Analysis of heat dissipation

The heat dissipation was analysed by thermal impedance spectroscopy (TIS). A similar method was used in (Fleckenstein et al., 2013) for the determination of the cylindrical cell specific heat capacity and the thermal conductivity. The method requires generation of sinusoidal varying heat losses in the cells. Such losses produce a sinusoidal variation

in the temperatures of the LTO pouch cell and the module walls. The analysis of the heat generation and temperature variation can show how heat is dissipated from the cells in the module, and it can be used to model this process.

The sinusoidal heat losses in the cells were generated by using short charging and discharging cycles with different values of current. The electrical power source Amrel SPS60X333 and the programmable electrical load Amrel PLW9K-60-1500E were controlled by a LabVIEW program. The operating cycle was obtained by multiplication of the charging and discharging impulses on the discrete sinusoidal signal as shown in Fig. 5.2.

Fig. 5.2: Generation of the operating cycle and heat losses of one Altairnano battery module.

The frequency of all charging and discharging impulses was kept constant. The values of the operating currents were varied so that the SoC of the cells remained constant on average. This was achieved by using the same current value for the charging impulses as for the previous discharging impulses.

The heat losses in the battery module were estimated as in (Javani et al., 2014) by



where N is the number of LTO pouch cells, I is the operating current (A), Uocv is the OCV of the LTO pouch cell (V), Ucell is the terminal voltage of the LTO pouch cell (V), and T is the average temperature of the LTO pouch cells (K).

The values of the charging and discharging current I (A) were measured in the experiments by using a shunt of a 0.6 mΩ resistance, and the terminal voltage of the cell was measured directly from the special terminal in the battery module. The temperature variation in the battery module was measured in the steady state at the average

temperature of the module walls. Further, it was assumed that all LTO pouch cells in the module can be regarded as a single source of losses. Based on this assumption, the average temperature of the cells can be described by measuring data from the temperature sensor, which was installed in the centre of the module by the battery manufacturer. In the analysis of the heat dissipation, it was also assumed that heat is dissipated from three parts of the module: from the aluminium bottom, vertical walls and top of the battery module.

To verify the assumption, the temperature values in points 2 and 3 were measured in all tests, and the temperature differences in these points were analysed. The sinusoidal heat losses were generated by 1, 0.6, 0.4, 0.3, 0.2, 0.15 and 0.1 mHz frequencies of the battery pack operating cycle. For all tests, the initial SoC of the battery module was 64 %.

After the tests, the measured variation in temperature and the calculated values of heat losses were analysed in MATLAB by using a fast Fourier transform. The fast Fourier transforms of the calculated losses and the average temperatures of the cells for the 0.2 mHz frequency of the operating cycle are shown in Figs. 5.3 (a) and (b), respectively.

Fig. 5.3: Fourier transform of the heat losses (a) and the average cell temperatures (b) in the battery module.

The fast Fourier transform showed two main harmonics. The harmonic at the zero frequency shows the average value of the signal. The second largest harmonic is detected at the 0.2 mHz frequency, which is the main frequency of the battery module operating cycle. Therefore, this operating cycle of the battery module could be used to generate the sinusoidal heat losses, which produce a sinusoidal temperature variation in the average temperature of the LTO pouch cells.

The analysis of the heat dissipation from the bottom of the battery module was made by analysing the measured sinusoidal signals of the temperature difference between the

module bottom plate and the cooling liquid, and heat flux from the module bottom plate.

The fast Fourier transform results of these signals for the 0.2 mHz frequency of the operation cycle are shown in Figures 5.4 (a) and (b), respectively.

Fig. 5.4: Fourier transform of the heat dissipation from the module bottom (a) and the temperature difference between the module bottom plate and the cooling liquid (b).

PT 100 temperature sensors were used for the measurements of the temperature values of the module aluminium bottom and the cooling liquid. The heat dissipation from the module bottom was measured by a GHFS. The same analysis was performed for all frequencies under study. The magnitude difference and phase shift between the signals were calculated as:

 

T H

Y

A Y , (5.2)

 

Δ 180





  t



 , (5.3)

where ∆t is the time-lag of the responce signal (s), and YT and YH are the magnitudes of the measured temperatures and heat, respectively. The values of the magnitudes were calculated by a fast Fourier transform of the measured temperature and heat waveforms as a function of time.

The calculated magnitude ratio on a logarithmic scale and the phase shift are shown as a Bode plot in Figure 5.5.

Fig. 5.5: Magnitude ratio on a logarithmic scale and the phase shift presented as a Bode plot, which describes heat dissipation from the battery module bottom.

The Bode plot of the measured thermal impedance of the cooling system shows that at the frequencies under study, the magnitude and phase shift of the measured data are almost constant. Such a result shows that the heat dissipation from the module bottom is mostly determined by the module bottom temperature, which allows neglecting the cooling system heat capacity in the modelling.

Heat transfer from the cells to the bottom, top and vertical walls can be presented by temperature transfer functions, which describe the dependence of the average cell temperature on the temperature of the bottom, top and vertical walls of the battery module. The difference between the measured temperatures of the module walls in points 2 and 3 (Fig. 5.1) was less than 1 °C for all experiments. Therefore, to simplify the thermal model of the module, the average temperature between points 2 and 3 was taken as the wall temperature of the module. The Bode plots of the temperature transfer functions from the centre of the cell to the module bottom, module top and vertical walls of the battery module are shown in Fig. 5.6 (a), (b) and (c), respectively.

As it can be seen in Fig. 5.6, the phase shift for the temperature transfer functions, which describes the heat transfer from the cells to the aluminium bottom, is larger than -90° for the smallest frequency under study. The phase shifts for other directions are smaller than -90° for the smallest frequency. The result can be explained by considering the battery module structure. The heat from the cell goes directly to the aluminium plates, which are connected to the aluminium bottom. In this direction, the heat transfers through one type of material to the battery module cooling system. In the horizontal directions, the heat transfers through at least two materials such as the phase change material (PCM) and the module plastic walls. When the heat transfers from the cell to the top of the battery module, it passes through two different materials. These materials may be the plastic top

of the module and an additional system, which provides a series connection of the cells inside the battery module.

Fig.5.6: Bode plots of the measured battery module thermal impedances in the directions from module centre to the module bottom (a), to the module top horizontal plate (b) and to the vertical walls (c).

The analysis of the heat transfer from the cells to the module bottom, top and vertical walls allows an assumption that a Cauer network can be used. A first-order Cauer network can be used to model the heat transfer from the cells to the module bottom as only heat transfer through only one material was found (Davidson et al., 2014). A second-order Cauer network was chosen to model the heat transfer from the cells to the vertical walls and to the top of the battery module. It was chosen as the measured data showed at least two different materials, through which the heat flux transferred in these directions. The total lumped-parameter thermal model, which was chosen to model the heat transfer and temperature in the battery module, is shown in Fig. 5.7.

Fig. 5.7: Lumped-parameter thermal model of the battery module.

In the presented lumped-parameter thermal model, the heat generated in the cells increases the average cell temperature Tbat. This process is modelled by an element similar to the current source in an electrical circuit Qbat and the thermal capacitance Cth, bat. The heat dissipation from the cells takes place in three ways. The largest amount of heat is dissipated through the aluminium bottom of the module. This process is modelled by the thermal resistance Rth, 11, which indicates heat transfer from the cell to the aluminium bottom. The thermal resistance Rth, 12 indicates heat transfer from the aluminium bottom to the water cooling system. The thermal capacitance Cth, 11 is used for the modelling of the module cooling system heat capacity. The element that is similar to the voltage source in an electrical circuit is used to model the cooling liquid temperature Twat. The heat dissipation from the module top and temperature on the model top Ttp are modelled by the thermal resistances Rth, 21, Rth, 22 andRth, 23 and the thermal capacitances Cth, 21 and Cth,22. The heat dissipations from the vertical walls and temperature on the walls of the module Tw are modelled by the thermal resistances Rth, 31, Rth, 32 andRth, 33 and the thermal capacitances Cth, 31 and Cth, 32. The ambient temperature is modelled by an element that is analogous to the voltage source in an electrical circuit, Tamb. The lumped-parameter thermal model parameters were estimated by approximating the measured thermal impedances of the battery module in the direction under consideration.

5.2