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ADE7518
Voltage Channel RMS Calculation
Figure 50 shows details of the signal processing chain for the
rms calculation on the voltage channel. The voltage channel
rms value is processed from the samples used in the voltage
where:
v is the rms voltage.
i is the rms current.
p ( t ) = v ( t ) × i ( t )
channel waveform sampling mode and is stored in the unsigned
24-bit V rms register.
p ( t ) = VI ? VI cos( 2 ω t )
(8)
The update rate of the voltage channel rms measurement is
MCLK/5. To minimize noise in the reading of the register, the
The average power over an integral number of line cycles (n) is
given by the expression in Equation 9.
∫ 0
V rms register can also be configured to update only with the
zero crossing of the voltage input. This configuration is done
P =
1
nT
nT
p ( t ) dt = VI
(9)
by setting the ZXRMS bit in the MODE2 register (0x0C).
With the specified full-scale ac analog input signal of 0.4 V, the
output from the LPF1 in Figure 50 swings between 0x28F5 and
0xD70B at 60 Hz (see the Voltage Channel ADC section). The
equivalent rms value of this full-scale ac signal is approximately
0d1,898,124 (0x1CF68C) in the V rms register. The voltage rms
measurement provided in the ADE7518 is accurate to within
±0.5% for signal input between full scale and full scale/20.
The conversion from the register value to volts must be done
externally in the microprocessor using a V/LSB constant.
Voltage Channel RMS Offset Compensation
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 9, that is, VI. This
is the relationship used to calculate active power in the ADE7518.
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 49.
The ADE7518 incorporates a voltage channel rms offset compensa-
INSTANTANEOUS
POWER SIGNAL
p(t) = v × i – v × i × cos(2 ω t)
tion register (VRMSOS). This is a 12-bit signed register that can
be used to remove offset in the voltage channel rms calculation.
An offset can exist in the rms calculation due to input noises
and dc offset in the input samples. One LSB of the voltage
channel rms offset is equivalent to 64 LSBs of the rms register.
Assuming that the maximum value from the voltage channel
rms calculation is 0d1,898,124 with full-scale ac inputs, then
1 LSB of the voltage channel rms offset represents 3.37% of
measurement error at ?60 dB down from full scale.
0x19999A
VI
0xCCCCD
0x00000
ACTIVE REAL POWER
SIGNAL = v × i
V rms = V rms0 + 64 × VRMSOS
(5)
CURRENT
i(t) = √ 2 × i × sin( ω t)
where V rms0 is the rms measurement without offset correction.
ACTIVE POWER CALCULATION
Active power is defined as the rate of energy flow from source
to load. It is 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 watt or joules/second. Equation 8 gives an
expression for the instantaneous power signal in an ac system.
v ( t ) = 2 × V sin( ω t ) (6)
VOLTAGE
v(t) = √ 2 × v × sin( ω t)
Figure 49. Active Power Calculation
Because LPF2 does not have an ideal brick wall frequency response
(see Figure 51), 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 of its
sinusoidal nature, the ripple is removed when the active power
signal is integrated to calculate energy (see the Active Energy
Calculation section).
i ( t ) = 2 × I sin( ω t )
(7)
VOLTAGE SIGNAL (V(t))
0x28F5
VRMSOS[11:0]
0x00
VOLTAGE CHANNEL
LPF1
0x0
0xD70B
LPF3
sgn 2 16 2 15
+
2 8 2 7 2 6
VRMSx[23:0]
0x28F5C2
+
Figure 50. Voltage Channel RMS Signal Processing
Rev. 0 | Page 48 of 128
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