# Battery Charge and Discharge Time Calculations

## Main Question or Discussion Point

I am performing some calculations but struck with confusion whether I am doing it correct or wrong due to contradictions of these calculations on different calculators websites. I hope here someone will help me with the validation of my calculations.

Code:
Battery Capacity            = 150 Ah
Battery Nominal Voltage     = 666 V
Efficiency Charge/Discharge = 0.87
Power Demand                = 100 kW
Current Demand              = 150 A

Battery Discharge Time = (Battery Capacity x Battery Voltage x Efficiency ) / Power Demand
Battery Discharge Time = (150 x 666 x 0.87) / 100000
Battery Discharge Time = 0.87 Hours
Battery Discharge Time = 51 Minutes

Alternative Method

Battery Discharge Time = (Battery Capacity x Efficiency) / Current Demand
Battery Discharge Time = (150 *0.87)/150
Battery Discharge Time = 0.87 Hours
Battery Discharge Time = 51 Minutes
Q1) If above both calculations are correct does it mean that I can constantly draw 100 kW from the battery for 51 minutes?

Q2) This website tells a different story for calculating a run time when you put 150 Ah and 100000 W Load = 0.015 Hour Run time

Q3) What is 10 in the equation given on this website for calculating run time. Run time = (10 * Ampere Hours) / Load in Watts

Thank You

Last edited by a moderator:

Related Electrical Engineering News on Phys.org
BvU
Homework Helper
Hello shahabkhan, $\quad$ $\quad$ !

Q1) Yes. But they are not correct
Q2) Yes it does
Q3) It has the dimension of voltage, so I suspect the calculation is for a 12 V car battery which should not be discharged more than down to 20% of capacity (either that, or they use an assumed efficiency of 0.8)

Trying to discharge a 100 kWh battery with 100 kW is a very, very bad idea.

(Step 3 here, among other much more dangerous things)

I actually read the link you gave and the equations I used in my first post are also referenced from there.

Q1) If the calculations are not correct can you please help me fixing them. Once I have found the correct calculations I can limit the charge and discharge cap from 20% to 80% in matlab.

Drawing 100 kW from 100 kWh battery is not essential in my case. I was just referencing it so i can find the correct equations. Power demand will fluctuate between 1 kW to 70 kW just when needed for few minutes.

Hello shahabkhan, $\quad$ $\quad$ !

Q1) Yes. But they are not correct
Q2) Yes it does
Q3) It has the dimension of voltage, so I suspect the calculation is for a 12 V car battery which should not be discharged more than down to 20% of capacity (either that, or they use an assumed efficiency of 0.8)

Trying to discharge a 100 kWh battery with 100 kW is a very, very bad idea.

(Step 3 here, among other much more dangerous things)

tech99
Gold Member
Q3) What is 10 in the equation given on this website for calculating run time. Run time = (10 * Ampere Hours) / Load in Watts

Thank You
A battery is inefficient when you discharge it quickly. I think the 10 means that for maximum energy transfer, it is best to do it over 10 hours - the 10 hour rate as it is called. Similarly with charging.

BvU
Homework Helper
A battery is inefficient when you discharge it quickly. I think the 10 means that for maximum energy transfer, it is best to do it over 10 hours - the 10 hour rate as it is called. Similarly with charging.
As I said, the 10 has the dimension of voltage, not time.
Power demand will fluctuate between 1 kW to 70 kW just when needed for few minutes
So what's it used for ? And how is the battery put together ?

So what's it used for ? And how is the battery put together ?
It will be used in hybrid vehicle along with 100 kW fuel cell.

Battery will be used along side fuel cell to meet higher power demand.

In current duty cycle maximum power demand is 150 kW for approximately 10-15 minutes throughout 40 minutes journey.

BvU
russ_watters
Mentor
Q1) If above both calculations are correct does it mean that I can constantly draw 100 kW from the battery for 51 minutes?
The calculation/answer looks correct to me. But as said, results of an actual test may vary due to the high discharge rate.

Tom.G
It would depend on the battery chemistry, Lead-Acid vs Li-Ion for instance.

Lead-Acid batteries are generally rated in AH based on a 10 hour discharge rate. If you discharge at 10 times that rate, 1 hour in your case, they can supply around 5% of their rated capacity.

You could probably get 65%-75% from a Li-Ion battery under the same discharge conditions.

Here are some curves for the two chemistries:

url=https://electronics.stackexchange.com/questions/273345/how-does-voltage-progress-during-discharge-of-a-battery&psig=AOvVaw1IGYYBVunaPhzD6P0kvhG2&ust=1574661829762700

Li-Ion curve from:
https://www.mpoweruk.com/images/discharge-C-rate.gifFrom https://www.mpoweruk.com/performance.htm

Cheers,
Tom

anorlunda
Mentor
It will be used in hybrid vehicle along with 100 kW fuel cell.
If that is your project, then you need to go much deeper into the real battery characteristics than those extremely simple formulas.

You need the discharge curves that @Tom.G linked.

You need the condition and age of the batteries.

You need temperatures, and sensitivity of batteries.

You need to consider battery lifetime.

You need to consider power versus time. It will not continue to deliver the same power all the way down to zero charge.

Efficiency is a function of discharge rate.

It goes on and on. My point is that you need to go much deeper.

You need the discharge curves that @Tom.G linked.
You need the condition and age of the batteries.
You need temperatures, and sensitivity of batteries.
You need to consider battery lifetime.
You need to consider power versus time. It will not continue to deliver the same power all the way down to zero charge.
Efficiency is a function of discharge rate.
It goes on and on. My point is that you need to go much deeper.
Amusing that if I control the charge discharge rate, health, temperature and power demand in matlab according to battery specifications, the above calculation I have done in first pose are theoretically correct? Can I use them as a base for my rest of calculations and state of charge calculations?

anorlunda
Mentor
Amusing that if I control the charge discharge rate, health, temperature and power demand in matlab according to battery specifications, the above calculation I have done in first pose are theoretically correct?
Did you look at the links that @Tom.G provided? One of them is a curve.
Did you read the articles at batteryuniversity.com?

Things like that are normally treated empirically, not theoretically.

Did you look at the links that @Tom.G provided? One of them is a curve.
Did you read the articles at batteryuniversity.com?

View attachment 253361

Things like that are normally treated empirically, not theoretically.
Based on above curves, If I design a look up table and then use it in matlab would be a good idea?

sophiecentaur
Gold Member
It will be used in hybrid vehicle along with 100 kW fuel cell.

Battery will be used along side fuel cell to meet higher power demand.

In current duty cycle maximum power demand is 150 kW for approximately 10-15 minutes throughout 40 minutes journey.
I imagine a lot of the really important and recent design information for electric cars will be industrial secrets but have you read around this subject as much as humanly possible? Look at the detailed specifications of as many existing models that you can get hold of. (And also test reviews in the magazines) You need to do this before you start considering any alternative designs of your own. You can benefit by other people's mistakes.

I imagine a lot of the really important and recent design information for electric cars will be industrial secrets but have you read around this subject as much as humanly possible? Look at the detailed specifications of as many existing models that you can get hold of. (And also test reviews in the magazines) You need to do this before you start considering any alternative designs of your own. You can benefit by other people's mistakes.

I guess the discussion is going way off from the original question. I can manage the life and health calculation of the battery with algorithm with some estimations and efficiencies.

What actually I was asking for the validation of my equations in general.

anorlunda
Mentor
What actually I was asking for the validation of my equations in general.
Efficiency relates energy out to energy in. It should not be in the formula of discharge time.

Other than that, yes you can use that formula to get an estimate of discharge time with an accuracy of maybe plus/minus 50%.