR model obtained
through
iterative
calculation
are
(0.15,0.11,0.375)
and
(0.23,0.15,0.392), respectively.
After obtaining the optimal values of the three hyperparameters of
the SVR model through the PSO algorithm, the three parameter values
are brought into the SVR model to predict the system COP and cooling
capacity of the liquid-cooled BTMS based HPACS. In order to further
verify the generality and generalization ability of PSO-SVR model with
RBF kernel function, the comparison between the prediction results of
the SVR model and the PSO-SVR model is shown in Fig. 8. After PSO is
introduced to optimize three hyper parameters of SVR model, regardless
of the cooling capacity or COP of the system, the MSE of the training
samples and testing samples is reduced and R is increased. To be specific,
R of cooling capacity and system COP for the proposed PSO-SVR model
in this paper is improved 2.1% and 2.8% respectively, MSE of and
3.4. Prediction result and discussion for SVR model
When the SVR model is trained, the datasets are provided by the
experimental results and the datasets were randomly separated into two
different parts, namely training and test datasets. 80% of datasets were
assigned as training datasets, and the remaining 20% were assigned as
test datasets. The prediction performance of the proposed SVR model in
this paper is measured by MSE and R, and the calculation formula is as
follows:
MSE =
n
1∑
(yi − f (xi ))2
n i=1
(
)
(yi − y)⋅ f (xi ) − f
i=1
R2 = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
)2
n
n (
∑
∑
f (xi ) − f
(yi − y)2
(17)
n
∑
i=1
(19)
(18)
i=1
where n is the number of samples, yi is the prediction result and f(xi ) is
11
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Fig. 8. Comparison on the prediction results between training sample and test sample.
cooling capacity and system COP is reduced 87.8% and 82.9% respec­
tively, which indicated that compared to SVR model, PSO-SVR model
can better express complex nonlinear relations among the system COP,
cooling capacity of the liquid-cooled BTMS based HPACS and other
influencing factors including ambient temperature, compressor speed
and air flow rate of the external heat exchanger.
the air flow rate of the external heat exchanger and compressor speed on
performances of the liquid-cooled BTMS and construction of automatic
calibration model for liquid-cooled BTMS are summarized as follow:
(1) The liquid-cooled BTMS designed has high energy efficiency and
cooling capacity. When the ambient temperature was 42 ◦ C, the
coolant temperature of the battery inlet could reach 19.8 ◦ C and
the COP at this time is 2.36 under the operating conditions of the
liquid-cooled BTMS. In fact, for the liquid-cooled BTMS based
HPACS designed in this paper even if the ambient temperature
exceeds 40 ◦ C, as long as the compressor speed is greater than
4000 rpm, the coolant temperature of the battery inlet can be
lower than 25 ◦ C.
4. Conclusions
In order to analyze the performances of liquid-cooled BTMS
comprehensively, the performances of liquid-cooled BTMS designed are
concerned and analyzed from the perspective of air conditioning based
experimental data in this paper. The influence of ambient temperature,
12
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
(2) For SVR model that predict cooling performance of liquid-cooled
BTMS based HPACS, the best kernel function is the RBF kernel
function. It is found that for system COP and cooling capacity, the
R between the measured value and the predicted value of the SVR
model with RBF kernel function is at least 2.7% and 2.2% higher
than the model using the other three kernel functions (Linear,
Polynomial and Sigmoid kernel function), and the MSE is at least
10.1% and 6.7% lower than the model using the other three
kernel functions, respectively.
(3) To optimize the performance of the SVR model, PSO algorithm is
introduced to optimize three hyper parameters of SVR model. The
three optimal hyper parameters (C, ε,γ)of the SVR model obtained
through
PSO
algorithm
are
(0.15,0.11,0.375)
and
(0.23,0.15,0.392), respectively. The results show that compared
to SVR model, R of cooling capacity and system COP for the
proposed PSO-SVR model in this paper is improved 2.1% and
2.8% respectively, MSE of and cooling capacity and system COP
is reduced 87.8% and 82.9% respectively.
(4) The machine learning method mentioned in this paper for pre­
dicting the performance of liquid-cooled BTMS based HPACS
makes it possible to get satisfactory performance parameter of
liquid-cooled BTMS based HPACS without the complicated
thermodynamics theory and equations. Meanwhile, Using the
automatic calibration model based PSO-SVR algorithm to predict
performances of liquid-cooled BTMS based HPACS for BEV also
avoids a lot of high-cost and long-term experiments and it can be
used as a new method to fit the complex nonlinear relationship
among the system COP, cooling capacity and other influencing
factors of the liquid-cooled BTMS based HPACS.
In order to further develop the liquid-cooled BTMS based HPACS for
BEV, the internal thermal characteristics of battery should be considered
in the automatic calibration model for liquid-cooled BTMS in the future.
Namely, the battery electrochemical model and machine learning model
of HPACS should be coupled and the liquid-cooled battery thermal
management system can be better optimized based on the automatic
calibration model and the battery electrochemical model.
CRediT authorship contribution statement
Xingwang Tang: Investigation, Validation, Formal analysis, Writing
– original draft. Qin Guo: Software, Formal analysis, Writing – original
draft. Ming Li: Conceptualization, Methodology. Changhua Wei:
Investigation, Validation. Zhiyao Pan: Visualization, Writing – review
& editing. Yongqiang Wang: Investigation.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgments
The authors wish to acknowledge for the financial support from
Technology Breakthrough Project of Department of Science and Tech­
nology of Jilin Province (No.20190302120GX) and State Key Laboratory
of Automotive Simulation and Control (ASCL) Foundation (ascl-zytsxm202029), for the work reported in this paper.
Appendices.
Table A.1
Operating conditions of liquid-cooled BTMS based HPACS
Samples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Input variables
Output variables
x1
x2
x3
y1
y2
Vcomp (rpm)
2000
2000
2000
2000
2000
3000
3000
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
2000
2000
2000
2000
2000
3000
3000
T0 (◦ C)
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
34
34
34
34
34
34
34
Vair (m s¡1)
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
COP
5.17546
5.89625
6.08945
6.02152
6.05875
4.10254
4.69458
4.53214
4.54218
4.54017
3.1568
3.63689
3.5021
3.51865
3.51245
2.91247
3.25487
3.19451
3.23458
3.25124
2.32557
2.65706
2.72354
2.74038
2.75587
5.01824
5.66723
5.85456
5.78654
5.81258
4.12548
4.62387
Cooling capacity (kw)
4.25225
4.26912
4.21785
4.23652
4.24001
4.59873
4.61548
4.55681
4.58327
4.61024
4.9596
4.9568
4.96543
4.91205
4.95242
5.06874
5.06217
5.07874
5.01248
5.05987
5.12022
5.13903
5.15015
5.13432
5.11982
4.27968
4.29044
4.23652
4.25125
4.27652
4.62189
4.65487
(continued on next page)
13
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Table A.1 (continued )
Samples
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
Input variables
Output variables
x1
x2
x3
y1
y2
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
2000
2000
2000
2000
2000
3000
3000
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
2000
2000
2000
2000
2000
3000
3000
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
2000
2000
2000
2000
2000
3000
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
40
40
40
40
40
40
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
4.60125
4.61354
4.61017
3.09875
3.51009
3.49539
3.50564
3.50124
2.76842
3.02389
3.10287
3.12548
3.13547
2.24896
2.57637
2.64254
2.65745
2.66986
4.86242
5.46974
5.29654
5.2357
5.2634
4.01257
4.42158
4.53278
4.55012
4.54963
2.98485
3.39481
3.49682
3.5087
3.5032
2.65481
2.91257
3.03548
3.08562
3.31254
2.19548
2.49568
2.56458
2.58564
2.89063
4.6532
5.23919
5.34898
5.34212
5.34698
4.59268
4.40189
4.52381
4.53521
4.53139
2.8364
3.26801
3.3764
3.38754
3.38254
2.57542
2.89645
2.81263
2.83654
2.84821
2.1687
2.41499
2.35887
2.36879
2.3784
4.41273
5.01615
5.18121
5.12707
5.15027
3.76542
4.59874
4.62127
4.64328
4.95128
4.94717
4.960121
4.91942
4.96127
5.04874
5.03698
5.06321
5.00854
5.05976
5.12024
5.13285
5.146822
5.12028
5.11682
4.28965
4.30145
4.25864
4.28125
4.29246
4.65327
4.68764
4.61985
4.64578
4.65782
4.95324
4.95818
4.97004
4.92852
4.96867
5.07019
5.07824
5.10538
5.04982
5.09324
5.11996
5.13009
5.14285
5.11965
5.10362
4.29085
4.30213
4.24865
4.26125
4.27156
4.63017
4.64871
4.57954
4.59124
4.61248
4.96
4.95886
4.97085
4.92651
4.96025
5.03498
5.02964
5.04127
4.99127
5.03421
5.12732
5.13421
5.14265
5.12623
5.11762
4.30147
4.31314
4.25172
4.27241
4.28621
4.61327
(continued on next page)
14
X. Tang et al.
Journal of Power Sources 494 (2021) 229727
Table A.1 (continued )
Samples
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Input variables
Output variables
x1
x2
x3
y1
y2
3000
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
2000
2000
2000
2000
2000
3000
3000
3000
3000
3000
4000
4000
4000
4000
4000
5000
5000
5000
5000
5000
6000
6000
6000
6000
6000
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
42
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
1.5
2.5
3.5
4.5
5.5
4.23657
4.34592
4.34964
4.35124
2.78809
3.17235
3.27291
3.28321
3.28065
2.38624
2.68675
2.79124
2.79854
2.81625
2.06607
2.34714
2.40902
2.41932
2.42963
4.2158
4.80115
4.98745
4.92154
5.02541
3.79854
4.12971
4.25362
4.27931
4.28011
2.74564
3.03746
3.15481
3.17541
3.17124
2.28671
2.65245
2.75015
2.77983
2.78541
1.97385
2.24207
2.3245
2.3456
2.35987
4.62579
4.57324
4.59127
4.6012
4.95517
4.95172
4.96207
4.91034
4.95517
5.05498
5.05013
5.06547
5.01048
5.05987
5.13448
5.14178
5.15172
5.13628
5.12759
4.31768
4.32069
4.25587
4.28156
4.30312
4.60182
4.61287
4.52387
4.55624
4.57421
4.95337
4.94994
4.96482
4.91512
5.00151
5.03349
5.02178
5.04129
4.98657
5.07124
5.12789
5.13559
5.14688
5.1263
5.11861
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