YOKOGAWA wt3000, User Manual, Page: 351 / 384

App-19
IM 760301-01E
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App App
Index
Appendix
• AC Power
Because there is phase difference between the voltage and current due to the load,
AC power cannot be determined as easily as DC power.
If we denote the instantaneous voltage as u = U
m
sin ω t and the instantaneous current
as i = I
m
sin( ω t – φ ), the instantaneous power of AC power p is as follows:
p = u × i = U
m
sin ω t × I
m
sin( ω t – φ ) = UIcos φ – UIcos(2 ω t – φ )
U and I represent the rms voltage and current, respectively.
p is the sum of the time-independent term “UIcos φ ” and the AC component term of the
voltage or current at twice the frequency “–UIcos(2
ω
t –
φ
).”
AC power refers to the average power over 1 period. By taking the average over 1
period, AC power P becomes
P=UIcos φ [W]
The power varies even with the same voltage and current 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 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.
p
0
π
2
π
i
u
ω
t
Average power
P = UI
When the phase difference between voltage and current is 0
Positive
power
p
0
π
i
u
ω
t
Average power
P = UIcos
φ
Negative
power
φ
Positive power
When the phase difference between voltage and current is
φ
2
π
p
0 2
π
i
u
ω
t
Average power
P = UIcos
The positive and negative powers are the same.
2
π
= 0
2
π
When the phase difference between voltage and current is 2
π
π
Appendix 4 Power Basics (Power, Harmonics, and RLC of AC Circuits)