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ADE7761A
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).
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°.
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.
V×I
2
0V
INSTANTANEOUS
POWER SIGNAL
CURRENT
VOLTAGE
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS
ACTIVE POWER SIGNAL
INSTANTANEOUS
ACTIVE POWER SIGNAL
CH1
PGA
ADC
HPF
DIGITAL-TO-
FREQUENCY
F1
F2
V×I
2
× cos(60°)
0V
CH2
ADC
MULTIPLIER
LPF
DIGITAL-TO-
FREQUENCY
CF
VOLTAGE
60°
CURRENT
Figure 23. Active Power Calculation over PF
INSTANTANEOUS
INSTANTANEOUS
POWER SIGNAL –p(t)
ACTIVE POWER SIGNAL
If one assumes that the voltage and current waveforms are
V×I
p(t) = i(t).v(t)
sinusoidal, the active power component of the instantaneous
v(t) = V × cos( ω t)
WHERE:
V×I
i(t) = I × cos( ω t) 2
p(t) = V × I {1 + cos (2 ω t)}
2
TIME
Figure 22. Signal Processing Block Diagram
The low frequency output of the ADE7761A 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
power signal (dc term) is given by
( V × I /2) × cos(60°)
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
v ( t ) = V O + 2 × ∑ V h × sin( h ω t + α h )
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.
∞
h ≠ 0
where:
v(t) is the instantaneous voltage.
(1)
V O is the average value.
V h is the rms value of voltage harmonic h.
α h is the phase angle of the voltage harmonic.
Rev. 0 | Page 14 of 24
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