Datasheet ADE7751 (Analog Devices) - 10

ADE7751 THEORY OF OPERATION
are sinusoidal, the real power component of the instantaneous The two ADCs digitize the voltage and current signals from the power signal (i.e., the dc term) is given by: current and voltage transducers. These ADCs are 16-bit second order sigma-delta converters with an oversampling rate of 900 kHz. V × I  cos (60 ) This analog input structure greatly simplifies transducer interfacing  (1) 2  × ° by providing a wide dynamic range for direct connection to the transducer and also by simplifying the antialiasing filter design. This is the correct real power calculation. A programmable gain stage in the current channel further facilitates easy transducer interfacing. A high-pass filter in the
INSTANTANEOUS INSTANTANEOUS POWER SIGNAL REAL POWER SIGNAL
current channel removes any dc component from the current signal. This eliminates any inaccuracies in the real power calcu- lation due to offsets in the voltage or current signals—see
V
ⴛ
I
HPF and Offset Effects section.
2
The real power calculation is derived from the instantaneous power signal. The instantaneous power signal is generated by a
0V
direct multiplication of the current and voltage signals. In order
CURRENT VOLTAGE
to extract the real power component (i.e., the dc component), the instantaneous power signal is low-pass filtered. Figure 2 illustrates the instantaneous real power signal and shows how the real power
INSTANTANEOUS INSTANTANEOUS POWER SIGNAL REAL POWER SIGNAL
information can be extracted by low-pass filtering the instantaneous power signal. This scheme correctly calculates real power for nonsinusoidal current and voltage waveforms at all power factors.
V
ⴛ
I
ⴛ
cos(60
ⴗ
)
All signal processing is carried out in the digital domain for
2
superior stability over temperature and time.
0V DIGITAL-TO- VOLTAGE CURRENT FREQUENCY HPF 60
ⴗ
F1
⌺
CH1 PGA ADC LPF F2
Figure 3. DC Component of Instantaneous Power Signal
MULTIPLIER DIGITAL-TO-
Conveys Real Power Information PF < 1
FREQUENCY CH2 ADC
⌺
Nonsinusoidal Voltage and Current CF
The real power calculation method also holds true for nonsinu- soidal current and voltage waveforms. All voltage and current
INSTANTANEOUS INSTANTANEOUS REAL
waveforms in practical applications will have some harmonic
POWER SIGNAL – p(t) POWER SIGNAL
content. Using the Fourier Transform, instantaneous voltage
V
ⴛ
I
and current waveforms can be expressed in terms of their
p(t) = i(t)
ⴛ
v(t) WHERE:
harmonic content.
V v(t) = V
ⴛ
I V
ⴛ
I
ⴛ
cos(
␻
t) i(t) = I
ⴛ
cos(
␻
t) 2
∞
2 p(t) = V
ⴛ
I {1+cos(2
␻
t)}
v(t) = V + 2 × ∑ V × sin(h t ω + α ) (2)
2
O h h h≠0
TIME
where: Figure 2. Signal Processing Block Diagram v(t) = The instantaneous voltage The low-frequency output of the ADE7751 is generated by VO = The average value accumulating this real power information. This low frequency Vh = The rms value of voltage harmonic h inherently means a long accumulation time between output and ␣ pulses. The output frequency is therefore proportional to the h = The phase angle of the voltage harmonic average real power. This average real power information can in turn be accumulated (e.g., by a counter) to generate real-energy ∞ information. Because of its high output frequency, and hence i(t ) = I + 2 × ∑ I × sin(h t ω + β O h h ) (3) h≠0 shorter integration time, the CF output is proportional to the where: instantaneous real power. This is useful for system calibration purposes that would take place under steady load conditions. i(t) = The instantaneous current IO = The dc component
Power Factor Considerations
Ih = The rms value of current harmonic h The method used to extract the real power information from the and instantaneous power signal (i.e., by low-pass filtering) is still ␤h = The phase angle of the current harmonic valid even when the voltage and current signals are not in phase. Figure 3 displays the unity power factor condition and a DPF (displacement power factor) = 0.5, i.e., current signal lagging the voltage by 60°. If we assume the voltage and current waveforms –10– REV. 0