ade7762 Analog Devices, Inc., ade7762 Datasheet - Page 13

• Manufacturer Part Number: ade7762
• Description: Polyphase Energy Metering Ic With Phase Drop Indication
• Manufacturer: Analog Devices, Inc.

NONSINUSOIDAL VOLTAGE AND CURRENT
The active power calculation method also holds true for
nonsinusoidal current and voltage waveforms. All voltage and
current waveforms in practical applications have some har-
monic 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
α
V × I
2
O
n
n
is the average value.
is the rms value of voltage harmonic n.
is the phase angle of the voltage harmonic.
× cos(60°)
v
) (
t
Figure 13. DC Component of Instantaneous Power Signal
=
V × I
2
0V
0V
V
O
+
VOLTAGE
2
CURRENT
VOLTAGE
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS
POWER SIGNAL
×
n
∑
∞
=
0
V
n
×
sin
60°
(
n
ω
t
+
α
INSTANTANEOUS
ACTIVE POWER SIGNAL
n
CURRENT
INSTANTANEOUS
ACTIVE POWER SIGNAL
)
Rev. 0 | Page 13 of 28
(3)
where:
i(t) is the instantaneous current.
I
I
β
Using Equation 3 and Equation 4, the active power, P, can be
expressed in terms of its fundamental active power (P
harmonic active power (P
where:
As can be seen from Equation 6, 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 because
harmonics are made up of a series of pure sinusoids. A limiting
factor on harmonic measurement is the bandwidth. On the
ADE7762, 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.
P = P
t i
φ
φ
P
P
( )
1
H
1
n
=
=
=
=
=
1
V
α
α
n
∑
I
+ P
∞
=
O
1
n
1
1
V
×
−
−
+
H
n
β
I
β
×
1
n
1
2
cos
I
n
×
cos
n
∑
∞
φ
=
1
1
I
φ
H
n
n
).
×
sin
(
(
n
ω
t
)
( )
β
n
)
ADE7762
1
) and
(4)
(5)
(6)