 # Electrical and Power Protection Formulas

The information below is provided for guidance only and general project discussions. Measurements and calculations for your specific project must be made by certified engineers. A summary of terms can be found in our website glossary.

## Apparent Power (VA, kVA or MVA)

Apparent Power is the current drawn by a load at a given supply voltage measured in VA or kVA or MVA. This is the generally accepted formula for UPS and voltage stabiliser sizing when considering IT-related hardware (non-linear loads).

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.

Single Phase Loads: if an electrical device is connected to a 230Vac single-phase supply and the current drawn by this device is 10 Amps, the resulting VA value would be:

10 × 230 = 2300VA or 2.3kVA

Three Phase Loads: a 15kVA three phase UPS supplies 5kVA per phase. To size a three-phase UPS the total kVA per phase must first be calculated and then compared to ensure balanced load sharing across the phases. The maximum kVA per phase should then be used to size the overall UPS. For example if the maximum load is 10kVA then the UPS should be sized for 30kVA (3×10kVA).

## Real Power (W, kW, MW, GW)

Watts is a unit of measure for the Real Power (also referred to as Active Power) dissipated by a load. This value is generally used to calculate a generator or battery size. Some UPS now use Real Power as their rating as they have a Unity Power Factor and therefore can be considered to draw their power like as a linear-type load.

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 × 230 = 2300W or 2.3kW

Three Phase Loads: the maximum kW per phase should be identified and used to calculate the three-phase requirements. If this is 10kW maximum per phase, the power protection device should be sized at 30kW (3×10kW).

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

Total kVA or kW x 1.25

It is also sound engineering practice to build in headroom of 10-20% for reduced component stress and ‘wear and tear’ i.e. run a UPS at 80-90% of its rating. So a 100kW generator would have a load of 80-90kW maximum.

(Total kVA or kW x 1.25) / 0.8 or 0.9

## Power Factor

Power factor is the ratio of real power (W) to 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

Therefore, 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)

## Reactive Power

Reactive power is effectively wasted power and is typically only considered when considering a generator or power factor correction system.

Reactive Power (VAr) = √(Apparent Power² – Real Power²)

## Battery Sizing

The battery load can be calculated using the formula:

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

The overall load on the battery to take into account the load on the UPS and efficiency losses within the UPS itself. The Battery Load and 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 × 150Ah Battery Strings

Total number of battery blocks = 2 × 40 = 80

## Battery Recharge Time

The recharge curve is non-linear. A general rule of thumb to an 80% recharge is:

Recharge Time (Hrs) = Battery Ah / Charging Amps

## Solar PV Panel Battery Charging

Solar PV panels have a Peak Power Watt (Wp) rating under standard test conditions. For example: 1000W/m² of sunlight (‘peak sun’), 25ºC and air mass of 1.5. Their output varies depending on the amount of solar radiation then receive, module temperature (decreases with temperature) and connected load voltage.

Sunlight data is given in terms of ‘mean daily peak sun hours’ at a given site. For example, daily solar radiation is averaged out to give equivalent number of hours of ‘peak sun’ (or kWh/m²).

For battery charging applications the Peak Current rating should be used as solar PV modules only produce their Peak Power at their Peak Voltage.

Expected Output (Ah) = Current at Peak Output (Amps) x Peak Sun Hours

The Expected Output (Ah) can be multiplied by the battery voltage to give energy output (Wh). Where a solar PV inverter has a wide input voltage range, the Maximum Power Point Tracking (MPPT) will allow the solar PV modules to work at their optimum voltage allowing the following formula to be used:

Expected Output (Wh) = Peak Power (Wp) x Peak Sun Hours (h)

## Energy Savings

From Ohms Law we can calculate the Real Power (W, kW, MW, GW) used by a load or total loads within a building:

Power = Supply Voltage (V²) / R

R = Resistance and is a constant factor of a load and associated supply cabling. Electricity is charged for in kWh (KiloWattHours) and so the more the supply voltage is reduced the lower the number of kWh charged for within a given period.

## Energy Efficiency

The most commonly used data centre energy efficiency ratio is Power Usage Effectiveness (PUE):

PUE = Total Facility Energy / IT Equipment Energy

Uninterruptible Power Supplies form part of the Total Facility Energy and therefore the higher the UPS efficiency the lower the PUE ratio with 1 being the ideal target number.

GPUE adds a green element to PUE calculations. GPUE includes how much sustainable energy a data centre uses, its carbon footprint per usable kilowatt hour (kWh).