ADE7878 datasheet(42/92 Pages) AD

42 / 92 page

ADE7878

Rev. 0 | Page 42 of 92

AVGAIN

HPFDIS

[23:0]

HPF

LPF

AIGAIN

HPFDIS

[23:0]

DIGITAL

INTEGRATOR

HPF

AWGAIN

AWATTOS

APHCAL

INSTANTANEOUS

PHASE A ACTIVE

POWER

DIGITAL SIGNAL PROCESSOR

Figure 58. Total Active Power Datapath

If the phase currents and voltages contain only the fundamental

component, are in phase (that is φ1 = γ1 = 0) and correspond to

full-scale ADC inputs, then multiplying them results in an

instantaneous power signal that has a dc component, V1 × I1,

and a sinusoidal component, V1 × I1 cos(2ωt). Figure 59 shows

the corresponding waveforms.

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER

SIGNAL: Vrms × Irms

p(t)= Vrms × Irms – Vrms × Irms × cos(2ωt)

0x3FED4D6

67,032,278

Vrms × Irms

0x1FF6A6B =

33,516,139

0x000 0000

i(t) = √2 × Irms × sin(ωt)

v(t) = √2× Vrms × 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 the ripple is sinusoidal in nature, it is

removed when the active power signal is integrated over

time to calculate the energy.

–5

–10

–15

–20

–25

0.1

FREQUENCY (Hz)

Figure 60. Frequency Response of the LPF Used

to Filter Instantaneous Power in Each Phase

The ADE7878 stores the instantaneous total phase active

powers into the AWATT[23:0], BWATT[23:0], and

CWATT[23:0] registers. Their expression is

∑

∞

xWATT

cos(φk – γk) × PMAX ×

(20)

where:

UFS, IFS are the rms values of the phase voltage and current when

the ADC inputs are at full scale.

PMAX = 33,516,139; it is the instantaneous power computed

when the ADC inputs are at full scale and in phase.

The xWATT[23:0] waveform registers can be accessed using

various serial ports. Refer to the Waveform Sampling Mode

section for more details.

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