YOKOGAWA WT1800 User Manual page 121

AC Power
AC power cannot be determined as easily as DC power, because of the phase difference between the
voltage and current caused by load.
If the instantaneous voltage u = U
instantaneous AC power p is as follows:
p = u × i = U
U and I represent the rms voltage and rms current, respectively.
p is the sum of the time-independent term, UIcosΦ, and the AC component term of the voltage or
current at twice the frequency, –UIcos(2ωt – Φ).
AC power refers to the mean power over 1 period. When the mean over 1 period is taken, AC power P
is as follows:
P = UIcosΦ [ W ]
Even if the voltage and current are the same, the power varies depending on the phase difference Φ.
The section above the horizontal axis in the figure below represents positive power (power supplied
to the load), and the section below the horizontal axis represents negative power (power fed back
from the load). The difference between the positive and negative powers is the power consumed by
the load. As the phase difference between the voltage and current increases, the negative power
increases. At Φ = π/2, the positive and negative powers are equal, and the load consumes no power.
When the phase difference between voltage and current is 0
u
0
When the phase difference between voltage and current is Φ
u
p
0
Negative
Φ
power
When phase difference between voltage and current is
u
p
π
2
0
The positive and negative powers are the same
IM WT1801-03EN
Appendix 2 Power Basics (Power, harmonics, and AC RLC circuits)
sinωt and the instantaneous current i = Imsin(ωt – Φ), the
m
sinωt × I sin(ωt – Φ) = UIcosΦ – UIcos(2ωt – Φ)
m m
p
Positive
power
Average power
P = UI
π
2π ωt
i
Positive power
i
π
2π ωt
i Average power
P = UIcos
π ωt
2π
Average power
P = UIcosΦ
π
2
π
= 0
2
1
2
3
4
5
6
App
Index
App-15