Datasheet

ADE7953 Data Sheet
Rev. B | Page 28 of 72
REACTIVE POWER CALCULATION
Reactive power is defined as the product of the voltage and
current waveforms when one of these signals is phase shifted
by 90°. The resulting waveform is called the instantaneous
reactive power signal.
Equation 16 provides an expression for the instantaneous
reactive power signal in an ac system when the phase of the
current channel is shifted by +90°.
RP(t) = V(t) × I’(t) (16)
RP(t) = VI × sin(θ) + VI × sin(2ωt + θ) (17)
)sin(2 θωt V V(t) +××=
(18)
)sin(2 ωt I I(t) ××=
(19)
I’(t) =






π
+××
2
sin2 ωt I
(20)
where:
V is the rms voltage.
I is the rms current.
θ is the phase difference between the voltage and current channel.
The average reactive power over an integral number of line
cycles (n) is given by the expression in Equation 21.
∫
×
=
=
nT
θ
VI
dt
tRP
nT
RP
0
)
sin()
(
1
(21)
where:
RP is the reactive power.
T is the line cycle period.
The reactive power is equal to the dc component of the
instantaneous reactive power signal (RP(t) in Equation 16).
This relationship is used to calculate reactive power in the
ADE7953. The signal chain for the reactive power and energy
calculations in the ADE7953 is shown in Figure 51.
The instantaneous reactive power signal RP(t) is generated by
multiplying the current signal and the voltage signal. Simulta-
neous calculations are performed using Current Channel A and
Current Channel B. The multiplication is performed over the full
1.23 kHz bandwidth and results in a reactive power measurement
that includes all harmonics included in this range.
The ADE7953 reactive power measurement is stable over the
full frequency range. The dc component of the instantaneous
reactive power signal is then extracted by a low-pass filter to
obtain the reactive power information.
The frequency response of the LPFs in the reactive power signal
paths is identical to the frequency response of the LPFs used in
the active power calculation. Because the LPF does not have an
ideal “brick wall” frequency response, the reactive power signal
has some ripple associated with it. 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 reactive
power signal is integrated to compute the reactive energy (see
the Reactive Energy Calculation section).
The ADE7953 computes the reactive power simultaneously
on Current Channel A and Current Channel B and stores the
resulting measurements in the AVAR (Address 0x214 and
Address 0x314) and BVAR (Address 0x215 and Address 0x315)
registers, respectively. With full-scale inputs, the expected
reading in the AVAR and BVAR registers is approximately
4862401 LSBs (decimal).
The reactive power registers are updated at a rate of 6.99 kHz
and can be read using the waveform sampling mode (see the
Instantaneous Powers and Waveform Sampling section).
SIGN OF REACTIVE POWER CALCULATION
The reactive power measurement in the ADE7953 is a signed
calculation. If the current waveform is leading the voltage wave-
form, the reactive power is negative. Negative reactive power
indicates a capacitive load. If the current waveform is lagging
the voltage waveform, the reactive power is positive. Positive
reactive power indicates an inductive load. The ACCMODE
register (Address 0x201 and Address 0x301) includes two sign
indication bits that show the sign of the reactive power of
Current Channel A (VARSIGN_A) and Current Channel B
(VARSIGN_B). See the Sign Indication section for more
information.
CURRENT
CHANNEL
A OR B
48 0
+
+
xVAROS
09320-120
VOLTAGE
CHANNEL
INTERNA
L
ACCUMULATION
FIXED INTERNAL
THRESHOLD
REACTIVE
POWER
SIGNAL
RENERGYx
23 0
REACTIVE
POWER
ALGORITHM
x
VARGAIN
Figure 51. Reactive Energy Signal Chain