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kVA, kW, KVAr and Power Factor
AC power is made up of three components, VA (apparent power), W (real power) and VAr (reactive power). This
document is intended to describe these three elements with specific interest to generator engineers.
o VA = Volts x Amps (resistive load)
VA is called Apparent Power
• Typical resistive loads are filament bulbs, strip heaters, domestic cookers.
o VAr = Volts x Reactive Amps (capacitive and inductive load)
VAr is called Reactive Power or Wattless Power as none of the VAr is absorbed
by the load. Although VAr is of no use to use, we still have to be aware of it as
extra current is required from the alternator to create the reactive power, which
means the generator is doing more work, and switchgear, cables etc must be
made larger to cater for this extra power transmission, even though it is not being
used by the load. This means inefficiency and more cost.
VAr is produced only by the alternator. More VAr = higher alternator field
excitation. The engine does not see the work required to create VAr, no extra fuel
is required to create more VAr.
Capacitive load is negative (-VAr)
• Typical capacitive loads are fluorescent lights, Switched mode power
supplies such as Personal Computers, Uninterruptable Power Supplies,
Inductive load is positive (+VAr)
• Typical inductive loads are electric fans, other motors, induction cookers.
o W = V x A x Power Factor
W is called Watts or Real Power.
Watts are created by the engine. Increasing W while maintain a fixed voltage
from the alternator requires more fuel for the engine.
A typical site load consists of :
Resistive loads (VA), Inductive loads (+VAr) and Capacitive loads (-VAr)
056-026 kW and kVAr Issue 1 – A.D.Manton
o Power factor = Cos Φ (see overleaf for explanation)
Power factor is abbreviated to pf
pf = A power factor of 1 indicates that all the power provided by the generator is
Real Power, being absorbed by the load. There is no reactive power.
A power factor factor of 0 indicates that there is no real power, only reactive
power and it is all being returned to the source, the load is not absorbing any
A power factor between 0 and 1 indicates varying amounts of Real and Reactive
Where the VAr is a negative value, the power factor is said to be Leading
Where the VAr is a positive value, the power factor is said to be Lagging
Generators are designed to operate with a Lagging power factor. Alternator
manufacturers provide capability curves to show the desired region of operation.
All this information can be shown in a phasor diagram :
Apparent Power (VA) is
given by adding together the
W and the VAr vectors.
Reactive Power
(VAr) is at 90° to the
Real Power (W) so
is drawn on the
vertical axis.
We call this angle Φ
(pronounced phi)
Real Power (W) is drawn on the
horizontal axis (0°)
o This shows that the VA is a larger value than the W (If the VAr is zero, VA=W)
Calculating the VAr rating of a genset
o Most generators are rated for a power factor (W \ VA) of 0.8
o From Pythagoras :
Cos Φ = W / VA
Cos Φ = 0.8
Φ = Cos-1 0.8 = 36.87°
o From this we can calculate the VAr rating of the typical 0.8 pf rated generator as :
Tan Φ = VAr / W
VAr = Tan 36.87 x W
VAr = 0.75 x W
o Or to simplify this, the VAr rating of a 0.8 pf rated generator is ¾ of the W rating.
056-026 kW and kVAr Issue 1 – A.D.Manton