UPS Battery Size & Runtime Calculations
How to size a battery back-up systems!
AC power measurements are related as follows:
VA = Volts x Amps only if PF = 1. If PF is smaller than 1 then Volts x Amps = Watts and Watts ÷ PF = VA
Volts = 230 typical, Amps = Load Current and Power Factor = between 0 and 1
Power factor is a number between 0 and 1 which represents the fraction of the load current which provides useful energy (Watts) to the load. Only in an electrical heater or incandescent light bulb is the power factor equal to 1; for all other equipment, some of the load current flows into and then back out of the load without delivering watts. This current, composed of distortion or reactive currents, is the result of the nature of the electronic load. The important point to understand is this distortion or reactive current, which is forced to exist due to the load, causes the load V-A rating to be larger than the load-watt rating. The Watt rating system can be thought of as a special case of the V-A measurement system, namely, the case where the power factor is equal to 1.
How to calculate battery runtimes
With over 25 years experience in the backup power industry, the directors at PHD Powerhouse have pretty much seen it all. However, the one thing that consumers consistently fail to understand is battery sizing for backup power systems. Very often consumers will opt for a lower cost quote on a backup system without looking at the finer detail. In an attempt to win orders, unscrupulous vendors will often skimp on the batteries, making ludicrous claims on runtimes. By offering smaller battery capacities, huge savings can be realised but the runtime claims are often unachievable. Here’s how PHD Powerhouse recommends you calculate battery requirements to ensure that you get what you are asking for. There are a number of factors which influence battery selection:
It stands to reason that the bigger the load that one wants to support, the greater the capacity of the batteries should be. In our example we will use a load of 1000W.
2. Required runtime
As in point 1 above, the longer the required runtime, the greater the battery capacity will have to be. In our example we will use a required runtime of 1 hour.
3. Charger Type
UPS’s cannot accommodate an infinite battery capacity. The battery capacity is therefore limited to the size of the charger. Usually, the battery capacity should be no more than 12x the maximum charge current ie. a 5A charger can only accommodate 60AH of batteries (5 x 12 =60). however, if discharges are expected to be less frequent than once in every 10 days, one may in extreme cases go to 20x the maximum charge current. We will assume that our UPS has a 10A charger.
4. DC Bus
The DC Bus is the voltage required by the inverter to operate and dictates the number of batteries in series required to drive the inverter. This information is available from the UPS supplier and should be clearly indicated in their spec sheets. DC busses range from 12V (1 x battery) to 480V (40 x batteries). We will assume a DC bus of 36V (3 x batteries).
5. UPS Efficiency (Inverter)
Inverters use some of the energy supplied by the batteries to run the internal electronics and so not all of the battery capacity is available to run the load. Also, some of the energy is lost due to cabling and connections particularly if there are long run’s of DC cables. For our example we’ll assume a 70% inverter efficiency.
6. Battery Type
There are many types of batteries available on the market today and since PHD is not a battery specialist, we will not make recommendations here. However, as a rule we use fully sealed, maintenance-free, deep cycle lead-acid batteries which are common to the industry. It is important to remember that batteries discharge exponentially faster at higher loads than at lower loads, so if a battery provides 1 hour runtime at 5A it will provide significantly less than 30min at 10A – usually in the order of 10 to 15% less. For total accuracy it is important to refer to the discharge curves of the particular battery manufacturer however, PHD uses a few rules of thumb to increase runtime accuracies.
1. For runtimes below 2 hours, a factor of 1.5 is applied to the final required battery current.
2. For runtimes above 2 hours, a factor of 1.3 is applied to the final required battery current.
From the above information we have the following:
Load = 1000W
DC Bus = 36V (3 x 12V batteries)
Required runtime = 60mins
Inverter efficiency = 70%
Charger = 10A
First we need to calculate the current required to run the load and the inverter:
I = Load / (70%) / (DC Bus)
I = 1000 / 0.7 / 36
I = 39.68A
From the above we can see that to supply our load and inverter for 1 hour, the battery will have to supply 39.68A for 1 hour = 39.68AH. However, using our rule of thumb for the exponential nature of battery discharge curves, we need to increase the required current by a factor of 1.5
I = 39.68 x 1.5
I = 59.52
A 59.52AH battery will therefore be required to provide 1 hour’s runtime to the load of 1000W. However, manufacturers do not manufacture batteries of 59.52AH so the next biggest standard size should be selected. In this case a 65AH battery. Finally, since the DC Bus requires a 36V input 3 x 12V, 65AH batteries connected in series will be required to complete the system. The above calculations may seem a little daunting
and many consumers may feel it unnecessary to learn something that they may need once in a lifetime. So here’s a basic rule to ensure that when comparing quotes one compares apples with apples. Remember “the devil is in the details” so always ask for a breakdown when getting a quote for a backup system. Ensure that the UPS, batteries, cabinets and installation are each quoted on a separate line with a full description including the number and capacity of batteries. That way, one is easily able to understand the discrepancies between competing quotes.