ADE7761
Using Equations 1 and 2, the active power P can be expressed in
terms of its fundamental active power (P1) and harmonic active
power (PH):
DC COMPONENT (INCLUDING ERROR TERM)
IS EXTRACTED BY THE LPF FOR ACTIVE
POWER CALCULATION
V
× I
1
1
2
P = P1 + PH
where:
V
V
× I
× I
1
0
0
1
P1 = V1 × I1 cos(Φ1 )
(3)
Φ1 = α1 −β1
2v
FREQUENCY (RAD/S)
0v
and
Figure 22. Effect of Channel Offsets on the Active Power Calculation
PH
=
∞ V ×I ×cos(Φ )
∑
0.30
0.25
0.20
0.15
h
h
h
h =2
(4)
Φh = αh −βh
As can be seen from Equation 4, 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 previously been shown to be
accurate in the case of a pure sinusoid; the harmonic active
power must, therefore, also correctly account for power factor,
because it is made up of a series of pure sinusoids.
0.10
0.05
0
–0.05
–0.10
Note that the input bandwidth of the analog inputs is 7 kHz
with the internal oscillator frequency of 450 kHz.
0
100 200 300 400 500 600 700 800 900 1000
FREQUENCY (Hz)
HPF and Offset Effects
Figure 23. Phase Error between Channels (0 Hz to 1 kHz)
Equation 5 shows the effect of offsets on the active power
calculation. Figure 22 shows the effect of offsets on the active
power calculation in the frequency domain.
0.30
0.25
0.20
0.15
0.10
V(t)× I(t) =
(V0 +V1 × cos(ωt))×(I0 + I1 × cos(ωt)) =
V1 × I1
(5)
V0 × I1 +
+V0 × I1 × cos(ωt) +V1 × I0 × cos(ωt)
2
0.05
0
As can be seen from Equation 5 and Figure 22, an offset on
Channel 1 and Channel 2 contributes a dc component after
multiplication. Because this dc component is extracted by the
LPF and used to generate the active power information, the
offsets contribute a constant error to the active power calcula-
tion. This problem is easily avoided in the ADE7761 with the
HPF in Channel 1. By removing the offset from at least one
channel, no error component can be generated at dc by the
multiplication. Error terms at cos(ωt) are removed by the LPF
and the digital-to-frequency conversion (see the Digital-to-
Frequency Conversion section).
–0.05
–0.10
40
45
50
55
60
65
70
FREQUENCY (Hz)
Figure 24. Phase Error between Channels (40 Hz to 70 Hz)
The HPF in Channel 1 has an associated phase response that is
compensated for on-chip. Figure 23 and Figure 24 show the
phase error between channels with the compensation network
activated. The ADE7761 is phase compensated up to 1 kHz as
shown, which ensures correct active harmonic power
calculation even at low power factors.
Rev. A | Page 17 of 28
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