App-10
IM WT310E-01EN
Active Power and the Power Factor
In alternating electrical current, not all of the power calculated by the product of voltage and current,
UI, is consumed. The product of U and I is called the apparent power. It is expressed as S. The unit of
apparentpoweristhevolt-ampere(VA).Theapparentpowerisusedtoexpresstheelectricalcapacity
of a device that runs on AC electricity.
The true power that a device consumes is called active power (or effective power). It is expressed as P.
This power corresponds to the AC power discussed in the previous section.
S=UI[VA]
P=UIcos
Φ
[W]
cosΦiscalledthepowerfactorandisexpressedasλ.Itindicatestheportionoftheapparentpower
that becomes true power.
Reactive Power
IfcurrentIlagsvoltageUbyΦ,currentIcanbebrokendownintoacomponentinthesamedirection
asvoltageU,IcosΦ,andaperpendicularcomponent,IsinΦ.ActivepowerP,whichisequaltoUIcosΦ,
istheproductofvoltageUandthecurrentcomponentIcosΦ.TheproductofvoltageUandthecurrent
componentIsinΦiscalledthereactivepower.ItisexpressedasQ.Theunitofreactivepoweristhe
var.
Q=UIsin
Φ
[var]
Φ
U
I
IcosΦ
IsinΦ
The relationship between S, the apparent power, P, the active power, and Q, the reactive power is as
follows:
S
2
=P
2
+ Q
2
Appendix 2 Power Basics (Power, harmonics, and AC RLC circuits)
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