Datasheet
Data Sheet ADE5166/ADE5169/ADE5566/ADE5569
Rev. D | Page 65 of 156
When a new half-line cycle is written in the LINCYC register
(Address 0x12), the LWATTHR register (Address 0x03) is reset,
and a new accumulation starts at the next zero crossing. The
number of half-line cycles is then counted until LINCYC is
reached. This implementation provides a valid measurement at
the first CYCEND interrupt after writing to the LINCYC register
(see Figure 71). The line active energy accumulation uses the
same signal path as the active energy accumulation. The LSB
size of these two registers is equivalent.
LINCYC
VALUE
CYCEND IRQ
LWATTHR REGISTER
07411-045
Figure 71. Energy Accumulation When LINCYC Changes
Using the information from Equation 8 and Equation 9
( )
( )
dtft
f
VI
dtVItE
nTnT
π
+
−=
∫∫
2cos
9.8
1
0
2
0
(16)
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,
0
0
+=
∫
nT
VIdtE
(17)
E(t) = VInT (18)
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 65,535 half-line cycles. At a 60 Hz
line frequency, the total duration of 65,535/120 Hz = 546 sec.
REACTIVE POWER CALCULATION
(ADE5169/ADE5569 ONLY)
Reactive power, a function available for the ADE5169/ADE5569,
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 instantaneous reactive
power signal in an ac system when the phase of the current
channel is shifted by 90°.
)sin(2)( θtVtV +ω×=
(19)
)sin(2)( tItI ω×=
π
+ω×=
2
sin2)(' tItI
(20)
where:
θ is the phase difference between the voltage and current channel.
V is the rms voltage.
I is the rms current.
q(t) = V(t) × I’(t) (21)
q(t) = VI sin (θ) + VI sin(2ωt + θ)
The average reactive power over an integral number of lines (n)
is given in Equation 22.
∫
θ==
nT
VIdttq
nT
Q
0
)sin()(
1
(22)
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
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 72).
In addition, the phase-shifting filter has a nonunity magnitude
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
characteristic of the phase shifting filter, the weight of the reactive
power is slightly different from 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 65), the reactive power signal
has some ripple due to the instantaneous reactive power signal.
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 to
calculate energy.
The reactive power signal can be read from the waveform register
by setting the WAVMODE register (Address 0x0D) and the
WFSM bit (Bit 5) in the Interrupt Enable 3 SFR (MIRQENH,
Address 0xDB). Like the current and voltage channels waveform
sampling modes, the waveform data is available at sample rates
of 25.6 kSPS, 12.8 kSPS, 6.4 kSPS, and 3.2 kSPS.