In simple terms this will be based on the energy and power demands of the application.
The application of the battery pack is quite fundamental to sizing it and setting the usable SoC window.
High power packs need to operate over a narrower state of charge window if the power delivery is to be consistent.
A long range BEV will have a very ‘wide’ usable SoC of around 90 to 95%. A HEV that discharges and charges the pack in an aggressive way would need a ‘narrow’ usable SoC of around 30%. Use high level numbers as a starting point, but be mindful that these might change depending on chemistry, ageing profiles and user cases.
The usable energy of a battery is dependent on a number of parameters at any given time:
- variation in cells
- absolute temperature
- temperature gradient within a cell
- temperature gradient across the pack
- available coolant capacity
- power demand
- state of health (SoH)
- capacity at discharge rate
- internal resistance increase
- degradation of other components
- usable window
Hence, most battery pack sizing studies start with the Energy, Power and Working Voltage Range (Inputs to Pack Sizing is a more complete list).
The operating voltage of the pack is fundamentally determined by the cell chemistry and the number of cells joined in series.
As the pack size increases the rate at which it will be charged and discharged will increase. In order to manage and limit the maximum current the battery pack voltage will increase.
When we plot the nominal battery voltage versus pack total energy content we can see the voltage increasing in steps.
Typical nominal voltages:
The usable energy (kWh) of the pack is fundamentally determined by:
- Number of cells in series (S count)
- Number of cells in parallel (P count)
- Capacity of a single cell (Ah)
- Nominal voltage of a single cell (Vnom)
- Usable SoC window (%)
Energy (kWh) = S x P x Ah x Vnom x SoCusable / 1000
Note: this is an approximation as the nominal voltage is dependent on the usable window. Also, the variation in cell capacity will be needed to be understood to establish accurate pack capacity values in production. However, all of this takes time and hence please use this as a first approximation.
An overview of the basics from how a battery works to End of Life.
The power is determined by the C-rate of the cell and as a very rough first guess you can multiply the energy of the pack in kWh by the C-rate. Hence a 50kWh pack with a cell capable of delivering a 2C discharge rate will give approximately 100kW.
However, this is a very rough approximation.
- Resistance of the cells, connections, busbars and HV distribution system will determine the power and energy capability of the pack.
- Variation in cell capacity and resistance along with number of cells in series and parallel will determine the actual energy capacity of any pack.
- Temperature management of the cells and variations across the pack will influence power and energy.
The pack capability is always determined by the weakest cell and the weakest cell can be a different cell depending on the parameters under which the pack is being required to work.
The options for the cooling system depend on the usage cycles, selected cell, ambient conditions and what cooling systems are available for the installation. The high level goals are:
- minimise the temperature gradient across the cell <3°C
- minimise the cell to cell temperature <3°C
- do not exceed cell maximum temperature <60°C
- assist the cells in heating up to a fully operational temperature, typically >0°C
These are typical/indicative values and all cells have variations on these parameters.
There may also be a requirement to size a battery pack to have a passive thermal system, as such the heat capacity of the pack would need to be sized to suit the typical usage cycle.
The thermal and electrical performance of the pack are the first things to look at when sizing a battery pack.
Remember: the pack is only as good as the weakest cell. This weakest cell can be the one that is too cold or too hot.
A look at the inputs you will need to do a basic conceptual pack sizing exercise. This is a list of data grouped by major subject along with comments based on experience of doing this work.
Aircraft Battery Pack Sizing
- 400 Wh/kg required at the system level
- 1000’s of cycles
- Extremely high power requirements (C-rates) during takeoff and landing
- Cruise power for long range flights
- High reliability, limited maintenance
- Improved safety for thermal runaway events