*2.2. Temperature Control System*

The control of the cell temperature as well as the temperature homogeneity at the cells were decisive tasks for the test bench in order to fulfill reliable and trustful measurements. In order to validate these requirements, nine temperature sensors were fixed on the cell adjacent subarea of the aluminum plate, Figure 3a, and an exemplary regulation from *T* = 10 ◦C to *T* = 30 ◦C and further to *T* = 40 ◦C, Figure 3b, was conducted.

Figure 3f–h demonstrates the temperature homogeneity of the aluminum plate. The temperature distribution on the plate was determined by weighting each temperature sensor depending on their distance to the respective point. In the stationary state, the maximum temperature difference within the plate was about Δ*T* = 0.71 ◦C. The differences can be caused, on the one hand, by the smaller area of the Peltier Element compared to the aluminum plate and, on the other hand, by the energy exchange with the environment.

**Figure 3.** Investigation of the temperature homogeneity and the heating rate of the aluminum plate with the position of the Pt100 sensors and the PE (gray box) in (**a**), the time curve of the Pt100 sensors with an exemplary regulation from *T* = 10 ◦C to *T* = 30 ◦C and further to *T* = 40 ◦C (**b**), the heating rate of the aluminum plate (**<sup>c</sup>**–**<sup>e</sup>**) and the temperature homogeneity of the aluminum plate (**f**–**h**).

Another important requirement of the temperature control system is to realize a higher heating rate of the aluminum plates *T* ˙ Plate compared to the maximum heating rate of the cells *T* ˙ Cell caused by dissipation *Q* ˙ Diss,max, which can be estimated by

$$\mathcal{T}\_{\text{Cell}} = \frac{1}{m\_{\text{Cell}} \mathfrak{C}\_p} \cdot \mathbf{Q}\_{\text{Diss,max}} \tag{1}$$

$$
\dot{\mathcal{Q}}\_{\text{Diss, max}} = \mathcal{R}\_{\text{Cell, max}} \cdot I\_{\text{Cell}'}^2 \tag{2}
$$

with the maximum cell resistance *<sup>R</sup>*Cell,max, the cell current *I*Cell, the cell's heat capacity *<sup>c</sup>*p,Cell and the cell mass *<sup>m</sup>*Cell. The cell's resistance was determined by pulse tests as described in Section 3.2 and ranges between *R*Cell = 21.3 mΩ and *R*Cell = 99.44 <sup>m</sup>Ω, depending on the SoC, temperature and time. With a maximum cell current of *I*Cell = 2*C*, the required heating rate can be calculated with Equation (2) from *T* ˙ Cell = 23.4 mK·s<sup>−</sup><sup>1</sup> to *T*˙Cell = 114 mK·s<sup>−</sup>1. However, as the maximum currents

of *I*Cell = 2C are only permitted at cell temperatures above *T*Cell = 10 ◦C and the voltage limits are reached at about SoC = 8% for these high currents, the practical limit can be set to *T*˙Cell = 74.8 mK·s<sup>−</sup>1.

The heating rate of the aluminum plate is approximately limited to *T*˙Plate = 250 mK·s<sup>−</sup>1, as shown in Figure 3c–e. This enables a precise temperature adjustment of the cells and the reconstruction of temperature gradients within a battery module due to varying thermal connections of the cells to neighboring cells and cooling.

### *2.3. Impacts of the Test Bench on the Current Distribution*

The ratios of the resistances and capacities of the parallel-connected cells have one of the main influences on the current distribution. This was shown qualitatively by measurements and simulations in [1], the quantitative influences of these parameters were mathematically proven in previous work [8,9].

For this reason, additional resistors induced by the test bench can significantly influence the current distribution. Due to the electrical connection of the cell tester and the lithium-ion cells, additional resistances arise in series with the cells, which are demonstrated in Figure 4.

**Figure 4.** Possible induced resistances by the test bench influencing the current distribution of *p* parallel-connected cells, with the contact resistances at the positive *R*Tab+ and negative tab *R*Tab−, the positive *R*Cab+ and negative cable resistances *R*Cab- as well as the cell resistance *R*Cell.

The contact resistances at the cell tabs as well as the cable resistances must on the one hand be well-known and on the other hand be kept low, at least their difference. As a result of the first Kirchhoff's law the following is valid

$$\begin{aligned} &lL\_{\text{Cab}\star,\text{i}} + lL\_{\text{Tab}\star,\text{i}} + lL\_{\text{Cell},\text{i}} + lL\_{\text{Tab}\star,\text{i}} + lL\_{\text{Cab}\star,\text{i}} \\ &= lL\_{\text{Cab}\star,\text{i}+1} + lL\_{\text{Tab}\star,\text{i}+1} + lL\_{\text{Cell},\text{i}+1} + lL\_{\text{Tab}\cdot,\text{i}+1} + lL\_{\text{Cab}\cdot,\text{i}+1} \\ &= lL\_{\text{Cab}\star,\text{p}} + lL\_{\text{Tab}\star,\text{p}} + lL\_{\text{Cell},\text{p}} + lL\_{\text{Tab}\cdot,\text{p}} + lL\_{\text{Cab}\cdot,\text{p}'} \end{aligned} \tag{3}$$

with the cell voltage *<sup>U</sup>*Cell,i, the positive *<sup>U</sup>*Tab+,i and negative tab voltages *<sup>U</sup>*Tab-,i as well as the voltages of the positive *<sup>U</sup>*Cab+,i and negative load cable *<sup>U</sup>*Cab-,i of cell *i*. In order to keep these disturbing values of the test bench on the current distribution low, the following conditions must be fulfilled

$$\mathcal{U}\_{\text{Cell},1} \approx \mathcal{U}\_{\text{Cell},2} \approx \mathcal{U}\_{\text{Cell},\mathbb{R}^\nu} \tag{4}$$

$$\|L\_{\rm Cap,i} + \|L\_{\rm Tab}\mathbf{}\_{\rm i} + \|L\_{\rm Cap,i} + \|L\_{\rm Tab}\mathbf{}\_{\rm i}\| < \cdot \tag{5}$$

The contact resistance at the tabs were examined and the cable resistances were varied in order to validate their impacts on the current distribution.

### 2.3.1. Contact Resistance at the Tabs

In order to keep the contact resistance at the cell tabs low, different influences on these resistances were investigated. The contact resistances were calculated by a four terminal measurement using a micro ohmmeter (MPK, 2000e). The influences of surface cleaning, torque and air insulation were researched. Therefore the tabs were treated with a non-woven abrasive cloth and then cleaned with an oxide-dissolving spray (CRC-Kontaktchemie, Kontakt 60). In addition, tests with varied contact pressure and conductive epoxy resin were conducted in order to isolate the tabs. For the investigation of the contact pressure, the resistances of twelve cathode and anode tabs were examined. To research the impacts of air seal, six of the cathode tabs were treated with conductive epoxy resin. The other six cathode tabs and the twelve anode tabs were not sealed with epoxy resin. The results are presented in Figure 5, whereby for each point the mean, minimum and maximum value is shown.

The influences of surface cleaning and contact pressure, as presented in Figure 5a,b, have already been investigated in [38,39] with the same findings. Figure 5c shows the influence of the air seal. While the contact resistances at the cathode tabs with air seal remained almost constant over the test period of 51 days, the resistances without air seal increased 2.5 times from *<sup>R</sup>*Tab,+ = 57.4 μΩ to *<sup>R</sup>*Tab,+ = 133.6 μΩ. It is assumed that oxidation on the tabs will lead to this increase. A relaxation of the surface pressure during the test period could additionally have led to an increasing contact resistance. However, since the resistances at the anode tabs remained unchanged, this effect should be not that significant. The anode tabs do not require an air seal due to their nickel coating, which shows up in an unchanged resistance over the test period. Furthermore, the contact resistances at the tabs and therefore the corresponding disturbing voltage drops *U*Tab+ and *U*Tab− are low compared to the cell resistance with 

$$\max\left(\frac{R\_{\text{Tab}}}{R\_{\text{Cell}}}\right) < 1\%\_{\text{\textdegree}}\tag{6}$$

which should lead to no significant impacts on the current distribution.
