ADE7761ARSRL datasheet(16/28 Pages) AD

16 / 28 page

ADE7761

Rev. A | Page 16 of 28

The low frequency output of the ADE7761 is generated by

accumulating this active power information. This low frequency

inherently means a long accumulation time between output

pulses. The output frequency is, therefore, proportional to the

average active power. This average active power information can

in turn be accumulated (for example, by a counter) to generate

active energy information. Because of its high output frequency

and therefore shorter integration time, the CF output is propor-

tional to the instantaneous active power. This is useful for

system calibration purposes that would take place under steady

load conditions.

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

HPF

MULTIPLIER

LPF

ADC

CH1

CH2

INSTANTANEOUS

POWER SIGNAL –p(t)

INSTANTANEOUS

ACTIVE POWER SIGNAL

V× I

TIME

p(t) = i(t).v(t)

WHERE:

v(t) = V × cos(

ϖt)

i(t) = I × cos(

ϖt)

p(t) =

V× I

{1 + cos (2

ϖt)}

Figure 20. Signal Processing Block Diagram

Power Factor Considerations

The method used to extract the active power information from

the instantaneous power signal (by low-pass filtering) is still

valid even when the voltage and current signals are not in

phase. Figure 21 displays the unity power factor condition and

a displacement power factor (DPF = 0.5), that is, current signal

lagging the voltage by 60°. If one assumes that the voltage and

current waveforms are sinusoidal, the active power component

of the instantaneous power signal (dc term) is given by

(V × I/2) × cos(60°)

This is the correct active power calculation.

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL

60°

CURRENT

VOLTAGE

V× I

× cos(60°)

Figure 21. Active Power Calculation over PF

Nonsinusoidal Voltage and Current

The active power calculation method also holds true for

nonsinusoidal current and voltage waveforms. All voltage and

current waveforms in practical applications have some

harmonic content. Using the Fourier transform, instantaneous

voltage and current waveforms can be expressed in terms of

their harmonic content:

)

sin(

)

(

∑

∞

≠

(1)

where:

v(t) is the instantaneous voltage.

VO is the average value.

Vh is the rms value of voltage harmonic h.

αh is the phase angle of the voltage harmonic.

)

sin(

)

(

∑

∞

≠

(2)

where:

i(t) is the instantaneous current.

IO is the dc component.

Ih is the rms value of current harmonic h.

βh is the phase angle of the current harmonic.

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