Battery Power Demand Solution

Knowing the power demand for a battery cell or pack is really useful, but how do you turn that into a current demand?

The following image shows the solution we use in the Battery Calculations Workbook and in the Vehicle Model. At first it can look daunting, but it is quite simple, maybe too simple but it gives a good first estimation.

First of all we need to consider a battery cell and remember that it is not a perfect voltage source as it has an internal resistance. Hence, as we demand current the voltage will drop.

V_OCV is the Open Circuit Voltage of the cell and this changes with state of charge and with chemistry.

R_int is the internal resistance of the cell and this is dependent on my factors.

The resultant voltage V or V_Lpack as shown in the equations is then described by Ohm’s Law.

This post has been built based on the support and sponsorship from: Thermo Fisher Scientific, Eatron Technologies, About:Energy, Quarto Technical Services and Alvatek.

If we look at the simple circuit showing a cell or pack and the internal resistance. We have a power demand, P_pack applied across the terminals and a resultant current of I_Lpack.

We can write an equation for the voltage across the terminals under load:

We need to rearrange this so that we can solve it:

Then rearranging again we see that we have a quadratic to solve:

The quadratic has two solutions:

the solution for the voltage under load is:

now we know the voltage under load it means we can easily calculate the current under load:

This can be applied to a cell, module or a pack.

Battery Calculations Workbook

If you don’t want to code this then you can use the workbook. This allows you to enter the fields and solve the equations to estimate current, heating and battery temperature.