## When sizing a UPS and Generator Power Protection System – What are the factors in calculating power?

Selection of the respective power values must take into account the factors presented below.

NOTE – Quick Calculation

## Uninterruptible Power Supplies ( UPS )

**REMEMBER –**

It usually takes up to 4 hours to recover from a one-hour power loss

• Scale your UPS allowing for future growth of 25% as a minimum growth factor and bearing in

mind that any UPS should never run consistently with more than 75% load

• Choose a UPS equipped with a built-in active filter or a PFC rectifier (drawing a sinusoidal signal) to avoid the negative effects of harmonics on a Diesel Generator and the need for the generator to be twice the size of the UPS in kVA

To calculate these easily you can download our Power Calculator app from the Apple App Store for free – Click Here to download.

## Diesel Generators (Gensets)

• The increase in the size of the Diesel Generator 2:1 ( rule of thumb is 2 to 1), so for example a 100kVA UPS requires a 200kVA Diesel Generator

• Make sure the Diesel Generator power rating can also handle battery charging at Diesel Generator start (see the example below)

• Calculate how many minutes you require the UPS battery backup to have, as well as how many hours you wish the Diesel Generator tanks to run (at least 8- 12 hours of running time)

To calculate these easily you can download our Power Calculator app from the Apple App Store for free – Click Here to download.

Example

This example presents how to calculate the Diesel Generator power rating, assuming that appropriate filtering is installed (active or PFC) and that load-shedding is not an option.

The rated power Pn (kVA) of a UPS is the maximum output power given an output power factor of 0.8. It is necessary to calculate the corresponding input power to determine the Diesel Generator power rating

**UPS**

A 100 kVA UPS supplies the load with a maximum output power factor of 100 x 0.8 = 80 kW.

And surprisingly a Generator is virtually the same power factor

**GENERATOR**

A 100 kVA DIESEL GENERATOR supplies the load with a maximum output power of 100 x 0.75 = 75 kW

### Power Factor

NOTE – Diesel Generators have a power factor of around 0.75

Gas Generators have a power factor of around 0.50

LPG Generators have a power factor of around 0.45

Given UPS efficiency and the current required to charge the battery, the input power is greater than the output value.

For example,

if the increase is 18% (value supplied by the manufacturer), the necessary input power is Pe = 80 x 1.18 = 94.4 kW.

The Diesel Generator must be sized to supply power Pg such that:

if the input power factor is 0.8, then Pg > 94.4 / 0.8 = 118 kVA. In this case where both the

• input and output power factors are equal to 0.8, it is possible to calculate the result as 100kVA x 1.18 = 118 kVA

• if the UPS has a PFC rectifier with a power factor close to 1 (> 0.95), then Pg > 94.4 / 0.95 = 99.3 kVA

UPS input current when charging the battery

Diesel Generator rated power must be sufficient to supply the UPS when the rectifier-charger is both supplying the load (load current) and recharging the battery (lb current) .

This is the situation when the Diesel Generator starts to supply the UPS, i.e. approximately 60 to 90 seconds after the beginning of the power outage, when the battery is partially discharged.

Possible harmonics and harmonic filter at the UPS input

To supply the inverter with DC current, the UPS is equipped with an SCR-based rectifier that draws harmonics which distort the sinusoidal waveform of the input current (see fig. 3) and the upstream voltage.

Distortion is measured as Total Harmonic Distortion (THD):

THD% = (rms value of all harmonics) / (rms value of the fundamental) in %

Depending on whether current or voltage distortion is measured, the terms used are:

• THDI where I stands for current

• THDU where U stands for voltage

To eliminate the harmonic currents, UPSs are equipped with :

• either an input filter, which can be:

– a passive LC filter, compensated or non-compensated, with or without a contactor,

– a double-bridge or phase-shifting filter (harmonic recombination),

– an active filter, derived from active harmonic conditioners.

These filters reduce distortion from approximately 30%) to less that 5%

• or a “clean” rectifier of the PFC (Power Factor Correction using control electronics) type that does not draw harmonics. In this case (without a filter), THDI drops to under 3%. Both solutions meet the requirements of standard IEC / EN 61000-3-4 for low-voltage devices drawing less than 16 A, i.e

• THDI < 5% at the UPS input

• THDU = 5% on the upstream busbars

• no individual harmonic order higher than 5%

**Behaviour of a Diesel Generator with harmonics**

The Diesel Generator is designed to supply linear loads. The presence of harmonics makes it necessary to take action to ensure compatibility, due to the possible repercussions on the Diesel Generator.

• Regulation difficulties

The distortion increases the rms value of the output voltage and thus disturbs Diesel Generator regulation, which is based on the rms value of sinusoidal voltage. What is more, the high time constant of the flux variations in the windings makes corrections difficult.

• Temperature rise in generator winding because the harmonics increase the rms current

• Amplification of the harmonics (1) with a number of consequences:

– an increase in voltage distortion (THDU, normally limited to 5%) on the upstream busbars during operation on Diesel Generator power,

– a reduction in the input power factor (< 0.8)

The subtransient reactance X”d of a generator is approximately 10 to 12%, compared to 3 or 4% for the short-circuit voltage of a transformer.

In other words, the output impedance of a Diesel Generator is 2 to 4 times higher than that of a transformer. Each harmonic order lHk, a sinusoidal current k times the fundamental frequency, is amplified compared to normal operation on utility power with the output impedance of the transformer.

**What are the possible solutions?**

Oversize the Diesel Generator

A classic solution to avoid the effects of harmonics is to oversize the Diesel Generator.

The power rating of the diesel generator is 2 times greater than that of the UPS. For example 2:1 ratio

This increase in power makes it possible to handle the temperature rise in coils, to ensure correct regulation and to obtain a higher output impedance.

Reduce the level of harmonics drawn by the UPS

First we need to understand that the industry average of THDi is around 5%.

A modern True On-Line UPS designed to reduce the level of harmonics drawn by the rectifier is built to be around 5%. Should there be any requirement to have a lower THDi then this is possible using either.

• a built-in active filter optimised for the UPS power rating and input rectifier. This type of filter eliminates a large part of the harmonic spectrum and reduces the THDI to less than 3%

• a clean PFC (Power Factor Correction) rectifier that draws a sinusoidal signal. The residual THDI is less than 2%. UPS systems of less than 2% are rare and extremely expensive

Either of these two options are costly and only ever required where extremely sensitive equipment is used – military / medical.

To calculate these easily you can download our Power Calculator app from the Apple App Store for free – Click Here to download.