# How to Size UPS Systems

It is relatively easy to calculate the size of UPS system you need to support a specific load using the following formulas:

## Apparent Power (VA)

UPS systems are typically quoted as having a VA rating. VA measures the ‘Apparent Power’ current drawn by the load multiplied by the voltage of the mains power supply.

Apparent Power (VA) = Supply Voltage (V) x Amps (A)

In the formula (V) is the Root Mean Square (RMS) of the supply voltage. Amps is the current drawn by the load and should be measured at start-up and whilst running.

Examples:

560VA = 230V x 2A

1000VA = 230V x 4A

For larger VA numbers the VA may be expressed as kVA by dividing the calculated sum by 1000.

1000VA divided by 1000 = 1kVA.

MVA is a larger unit of measure and is used for large UPS systems. 1MVA=1,000,000VA.

The above formula is suitable for calculating single-phase and non-linear loads such as IT servers and computers at the nominal voltage. In the UK the nominal single phase voltage is 230Vac.

For three phase loads, the VA or kVA is calculated per phase and the largest number is then multiplied by a factor of 3 to calculate the UPS size required. It is important to ensure that the phases are equally balanced to ensure load sharing across the phases.

For example if the maximum load is 20kVA then the UPS should be sized for 60kVA (3x10kVA).

Alternatively if the phases are balanced the individual calculations can be added together i.e.

12kVA+13kVA+11kVA = 36kVA or 40kVA being the nearest UPS size

## Safety Margin

It is recommended to add 20% to the calculated load to allow head-room for overload.

kVA size x 1.2 = Final UPS size

## Real Power (Watts)

Watts is a unit of measure for the Real Power (also referred to as the ‘Active Power’) dissipated by a load.

The Watts value is also used to calculate a generator or battery size.

Some UPS use Real Power as their size rating as they are rated at unity power factor and can be considered to draw their power as a linear-type load. At unity power factor:

Real Power (W) = Supply Voltage (V) x Amps (A)

Single Phase Loads: if a linear electrical device is connected to a 230Vac single-phase supply and the current drawn is 10 Amps, then the Watts dissipated will be:

10 x 230 = 2300W or 2.3kW

Three Phase Loads: the maximum kW per phase should be calculated and used to calculate the three-phase size. If this is 20kW maximum per phase, the power protection device should be sized at 60kW (3x20kW).

## Right-Sizing and Growth Factor

If the load is steady with no planned expansion it may not necessary to add a factor for future growth. Where expansion is required a factor from 20-25% should be added.

For most applications a typical growth factor for future expansion would be 25%.

Total kVA or kW x 1.25

## Load Power Factors

Power factor is the ratio of Real Power (W) / Apparent Power (VA) in an AC circuit and corresponds to the phase angle difference between the voltage and current waveforms drawn.

Power factor is calculated as a decimal number or percentage i.e. 0.65pF = 65% between 0-1pF and 0-100% respectively. Power Factor formulae include:

Power Factor (pF) = Real Power (W) ÷ Apparent Power (VA) = CosØ

If we know the Power Factor and Real Power we can calculate:

Apparent Power (VA) = Real Power (W) ÷ Power Factor (pF)

If we know the Apparent Power and Power Factor we can calculate:

Real Power (W) = Apparent Power (VA) x Power Factor (pF)

## UPS Battery Sizing

A UPS battery size can be be calculated using the formula:

Battery Load (kW) = (UPS kVA x Power Factor) / UPS Efficiency

The overall load on the battery should take into account the load on the UPS and the efficiency losses within the UPS itself.

The Battery Load and back-up time (runtime) required (minutes) is used to calculate the overall battery Ampere-Hour (Ah) size required of the battery string.

UPS and AC Inverters have a Vdc input voltage rating. This DC voltage can be supplied by a single battery or number of battery blocks in a battery string.

Number of batteries per string = Inverter Vdc Bus / Vdc Battery Block

For example a 480Vdc inverter using 12Vdc battery blocks will require one string of 40 batteries.

If the battery Ah required is 300Ah and we have a 150Ah Battery Blocks available, the Battery Set will require 2 strings to reach 300Ah.

300Ah Battery Set = 2 x 150Ah Battery Strings

Total number of battery blocks = 2 x 40 = 80

## Battery Recharge Time

Battery recharge curves are non-linear. A general rule of thumb to reach an 80% recharge is:

Recharge Time (Hrs) = Battery Ah / Charging Amps

This information on UPS and battery sizing is provided for guidance. Please contact the projects team at Server Room Environments who can guide you through the calculations and help you select the right uninterruptible power supply and battery runtime combination for your application.