ADE7761A

Rev. 0 | Page 14 of 24

ACTIVE POWER CALCULATION

The ADCs digitize the voltage signals from the current and

voltage transducers. A high-pass filter in the current channel

removes any dc component from the current signal. This

eliminates any inaccuracies in the active power calculation

due to offsets in the voltage or current signals (see the HPF and

Offset Effects section).

The active power calculation is derived from the instantaneous

power signal. The instantaneous power signal is generated by a

direct multiplication of the current and voltage signals. To

extract the active power component (dc component), the

instantaneous power signal is low-pass filtered. Figure 22

illustrates the instantaneous active power signal and shows how

the active power information can be extracted by low-pass

filtering the instantaneous power signal. This scheme correctly

calculates active power for nonsinusoidal current and voltage

waveforms at all power factors. All signal processing is carried

out in the digital domain for superior stability over temperature

and time.

F2

CF

F1

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

HPF

MULTIPLIER

LPF

ADC

ADC

CH1

CH2

INSTANTANEOUS

POWER SIGNAL –p(t)

INSTANTANEOUS

ACTIVE POWER SIGNAL

V × I

V × I

2

TIME

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

WHERE:

v(t) = V × cos(ωt)

i(t) = I × cos(ωt)

p(t) = V × I {1 + cos (2ωt)}

2

PGA

Figure 22. Signal Processing Block Diagram

The low frequency output of the ADE7761A 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 proportional to the instantaneous active power. This is

useful for system calibration purposes that take place under

steady load conditions.

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 23 displays the unity power factor condition and a

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

lagging the voltage by 60°.

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL

60°

CURRENT

CURRENT

VOLTAGE

0V

0V

VOLTAGE

V × I

2

V × I

2

× cos(60°)

Figure 23. Active Power Calculation over PF

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.

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(

2

)

(

0

h

h

h

O

t

h

V

V

t

v

α

+

ω

×

×

+

=

∑

∞

≠

(1)

where:

v(t) is the instantaneous voltage.