Calculating required amount of batteries for powering a motor

Hi everyone, I have spent a long time trying to work the following calculation out however feel as though my lack of understanding in electronics is letting me down somewhere.

I am trying to power a motor with 65kW of power at 300V, the source of power is from 18650 cells. A single cell provides a nominal voltage of 3.6V and has a capacity of 3.45 Ah. The motor must be powered by these cells for at least 30 minutes.

I first began by calculating the amount of batteries I require in series which was given by dividing the required supply voltage by the nominal battery voltage, this gave me a rough requirement of 84 cells to achieve 302.4V which is sufficient.

Knowing that when cells are connected in series the capacity remains the same, I can say that I will have 84 cells giving 302.4V with a capacity of 3.45Ah.

Now I must address my need to power the motor for 30 minutes, to do this I need to work out how many parallel banks are required. First I begin by determining how much current the motor requires to produce 65kW at 300V. This is done by dividing the power requirement by the voltage input - 65000/300=217A. I convert this to Ah by multiplying by 0.5 (for half an hour run time) and get a value of 108.33Ah.

So now I know my capacity requirement is 108.33 Ah I can calculate the amount of parallel cells I will need as follows:

108.33/3.45=31.4 which I can round up to 32 banks. This means I need 34 sets of 84 cells connected in series to power the motor for half an hour. The configuration can be written as 84S34P.

Overall this gives me a requirement of 32*84=2688 cells, with a rough mass of 45g per cell I get a total weight of 120kg.

I have tried my best to work this out to the best of my knowledge but still feel like I may have made an incorrect assumption somewhere along the calculations. If someone could please let me know if I have gone wrong somewhere then I would be very grateful. Thank you for your help.

Looks about right to me, except that you should derate the battery capacity by about 50% to account for the manufacturers’ tendencies to exaggerate, the effects of age, temperature variations, etc.

So double the battery banks to 64, or about 5000 cells total. Spendy project!

Note that lithium based cells have special charge/discharge requirements that must be rigorously obeyed. If you do not understand these requirements well enough or do not have the professional skills to design the circuitry, you are much more likely to create a death trap than a useful power source. Think early model Samsung Note7, multiplied by 1000.

NiMH cells are much safer.

Thank you for confirming my calculations Jim. I was hoping I would be wrong somewhere as the battery pack will be powering a race car and I cant imagine packing it with 240kg of batteries when the car itself is meant to weight around 250kg total! Back to the drawing board for me.

In terms of charging I am hoping to break the battery pack up into smaller banks to reduce the voltage of each bank and then have them all connected up in series but also include some type of BMS for all of them to reduce any risks that come with lithium cells.

Half an hour is a long time to drive, with the motor putting out the full 65 kW.

That might be the equivalent of driving 100 kilometers in a full sized vehicle, so you would be in the performance ballpark of a commercial electric vehicle.

Companies that make those vehicles employ teams of professional electrical and mechanical engineers, combined with stringent real world testing to refine their designs.

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