ADE7752BARWZ datasheet(14/27 Pages) AD

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ADE7752B

Preliminary Technical Data

Rev. PrA | Page 14 of 27

This is the correct active power calculation.

INSTANTANEOUS

ACTIVE POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

V× I

×cos(60

°)

V× I

CURRENT

VOLTAGE

Figure 16. DC Component of Instantaneous Power Signal

NONSINUSOIDAL VOLTAGE AND CURRENT

The active power calculation method also holds true for non-

sinusoidal 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)

where:

(t) is the instantaneous voltage.

is the average value.

is the rms value of voltage harmonic n.

and α n is the phase angle of the voltage harmonic.

()

∑

∞

sin

(3)

where:

i(t) is the instantaneous current.

IO is the dc component.

In is the rms value of current harmonic n.

βn is the phase angle of the current harmonic.

Using Equations 2 and 3, the active power, P, can be expressed

in terms of its fundamental active power (P1) and harmonic

active power (PH).

P = P1 + PH

where:

cos

−

(4)

−

∑

∞

cos

(5)

As can be seen from Equation 5, a harmonic active power

component is generated for every harmonic, provided that

harmonic is present in both the voltage and current waveforms.

The power factor calculation has been shown to be accurate in

the case of a pure sinusoid. Therefore, the harmonic active

power also correctly accounts for power factor since harmonics

are made up of a series of pure sinusoids. A limiting factor on

harmonic measurement is the bandwidth. On the ADE7752B,

the bandwidth of the active power measurement is 14 kHz with

a master clock frequency of 10 MHz.

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