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ADE7518
When a new half-line cycle is written in the LINCYC register,
the LWATTHR register is reset, and a new accumulation starts
at the next zero crossing. The number of half-line cycles is then
v ( t ) = 2 V sin( ω t + θ )
i ( t ) = 2 I sin( ω t )
(19)
i ′ ( t ) = 2 I sin ? ? ω t +
π ?
2 ?
counted until LINCYC is reached. This implementation provides a
valid measurement at the first CYCEND interrupt after writing
to the LINCYC register (see Figure 57). The line active energy
?
?
(20)
accumulation uses the same signal path as the active energy
accumulation. The LSB size of these two registers is equivalent.
where:
θ is the phase difference between the voltage and current channel.
v is the rms voltage.
i is the rms current.
LWATTHR REGISTER
q ( t ) = v ( t ) × i ’( t )
q ( t ) = VI sin (θ) + VI sin ( 2 ω t + θ )
(21)
CYCEND IRQ
The average reactive power over an integer number of lines (n)
is given in Equation 22.
LINCYC
VALUE
Figure 57. Energy Accumulation When LINCYC Changes
Q =
1
nT
nT
∫ q ( t ) dt = VI sin( θ )
0
(22)
? ? nT
cos ( 2 π ft ) dt
VI
? 1 + ?
? 8 . 9 ? ?
From the information in Equation 8 and Equation 9,
? ?
? ?
nT
E ( t ) = ∫ VI dt ? ? 2 ? ∫
0 ? ? f ? ? 0
? ?
?
(16)
where:
T is the line cycle period.
q is referred to as the reactive power.
Note that the reactive power is equal to the dc component of
the instantaneous reactive power signal q(t) in Equation 21.
The instantaneous reactive power signal q(t) is generated by
multiplying the voltage and current channels. In this case, the
where:
n is an integer.
T is the line cycle period.
Because the sinusoidal component is integrated over an integer
number of line cycles, its value is always 0. Therefore,
phase of the current channel is shifted by 90°. The dc component
of the instantaneous reactive power signal is then extracted by
a low-pass filter to obtain the reactive power information (see
Figure 58).
In addition, the phase-shifting filter has a nonunity magnitude
nT
E = ∫ VIdt + 0
0
E ( t ) = VInT
(17)
(18)
response. Because the phase-shifted filter has a large attenuation
at high frequency, the reactive power is primarily for calculation
at line frequency. The effect of harmonics is largely ignored in
the reactive power calculation. Note that, because of the magnitude
Note that in this mode, the 16-bit LINCYC register can hold
a maximum value of 65,535. In other words, the line energy
accumulation mode can be used to accumulate active energy
for a maximum duration of over 65,535 half-line cycles. At
a 60 Hz line frequency, this translates to a total duration of
65,535/120 Hz = 546 sec.
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 21 gives an expression for the instanta-
neous reactive power signal in an ac system when the phase of
the current channel is shifted by 90°.
characteristic of the phase shifting filter, the weight of the reactive
power is slightly different from that of the active power calculation
(see the Energy Register Scaling section).
The frequency response of the LPF in the reactive signal path is
identical to the one used for LPF2 in the average active power
calculation. Because LPF2 does not have an ideal brick wall
frequency response (see Figure 51), the reactive power signal
has some ripple due to the instantaneous reactive power signal.
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 calcu-
late energy.
The reactive power signal can be read from the waveform register
by setting the WAVMODE register (0x0D) and the WFSM bit in
the Interrupt Enable 3 SFR (MIRQENH, 0xDB). Like the current
and voltage channels waveform sampling modes, the waveform
data is available at a sample rate of 25.6 kSPS, 12.8 kSPS, 6.4 kSPS,
or 3.2 kSPS.
Rev. 0 | Page 53 of 128
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