ADE7761AARS-REF Analog Devices Inc, ADE7761AARS-REF Datasheet - Page 15

• Manufacturer Part Number: ADE7761AARS-REF
• Description: IC DETECTOR ENERGY METER 20-SSOP
• Manufacturer: Analog Devices Inc

Specifications of ADE7761AARS-REF

• Lead Free Status / RoHS Status: Contains lead / RoHS non-compliant

where:
i(t) is the instantaneous current.
I
I
β
Using Equation 1 and Equation 2, the active power P can be
expressed in terms of its fundamental active power (P
harmonic active power (P
where:
and
As can be seen in Equation 4, a harmonic active power component
is generated for every harmonic provided that the harmonic is
present in both the voltage and current waveforms. The power
factor calculation was previously shown to be accurate in the
case of a pure sinusoid; therefore, the harmonic active power
must also correctly account for the power factor because it is
made up of a series of pure sinusoids.
Note that the input bandwidth of the analog inputs is 7 kHz
with an internal oscillator frequency of 450 kHz.
HPF and Offset Effects
Equation 5 shows the effect of offsets on the active power
calculation. Figure 24 shows the effect of offsets on the active
power calculation in the frequency domain.
As can be seen in Equation 5 and Figure 24, 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 calculation. This problem is
easily avoided in the ADE7761A 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).
V
(
V
O
h
V
h
is the rms value of current harmonic h.
0
) (
is the dc component.
is the phase angle of the current harmonic.
0
t
×
+
P = P
P
Φ
t i
×
P
Φ
I
) (
1
V
1
H
1
t I
h
= V
) (
1
= α
+
=
=
=
×
V
1
h
∑
α
I
=
1
1
+ P
∞
cos(
=
1
O
× I
h
− β
2
×
2
V
−
+
H
h
I
1
ω
1
β
×
1
cos(Φ
h
t
2
I
+
))
h
×
V
×
×
h
∑
0
∞
(
cos(
≠
1
I
×
0
)
0
I
h
I
+
H
Φ
1
×
).
I
×
sin(
h
1
)
×
cos(
h
cos(
ω
ω
t
t
ω
+
)
β
t
+
))
h
V
)
=
1
×
I
0
×
cos(
1
ω
) and
t
)
Rev. 0 | Page 15 of 24
(2)
(3)
(4)
(5)
The HPF in Channel 1 has an associated phase response that is
compensated for on-chip. Figure 25 and Figure 26 show the
phase error between channels with the compensation network
activated. The ADE7761A is phase compensated up to 1 kHz as
shown, which ensures a correct active harmonic power calculation
even at low power factors.
Figure 24. Effect of Channel Offsets on the Active Power Calculation
–0.05
–0.10
–0.05
–0.10
0.30
0.25
0.20
0.15
0.10
0.05
0.30
0.25
0.20
0.15
0.10
0.05
V
1
0
0
2
Figure 26. Phase Error Between Channels (40 Hz to 70 Hz)
× I
0
40
Figure 25. Phase Error Between Channels (0 Hz to 1 kHz)
1
0ϖ
100
45
200
DC COMPONENT (INCLUDING ERROR TERM)
IS EXTRACTED BY THE LPF FOR ACTIVE
POWER CALCULATION
300
50
V
V
FREQUENCY (RAD/S)
1
0
FREQUENCY (Hz)
400
FREQUENCY (Hz)
× I
× I
0
1
500
55
2ω
600
60
700
800
ADE7761A
65
900
1000
70