ADE7758 Analog Devices, ADE7758 Datasheet - Page 35

• Manufacturer Part Number: ADE7758
• Description: Poly Phase Multifunction Energy Metering IC with Per Phase Information
• Manufacturer: Analog Devices

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
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
when the LWATT bit is set resets the zero-crossing counter, thus
ensuring that the first energy accumulation result is accurate.
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. This eliminates any ripple in the energy calculation. Therefore,
total energy accumulated using the line-cycle accumulation
mode is
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 17 gives an expression for the instantaneous reactive
power signal in an ac system when the phase of the current
channel is shifted by +90°.
t i
i
v
E
( )
′
( )
( )
t
t
( )
t
=
=
=
=
VRMS
2
2
2
I
V
I
sin
sin
sin
×
( )
⎛
⎜
⎝
ω
(
ω
ω
IRMS
t
t
t
–
+
θ
π
2
×
)
⎞
⎟
⎠
t
(14)
(15)
(16)
Rev. A | Page 35 of 68
where 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
where
that q(t) can be rewritten as
The average reactive power over an integral number of line
cycles (n) is given by the expression in Equation 18.
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 71. The reactive power of
each phase is accumulated in the corresponding 16-bit VAR-
hour register (AVARHR, BVARHR, or CVARHR). The input to
each reactive energy register can be changed depending on the
accumulation mode setting (see Table 17).
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 65).
The low-pass filter is nonideal so the reactive power signal has
some ripple. This ripple is sinusoidal and has a frequency equal
VRMS
×
q
q
q
Q
IRMS
( )
( )
( )
i ′
t
t
t
=
( )
t
×
=
00000h
=
=
nT
1
sin(
VI
v
VI
is the current waveform phase shifted by 90°. Note
( )
φ
nT
∫
t
0
)
sin
cos
q
Figure 71. Reactive Power Calculation
( )
×
VOLTAGE
v(t) = 2
t
( )
⎛
⎜
⎝
θ
dt
INSTANTANEOUS
REACTIVE POWER SIGNAL
q(t) = VRMS
–
i
′
( )
θ
=
+
t
×
–
V
I V
VRMS
π
2
×
sin
×
⎞
⎟
⎠
I
×
IRMS
–
×
(
sin(
2
VI
sin
ω
ω
×
t
t–
sin(
θ
( )
cos
θ
–
θ
)
φ
θ
) + VRMS
⎛
⎜
⎝
)
AVERAGE REACTIVE POWER SIGNAL =
VRMS
2
ω
t
CURRENT
i(t) = 2
×
×
–
IRMS
IRMS
θ
–
×
×
×
IRMS
sin(
π
2
sin(2
ADE7758
⎞
⎟
⎠
θ
)
×
ω
sin(
t+
θ
)
ω
t)
(17)
(18)