Determination of the through-plane thermal conductivity and specific heat capacity of a Li-ion cylindrical cell
K.A. Murashkoa,∗, J. Pyrh¨onenb, J. Jokiniemia
aFine Particle and Aerosol Technology Laboratory, Department of Environmental and Biological Sciences, University of Eastern Finland, Post Office Box 1627, FI-70211 Kuopio, Finland
bLUT School of Energy Systems, Lappeenranta University of Technology, Skinnarilankatu 34, 53850 Lappeenranta, Finland
Abstract
Despite the high popularity of lithium-ion batteries there are still lack of the simple and eas- ily applicable methods for determining the Li-ion cell thermal parameters. The information about specific heat capacity and thermal conductivity of Li-ion cells is necessary to ensure appropriate operation of the Li-ion battery thermal control system, which prevents battery operation in an unacceptable temperature range. The method presented in this paper allows to determine simultaneously the specific heat capacity and a through-plane thermal conduc- tivity of any Li-ion cylindrical cell by a simple and cheap way with help of temperature and heat flux measurements on the cell surface. Moreover, the presented method allows to estimate the temperature dependence on the considered thermal parameters. The method is applied to measure the thermal parameters at different values of temperature and SoC for 18560 and 26650 types cylindrical Li-ion cells. In addition, the applicability of the presented method is evaluated on the reference sample whose thermal parameters are close to the ther- mal parameters of Li-ion cylindrical cells and are well known. Furthermore, the uncertainty of the method presented is analyzed and recommendations to decrease the uncertainty of thermal parameter determination are given.
Keywords: Cylindrical Li-ion batteries, Specific heat capacity, Through-plane thermal conductivity, Heat flux measurements, Thermal modelling
∗I am the corresponding author
Email address: [email protected](K.A. Murashko)
1. Introduction
Currently lithium-ion batteries (LIBs) are extensively used in the manufacturing of au- tomotive energy storage systems. LIBs are popular because of their advantages, such as high energy and power densities and long cycle life. However, a battery management system (BMS) must be used to ensure a safe and reliable operation of LIBs. Thermal protection and accurate control of the temperature distribution inside of the energy storage system are important tasks of an advanced BMS. The operation temperature of LIBs has significant effect on their operation performances. The operation of LIBs outside of the specified tem- perature range reduces the capacity, power and the lifetime of the battery and may lead to a thermal runaway and even fire [1].
The traditional way of thermal protection and temperature control, which is based on the surface temperature measurements, does not take into account the inertia of the system and may not give an acceptable quality of the thermal protection and control of the temperature distribution inside of battery system. The temperature control based on the temperature prediction with the help of LIB thermal model may give more accurate temperature control and improve the thermal protection of a battery system [2]. Different thermal models of LIBs were proposed in literature for temperature prediction [1, 3–5]. To ensure appropriate operation of these models a proper thermal characterization of a Li-ion cell including the determination of the specific heat capacity, in-plane and through-plane thermal conductivity is necessary.
In recent years, different methods have been proposed to determine the required thermal properties of Li-ion cells. A review of the thermal properties measurement methods for a Li-ion cell is given in Ref. [6]. The calorimeter method was widely used to measure the heat capacity of a Li-ion cell in [7–9]. However, this method requires using an expensive calorimeter. The specific heat capacity and the thermal conductivity can be measured by using an internal thermocouple as it was done by Forgez et al. in [10]. However, installing a temperature sensor inside of a cell is necessary and the cell can be damaged. The thermal impedance spectroscopy (TIS) method was suggested to measure the specific heat capacity and the thermal conductivity of Li-ion battery in [11, 12]. The required value can be obtained by fitting of thermal impedance curves, which describe the cell temperature response on the excitation signal. The main disadvantages of the TIS method is a low frequency of
the battery thermal response that is usually in the range of mHz. Therefore, the TIS method is a very time-consuming method [13]. The applicability of the lumped capacitance method for the determination of the average cell specific heat capacity of pouch cells was presented in [14]. The simplicity of the test setup is considered as the main advantage of the method. An external heat source was used to determine the thermal properties of pouch cells in [2, 15]. The presented methods allow measuring the specific heat capacity and through-plane thermal conductivity in a single experiment with acceptable accuracy by using a relatively simple and cheap test setup. An external heat source was also used in determining cylindrical cell thermal parameters in [9, 16]. However, the presented method requires that the measurements of the thermal parameters should be done in vacuum and, therefore, special equipment is necessary. Despite the intensive research in the field of determining the thermal parameters of LIBs, there is still a lack of the simple and easily applicable methods, which should allow to obtain the desirable information for cylindrical Li-ion cells with acceptable accuracy.
This paper presents a method to determine the thermal parameters of cylindrical Li- ion cells. Specific heat capacity and through-plane thermal conductivity are determined.
The measurement of the thermal parameters is done in a single experiment by using an external heat source. A simple and an affordable test setup is used to determine the thermal parameters of a cylindrical Li-ion cell. All measurements are done in ambient conditions and using a temperature chamber or vacuum is not necessary. The proposed method is verified with a reference sample, whose thermal properties are well known. The limitations and the uncertainty of the presented method are analyzed. The proposed method is used to determine the thermal parameters of 18650-type and 26650-type Li-ion cylindrical cells.
Moreover, the applicability of the suggested method to determine the required thermal parameters at different values of temperature and SoC is investigated.
2. Determination of thermal parameters
2.1. Cylindrical cell
This work aims to measure the through-plane thermal conductivity and the specific heat capacity of 18650 and 26650 types Li-ion cylindrical cells. The A123 lithium iron phosphate (LFP/C) cylindrical cell (ANR26650M1B) and Panasonic nickel cobalt aluminium (NCA/C)
cylindrical cell (NCR18650PF) are considered. Detailed specifications of the selected Li-ion cells are given in Table 1.
Table 1
Specifications of selected Li-ion cylindrical cells.
Cell product codes Chemistry Capacity, Ah
Mass, g
Max./Min.
voltage, V
Diameter/Length, mm
ANR26650M1B LFP/C 2.5 70 3.6/1.6 25.85/65.15
NCR18650PF NCA/C 2.7 48 4.2/2.5 18.5/65.3
2.2. Theory
The determination of the thermal parameters of the cylindrical Li-ion cell is based on the thermal model of an infinite cylinder with external heater. The method was described in [17, 18]. The thermal model of an infinite cylinder can be applied to the cylindrical cell when the tabs of the cell are thermally isolated. A schematic representation of such a cylindrical cell with boundary conditions is shown in Figure 1 (d).
The temperature of the cell surface, when a constant heat flux is penetrating to the cell, can be calculated as:
T =T0+ r
k ·θ·S, (1)
where T is the temperature of the cylindrical cell surface [K], T0 is the initial temperature of the cylindrical cell [K],r is the cylindrical cell radius [m], k is the through-plane thermal conductivity [W m−1 K−1], S is the heat flux [W m−2] and θ is the temperature coefficient.
The temperature coefficient in the beginning of the cylindrical cell heating or cooling is calculated as:
θ = 2·
v u u t Fo
π
!
+Fo
2 , (2)
where Fo is the thermal Fourier number. The thermal Fourier number is calculated as:
Fo = α·t
r2 , (3)
wheret is time (s), α is thermal diffusivity [m2 s−1], which is calculated as:
α= k
Cth·ρ, (4)
whereCth is heat capacity [J kg−1 K−1] and ρ is average density [kg m−3].
Equation (1) should be modified by using the superposition principle, if a variable heat flux is supplied into the cell. The variable heat flux should be divided on N small intervals during which a constant heat flux is assumed. This value is equal to the average value of the heat flux during the considered time interval. In this case equation (1) can be rewritten in the following form:
T =T0+ r k ·
N
X
i=1
(θi·Si), (5)
whereθi andSi are the temperature coefficients and the constant heat flux in theith interval (i= 1. . .N).
When the temperature on the cylindrical surface and the heat flux supplied into the cell are measured the through-plane thermal conductivity (k) can be calculated by substituting the equations (2), (3) and (4) to equation (5).
k = 4·PNi=1Si·√
∆ti2 Cth·ρ·π·
T −T0−
PN
i=1(Si·∆ti) 2·Cth·ρ·r
2, (6)
where ∆ti is a time interval (s), which is calculated as a difference between time when the sample heating or cooling was stopped and the starting time of theith interval at which the average value of the heat flux (Si) is calculated.
The average specific heat capacity of the cylindrical cell is calculated in a steady-state during heating and cooling processes as:
C¯th = 2·PNi=1(Si·∆ti)
r·ρ·T¯−T0 , (7)
where ¯T is the steady-state temperature of the cell at the end of the cell heating or cooling (K).
2.3. Test setup
The test setup is shown in Figure 1.
Fig 1. Test setup: samples and heaters (a), structure of the heater (b), test setup with thermal isolation and cooling (c) and the Li-ion cell boundary conditions (d).
The tabs of the cylindrical cell were thermally isolated by using an extruded polystyrene foam Fig. 1 (c). The thermal isolation of the cylindrical cell tabs was necessary to consider the Li-ion cell as an infinitely long cylinder. The temperature of the cylindrical cell surface was measured by PT100 temperature sensor and the green TEG heat flux sensor (gSKIN® XM 26 9C) was used to measure the heat flux to and from the cylindrical Li-ion cell surface.
The temperature and heat flux sensors were installed on the Li-ion cell surface in the middle of the cylindrical cell. Further, the cell surface was covered by a 2.5 mm vacuum rubber with purpose to improve the contact with the heater and to remove the air gap between the cylindrical cell and the heater Fig 1 (b). The heater was made of 0.1 mm copper foil, which was cut and wrapped around the cylindrical cell. The outer surface on the copper foil was isolated by Kapton tape and a nickel-chrome wire was uniformly wound on the device. Further Kapton tape was used to fix and isolate the nickel-chrome wire and
finally the surface of the device was covered by several layers of a copper tape to equalize the temperature distribution during the cylindrical cell heating and cooling. Sorensen LXI SGX1K0X5D DC power source was used to heat the nickel-chrome wire. The adjustment of the DC power supply voltage to heat the cylindrical cell to the selected temperature was done by trial and error method. Moreover, two 24 VDC Jamicon fans (JF0925-2SR00) were used to cool of the cylindrical cell. Tenma 72-10480 DC power supply was used to run the fans. Temperature and heat flux signals were recorded by Pico Technology PT-104 data logger.
The verification of the applicability of test setup was done by measuring the thermal parameters of the reference sample. A fused quartz cylinder whose thermal parameters are well known and were presented in [19, 20] at different temperatures, was selected as the reference sample. The length and diameter of the reference sample are 65 mm and 25 mm, correspondingly. The mass of the quartz cylinder equals 70.2 grams.
2.4. Limitations
The following limitations for the application of Eqs. (6) and (7) should be considered before performing the experiments and calculations of the cylindrical cell thermal parame- ters:
• The extruded polystyrene is attached to the cylindrical cell tabs to minimize the heat dissipation from the tabs and to simplify the cylindrical cell thermal model. However, despite the thermal diffusivity of the extruded polystyrene is small (0.026·10−6m2 s−1), a small amount of heat still dissipates from the tabs of the cell and is stored in the isolation material. Therefore, the specific heat capacity of the cylindrical cell should be calculated by equation (7) after heating and cooling of the cell from and to the ambient temperature. Further, the average value between the calculated values of the specific heat capacity should be found.
• Equation (6) requires information about the specific heat capacity at temperature at which the through-plane thermal conductivity is determined. If the average specific heat capacity obtained after cell heating and cooling in the some temperature range is used in equation (6), the average through-plane thermal conductivity should be cal-
culated as an average value between the values of through-plane thermal conductivity obtained in the beginning of the heating and cooling processes.
• The calculation of the though-plane thermal conductivity by equation (6) should be done in the beginning of the cell heating or cooling.
The last requirement is necessary when a simplified equation (2) for the temperature coefficient calculation is used instead of the full equation presented below:
θ = 2·Fo + 1 4 −
∞
X
n=1
An·J0(µn)·exp−µ2n·Fo, (8) whereJ0 is the zero-order Bessel function, µn and An are auxiliary variables.
The auxiliary variables are calculated as:
J1(µn) = 0, (9)
An= 2
µ2n·J1(µn), (10)
whereJ1 is the first order Bessel function.
Simplifying equation (8) results in an error shown in Figure 2.
Fig 2. Error resulting from the simplification of equation (8).
As it can be seen in Fig. 2, the error resulting from the simplification of equation (8) is proportional to the thermal Fourier number. Moreover, it should be mentioned that in the range 0.15<Fo<0.5, the error has a linear dependence on the thermal Fourier number. As
the thermal Fourier number is proportional to the heating and cooling time, the through- plane thermal conductivity of the cylindrical cell should be calculated at the beginning of the cell heating or cooling to achieve acceptable accuracy for the through-plane thermal conductivity determination.
2.5. Uncertainty
The uncertainty was calculated according to EA-4/02 [21]. The standard uncertainty for a single measured value is calculated as:
u2(y) =XN
i=1
∂f
∂xi
·u(xi)
!2
, (11)
whereu(y) is the uncertainty of the output estimatey,u(xi) is the uncertainty of the input estimate xi, where i is the number of the input estimates i = 1. . .N, and f is function showing the dependence between the input and the output. The values of the uncertainty of the input estimates for the equipment used for the cylindrical cell thermal parameters determination are given in Table 2.
Table 2
Uncertainty of the input estimates.
Equipment Input estimates Uncertainty
Time, s 0.5
Pico Technology PT-104 Temperature, K 0.019 Voltage, µV 4
Electric Lab Scale Mass, g 0.0005
Electronic digital caliper Dimensions, mm 0.005
3. Results and discussion
The thermal parameters of the quartz cylinder were calculated by the described equa- tions. The cylinder was heated from ambient temperature up to 41 ◦C and further cooled
to ambient temperature. The temperature of the cylinder surface and the heat flux to and from the cylinder surface during the test are shown in Figure 3.
Fig 3. Measured temperature of the quartz cylinder surface (a) and the heat flux to and from the cylinder surface (b) during the test
To calculate the specific heat capacity, it was assumed that the temperature of the quartz cylinder surface reached a steady-state value when the change of temperature was smaller than 0.2 ◦C per 5 minutes. Such requirement for the determination of the steady- state temperature was selected to neglect the fluctuation of the ambient temperature in the laboratory and therefore the small deviation of the heat flux values from zero at steady- state condition caused by this fluctuation. The average specific thermal conductivity was calculated by equation (7) and it is equal to 752.3±4.8 J kg−1 K−1. The average thermal conductivity was calculated in the beginning of the quartz cylinder heating and cooling and the values of quartz cylinder average thermal conductivity are given in Figure 4 for different values of the thermal Fourier number.
Fig 4. Calculated values of the quartz cylinder thermal conductivity.
As it can be seen in Fig. 4 the calculated values of the average thermal conductivity do not change significant at thermal Fourier numbers from 0.1 to 0.2. Moreover, the uncertainty of the thermal conductivity measurements decreases with thermal Fourier number increasing, which is explained by increasing of the time interval at which the measurements of the thermal conductivity is performed. Increasing the time interval leads to an increase of the variation of the temperature and the heat flux values within this interval, which can be measured with higher accuracy. However, a small linear decrease of the calculated values is noticeable with increasing of thermal Fourier number beyond 0.2. The linear decrease of the thermal conductivity is caused by the linear increase of the error of equation (2), which was previously shown in Fig. 2. Therefore, with aim to decrease the uncertainty of the thermal conductivity measurement and the effect of simplifying equation (8), it is recommended to measure the values of the thermal conductivity by the suggested method in the range of the thermal Fourier number from 0.15 to 0.2. The Fo = 0.2 was selected for the thermal conductivity determination in all further tests.
The analysis of the heating temperature and the cooling intensity effects are shown in Figure 5. The quartz cylinder was heated from 295 K to about 305, 315, 325 and 335 K at different rotation speed of the fans. The difference between initial temperature and temper- ature to which the quartz cylinder was heated is denoted as heating temperature (∆T). The measured average thermal parameters were compared with average thermal parameters of
the quartz sample in considered temperature ranges. These thermal parameters as function of temperature are given in [19, 20] and are considered in this work as reference values.
Moreover, the uncertainty of the measured values was calculated and presented in Fig 5 (c) and (d) for the calculated values of the specific heat capacity and the thermal conductivity, correspondingly.
Fig 5. Comparison of calculated values with reference values at different ∆T and angular velocity of the fans (a) and (b), and uncertainties of calculated values (c) and (d) for specific heat capacity and thermal conductivity determination correspondingly.
The analysis showed that the effect of the fan speed and∆T on the specific heat capacity is small. The deviation of the measured parameters from the reference values was smaller than 0.5% and the measured uncertainty was smaller than 1.13% for all cases considered.
However, the effect of the heating temperature and the fans speed on the thermal conduc- tivity was more noticeable as it can be seen in Fig. 5 (d). The maximum deviation of the measured values of the quartz thermal conductivity from the reference values was equal to 3.2% at 31.1 rad s−1 fan speed and about 10 K of ∆T. Moreover, the maximum uncertainty of the thermal conductivity measured values was obtained at these test conditions. The
increase of the fan speed and the heating temperature leads to decreasing uncertainty of measurements, which at the highest heating power and cooling intensity becomes less than 2% (Fig. 5 (b)). Such effect of the test conditions is explained by the increasing of the vari- ation of the temperature and the heat flux in the considered time interval with increasing of the heating power that should be supplied to the heater to heat the quartz cylinder up to a selected steady-state temperature at considered speed of the fans. Therefore, to decrease the uncertainty of the thermal conductivity measurements it is recommended to use the highest possible heating power and cooling intensity during the test.
The method presented allows to measure the average thermal parameters of a cylinder in a selected temperature range. However, in some cases the temperature dependence of the specific heat capacity and thermal conductivity must be consider. It may be important while creating a high-quality thermal model for a Li-ion cell and for a proper design of the thermal control system for a Li-ion battery pack. The average values of the considered parameters measured in different temperature ranges can be recalculated to the actual values at the considered temperature in case of linear temperature dependence. Linear temperature dependence of the specific heat capacity and through-plane thermal conductivity of a Li- ion cell were reported in many previous researches [15, 22–24]. Moreover, such assumption can be done for the quartz in temperature range from 293 to 343 K as it was shown in [19, 20]. Recalculation of the average values of the thermal parameter measured in different temperature ranges can be done by considering the similarity of triangles, which is presented in Figure 6 (a) as an example.
Based on the simplicity of the triangles the tanα and Cth0 can be calculated using the least square method as:
tanα Cth0
= (A×A|)×A×b|, (12) whereA is the 2x4 matrix andb is the 1x4 string.
A =
∆T1
2 ∆T2
2 ∆T3
2 ∆T4
2
1 1 1 1
andb=C¯th1 C¯th2 C¯th3 C¯th4
, (13)
where ¯Cth1... ¯Cth4 are the average values of the specific heat capacity at temperature range
∆T1...∆T4, correspondingly. The values of the specific heat capacity can be calculated as:
Cthi = tanα·∆Ti+Cth0, (14)
wherei is the index, which is equal to 1, 2, 3 and 4.
The values of the thermal conductivity are calculated by similar approach from the measured average values of the thermal conductivity in the considered temperature ranges. If the values of the thermal conductivity or/and specific heat capacity decrease with increasing temperature, the equations (13) and (14) should be modified by the following way:
A=
1 1 1 1
−∆2T1 −∆2T2 −∆2T3 −∆2T4
andb =C¯th1 C¯th2 C¯th3 C¯th4
, (15) Cthi =Cth0−tanα·∆Ti, (16) The calculated values of the specific heat capacity and thermal conductivity of the quartz cylinder by the method presented above are compared with the reference values at different values of temperature given in [19, 20]. The result of comparison and the uncertainty of the quartz thermal parameters calculation are shown in Figure 6 (b) and (c). The actual values of thermal parameters were calculated from the average values measured at fan speed 335.1 rad s−1.
Fig 6. Triangles considered for the calculation of the actual values of specific heat capacity (a) and calculated values of quartz specific heat capacity (d) and thermal conductivity (c).
As it can be seen in Fig. 6, there is a good correlation between the calculated and the reference values. The specific heat capacity is measured with lower than 1% uncertainty.
However, the possible uncertainty of the thermal conductivity calculation for the quartz cylinder reached 8.9% at the highest considered temperature, which is higher than the effect
of temperature on the quartz thermal conductivity values. As it was previously discussed, the uncertainty can be decreased by increasing the heating power and the cooling intensity for example a liquid cooling system can be used instead of the force air cooling system.
Moreover, the uncertainty in determining the actual thermal parameters can be decreased also by repetition of the measurements.
The method presented was then used to determine the parameters of ANR26650M1B and NCR18650PF cells. The results are given in Figures 7 and 8, correspondingly. The average thermal parameters of the Li-ion cells were measured at different values of SoC and temperature range. The 335.1 rad s−1 fan speed was used during all tests. Before measurements, the considered Li-ion cells were fully charged by a constant-current constant- voltage (CCCV) charging method. The charging in the constant current (CC) mode was done by 1/2 C-rate continuous current up to cut-off charging voltage and further constant voltage (CV) mode was applied during 2 h. Further, the considered Li-ion cells were heated and cooled in different temperature ranges to measure the average thermal parameters.
Discharging of the cell to a new value of the SoC was done by 1/2 C-rate continuous current.
The relaxation period of the cell after discharging and before average thermal parameters measurement was more than 3 hours. The average specific heat capacity and through-plane thermal conductivity were measured at 0%, 50% and 100% of SoC. The actual values of the considered thermal parameters were recalculated from the average values in different temperature ranges and are shown in Figure 7 and 8 for the both ANR26650M1B and NCR18650PF. The temperature ranges are denoted as a heating temperature (∆T) of the cylindrical Li-ion cells starting from the ambient temperature, which was equal to 295 K.
Fig 7. Average values of ANR26650M1B cylindrical cell thermal parameters(a) and (c), and the dependence of the thermal parameters on temperature (b) and (d).
As it can be seen in Fig. 7 (a) and (b) the thermal conductivity of the LFP/C cylindrical cell increase with increasing temperature and SoC, which is corresponding to the previously reported results in [23]. The maximum uncertainty of the average specific heat capacity in the temperature range from 295 to 333 K and the maximum value of actual specific heat capacity at each temperature is equal to 0.7% and 1.2%, correspondingly. The measured average value of the specific heat capacity in the temperature range from 298 to 328 K at 50% of SoC is equal to the 1127±13.5 J kg−1 K−1 which in a good correlation with the calorimetric measurement of the ANR26650M1B cylindrical cell given in [25]. The thermal conductivity of the LPF/C cylindrical cell decreases with increasing of the temperature which was also previously reported in [23] for the LFP/C pouch cell and in [22, 26] for other Li-ion cell types and chemistries. The analysis of the dependence of the thermal conductivity on SoC showed that for the ANR26650M1B cell the through-plane thermal conductivity decreases with increasing SoC which was also reported in [23]. However, the effect of the SoC is almost comparable with the uncertainty of the average through-plane thermal conductivity determination, which is equal to 0.8% and shown in Fig. 7 (c), and it is significantly smaller than the uncertainty of the actual values determined. They did
not exceed 3.0% for all measured points. Therefore, this result should be considered with precaution and the repetition of measurements or the improvement of the test setup should be done to analyze the effect of the SoC on the through-plane thermal conductivity with higher accuracy.
Fig 8. Average values of NCR18650PF cylindrical cell thermal parameters (a) and (c) and the dependence of the thermal parameters on temperature (b) and (d).
The considered thermal parameters of the NCA/C cylindrical cell have similar depen- dence on temperature as the thermal parameters of the LPF/C cell. However, the effect of the SoC on the though-plane thermal conductivity is opposite compered to LFP/C cell. The through-plane thermal conductivity is significantly increased with increasing SoC. Similar ef- fect of SoC on the thermal conductivity of Sony US-18650 lithium-ion battery, where LiCoO2 was used as the active material for the positive electrode, was reported in [7]. The different effect of the SoC on the through-plane thermal conductivity may be caused by a different intensity of the structural changes caused by delithiation of the positive electrodes with in- creasing of SoC that affect the phonon modes of vibration in positive electrode active material [7]. However, more detailed research is necessary for the explanation of this phenomenon.
The uncertainty of the average specific heat capacity and average through-plane thermal
conductivity in the temperature range from 296 to 330 K are 1% and 1.6%, correspondingly.
The maximum uncertainties of the specific heat capacity and thermal conductivity are equal to 1.5% and 9.2%, correspondingly. The uncertainty of the through-plane thermal conduc- tivity determination is significantly higher in case of the NCR18650PF NCA/C cylindrical cell than in case of the ANR26650M1B LFP/C as the diameter of NCA/C cells is smaller and the calculated values of the through-plane thermal conductivity are bigger, which has an effect on the duration of the time considered in the through-plane thermal conductivity determination. Decreasing this time range with decreasing cell diameter or/and increasing the through-plane thermal conductivity lead to decreasing variation of the measured values in this time range. Small variation is more difficult to detect by the equipment used. The deviation of the actual values of the through-plane thermal conductivity with temperature changing is much smaller than the uncertainty of the measurements. This requires the rep- etition of the tests or modification of the test setup, if the effect of the temperature on the NCR18650PF cell through-plane thermal conductivity should be investigated.
4. Conclusion
A simple and cheap method for the simultaneous measurements of the specific heat ca- pacity and through-plane thermal conductivity of cylindrical Li-ion cells was presented and verified in this paper. The method allows to determine the average values of the specific heat capacity and through-plane thermal conductivity in a selected temperature range with a high accuracy. The verification of the presented method was done by measuring the average thermal parameters of a quartz cylinder. Its specific heat capacity and thermal conductivity are close to the thermal parameter of cylindrical Li-ion cells and are well known. The ther- mal parameters of the quartz cylinder were measured in different temperature ranges and with different cooling intensity controlled by fans. The comparison of the measured quartz thermal parameters with previously reported values in literature showed high accuracy of the presented method and, therefore, it was recommended for the determination of Li-ion cylindrical cell thermal parameters. Moreover, the analysis of the effect of the test parame- ters such as cooling intensity and heating power on the uncertainty of the thermal parameter determination allows to give recommendation about necessity to use the maximum values of the considered parameters to get the lowest uncertainty. The applicability of the method
for the Li-ion cylindrical cells showed that the average values of the specific heat capacity and through-plane thermal conductivity can be obtained with uncertainties lower than 1%
and 1.6%, correspondingly at a maximum considered cooling intensity and heating power of the test setup used. The recalculation of the average values of the considered thermal parameters, measured in different temperature ranges, to exact values at each considered temperature showed slight increase of the thermal parameter determination uncertainty.
However, this uncertainty may become comparable and even bigger than the changes of the Li-ion thermal parameters when temperature changes. Similar situation may be observed when the effect of the SoC on the thermal parameters of the Li-ion cylindrical cells is inves- tigated by the method. Despite the relatively low uncertainties of the average specific heat capacity and average through-plane thermal conductivity for the LFP/C cell, which were 0.7% and 0.8% correspondingly, the change of these parameters with the change of SoC is almost in the same range as the values of the uncertainty. Therefore, if the temperature and SoC effects on the considered thermal parameters of cylindrical Li-ion cells should be investigated, repetition of the measurements or modification of the test setup may be needed to improve the accuracy of the determination of the thermal parameters.
Acknowledgements
This research was enabled by the financial support of Academy of Finland (project LIANA, grant number 309836).
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