ADE7761BARS-REF AD [Analog Devices], ADE7761BARS-REF Datasheet - Page 14

• Manufacturer Part Number: ADE7761BARS-REF
• Description: Energy Metering IC with On-Chip Fault and Missing Neutral Detection
• Manufacturer: AD [Analog Devices]

ADE7761B
ACTIVE POWER CALCULATION
The ADCs digitize the voltage signals from the current and
voltage transducers. A high-pass filter in the current channel
removes any dc component from the current signal. This eliminates
any inaccuracies in the active power calculation due to offsets in
the voltage or current signals (see the HPF and Offset Effects
section).
The active power calculation is derived from the instantaneous
power signal. The instantaneous power signal is generated by
a direct multiplication of the current and voltage signals.
To extract the active power component (dc component), the
instantaneous power signal is low-pass filtered. Figure 22 illustrates
the instantaneous active power signal and shows how the active
power information can be extracted by low-pass filtering the
instantaneous power signal. This scheme correctly calculates
active power for nonsinusoidal current and voltage waveforms
at all power factors. All signal processing is carried out in the
digital domain for superior stability over temperature and time.
The low frequency output of the ADE7761B is generated by
accumulating this active power information. This low frequency
inherently means a long accumulation time between output
pulses. The output frequency is, therefore, proportional to the
average active power. This average active power information
can, in turn, be accumulated (for example, by a counter) to
generate active energy information. Because of its high output
frequency and, therefore, shorter integration time, the CF
output is proportional to the instantaneous active power. This is
useful for system calibration purposes that take place under
steady load conditions.
CH1
CH2
V × I
PGA
TIME
Figure 22. Signal Processing Block Diagram
POWER SIGNAL –p(t)
ADC
ADC
INSTANTANEOUS
p(t) = i(t) × v(t)
WHERE:
MULTIPLIER
v(t) = V × cos(ωt)
i(t) = I × cos(ωt)
p(t) = V × I {1 + cos (2ωt)}
HPF
2
ACTIVE POWER SIGNAL
INSTANTANEOUS
LPF
V × I
2
FREQUENCY
FREQUENCY
DIGITAL-TO-
DIGITAL-TO-
CF
F1
F2
Rev. 0 | Page 14 of 24
Power Factor Considerations
The method used to extract the active power information from
the instantaneous power signal (by low-pass filtering) is still valid
even when the voltage and current signals are not in phase.
Figure 23 displays the unity power factor condition and a
displacement power factor (DPF = 0.5), that is, current signal
lagging the voltage by 60°.
If one assumes that the voltage and current waveforms are
sinusoidal, the active power component of the instantaneous
power signal (dc term) is given by
This is the correct active power calculation.
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
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
α
V × I
2
h
O
h
is the phase angle of the voltage harmonic.
is the rms value of Voltage Harmonic h.
is the average value.
× cos(60°)
( V × I /2) × cos(60°)
v
) (
t
V × I
2
0V
0V
=
V
O
CURRENT
VOLTAGE
Figure 23. Active Power Calculation over PF
+
VOLTAGE
2
INSTANTANEOUS
POWER SIGNAL
×
INSTANTANEOUS
POWER SIGNAL
h
∑
∞
≠
0
V
h
×
sin(
60°
h
ω
t
INSTANTANEOUS
ACTIVE POWER SIGNAL
+
α
h
CURRENT
INSTANTANEOUS
ACTIVE POWER SIGNAL
)
(1)