ADE7752AAR datasheet(13/24 Pages) AD

13 / 24 page

ADE7752/ADE7752A

Rev. C | Page 13 of 24

This is the correct real power calculation.

()

(

sin

∑

∞

)

(2)

INSTANTANEOUS

REAL POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

× I

× cos(60°)

× I

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS REAL

POWER SIGNAL

CURRENT

VOLTAGE

where:

i(t) is the instantaneous current.

IO is the dc component.

In is the rms value of current harmonic n.

β is the phase angle of the current harmonic.

Using Equations 1 and 2, the real power, P, can be expressed in

terms of its fundamental real power (P1) and harmonic real

power (PH).

+ P

P = P1

where:

−

cos

(3)

Figure 16. DC Component of Instantaneous Power Signal

Conveys Real Power Information PF < 1

−

∑

∞

cos

(4)

NONSINUSOIDAL VOLTAGE AND CURRENT

The real power calculation method also holds true for nonsin-

usoidal 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)

As can be seen from Equation 4, a harmonic real power compo-

nent 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 real power must also

correctly account for power factor since it is made up of a series

of pure sinusoids.

Note that the input bandwidth of the analog inputs is 14 kHz

with a master clock frequency of 10 MHz.

where:

v(t) is the instantaneous voltage.

VO is the average value.

Vn is the rms value of voltage harmonic n.

α n is the phase angle of the voltage harmonic.

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