The electrical design of a battery covers a wide array of topics. We will start simple and gradually add to the complexity and depth.

### Single Cell

The single battery cell is represented by the symbol:

The ‘+’ sign does not need to be there as the longest plate represents the positive terminal. This electrical symbol for a battery cell is used no matter what the battery chemistry is.

The Open Circuit Voltage (OCV) is a fundamental parameter of the cell. The OCV of a battery cell is the potential difference between the positive and negative terminals when no current flows and the cell is at rest.

More correctly the electrical symbol would have a resistor added to show the internal resistance of the cell, thus:

This internal resistance is a key cell parameter. Discharge the cell and you will see a voltage drop, on top of that given by the OCV curve, determined by Ohm’s Law. Charge the cell and you will see a voltage increase, this time on top of the OCV curve and based on Ohm’s Law.

The upper and lower voltage limits are set by the cell supplier for safety and lifetime reasons. Once we know the OCV and R_{int} then we know the maximum charge / discharge power available whilst remaining with the voltage limits.

However, this is a simplistic view as the cell must remain within the limits of the independent Anode and Cathode potentials. These are determined using a 3rd electrode inserted into the cell (a large topic of work in it’s own right). Hence the charge and discharge limits will normally be determined by the cell manufacturer.

### 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.

The schematic shows 3 cells in series, hence 3S. This would be written as 3S1P. If the nominal voltage of a single cell is 3.6V then this battery pack would be 3 x 3.6V = 10.8V

The Tesla Model 3 battery has 96 cells in series. Hence this is a 96S battery pack. A single Tesla Model 3 cell has a nominal voltage of 3.65V and so the series group of cells is 96 x 3.65V = 350.4V for the pack nominal voltage.

### Cells in Parallel

Cells that are in parallel have the positive terminals all connected together and the negative terminals all connected together. The voltage of the group of cells in parallel will be the same as a single cell. The nominal capacity of the group of cells will be P multiplied by the nominal capacity of a single cell.

The schematic shows 3 cells in parallel, hence 3P. This would be written as 1S3P. If the capacity of a single cell is 4.8Ah then the capacity of the 3 cells in parallel is 3 x 4.8Ah = 19.2Ah

### Series and Parallel

The Tesla Model 3 battery has 46 cells in parallel. Each cell has a nominal capacity of 4.8Ah and so the capacity of the group of cells is 46 x 4.8Ah = 220.8Ah

#### Single Side 21700 Busbars

In the case of cylindrical cells it is possible to connect to both the positive and negative terminals of the cell on the top surface.

Thus leaving the bottom of the cell free for cooling.

Hence we get the shorthand **96S46P** configuration of cells that we might see in a Tesla pack. This means 46 cells are connected together in a parallel group and this is then connected in series with 95 more of these groups.

If each cell was 5Ah then we would have a total capacity of 46 x 5Ah = 230Ah

and the total nominal voltage of the pack would be 3.7V x 96 = 355.2V

the total nominal energy content of the pack = nominal voltage x capacity = 355.2V x 230Ah = 81,696Wh or 81.696kWh

Watts are defined as 1 Watt = 1 Joule per second (1W = 1 Js^{-1})

time is simple 1 hour = 3600 seconds

Hence 1 Wh = 3600 Joules

So the Watt hour (Wh) is a strange unit as it is energy use per unit of time multiplied by time.

### Battery versus System Voltage

When we look at the battery versus system voltage we have to remember that these are working together. In fact we have to look at the complete system and all components to ensure they can work together over the maximum and minimum voltage range. This will normally be the maximum charge voltage and the minimum voltage will be the under load transient condition.

### Continuous Current Rating

At some point in the development of a battery pack design you need to consider the continuous current rating. Do this for charge and discharge as this then gives you one for the fundamental requirements to determine:

- cell to cell busbars
- HV joint requirements
- HV distribution busbar cross-sectional areas
- contactor sizing
- fuse sizing
- connector sizing

Plotting continuous power versus system nominal voltage it is possible to see the voltage/power/current design points.

### Higher Voltage Packs

As Power = IV this means to increase power we increase current or voltage. Increasing current increases losses due to heating, increasing the voltage means we can keep the heating losses fixed. It does though mean we need more cells in series and higher voltages brings other constraints once we go above the safe working voltage of 60V DC. As we increase the voltage further then creepage and clearance distances have to be increased.

### Electrical Isolation Resistance of the Pack

The isolation resistance of a pack to ground should be >500Ω/V and hence for a battery pack with a nominal voltage of 360V this resistance >180,000Ω/V.

It is important that a battery pack is designed around this criteria when new and during it’s lifetime of use. The BMS is expected to monitor the isolation resistance and act accordingly. There are a number of reasons why the isolation might reduce or breakdown over time:

- dirt ingress creating conductive pathways
- ageing of insulating materials
- coolant leakage
- cell venting or thermal runaway
- physical distortion or damage to the pack
- foreign bodies introduced to the pack, eg tools left in the pack during service