When connecting cells in parallel all of the negative terminals are connected together and all of the positive terminals are connected together. The capacity of the parallel group is the sum of the capacity of the cells. Hence three 5Ah cells connected in parallel will give a total capacity of 15Ah.

3 cells connected in parallel.

Nominal voltage of the group of cells is the same as just one cell.

Maximum and minimum voltage of the group is the same.

Operating voltage is the same, capacity is 3x one cell.

This is the ideal situation and as we learn in all areas of battery design it is more complex than this.

### Internal Resistance

A battery cell is not a perfect current source as it also has an **internal resistance**.

Symbolically we can show a cell with the internal resistance as a resistor in series.

R_{int} is the DC internal resistance, sometimes abbreviated as DCIR.

The DCIR is not just a single number for any given cell as it varies with State of Charge, State of Health, temperature and discharge time.

The internal resistance of new cells can also vary and hence when connected in parallel the cells with a lower internal resistance will deliver more than their fair share of the current. This means these cells will run hotter based on I^{2}R heating and hence will age faster. As cells age the internal resistance increases and hence there could be a level of feedback control.

### Resistance in Joints and Busbars

There is also resistance in the busbars and in any joints.

The busbar cross-sectional area, length and joints all need to be considered when connecting cells in parallel. Small differences in resistance will result in different currents being delivered by each cell.

### Equal Cooling

Differences in cell internal resistance can be due to differences in cell temperature. Or for large cells due to temperature gradients.

The DCIR of a cell typically follows this curve.

Hence if a cell is cold the internal resistance will be higher. If two cells are in parallel and one is colder than the other then it will have a higher internal resistance.

As a result the colder cell will deliver less current.

I^{2}R in the hotter cell will be greater and the temperature differential will increase.

The requirement to keep all cells at the same temperature and temperature gradients in cells at a minimum is important. Particularly if you want optimise the overall performance and reduce the likelihood of early ageing.

In the case of extreme performance battery packs the cells are immersed in a dielectric cooling fluid. This allows heat to be removed from all surfaces of the cells. In some cases the tabs and busbars interconnecting the cells are also immersed in dielectric coolant.

The electrical connections to the cell active materials also provide a good thermal connection to the active core of the cell [2].

Careful design of the coolant flow to ensure no dead spots and equal cell temperatures is still required.

There are many different cooling options and more than just this particular parameter to consider when selecting the right design.

### Finite Element version of a Large Cell

In battery pack models it is useful to consider each cell as a single element, this will simplify the calculations and allow multiple scenarios and drive cycles to be analysed. However, a large cell is conceptually very similar to a number of cells in parallel. Using this idea we can understand the design of a cell and the optimum design for thermal control.

A single pouch cell consider as a single cell, a 2D breakdown of a pouch cell into 9 elements each with their own electrical and thermal parameters and the simplified electrical symbol for this parallel connection of cell elements.

Using this fundamental idea it is possible to model the cell in 3 dimensions and from this to optimise the design.

Fayaz et al [3] show a prediction of temperature distribution in 6 different pouch cell configurations.

The temperature distribution is shown near the beginning (20s) and then near the end (1140s) of the cycle.

Out of the 6 different designs, option (e) B2 appears to be the best based on this analysis. Tabs at each end and biased to each corner, along with a slightly wider and shorter electrode makes sense.

### Internal Current Flow

Thomas Bruen [1] shows experimental and model data for the re-balancing of 4 cells in parallel as they are subjected to a drive cycle. The drive cycle has step changes in current demand.

From 708 to 712 s, there are four increases in

Thomas Bruen, James Marco, Modelling and experimental evaluation of parallel connected lithium ion cells for an electric vehicle battery system, Journal of Power Sources, Volume 310, 2016, Pages 91-101

applied current magnitude, and each time the cell currents diverge after the step change. From 712 to 714 s there are two reductions in cell current and the cells self-balance following the voltage differences driven by the previously large currents. Note also the current response at 716e717 s where the applied current magnitude is quite low. In this case the convergent and divergent responses largely cancel each other out resulting in a consistent current over the 1 s period.

The BMS will only see the total response of any cells in parallel or the response from a large cell. Hence some of the cells (regions of a larger cell) might deliver a higher current than specified, thus increasing the ageing in the cell (or region of the cell).

### Cell Level Fusing

When we connect cells in parallel to increase the capacity we might also want cell level fusing. This fusing being by definition designed to disconnect a cell that for some reason is sinking or delivering high currents.

The fusing can be inside the cell and sealed or external to the cell, sometimes both internal and external fuses are used.

#### References

- Thomas Bruen, James Marco, Modelling and experimental evaluation of parallel connected lithium ion cells for an electric vehicle battery system, Journal of Power Sources, Volume 310, 2016, Pages 91-101
- Ian A. Hunt, Yan Zhao, Yatish Patel and G. J. Offer, Surface Cooling Causes Accelerated Degradation Compared to Tab Cooling for Lithium-Ion Pouch Cells, Journal of The Electrochemical Society, Volume 163, Number 9
- H. Fayaz, Asif Afzal, A. D. Mohammed Samee, Manzoore Elahi M. Soudagar, Naveed Akram, M. A. Mujtaba, R. D. Jilte, Md. Tariqul Islam, Ümit Ağbulut, C. Ahamed Saleel, Optimization of Thermal and Structural Design in Lithium‑Ion Batteries to Obtain Energy Efficient Battery Thermal Management System (BTMS): A Critical Review, Archives of Computational Methods in Engineering (2022) 29:129–194

#### Cells in Series

When connecting cells in series the negative terminal of the first cell is connected to the positive terminal of the second cell. The negative terminal of the second cell is connected to the positive terminal of the third cell. This continues until we reach the total number of cells required in series.

The nominal voltage of the final set of cells is the number of cells in series times the nominal voltage of a single cell.