ampere hour calculation

The ampere hour capacity of a battery cannot be directly calculated by practical method. For instance, a 12V battery connected to DG set has a rating of 180 Ampere Hour (AH). This means, it can give 180 amps continuous current for one hour. It DOES NOT mean battery can give 90 ampere of current for two hours. But it may supply 18 ampere for close to ten hours. It has to be obtained from the battery manufacturer only.

First you need to establish how low you want to discharge the battery. Some batteries can be taken to almost 0.0 charge while others need to remain above, for example, 0.4 charge. This number is a characteristic of the battery type and relates to battery life. Lets call this "floor" = β.

Then, you have to look at the discharge curve to see what Voltage you can expect between 1.0 and β charge. You will end up having to calculate for the Voltage at β charge even if the Voltage at 1.0 charge is much higher. Call this Voltage λ; depending on the battery characteristics and your operating point, λ may be even higher than 24 VDC.

Now, you might be tempted to calculate the Amp-hrs as

(4000 W)(2 hr)/λ and, on paper, this looks good. However, very few large batteries will tolerate being greatly drained in two hours. You can do this to a 6 VDC lantern battery, but not to a 600 Amp-hr lead-acid battery.

So now you have to go back to the discharge characteristics of the battery and determine the maximum continuous current draw from the battery.

Sorry for such a long answer to get to the answer, but here it is: You really have to know the battery characteristics to answer this question.

I = P/V

I = 4000 / 24 = 167 amp hrs. x 2 hrs = 333amp hrs. Since we should not discharge a battery below 50% which is about 12v (100% = 12.65 volts or so). (I am assuming your 24 volt battery is made up of (2) 12 v batteries in series). You would need 333 / 50% = 666 amp hrs of capacity per battery.

From battery point of view you may be right that 50% discharge is acceptable. But if you look on the system performance I doubt that one can go that low, Just imaging what performance a 24volts motor can give at 12Volts,

Pout = V²/R

rakesh_semwal I was speaking of a 12v minimum charge on a 12v battery assuming the 24v bank was built with 2 12v batteries in series. I don't have direct experience with 24v systems, but I would assume that the fully charged voltage of a 24 volt system is actually 25.1 volts. A 50% discharge would be 24 volts across the 24 volt bank.

sail4evr Point taken,I don't remember exact formula this point of time but i doubt that top 1.1 volts out of 25.1 can hold half of the charge.