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Data Sheet
Voltage RMS Offset Compensation
The ADE78xx incorporates voltage rms offset compensation
ADE7854/ADE7858/ADE7868/ADE7878
ac system is supplied by a voltage, v(t), and consumes the current,
i(t), and each of them contains harmonics, then
v ( t ) ? ? V k 2 sin ( kωt + φ k )
registers for each phase: AVRMSOS, BVRMSOS, and CVRMSOS.
These are 24-bit signed registers used to remove offsets in the
?
k ? 1
(16)
i ( t ) ? ? I k 2 sin ? k ω t ? γ k ?
p ( t ) = v ( t) × i ( t ) = ? V k k cos( φ k – γ k ) ? ? V k k cos(2 kωt + φ k + γ k ) +
? V k I m {cos[( k ? m ) ωt + φ k – γ m ] – cos[( k + m ) ωt + φ k + γ m ]}
voltage rms calculations. An offset can exist in the rms calculation
due to input noises that are integrated in the dc component of
V 2 (t). The voltage rms offset register is multiplied by 128 and
added to the squared current rms before the square root is
executed. Assuming that the maximum value from the voltage
rms calculation is 4,191,910 with full-scale ac inputs (50 Hz), one
LSB of the voltage rms offset represents 0.00037%
(( 4191 2 ? 128 /4191 ? 1) × 100) of the rms measurement at
60 dB down from full scale. Conduct offset calibration at low
current; avoid using voltages equal to zero for this purpose.
2
V rms ? V rms 0 ? 128 ? VRMSOS (15)
where V rms 0 is the rms measurement without offset correction.
As stated in the Current Waveform Gain Registers section, the
serial ports of the ADE78xx work on 32-, 16-, or 8-bit words
and the DSP works on 28 bits. Similar to registers presented in
?
k ? 1
where:
V k , I k are rms voltage and current, respectively, of each
harmonic.
φ k , γ k are the phase delays of each harmonic.
The instantaneous power in an ac system is
? ?
I I
k ? 1 k ? 1
?
k , m ? 1
k ? m
(17)
The average power over an integral number of line cycles (n) is
given by the expression in Equation 18.
1 nT
? p ? t ? dt ? ? V k k I cos( φ k – γ k )
registers are accessed as 32-bit registers with the four most
significant bits padded with 0s and sign extended to 28 bits.
P =
nT 0 k ? 1
?
(18)
? V k I k cos( φ k – γ k )
ACTIVE POWER CALCULATION
The ADE7854 / ADE7858 / ADE7868 / ADE7878 compute the
total active power on every phase. Total active power considers
in its calculation all fundamental and harmonic components of
the voltages and currents. In addition, the ADE7878 computes
the fundamental active power, the power determined only by
the fundamental components of the voltages and currents.
Total Active Power Calculation
Electrical power is defined as the rate of energy flow from source
to load, and 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
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 Equation 17, that is,
?
k ? 1
This is the expression used to calculate the total active power in
the ADE78xx for each phase. The expression of fundamental active
power is obtained from Equation 18 with k = 1, as follows:
FP = V 1 I 1 cos( φ 1 – γ 1 ) (19)
power on each phase. First, it multiplies the current and voltage
signals in each phase. Next, it extracts the dc component of the
instantaneous power signal in each phase (A, B, and C) using
LPF2, the low-pass filter.
HPFDIS
DIGITAL
[23:0]
INTEGRATOR
AIGAIN
I A
HPF
AWGAIN
AWATTOS
V A
APHCAL
HPFDIS
[23:0]
HPF
AVGAIN
LPF
INSTANTANEOUS
PHASE A ACTIVE
POWER
AWATT
DIGITAL SIGNAL PROCESSOR
Figure 64. Total Active Power Datapath
Rev. H | Page 47 of 100
2 4
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