8-9
IM WT5000-01EN
Apparent Power and Reactive Power Computation Types (S,Q
Formula)
There are three types of power: active power, reactive power, and apparent power. In general, they are defined
by the following equations.
Active power P = UIcosΦ
(1)
Reactive power Q = UIsinΦ (2)
Apparent power S = UI
(3)
U = rms voltage; I = rms current; Φ = Phase difference between voltage and current
The power values are related as follows:
(Apparent power S)
2
= (Active power P)
2
+ (Reactive power S)
2
(4)
The three-phase power is the sum of the power of each phase.
These definitions only apply for sine waves. The measured values for apparent power and reactive power
vary for distorted waveform measurement depending on which of the above definitions are combined for the
computation. Because the equations for deriving the apparent and reactive power for distorted waveforms are
not defined, none of the equations can be said to be more correct than the other. Therefore, this instrument
allows you to select the apparent power and reactive power equations.
Unlike apparent power and reactive power, active power is derived directly from the sampled data, so errors
resulting from different definitions do not occur.
Type 1 (Type 1) (The method used in the normal mode of conventional WT series power meters)
This instrument calculates the apparent power of each phase using equation 3, calculates the reactive power of
each phase using equation 2, and sums the results to derive the power.
Active power for a three-phase four-wire system
PΣ = P1 + P2 + P3
Apparent power for a three-phase four-wire system SΣ = S1 + S2 + S3 ( = U1 × I1 + U2 × I2 + U3 × I3)
Reactive power for a three-phase four-wire system QΣ = Q1 + Q2 + Q3
(= s1× (U1×I1)
2
−P1
2
+ s2× (U2×I2)
2
−P2
2
+ s3× (U3×I3)
2
−P3
2
)
The signs for s1, s2, and s3 are negative when the current leads the voltage and positive when the current lags
the voltage.
Type 2 (Type 2)
This instrument calculates the apparent power of each phase using equation 3 and sums the results to derive
the three-phase apparent power. This instrument calculates the three-phase reactive power from the three-
phase apparent power and the three-phase active power using equation 4.
Active power for a three-phase four-wire system
PΣ = P1 + P2 + P3
Apparent power for a three-phase four-wire system SΣ = S1 + S2 + S3 ( = U1 × I1 + U2 × I2 + U3 × I3)
Reactive power for a three-phase four-wire system
QΣ = SΣ
2
−PΣ
2
Type 3 (Type 3) (The method used in the harmonic measurement modes of the WT1600, WT3000 and
PZ4000)
This instrument calculates the reactive power of each phase using equation 2 and calculates the three-phase
apparent power using equation 4.
Active power for a three-phase four-wire system
P
Σ = P1 + P2 + P3
Apparent power for a three-phase four-wire system
SΣ = PΣ
2
+QΣ
2
Reactive power for a three-phase four-wire system QΣ = Q1 + Q2 + Q3
8 Computation Function
