ADE7753 View Datasheet(PDF) - Analog Devices
Part Name
Description
MFG CO.
'ADE7753' PDF : 60 Pages View PDF
ADE7753
0.4
0.3
0.2
0.1
0.0
–0.1
–0.2
–0.3
–0.4
54
56
58
60
62
64
66
FREQUENCY (Hz)
02875-0-059
Figure 60. Combined Gain Response of the HPF and Phase Compensation
ACTIVE POWER CALCULATION
Power is defined as the rate of energy flow from source to load.
It is defined as the product of the voltage and current wave-
forms. The resulting waveform is called the instantaneous
power signal and is equal to the rate of energy flow at every
instant of time. The unit of power is the watt or joules/sec.
Equation 9 gives an expression for the instantaneous power
signal in an ac system.
v(t) = 2 ×V sin(ωt)
(7)
i(t) = 2 × I sin(ωt)
(8)
where:
V is the rms voltage.
I is the rms current.
p(t) = v(t) × i(t)
p(t) = VI −VI cos(2ωt)
(9)
The average power over an integral number of line cycles (n) is
given by the expression in Equation 10.
P=
1
nT
∫ nT
0
p(t)dt = VI
(10)
where:
T is the line cycle period.
P is referred to as the active or real power.
Note that the active power is equal to the dc component of the
instantaneous power signal p(t) in Equation 8, i.e., VI. This is
the relationship used to calculate active power in the ADE7753.
The instantaneous power signal p(t) is generated by multiplying
the current and voltage signals. The dc component of the
instantaneous power signal is then extracted by LPF2 (low-pass
filter) to obtain the active power information. This process is
illustrated in Figure 61.
INSTANTANEOUS
POWER SIGNAL
0x19999A
p(t) = v×i-v×i×cos(2ωt)
ACTIVE REAL POWER
SIGNAL = v × i
VI
0xCCCCD
0x00000
CURRENT
i(t) = 2×i×sin(ωt)
VOLTAGE
v(t) = 2×v×sin(ωt)
Figure 61. Active Power Calculation
02875-0-060
Since LPF2 does not have an ideal “brick wall” frequency
response—see Figure 62, the active power signal has some
ripple due to the instantaneous 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 active power signal is integrated to calculate energy—see the
Energy Calculation section.
0
–4
–8
–12
–16
–20
–24
1
3
10
30
FREQUENCY (Hz)
Figure 62. Frequency Response of LPF2
100
02875-0-061
Rev. C | Page 28 of 60
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