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ADE7753
90°. The resulting waveform is called the instantaneous reactive
power signal. Equation 25 gives an expression for the instanta-
The average reactive power over an integral number of lines (n)
is given in Equation 26.
neous reactive power signal in an ac system when the phase of
the current channel is shifted by +90°.
v ( t ) = 2 V sin( ω t + θ ) (23)
2 I sin( ω t )
i ( t ) =
RP =
where:
1
nT
nT
∫ Rp ( t ) dt = VI sin( θ )
0
(26)
i ′ ( t ) = 2 I sin ? ? ω t +
π ?
2 ?
?
?
(24)
T is the line cycle period.
RP is referred to as the reactive power.
Note that the reactive power is equal to the dc component of the
where:
θ is the phase difference between the voltage and current
channel.
V is the rms voltage.
I is the rms current.
instantaneous reactive power signal Rp(t) in Equation 25. This
is the relationship used to calculate reactive power in the
ADE7753. The instantaneous reactive power signal Rp(t) is
generated by multiplying Channel 1 and Channel 2. In this case,
the phase of Channel 1 is shifted by +90°. The dc component of
Rp ( t ) = v ( t ) × i ’( t )
Rp ( t ) = VI sin (θ) + VI sin(2ωt + θ)
(25)
the instantaneous reactive power signal is then extracted by a
low-pass filter in order to obtain the reactive power informa-
tion. Figure 71 shows the signal processing in the reactive
power calculation in the ADE7753.
90 DEGREE
PHASE SHIFT
INSTANTANEOUS REACTIVE
POWER SIGNAL (Rp(t))
I
π
2
+
+
49
0
MULTIPLIER
LPF2
V
ACCUMULATE REACTIVE
ENERGY IN INTERNAL
REGISTER AND UPDATE
23
0
THE LVARENERGY REGISTER
FROM
CHANNEL 2
ADC
ZERO-CROSSING
DETECTION
CALIBRATION
CONTROL
LVARENERGY [23:0]
AT THE END OF LINECYC HALF
LINE CYCLES
LPF1
LINECYC [15:0]
Figure 71. Reactive Power Signal Processing
Rev. C | Page 34 of 60
02875-0-070
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