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Data Sheet
ADE7880
∑ V k I m { cos [ ( k – m ) ωt + φ k ? γ k ?
set to high again by writing to the STATUS0 register with the
corresponding bit set to 1.
Because the active power is integrated on an integer number of
∞
k , m = 1
k ≠ m
π
2
] ?
] }
cos [ ( k + m ) ωt + φ k + γ k +
(33)
1 nT
π
∫ q ( t ) dt = ∑ V k k I cos( φ k – γ k ? 2 )
half-line cycles in this mode, the sinusoidal 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 ∑ V k I k cos( φ k – γ k )
t k = 1
(29)
π
2
The average total reactive power over an integral number of line
cycles (n) is shown in Equation 34.
∞
Q = (34)
nT 0 k = 1
Q = ∑ V k k sin( φ k – γ k )
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.
FUNDAMENTAL REACTIVE POWER CALCULATION
The ADE7880 computes the fundamental reactive power, the
power determined only by the fundamental components of the
∞
I
k = 1
where:
T is the period of the line cycle.
Q is referred to as 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 32, that is,
∑ V k I k
voltages and currents.
The ADE7880 also computes the harmonic reactive powers, the
∞
k = 1
sin( φ k – γ k )
reactive powers determined by the harmonic components of the
voltages and currents. See Harmonics Calculations section for
details. A load that contains a reactive element (inductor or
capacitor) produces a phase difference between the applied ac
voltage and the resulting current. The power associated with
reactive elements is called reactive power, and its unit is VAR.
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 31 is an example of the instantaneous reactive power
signal in an ac system when the phase of the current channel is
shifted by +90°.
This is the relationship used to calculate the total reactive power
for each phase. The instantaneous reactive power signal, q(t), is
generated by multiplying each harmonic of the voltage signals by
the 90° phase-shifted corresponding harmonic of the current in
each phase.
The expression of fundamental reactive power is obtained from
Equation 33 with k = 1, as follows:
FQ = V 1 I 1 sin(φ 1 – γ 1 )
The ADE7880 computes the fundamental reactive power using
a proprietary algorithm that requires some initialization
function of the frequency of the network and its nominal
v ( t ) = ∑ V k 2 sin( kωt + φ k )
i ( t ) = ∑ I k 2 sin ( k ω t + γ k )
∞
k = 1
∞
k = 1
(30)
(31)
voltage measured in the voltage channel. These initializations
are introduced in the Active Power Calculation section and are
common for both fundamental active and reactive powers.
The ADE7880 stores the instantaneous fundamental phase
reactive powers into the AFVAR, BFVAR, and CFVAR registers.
i ' ( t ) = ∑ I k 2 sin ? ? k ω t + γ k + ? ?
π
× × sin( φ 1 – γ 1 ) × PMAX × 1 4
xFVAR =
U 1 I 1
∞
k = 1 ? 2 ?
where i’(t) is the current waveform with all harmonic
components phase shifted by 90°.
Next, the instantaneous reactive power, q(t), can be expressed as
Their equation is
(35)
U FS I FS 2
where:
U FS , I FS are the rms values of the phase voltage and current when
q(t) = v(t) × i ? (t)
(32)
the ADC inputs are at full scale.
q ( t ) = ∑ V k I k × 2 sin( kωt + φ k ) × sin( kωt + γ k +
∑ V k I m × 2sin( kωt + φ k ) × sin( mωt + γ m +
π
∞
k ≠ m
∞
k = 1
k , m = 1 2
)
π
2
)+
PMAX = 27,059,678, the instantaneous power computed when
the ADC inputs are at full scale and in phase.
The xFVAR waveform registers are not mapped with an address
in the register space and can be accessed only through HSDC
Note that q ( t ) can be rewritten as
Mode section for details). Fundamental reactive power
information is also available through the harmonic calculations
{
q ( t ) = ∑ V k k cos ( φ k ? γ k ?
∞
k = 1
I
π
2
) ? cos ( 2 kωt + φ k + γ k +
π
2
) } +
of the ADE7880 (see Harmonics Calculations section for details).
Rev. A | Page 49 of 104
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