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Data Sheet
Voltage RMS Offset Compensation
The ADE7880 incorporates voltage rms offset compensation
registers for each phase: AVRMSOS, BVRMSOS, and CVRMSOS.
These are 24-bit signed registers used to remove offsets in the
voltage rms calculations. An offset can exist in the rms calcula-
tion due to input noises that are integrated in the dc component
of V 2 (t). One LSB of the voltage rms offset compensation register is
equivalent to one LSB of the voltage rms register. Assuming that
ADE7880
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
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 )
i ( t ) = ∑ I k 2 sin ( k ω t + γ k )
the maximum value from the voltage rms calculation is 3,766,572
with full-scale ac inputs (50 Hz), one LSB of the current rms offset
represents 0.00045%
? ?
? 3767 2 + 128 / 3767 ? 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.
∞
k = 1
∞
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.
(17)
V rms = V rms 0 2 + 128 × VRMSOS
(16)
The instantaneous power in an ac system is
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 ]}
1 nT
∫ p ( t ) dt = ∑ V k k I cos( φ k – γ k )
∑ V k k I cos( φ k – γ k )
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 ADE7880 work on 32-, 16-, or 8-bit words
and the DSP works on 28 bits. Similar to registers presented in
registers are accessed as 32-bit registers with the four most
significant bits padded with 0s and sign extended to 28 bits.
Voltage RMS in 3-Phase Three Wire Delta Configurations
In 3-phase three wire delta configurations, Phase B is
considered the ground of the system, and Phase A and Phase C
voltages are measured relative to it. This configuration is chosen
using CONSEL bits equal to 01 in ACCMODE register (see
used). In this situation, all Phase B active, reactive, and apparent
powers are 0.
In this configuration, the ADE7880 computes the rms value of
the line voltage between Phase A and Phase C and stores the
result into BVRMS register. BVGAIN and BVRMSOS registers
may be used to calibrate BVRMS register computed in this
configuration.
ACTIVE POWER CALCULATION
The ADE7880 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. In
addition, the ADE7880 computes the fundamental active power,
the power determined only by the fundamental components of
the voltages and currents.
The ADE7880 also computes the harmonic active powers, the
active powers determined by the harmonic components of the
voltages and currents. See the Harmonics Calculations section
for details.
∞ ∞
I I
k = 1 k = 1
∞
+
k , m = 1
k ≠ m
(18)
The average power over an integral number of line cycles (n) is
given by the equation in Equation 19.
∞
P = (19)
nT 0 k = 1
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 18, that is,
∞
k = 1
This is the equation used to calculate the total active power in the
ADE7880 for each phase. The equation of fundamental active
power is obtained from Equation 18 with k = 1, as follows:
FP = V 1 I 1 cos( φ 1 – γ 1 ) (20)
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.
If the phase currents and voltages contain only the fundamental
component, are in phase (that is φ 1 = γ 1 = 0), and they correspond
to full-scale ADC inputs, then multiplying them results in an
instantaneous power signal that has a dc component, V 1 × I 1 ,
and a sinusoidal component, V 1 × I 1 cos(2ωt); Figure 71 shows
the corresponding waveforms.
Rev. A | Page 43 of 104
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