ADE7761B
Power Factor Considerations
ACTIVE POWER CALCULATION
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.
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).
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°.
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS
ACTIVE POWER SIGNAL
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
CURRENT
VOLTAGE
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS
ACTIVE POWER SIGNAL
DIGITAL-TO-
FREQUENCY
V × I
2
F1
F2
× cos(60°)
0V
CH1
CH2
PGA
ADC
ADC
HPF
MULTIPLIER
DIGITAL-TO-
FREQUENCY
LPF
VOLTAGE
CURRENT
CF
60°
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
sinusoidal, the active power component of the instantaneous
power signal (dc term) is given by
V × I
p(t) = i(t) × v(t)
WHERE:
v(t) = V × cos(ωt)
V × I
2
i(t) = I × cos(ωt)
(V × I/2) × cos(60°)
V × I
2
p(t) =
{1 + cos (2ωt)}
This is the correct active power calculation.
Nonsinusoidal Voltage and Current
TIME
Figure 22. Signal Processing Block Diagram
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.
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.
v(t) = V + 2 × ∞ V ×sin(hωt + α )
(1)
∑
O
h
h
h ≠0
where:
v(t) is the instantaneous voltage.
VO is the average value.
Vh is the rms value of Voltage Harmonic h.
αh is the phase angle of the voltage harmonic.
Rev. 0 | Page 14 of 24
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