App-16
IM 760201-01E
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
m
sin
ω
t and the instantaneous current i = I
m
sin(
ω
t –
f
),
the instantaneous AC power p is as follows:
p = u × i = U
m
sin
ω
t × I
m
sin(
ω
t –
f
) = UIcos
f
– UIcos(2
ω
t –
f
)
U and I represent the rms voltage and rms current, respectively.
p is the sum of the time-independent term UIcos
f
and the AC component term of the
voltage or current at twice the frequency –UIcos(2
ω
t –
f
).”
AC power refers to the average power over 1 period. When the average over 1 period is
taken, AC power P is as follows:
P = UIcos
f
[W]
Even if the voltage and current are the same, the power varies depending on the phase
difference
f
. 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
f
=
π
/2, the positive and negative
powers are equal, and the load consumes no power.
p
0
P
2
P
i
u
W
t
Average power
P=UI
When the phase difference between voltage and current is 0
Positive
power
p
0
P
i
u
W
t
Average power
P=UIcos
F
Negative
power
F
Positive power
When the phase difference between voltage and current is
F
2
P
p
0
2
P
i
u
W
t
Average power
P=UIcos
The positive and negative powers are the same
2
P
= 0
2
P
When phase difference between voltage and current is 2
P
P
Appendix 3 Power Basics (Power, harmonics, and AC RLC circuits)
