ade7880 Analog Devices, Inc., ade7880 Datasheet - Page 46

• Manufacturer Part Number: ade7880
• Description: Polyphase Multifunction Energy Metering Ic With Harmonic Monitoring
• Manufacturer: Analog Devices, Inc.

ADE7880
where nT is the accumulation time.
Note that line cycle active energy accumulation uses the same
signal path as the active energy accumulation. The LSB size of
these two methods is equivalent.
FUNDAMENTAL REACTIVE POWER CALCULATION
The ADE7880 computes the fundamental reactive power, the
power determined only by the fundamental components of the
voltages and currents.
The ADE7880 also computes the harmonic reactive powers, the
reactive powers determined by the harmonic components of the
voltages and currents. Please see Harmonics calculations
section for details. A load that contains a reactive element
(inductor or capacitor) produces a phase difference between the
applied ac voltage and the resulting current. The power associated
with reactive elements is called reactive power, and its unit is
VAR. Reactive power is defined as the product of the voltage and
current waveforms when all harmonic components of one of
these signals are phase shifted by 90°.
Equation 31 gives an expression for the instantaneous reactive
power signal in an ac system when the phase of the current
channel is shifted by +90°.
where i
components phase shifted by 90°.
Next, the instantaneous reactive power, q(t), can be expressed as
Note that q(t) can be rewritten as
+
q
k
k
∑
,
≠
) (
m
∞
m
t
=
V
1
=
q(t) = v(t) × i
e
v
t i
i
q
k
k
) (
k
'
∑
,
≠
) (
) (
m
k
) (
∑
∞
I
=
m
∞
t
t
t
ʹ
=
=
m
1
V
1
(t) is the current waveform with all harmonic
t
=
V
+
=
=
=
{
∫
t
k
nT
k
∑
k
I
p
∞
∑
k
cos
∑
k
∑
k
I
=
∞
∞
∞
=
m
=
=
1
k
1
( )
1
1
I
V
t
V
I
× 2sin(kωt + φ
{
k
[
k
k
k
dt
cos
(k – m)ωt + φ
I
2
k
2
ʹ
2
=
sin
×
(
(t)
sin
φ
nT
sin(kωt + φ
2
k
(
sin(kωt + φ



k
− γ
∑
k
k
t ω
∞
=
t ω
1
k
V
+
−
k
+
γ
I
k
γ
k
) × sin(mωt + γ
π
k
2
k
k
)
cos(φ
− γ
k
+
)
)
k
− cos
π
) × sin(kωt + γ
2
k
−



k
– γ
π
2
(
2 kωt + φ
k
]
)
}
m
+
k
π
k
2
+
+ γ
)
π
2
k
+
) +
π
2
Rev. PrE | Page 46 of 103
)
(28)
(29)
(30)
(31)
(32)
}
The average total reactive power over an integral number of line
cycles (n) is given by the expression in Equation 33.
where:
T is the period of the line cycle.
Q is referred to as the total reactive power. Note that the total
reactive power is equal to the dc component of the instantaneous
reactive power signal q(t) in Equation 32, that is,
This is the relationship used to calculate the total reactive power
for each phase. The instantaneous reactive power signal, q(t), is
generated by multiplying each harmonic of the voltage signals by
the 90° phase-shifted corresponding harmonic of the current in
each phase.
The expression of fundamental reactive power is obtained from
Equation 33 with k = 1, as follows:
FQ = V
The ADE7880 computes the fundamental reactive power using
a proprietary algorithm that requires some initialization
function of the frequency of the network and its nominal
voltage measured in the voltage channel. These initializations
are introduced in the Active Power Calculation section and are
common for both fundamental active and reactive powers.
The ADE7880 stores the instantaneous fundamental phase
reactive powers into the AFVAR, BFVAR, and CFVAR registers.
Their expression is
where:
U
the ADC inputs are at full scale.
PMAX =27,059,678, the instantaneous power computed when
the ADC inputs are at full scale and in phase.
The xFVAR waveform registers are not mapped with an address
in the register space and can be accessed only through HSDC
port in the waveform sampling mode (see Waveform Sampling
Mode section for details). Fundamental reactive power
information is also available through the harmonic calculations
of the ADE7880 (see Harmonics calculations section for
details).
Table 16 presents the settling time for the fundamental reactive
power measurement, which is the time it takes the power to
reflect the value at the input of the ADE7880.
FS
, I
Q
Q
FS
xFVAR
k
∑
∞
=1
are the rms values of the phase voltage and current when
1
=
=
I
V
1
nT
∑
k
∞
k
sin(φ
1
=
1
I
V
k
nT
∫
0
=
k
sin(φ
I
q
1
k
U
( )
– γ
U
t
sin(φ
FS
1
dt
1
k
Preliminary Technical Data
)
– γ
×
=
k
I
∑
k
– γ
k
I
∞
FS
=
)
1
1
V
k
)
×
k
I
sin(φ
k
cos(φ
1
– γ
k
– γ
1
) × PMAX ×
k
−
π
2
)
2
1
4
(33)
(34)