ADE7166 datasheet(58/144 Pages) AD

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ADE7566/ADE7569/ADE7166/ADE7169

Rev. A | Page 58 of 144

Voltage Channel RMS Calculation

The average power over an integral number of line cycles (n) is

given by the expression in Equation 11.

Figure 62 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

channel waveform sampling mode and is stored in the unsigned

24-bit Vrms register.

∫

)

(

(11)

where:

is the line cycle period.

is referred to as the active or real power.

The update rate of the voltage channel rms measurement is

MCLK/5. To minimize noise in the reading of the register, the

Vrms register can also be configured to update only with the zero

crossing of the voltage input. This configuration is done by

setting the ZXRMS bit in the MODE2 register (0x0C).

Note that the active power is equal to the dc component of the

instantaneous power signal p(t) in Equation 11, that is, VI. This

is the relationship used to calculate active power in the ADE7566/

ADE7569/ADE7166/ADE7169. 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

With the specified full-scale ac analog input signal of 0.4 V, the

output from the LPF1 in Figure 62 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 Vrms register. The voltage rms

measurement provided in the ADE7566/ADE7569/ADE7166/

ADE7169 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.

Figure 63.

INSTANTANEOUS

POWER SIGNAL

p(t) = v × i – v × i × cos(2ωt)

ACTIVE REAL POWER

SIGNAL = v × i

0x19999A

0xCCCCD

0x00000

CURRENT

i(t) = √2 × i × sin(ωt)

VOLTAGE

v(t) = √2 × v × sin(ωt)

Voltage Channel RMS Offset Compensation

The ADE7566/ADE7569/ADE7166/ADE7169 incorporate a

voltage channel rms offset compensation 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

of full scale.

Figure 63. Active Power Calculation

Because LPF2 does not have an ideal brick wall frequency

response (see Figure 64

Vrms

= Vrms0 + 64 × VRMSOS

(7)

), 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

where Vrms0 is the rms measurement without offset correction.

Active Energy Calculation section).

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 the watt or joules/second. Equation 10 gives an

expression for the instantaneous power signal in an ac system.

()

)

sin(

(8)

()

)

sin(

(9)

FREQUENCY (Hz)

–24

–20

310

–12

–16

–8

–4

where:

is the rms voltage.

is the rms current.

)

(

)

(

)

(

Figure 64. Frequency Response of LPF2

)

cos(

)

(

−

(10)

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