ADE7854AACPZ View Datasheet(PDF) - Analog Devices
Part Name
Description
MFG CO.
'ADE7854AACPZ' PDF : 96 Pages View PDF
Data Sheet
ADE7854A/ADE7858A/ADE7868A/ADE7878A
components are reduced to 0, eliminating any ripple in the energy
calculation. Therefore, total energy accumulated using the line
cycle accumulation mode is
t +nT
∞
e = ∫ p (t )dt = nT ∑Vk Ik cos(φk − γk)
(34)
t
k=1
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.
REACTIVE POWER CALCULATION—ADE7858A,
ADE7868A, ADE7878A ONLY
The ADE7858A/ADE7868A/ADE7878A can compute the total
reactive power on every phase. Total reactive power integrates
all fundamental and harmonic components of the voltages and
currents. The ADE7878A also computes the fundamental
reactive power, the power determined only by the fundamental
components of the voltages and currents.
A load that contains a reactive element (inductor or capacitor)
produces a phase difference between the applied ac voltage and
the resulting current. VAR is the unit for the power associated with
reactive elements (the reactive power). 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 38 is the expression for the instantaneous reactive
power signal in an ac system when the phase of the current
channel is shifted by 90°.
∞
v(t) = ∑Vk 2 sin(kωt + φk)
(35)
k =1
∞
i(t) = ∑ Ik
2 sin(kωt + γk )
(36)
k=1
∞
i′(t) = ∑ Ik
k =1
2
sin
kωt
+
γ
k
+
π
2
(37)
where iʹ(t) is the current waveform with all harmonic
components phase shifted by 90°.
Next, the instantaneous reactive power, q(t), can be expressed as
q(t) = v(t) × iʹ(t)
∞
q(t) = ∑Vk Ik × 2 sin(kωt + φk) × sin(kωt + γk +
k =1
π
2
)+
∞
∑Vk Im
k ,m=1
× 2sin(kωt + φk) × sin(mωt + γm +
π
2
)
(38)
k≠m
Note that q(t) can be rewritten as
q(t)
=
∞
∑Vk Ik
k =1
cosϕk
−
γ
k
−
π
2
−
cos 2kωt
+ ϕk
+
γ
k
+
π
2
+
∞
∑V kIm
k ,m =1
cos(k
−
m)ωt
+ϕk
−
γk
−
π
2
−
k≠m
cos(k
+
m)ωt
+ϕk
+
γk
+
π
2
(39)
Equation 40 expresses the average total reactive power over an
integral number of line cycles (n).
Q
=
1
nT
nT
∫
0
q(t
)dt
=
∞
∑Vk Ik
k=1
cos(φk − γk −
π
2
)
(40)
∞
Q = ∑Vk Ik sin(φk − γk)
k =1
where:
T is the period of the line cycle.
Q is 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 39, that is,
∞
∑Vk Ik sin(φk − γk)
k =1
This is the relationship used to calculate the total reactive power
in the ADE7858A/ADE7868A/ADE7878A for each phase. The
instantaneous reactive power signal, q(t), is generated by multiply-
ing each harmonic of the voltage signals by the 90° phase shifted
corresponding harmonic of the current in each phase.
The ADE7858A/ADE7868A/ADE7878A store the
instantaneous total phase reactive powers in the AVAR, BVAR,
and CVAR registers. Their expression is
xVAR
=
∞
∑
Vk
k=1 VFS
× Ik
I FS
× sin(φk − γk) × PMAX ×
1
24
(41)
where:
VFS, IFS are the rms values of the phase voltage and current when
the ADC inputs are at full scale.
PMAX = 33,516,139, which is the instantaneous power
computed when the ADC inputs are at full scale and in phase.
The xVAR waveform registers can be accessed using various
serial ports. For more information, see the Waveform Sampling
Mode section.
As described in the Active Power Calculation section, use the
LPFSEL bit in the CONFIG_A register to increase the filtering
on the power measurement. The LPFSEL bit is 0 by default and
when set to 1, the strength of the power filtering increases (see
Figure 68 and Figure 69). This filtering affects both the total
active and the total reactive power measurements.
The expression of fundamental reactive power is obtained from
Equation 40 with k = 1, as follows:
FQ = V1I1 sin(φ1 − γ1)
(42)
Rev. C | Page 53 of 96
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