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Data Sheet
Phase A, Phase B, and Phase C zero crossings are, respectively,
included when counting the number of half-line cycles by
setting ZXSEL[0:2] bits (Bit 3 to Bit 5) in the LCYCMODE
ADE7758
v = rms voltage.
i = rms current.
θ = total phase shift caused by the reactive elements in the load.
Then the instantaneous reactive power q(t) can be expressed as
q ( t ) = VI cos ? ? – θ –
? – VI cos ? 2 ωt – θ –
π ? ? π ?
?
2 ?
?
2 ?
register. Any combination of the zero crossings from all three
phases can be used for counting the zero crossing. Only one
phase should be selected at a time for inclusion in the zero
crossings count during calibration (see the Calibration section).
The number of zero crossings is specified by the LINECYC
register. LINECYC is an unsigned 16-bit register. The ADE7758
can accumulate active power for up to 65535 combined zero
crossings. Note that the internal zero-crossing counter is always
active. By setting the LWATT bit, the first energy accumulation
result is, therefore, incorrect. Writing to the LINECYC register
q ( t ) = v ( t ) × i ′ ( t )
?
where i ′ ( t ) is the current waveform phase shifted by 90°.
Note that q ( t ) can be rewritten as
q ( t ) = VI sin ( θ ) + VI sin ( 2 ωt – θ )
The average reactive power over an integral number of line
cycles (n) is given by the expression in Equation 31.
(29)
(30)
∫ q ( t ) dt = V × I × sin ( θ )
when the LWATT bit is set resets the zero-crossing counter, thus
ensuring that the first energy accumulation result is accurate.
Q =
1 nT
nT 0
(31)
At the end of an energy calibration cycle, the LENERGY bit
(Bit 12) in the STATUS register is set. If the corresponding
mask bit in the interrupt mask register is enabled, the IRQ
output also goes active low; thus, the IRQ can also be used to
signal the end of a calibration.
Because active power is integrated on an integer number of half-
line cycles in this mode, the sinusoidal component is reduced to
0, eliminating any ripple in the energy calculation. Therefore, total
energy accumulated using the line-cycle accumulation mode is
where:
T is the period of the line cycle.
Q is referred to as the average reactive power. The instantaneous
reactive power signal q ( t ) is generated by multiplying the
voltage signals and the 90° phase-shifted current in each phase.
The dc component of the instantaneous reactive power signal in
each phase (A, B, and C) is then extracted by a low-pass filter to
obtain the average reactive power information on each phase.
This process is illustrated in Figure 72. The reactive power of
E ( t ) = VRMS × IRMS × t
(26)
each phase is accumulated in the corresponding 16-bit VAR-
where t 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. Using the line cycle accumula-
tion to calculate the kWh/LSB constant results in a value that
can be applied to the WATTHR registers when the line
accumulation mode is not selected (see the Calibration section).
REACTIVE POWER CALCULATION
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
one of these signals is phase shifted by 90°.
Equation 30 gives an expression for the instantaneous reactive
power signal in an ac system when the phase of the current
hour register (AVARHR, BVARHR, or CVARHR). The input to
each reactive energy register can be changed depending on the
accumulation mode setting (see Table 21).
The frequency response of the LPF in the reactive power signal
path is identical to that of the LPF2 used in the average active
power calculation (see Figure 66).
INSTANTANEOUS
REACTIVE POWER SIGNAL
q(t) = VRMS × IRMS × sin( φ ) + VRMS × IRMS × sin(2 ω t + θ )
AVERAGE REACTIVE POWER SIGNAL =
VRMS × IRMS × sin( θ )
VRMS × IRMS × sin( φ )
0x00000
channel is shifted by +90°.
v ( t ) = 2 V sin ( ωt – θ )
i ( t ) = 2 I sin ( ωt )
(27)
θ
VOLTAGE CURRENT
v(t) = 2 × VRMS × sin( ω t – θ ) i(t) = 2 × IRMS × sin( ω t)
Figure 72. Reactive Power Calculation
The low-pass filter is nonideal, so the reactive power signal has
i ′ ( t ) = 2 I sin ? ? ωt +
π ?
2 ?
where:
?
?
(28)
some ripple. This ripple is sinusoidal and has a frequency equal
to 2× the line frequency. Because the ripple is sinusoidal
in nature, it is removed when the reactive power signal is
integrated over time to calculate the reactive energy.
Rev. E | Page 35 of 72
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