Datasheet

ADE7953 Data Sheet
Rev. B | Page 24 of 72
ACTIVE POWER CALCULATION
Power is defined as the rate of energy flow from the source to
the load. It is defined as the product of the voltage and current
waveforms. 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.
)sin(2 ωt V V(t) 
(3)
)sin(2 ωt I I(t) 
(4)
where:
V is the rms voltage.
I is the rms current.
P(t) = V(t) × I(t) (5)
P(t) = VI − VI × cos(2ωt) (6)
The average power over an integral number of line cycles (n)
is given by the expression in Equation 7.


nT
VIdttP
nT
P
0
)(
1
(7)
where:
P is the active or real power.
T is the line cycle period.
The active power is equal to the dc component of the instan-
taneous power signal (P(t) in Equation 5). The active power is
therefore equal to VI. This relationship is used to calculate active
power in the ADE7953. Figure 44 illustrates this concept.
The signal chain for the active power and energy calculations in
the ADE7953 is shown in Figure 45. 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. Because LFP2 does not have an ideal “brick
wall” frequency response, the active power signal has some
ripple associated with it. 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 compute the active energy (see the Active
Energy Calculation section).
INST
A
NT
A
NEOUS
POWER SIGNAL
INSTANTANEOUS
ACTIVE POWER SIGNAL:
VRMS × IRMS
P(t) = VRMS × IRMS – VRMS × IRMS × cos(2ωt)
VRMS
×
IRMS
0x0 0000
I(t) = √2 × IRMS × sin(ωt)
V(t) = √2×VRMS×sin(ωt)
09320-043
Figure 44. Active Power Calculation
The ADE7953 computes the active power simultaneously on
Current Channel A and Current Channel B and stores the
resulting measurements in the AWATT (Address 0x212 and
Address 0x312) and BWATT (Address 0x213 and Address 0x313)
registers, respectively. With full-scale inputs, the expected
reading in the AWATT and BWATT registers is approximately
4862401 LSBs (decimal).
The active power measurements are taken over a bandwidth of
1.23 kHz and include the effects of any harmonics within that
range. The active power registers are updated at a rate of 6.99 kHz
and can be read using the waveform sampling mode (see the
Instantaneous Powers and Waveform Sampling section).
09320-044
AVGAIN
CURRENT
CHANNEL
A
VOLTAGE
CHANNEL
HPF
AIGAIN
DIGITAL
INTEGRATOR
HPF
48 0
+
+
AWATTOS
PHCALA
INTERNAL
ACCUMULATION
FIXED INTERNAL
THRESHOLD
ACTIVE POWER
SIGNAL
AENERGYA
23 0
LPF2
AWGAIN
BIGAIN
CURRENT
CHANNEL
B
HPF
BVGAIN
HPF
DIGITAL
INTEGRATOR
48 0
+
+
BWATTOS
PHCALB
INTERNAL
ACCUMULATION
FIXED INTERNAL
THRESHOLD
ACTIVE POWER
SIGNAL
AENERGYB
23 0
LPF2
BWGAIN
Figure 45. Active Energy Signal Chain