ADE5169 datasheet(53/148 Pages) AD

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ADE5166/ADE5169

Rev. 0 | Page 53 of 148

Voltage Channel RMS Calculation

Figure 58 shows details of the signal processing chain for the

rms calculation on the voltage channel. This voltage rms esti-

mation is done in the ADE5166/ADE5169 using the mean

absolute value calculation, as shown in Figure 58. 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.

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 (Bit 2) in the MODE2 register (Address 0x0C).

With the specified full-scale ac analog input signal of 0.5 V, the

output from the LPF1 in Figure 58 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 ADE5166/ADE5169 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

The ADE5166/ADE5169 incorporate a voltage channel rms

offset compensation register (VRMSOS). This is a 12-bit signed

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.

Vrms = Vrms0 + 64 × VRMSOS

(5)

where Vrms0 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 the watt or joules/second. Equation 8 gives an

expression for the instantaneous power signal in an ac system.

()

)

sin(

(6)

()

)

sin(

(7)

where:

v is the rms voltage.

i is the rms current.

)

(

)

(

)

(

)

cos(

)

(

−

(8)

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

given by the expression in Equation 9.

∫

)

(

(9)

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 ADE5166/

ADE5169. 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 (see Figure 59).

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)

Figure 59. Active Power Calculation

Because LPF2 does not have an ideal brick wall frequency response

(see Figure 60), 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).

FREQUENCY (Hz)

–24

–20

100

–12

–16

–8

–4

Figure 60. Frequency Response of LPF2

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