ade7854 Analog Devices, Inc., ade7854 Datasheet - Page 34

• Manufacturer Part Number: ade7854
• Description: Poly Phase Multifunction Energy Metering Ic With Neutral Current Measurement
• Manufacturer: Analog Devices, Inc.

ADE7854
As previously stated, the serial ports of the ADE7854 work on
32, 16 or 8-bit words and the DSP works on 28 bits. Similar to
registers presented in Figure 16, 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 ADE7854 computes the total active power. 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:
where
The instantaneous power in an ac system is:
The average power over an integral number of line cycles (n) is
given by the expression in expression
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
the total active power in the ADE7854 for each phase.
Figure 42 shows how the ADE7854 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.
i
ϕ ,
p
+
P
v
) t (
k
) t (
∑
) t (
∞
k
, k
k
= 1
=
≠
∑
m
∞
V
m
=
=
nT
=
γ =phase delays of each harmonic.
=
V
1
k
1
k
k
v
I
∑
k
∞
k
=
V ,
∑
t (
k
∞
=
1
I
nT
I
0
cos
1
k
i )
∫
m
V
k
⋅
p
{
) t (
k
I = rms voltage and current of each harmonic,
cos
( )
(
k
t
ϕ
2
=
2
[
k
dt
sin
(
k
k
sin
∑
−
∞
=
−
=
1
(
γ
V
k
m
(
k
k
ω
k
k
∑
∞
= 1
)
)
I
ω
ω
t
k
. This is the expression used to calculate
V
+
t
t
cos
k
+
+
γ
I
ϕ
ϕ
k
k
(
ϕ
k
)
k
cos
k
−
)
−
γ
(
m
γ
ϕ
k
]
k
)
−
(15
−
−
cos
k
γ
∑
∞
), that is,
=
(16
k
1
[
V
(
)
k
).
k
+
I
k
m
cos
)
ω
(
t
k 2
+
ϕ
ω
k
t
+
+
ϕ
γ
k
m
(16)
(14)
(15)
−
]
}
γ
Rev. PrC| Page 34 of 71
k
)
+
If the phase currents and voltages contain only the fundamental
component, are in phase (that is
correspond to full scale ADC inputs, then multiplying them
results in an instantaneous power signal that has a dc
component
Figure 43 shows the corresponding waveforms.
Because LPF2 does not have an ideal brick wall frequency
response (see Figure 44), 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.
The ADE7854 stores the instantaneous total phase active
powers into AWATT[23:0], BWATT[23:0] and CWATT[23:0]
registers. Their expression is:
where: x=A, B, C,
U
the ADC inputs are at full scale.
PMAX=33,516,139 is the instantaneous power computed when
the ADC inputs are at full scale and in phase.
The xWATT[23:0], x=A,B,C waveform registers may be
accessed using various serial ports. See Waveform Sampling
Mode chapter for more details.
xWATT
VRMS x IRMS
v
0x1D1E1A0=
i
A
0x3A3C340=
FS
A
30,532,000
61,064,000
0x000 0000
, I
FS
APHCAL
are the rms values of the phase voltage and current when
=
∑
k
∞
=
V ⋅ and a sinusoidal component
INSTANTANEOUS
Figure 44. Frequency Response of the LPF Used
POWER SIGNAL
i
1
v
) t (
to Filter Instantaneous Power in Each Phase
1
) t (
U
AVGAIN
AIGAIN
U
=
Figure 42. Total Active Power Data Path
=
I
FS
1
2
k
Figure 43. Active Power Calculation
2
×
×
IRMS
HPFDIS[23:0]
HPFDIS[23:0]
⋅
VRMS
Preliminary Technical Data
I
HPF
HPF
I
FS
k
×
sin(
×
sin(
⋅
ω
cos
Integrator
) t
ω
Digital
p(t)=VRMS x IRMS - VRMS x IRMS x cos(2wt)
) t
(
ϕ
TBD
Digital Signal Processor
k
ϕ
−
1
γ
LPF2
=
k
)
γ
⋅
1
PMAX
AWATTOS
POWER SIGNAL: VRMS x IRMS
=
INSTANTANEOUS ACTIVE
Σ
0
) and they
⋅
V
AWGAIN
2
1
1
4
⋅
I
1
cos
Instantaneous
phase active
power
(17)
(
2
ω
t
)
.