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ADE7858 Fiches technique(PDF) 33 Page - Analog Devices

No de pièce ADE7858
Description  Poly Phase Multifunction Energy Metering IC with per Phase Active and Reactive Powers
PDF  76 Pages
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Fabricant  AD [Analog Devices]
Site Internet  http://www.analog.com
Logo AD - Analog Devices

ADE7858 Fiches technique(HTML) 33 Page - Analog Devices

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Preliminary Technical Data
ADE7858
Rev. PrA | Page 33 of 76
arguments only, the result of the square root operation is
erroneous, equal to 0x7FFFFF. It is recommended to avoid
using big, negative VRMSOS values and as the equivalent rms
value of a full-scale sinusoidal signal is 4,191,910(0x3FF6A6),
much smaller than 0x7FFFFF, such values may be easily
eliminated from consideration.
As previously stated, the serial ports of the ADE7858 work on
32, 16 or 8-bit words and the DSP works on 28 bits. Similar to
registers presented in Figure 15, AVRMSOS, BVRMSOS and
CVRMSOS 24-bit registers are accessed as 32-bit registers with
4 most significant bits padded with 0s and sign extended to 28
bits.
ACTIVE POWER CALCULATION
The ADE7858 computes the total active power on every phase.
Total active power considers in its calculation all fundamental
and harmonic components of the voltages and currents.
Total Active Power Calculation
Electrical power is defined as the rate of energy flow from
source to load. It is given by the product of the voltage and
current waveforms. The resulting waveform is called the
instantaneous power signal and it is equal to the rate of energy
flow at every instant of time. The unit of power is the watt or
joules/sec. If an ac system is supplied by a voltage v(t) and
consumes the current i(t) and each of them contains harmonics,
then:

k
1
k
k
t
k
sin
2
V
)
t
(
v
(16)

k
1
k
k
t
k
sin
2
I
)
t
(
i
where
k
V ,
k
I = rms voltage and current of each harmonic,
k
 ,
k
 =phase delays of each harmonic.
The instantaneous power in an ac system is:






m
k
1
m
,
k
m
k
m
k
m
k
k
k
1
k
k
k
1
k
k
k
k
k
t
m
k
cos
t
m
k
cos
I
V
t
k
2
cos
I
V
cos
I
V
)
t
(
i
)
t
(
v
)
t
(
p
(17)
The average power over an integral number of line cycles (n) is
given by the expression in Equation (18).


1
k
k
k
k
k
nT
0
cos
I
V
dt
t
p
nT
1
P
(18)
where: T is the line cycle period.
P
is referred to as the total active or total real power. Note that
the total active power is equal to the dc component of the
instantaneous power signal p(t) in expression (17), that is,

1
k
k
k
k
k
cos
I
V
. This is the expression used to calculate
the total active power in the ADE7858 for each phase.
Figure 38 shows how the ADE7858 computes the total active
power on each phase. First, it multiplies the current and voltage
signals in each phase. Then, extracts the dc component of the
instantaneous power signal in each phase (A, B and C) using
LPF2, the low pass filter.
v
A
i
A
HPF
HPF
AVGAIN
Digital
Integrator
AIGAIN
APHCAL
LPF
AWATTOS
Digital Signal Processor
AWGAIN
HPFDIS[23:0]
HPFDIS[23:0]
INSTANTANEOUS
PHASE A ACTIVE
POWER
Figure 38. Total Active Power Data Path
If the phase currents and voltages contain only the fundamental
component, are in phase (that is
0
1
1
) and they
correspond to full scale ADC inputs, then multiplying them
results in an instantaneous power signal that has a dc
component
1
1 I
V 
and a sinusoidal component
t
2
cos
I
V
1
1
.
Figure 39 shows the corresponding waveforms.
0x3FED4D6 =
67,032,278
0x000 0000
VRMS x IRMS
0x1FF6A6B =
33,516,139
INSTANTANEOUS
POWER SIGNAL
p(t)=VRMS x IRMS - VRMS x IRMS x cos(2wt)
INSTANTANEOUS ACTIVE
POWER SIGNAL: VRMS x IRMS
)
t
sin(
IRMS
2
)
t
(
i
)
t
sin(
VRMS
2
)
t
(
v
Figure 39. Active Power Calculation
Because LPF2 does not have an ideal brick wall frequency
response (see Figure 40), the active power signal has some
ripple due to the instantaneous power signal. This ripple is
sinusoidal and has a frequency equal to twice the line frequency.
Because the ripple is sinusoidal in nature, it is removed when
the active power signal is integrated over time to calculate the
energy.



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