# Determining Battery Charging and Discharging Rate Based on Max Current and Nominal Voltage

I am having difficulty in figuring out some basic stuff and confused with multiple equations.

I am working on a simulator which simulate a hybrid vehicle journey for some period of time. During journey the vehicle brakes and regenerate energy.

• How much energy vehicle is regenerating at each braking event in kWh.
• How long is each braking event in seconds (Time).

Battery specifications are:

Storage                = 30.6 kWh or 46 Ah

Max Peak Power         = 406 kW for 10 Sec

Voltage                = Nominal = 666 V , Min = 486 V , Max = 756 V

Battery Ratting        = 6C

Battery max Charge / max Discharge Rate per hour = 6C * 46 Ah = 276 A


Question:

All I want to know is that in one second time, how much energy I can send to battery and discharge from battery?

So in my algorithm I can automate the code to send only the amount of energy which battery can absorb for such given period of time and destroy rest in brake resistors.

I have tried this method but I am not sure if I am doing it correct.

please correct me if I am wrong.

Energy = V x I x T

Energy = 666(V) x 46(Ah) x 1 (hr) = 30636 Wh.

Now, Battery ratting is 6C. So,

Charge/Discharge current = 6 x 46 = 276 A.

Now, with 6C ratting:

Time to charge or Discharge (Run Time) = 46 (Ah) / 276 (A) = 0.17 hr

Run Time in Minutes = 0.17 x 60 = 10.20 Min

From this I can calculate 30636 Wh /10 min = 3063.6 Wh energy can be charged and discharged from battery each minute. (for 10 minutes period)

Considering this, 3063.6 wh / 60 sec = 51.06 wh energy can be charged or discharged from battery at each second at 6C rating.

Again for Ws = 30636*3600 = 110289600 Ws /10 min = 11028960 Ws energy can be charged and discharged from battery each minute. (for 10 minutes period)

Please correct me if I am wrong and guide me to perform these calculations properly.

• Energy is power multiplied by time, not divided by time. It'd Ws, not W/sec. – Transistor Dec 5 '18 at 23:42
• This one is going to need some fine tuning for clarity. First thing, when you include calculations, include units for everything, show the formula you start with and show you're work, so Energy = 666 x 540 = 35964 Wh should expand to Energy = \$formula = 666V * 540 (unit?) = 35964 Wh for example. It would help to include why you're doing the simulation and the desired performance. Is it something you['re putting together for practice or curiosity, or does it need to be accurate to a specific degree? – K H Dec 5 '18 at 23:45
• You may or may not want to take into account that the battery voltage will be changing as the battery drains/or is recharged, and that this will affect necessary output current at a given load and also system efficiency. – K H Dec 5 '18 at 23:50
• Some of your battery specs don't comport with others. For example, the peak power rating, the voltage range of the battery, the "C" rating and battery capacity don't all match up well. – jonk Dec 6 '18 at 1:42
• @Transistor You are right. I just realized my Current (I) value is also wrong, It should be 46 Ah in calculation. I figure out this, please correct me if I am wrong. W = V x I x T = 666(V) x 46(Ah) x 1 (hr) = 30636 Wh. Now, Battery ratting is 6C so Charge/Discharge current = 6 x 46 = 276 A. Now, Time to charge or Discharge (Run Time) = 46 (Ah) / 276( A) = 0.17 hr. Run Time in Minutes (0.17 x 60 = 10.20 Min. From this I can calculate 30636 Wh /10 min = 3063.6 Wh energy required per min to charge the battery and 3063.6 Wh / 60 Sec = 51.06 Wh energy required per second to charge my battery. – Sohail Naeem Dec 7 '18 at 1:09

I am having difficulty in figuring out some basic stuff and confused with multiple equations.

When in difficulty multiply out the units to see if they make sense. We'll see some errors below.

How much energy vehicle is regenerating at each braking event in kWh.

Good. Energy = Power x time = kW x h = kWh. This is correct.

Battery specifications are:

Storage = 30.6 kWh or 46 Ah

So you have assumed that battery voltage = $$\ \frac {P}{I} = \frac {30.6k}{46} = 665\ \text V \$$. That's fine.

Max Peak Power = 406 kW for 10 Sec

OK, but let's use 's' for seconds as in the SI standard units.

Continuous Power (RMS) = 77 kW

RMS is supposed to be used to find the equivalent DC voltage or current for a voltage or current waveform. It doesn't make sense in power measurements as the average is what is required.

Voltage = Nominal = 666 V, min = 486 V, max = 756 V

OK. Add a space between the numbers and the units for clarity. e.g., "6 cars", not "6cars". This is recommended in the SI standard. No spaces before commas.

Battery Rating = 6C

Battery max Charge / max Discharge Rate per hour = 6C * 46 Ah = 276 A

Here you're a little mixed up again. The ampere already is a rate measurement. It's the amount of charge (coulombs) per second. "Discharge rate per hour" doesn't make sense. Just say "max discharge rate = 276 A".

But now we see a problem. 276 A is the 6C rate which means that it will be all over (charging or discharging) in 1/6 hours = 10 minutes.

How can I calculate how much maximum energy my battery can absorb?

The battery can only absorb the amount of energy required to fully charge it from its current state + losses due to heat. I'm not a battery expert but I would expect that the maximum charge rate would be close to the maximum discharge rate.

So in my algorithm I can automate the code to send only the amount of energy which battery can absorb for such given period of time and destroy rest in brake resistors.

That seems fair.

Energy = Power Time = Voltage x Current x 1 Hour

Make that "power x time" and that is correct if you sustain it for one hour.

Energy = 666 x 276 x 1 = 183816 Wh

That's 183 kWh but at the start of the question you had calculated the actual capacity at 30.6 kWh. Your 1 hour needs to be divided by 6.

Energy = 183816 /60/60 = 51.06 Wsec

No, if you are converting Wh to Ws then you would multiply by 3600. So energy = 183 kWh = 183k x 3600 = 659 MWs (MJ, megajoules). (But don't forget that 183 kWh is wrong to start with.)

So the battery can absorb 0.05106 kW per second

No, kW/s is nonsense.

As @jonk has suggested, hit the edit link under your question, clean it up taking care with your numbers and units and then ask the question at the end.

Update after edit.

I think you're making it more complicated than you need to. Just figure out the charge / discharge power, $$\ P = VI = 666 \times 276 = 182484 \ \text W = 180 \ \text {kW} \$$ to two significant figures.

Energy transfer rate at this power will be 180 kWs or 180 kJ. (This should make it easy to convert back and forth between electrical and kinetic energy.

Considering this, 3063.6 Wh / 60 sec = 51.06 Wh energy can be charged or discharged from battery at each second at 6C rating.

To convert from kWs to kWh divide by 3600.