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
apparent power is the volt-ampere (VA). The apparent power is used to express the electrical capacity
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]
cosΦ is called the power factor and is expressed as λ. It indicates the portion of the apparent power
that becomes true power.
Reactive Power
If current I lags voltage U by Φ, current I can be broken down into a component in the same direction
as voltage U, IcosΦ, and a perpendicular component, IsinΦ. Active power P, which is equal to UIcosΦ,
is the product of voltage U and the current component IcosΦ. The product of voltage U and the current
component IsinΦ is called the reactive power. It is expressed as Q. The unit of reactive power is the
var.
Q = UIsin
Φ [var]
Φ
U
I
Icos
Φ
Isin
Φ
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)
