ADE7752BARW AD [Analog Devices], ADE7752BARW Datasheet - Page 14

• Manufacturer Part Number: ADE7752BARW
• Description: Polyphase Energy Metering IC with Pulsed Output
• Manufacturer: AD [Analog Devices]

ADE7752B
This is the correct active power calculation.
NONSINUSOIDAL VOLTAGE AND CURRENT
The active power calculation method also holds true for non-
sinusoidal current and voltage waveforms. All voltage and
current waveforms in practical applications have some
harmonic content. Using the Fourier Transform, instantaneous
voltage and current waveforms can be expressed in terms of
their harmonic content
where:
v ( t ) is the instantaneous voltage.
V
V
and α
V × I
v
2
( )
O
n
t
is the average value.
is the rms value of voltage harmonic n .
× cos(60°)
=
n
V
is the phase angle of the voltage harmonic.
Figure 16. DC Component of Instantaneous Power Signal
o
V × I
+
2
0V
0V
2
×
CURRENT
VOLTAGE
VOLTAGE
∑
n
∞
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS
POWER SIGNAL
=
0
V
n
×
sin
(
n
60°
ω
t
+
α
n
INSTANTANEOUS
ACTIVE POWER SIGNAL
)
CURRENT
INSTANTANEOUS
ACTIVE POWER SIGNAL
Rev. PrA | Page 14 of 27
(2)
where:
i(t) is the instantaneous current.
I
I
β
Using Equations 2 and 3, the active power, P, can be expressed
in terms of its fundamental active power (P
active power (P
where:
As can be seen from Equation 5, a harmonic active power
component is generated for every harmonic, provided that
harmonic is present in both the voltage and current waveforms.
The power factor calculation has been shown to be accurate in
the case of a pure sinusoid. Therefore, the harmonic active
power also correctly accounts for power factor since harmonics
are made up of a series of pure sinusoids. A limiting factor on
harmonic measurement is the bandwidth. On the ADE7752B,
the bandwidth of the active power measurement is 14 kHz with
a master clock frequency of 10 MHz.
O
n
n
is the rms value of current harmonic n.
is the dc component.
is the phase angle of the current harmonic.
φ
t i
P
φ
P
( )
1
1
n
H
=
=
=
=
=
α
V
α
I
∑
n
1
1
O
∞
n
=
−
×
1
−
+
V
H
β
β
I
n
).
1
n
1
2
cos
×
×
Preliminary Technical Data
I
n
∑
n
φ
∞
=
1
cos
0
V
P = P
φ
n
n
I
×
sin
1
+ P
(
n
H
ω
t
β
n
)
1
) and harmonic
(3)
(4)
(5)