Battery Calculations

for use with

Inverters & Portable Power Systems

If you are intent on buying a marine or deep cycle battery at some point as part of an inverter, battery and charger system to provide power for your equipment outdoors, then there are a few things you need to be aware of when calculating battery life, capacity, losses and discharge rates etc.

These issues are mostly covered in my sections on inverters, batteries and busking power, so have a read through them to get a better understanding of the different variables involved. You might then want to do a few calculations and see if this sort of set up is the right option for you.

In this section we’ll go through the basic things you need to consider and then work through some simple calculations to help you get an idea of how to go about choosing your system.

Here are some units of measurement you might need to know before you start.

Battery Capacity in Amp hour (Ah)
Current drawn in Amps (I)
Time taken in Hours (H)
Voltage of power source in Volts (V)
Power in Watts (W)

Battery Ratings, Variables and Losses

An approximate measurement of a battery’s ability to provide energy i.e it’s charge capacity, is it’s rating in ampere hours (Ah) or amp hours.

So a 100 Ah battery will produce 100 amps for 1 hour.

This capacity can be divided up any way you choose.

100 Ah could produce 1 amp for 100 hours, or 50 amps for 2 hours, 4 amps for 25 hours or 25 amps for 4 hours etc.

Battery capacity (Ah) = Current drawn (I) x Time (H)

or you could cross multiply and get..

Time = Battery capacity / Current drawn

Current drawn = Battery capacity / Time

So when choosing a battery for your set up, you need to know how many amps you will be drawing and for how long.

There are other things that also need to be taken into consideration when calculating a battery’s useable capacity.

When you discharge a battery by consuming the power stored in it, you should never discharge it beyond a certain point, otherwise you risk damaging it’s future storage capacity.

The maximum discharge level depends on the type and quality of the battery.

A true deep cycle battery from an RV, golf cart or forklift truck etc. can be expensive but should have a discharge capacity of up to 80%. Leisure batteries and marine batteries will be much less at around 50%, but no matter how good the battery is, if you want it to last and not pack up after a few months of use, it is generally accepted that you should never discharge a battery by more than 50% of it’s capacity.

You must also take into account, the battery’s listed ‘amp hour rating time’ when you buy it, and the speed that you intend to drain the battery when you use it. These two factors can dramatically affect the battery’s capacity. These are covered in my page on batteries.

Inverter losses also come into the equation when selecting batteries. This is also covered in my section on inverters and worked through in our calculations below.

Batteries are usually sold in voltages of 6v, 12v or 24v

To work out how much power you can get out of a battery you can use the equation..

P = V I

Power (Watts) = Voltage of battery (V) x Current drawn in amps (I)

The world’s first manned plane powered by 160 AA conventional dry-cell batteries. Produced by Japan’s Matsushita Electric Industrial Co.

Worked Example

Say we were in need of a power set up for a small outdoor gig and we needed enough power to enable us to play for at least 4 hours.

Firstly we work out how much power we will be using at our gig by adding together the power consumption used by each piece of equipment.

I have given an example of how to do this in my inverters guide.

Say the power consumption of all our gear put together is 400 watts rms (per hour)

Batteries become less efficient as they get older and the level of inefficiency really depends on the way you look after them. If you choose to take this into account you can always add an extra percentage (15 – 35 %) to your power consumption needs for a future buffer.

In this example we won’t worry about that too much, purely for the reason that we are not going to be drawing 400w constantly for the whole 4 hour event. As we are dealing with live music, the power consumption will vary greatly with volumes and song breaks etc. and as our batteries will be newly purchased, they should perform well.

As stated previously, for longevity it is unwise to discharge any battery to below 50% of its full capacity, even if it is a deep cycle battery capable of being discharged by up to 80%

So if we need to get 400 w of power using only half of our battery’s stored energy, it means the full capability of our battery bank should be able to supply at least 800 watts an hour over that 4 hour period. This would leave us with half a tank by the end of the event.

Needing 800 watts capacity to run our gear, and using a battery – inverter set up, we must also to take into consideration the inefficiencies of the inverter, this is explained in my inverter calculations guide.

Allowing for inverter efficiency of 90%, therefore using an inefficiency factor of 1.1 we would need to put

800 x 1.1 = 880 w

into the inverter to get 800 w out the other side.

So all in all, we need to buy a battery that can deliver 880 watts per hour for 4 hours. This will allow us to compensate for inverter losses and to only have to discharge the battery to 50% every time we use it to power our gig rig.

If we purchase 12 volt batteries and need 880 watts for 4 hours, then we can work out the Ah rating of the batteries we need to buy.

Battery Capacity (Ah) = Current in Amps (I) x Time (H)

We need to establish the current drawn (I) by our system.

P = V I

Power (watts) = Voltage (V) x Current drawn in Amps (I)

I = P/V

880/12 = 73.333 amps

So our battery capacity in Ah would need to be

Battery Capacity (Ah) = Current drawn (A) x Time (H)

4 x 73.33 = 293 Ah

In this instance, you would need to have around 300 Ah of battery power to do the job, cover losses and take care of your battery life.

You could achieve this with 3 x 100 Ah 12v batteries connected in parallel, giving you 300 Ah at 12v.

See my page on connecting batteries in series and parallel to find out how.

You might find in reality this gives you a much greater capacity than you actually need as we’ve originally calculated for a constant supply of 400w. The noise levels and power used in a live music situation is going to vary greatly over time so your average draw is probably going to be less than you have designed for.

In a live situation though, having a greater battery capacity than you need is never a bad thing.

More Compensations to Watch Out For

One thing you may have to watch out for is your ‘amp hour rating time’. This subject has been covered on my batteries page. We will assume the capacity figures we are given for the batteries we buy will be rated under the 8 hour amp rating time and not the 100 hour rating time. This means our batteries’ labeled capacities are accurate for our needs as they were tested and rated in similar circumstances to how we intend to use them.

(Had they been rated under the 100 hour amp rating and not the 8 hour time, then we might have had to compensate our final capacity by up to 20 %)

Also, as our batteries are to be drained to half their capacity over a 4 hour period (simulating an 8 hour full discharge) we don’t have to compensate for an excessive or quick current drain. Peukert’s law suggests that consuming a battery’s charge at very high current rates (i.e draining the whole cell in 1 hour) can reduce the capability of a battery by anything up to 50%.

In our case, none of the above conditions need to be considered. As long as you are aware of them, you can take steps to compensate if they arise in future.

The Easy Method

Let’s not forget the easy method of doing things. Using a clamp on ammeter, which you should be able to get for around £20, set your equipment up in your own home and measure the current draw on a normal household supply. Use the results and a few power equations to calculate the correct sized batteries for your needs.

Now you know what sort of battery bank you’ll need, go and check out my inverter page. You’ll also need to find a good charger to keep your batteries topped up.

If you need to step up your power requirements to greater levels, then increase the amount of batteries you use or if you’ve got the cash, go out and buy your self a honda gas generator.

By the end of my power guides, you should have a good idea of what will best suit your needs.

…

For time and legal reasons I don’t answer reader’s questions on calculations or individual set up’s, but if you need to know anything about creating your own power set up or need advice on calculations, make sure you fully read through my battery guide and posts on inverters, battery calculations and battery connections.

There you should find all you need to know to help you get started.

…

Other Posts of Interest

Batteries
Busking & Gigging Power – Outdoors
Battery Connections
Inverters

Back Home