8-8
IM WT1801-01EN
Apparent Power, Reactive Power, and Corrected Power
Equations (Formula)
Equation for Apparent Power (S Formula)
You can select the voltage and current to use to compute the apparent power (voltage × current) from the
following options.
• Urms*Irms
The product of the true rms values of the voltage and current
• Umean*Imean
The product of the voltage’s and current’s rectified mean values calibrated to the rms values
• Udc*Idc
The product of the simple averages of the voltage and current
• Umean*Irms
The product of the voltage’s rectified mean value calibrated to the rms value and the current’s true rms value
• Urmean*Irmean
The product of the voltage’s and current’s rectified mean values
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, the WT1800
provides three equations, Type 1 to Type 3, for determining the apparent power and reactive power.
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 (The method used in the normal mode of conventional WT series power meters)
The WT1800 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
The WT1800 calculates the apparent power of each phase using equation 3 and sums the results to derive
the three-phase apparent power. The WT1800 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
Q
Σ
= S
Σ
2
−
P
Σ
2
8 Computation
