Pack Sizing

In simple terms this will be based on the energy and power demands of the application.

usable SoC for different applications

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
  • temperature
    • 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.

pack series and paralle

Cell Capacity and Pack Size

There are very good reasons for selecting a battery cell and using it for multiple applications, thus leveraging the maximum buying opportunity for one cell rather than splitting this across 2 or 3 different cells.

This means that the specifications of the cell will be fixed. Let us suppose we select a 50Ah cell with a nominal cell voltage of 3.6V

A 400V pack would be arranged with 96 cells in series, 2 cells in parallel would create pack with a total energy of 34.6kWh

Changing the number of cells in series by 1 gives a change in total energy of 3.6V x 2 x 50Ah = 360Wh.

Increasing or decreasing the number of cells in parallel changes the total energy by 96 x 3.6V x 50Ah = 17,280Wh.

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:

  • 3.6V
  • 12V
  • 48V
  • 400V
  • 800V

One thing we have to remember is that it is extremely difficult to design a pack with a very high power density and a very high energy density.

Some of this is due to the trade in cell design requirements between energy and power.

However, at pack level high power designs require more cooling power, bigger busbars and larger contactors + fuses.

graph of actual battery pack data showing power density versus energy density

Peak vs continuous power is a recurring question across the electrification space. We need to deliver a repeatable amount of power for the user to have confidence in the machine and we need high power numbers to deliver the brochure wow factor. The transient peak power works well for a number of vehicle applications. However, a lot of commercial applications are all about the continuous power capability.

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.

The battery pack mass is roughly 1.6x the cell mass, based on benchmarking data from >160 packs.

However, there are a number of estimation options and always the fallback will be to list and weigh all of the components.

Battery Basics

Battery Basics

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.

Cooling System

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.

Thermal

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.

Ageing

Of course, with all of the sizing you need to consider the pack ageing, fundamentally over time the battery will:

  1. decrease in capacity
  2. increase in resistance

That means the available energy will decrease, the power will decrease and the charge time will increase. These factors are really important if this means the battery cannot meet the basic requirements:

  • vehicle range
  • gradient performance – eg fully loaded bus that traverses a hill on it’s route
  • maximum speed
  • usable time between charging – eg your mobile phone battery limited to 4 hours between charges

Ageing is complex and requires a lot of cell data to establish the cell behaviour under all use scenarios. However, it is important to set the target requirements for the battery pack so that you can use this to assess cell options.


Inputs to Pack Sizing

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

NASA electrified aircraft

Electrified Aircraft Propulsion Targets

  • 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