ADE7880 datasheet(49/104 Pages) AD

49 / 104 page

Data Sheet

ADE7880

Rev. A | Page 49 of 104

set to high again by writing to the STATUS0 register with the

corresponding bit set to 1.

Because the active power is integrated on an integer number of

half-line cycles in this mode, the sinusoidal components are

reduced to 0, eliminating any ripple in the energy calculation.

Therefore, total energy accumulated using the line cycle

accumulation mode is

()

∑

∫

∞

cos(φk – γk)

(29)

where nT is the accumulation time.

Note that line cycle active energy accumulation uses the same

signal path as the active energy accumulation. The LSB size of

these two methods is equivalent.

FUNDAMENTAL REACTIVE POWER CALCULATION

The ADE7880 computes the fundamental reactive power, the

power determined only by the fundamental components of the

voltages and currents.

The ADE7880 also computes the harmonic reactive powers, the

reactive powers determined by the harmonic components of the

voltages and currents. See Harmonics Calculations section for

details. A load that contains a reactive element (inductor or

capacitor) produces a phase difference between the applied ac

voltage and the resulting current. The power associated with

reactive elements is called reactive power, and its unit is VAR.

Reactive power is defined as the product of the voltage and current

waveforms when all harmonic components of one of these

signals are phase shifted by 90°.

Equation 31 is an example of the instantaneous reactive power

signal in an ac system when the phase of the current channel is

shifted by +90°.

∑

∞

)

(

sin(kωt + φk)

(30)

()

∑

∞

sin

)

(

(31)

⎟

⎠

⎞

⎜

⎝

⎛

∑

∞

sin

)

(

where i’(t) is the current waveform with all harmonic

components phase shifted by 90°.

Next, the instantaneous reactive power, q(t), can be expressed as

q(t) = v(t) × iʹ(t)

(32)

∑

∞

)

(

k I

sin(kωt + φk) × sin(kωt + γk +

) +

× 2sin(kωt + φk) × sin(mωt + γm +

∑

∞

≠

k I

)

Note that q(t) can be rewritten as

∑

∞

)

(

k I

{cos(φ

− γk −

π ) − cos(2 kωt + φ

+ γk +

π )} +

∑

∞

≠

{cos[(k – m)ωt + φ

− γk −

π ]−

cos

[(k + m)ωt + φk + γk +

π ]

}

(33)

The average total reactive power over an integral number of line

cycles (n) is shown in Equation 34.

()

∫

∑

∞

k I

cos(φk – γk −

)

(34)

∑

∞

k I

sin(φk – γk)

where:

T is the period of the line cycle.

Q is referred to as the total reactive power. Note that the total

reactive power is equal to the dc component of the instantaneous

reactive power signal q(t) in Equation 32, that is,

∑

∞

k I

sin(φk – γk)

This is the relationship used to calculate the total reactive power

for each phase. The instantaneous reactive power signal, q(t), is

generated by multiplying each harmonic of the voltage signals by

the 90° phase-shifted corresponding harmonic of the current in

each phase.

The expression of fundamental reactive power is obtained from

Equation 33 with k = 1, as follows:

FQ = V1I1 sin(φ1 – γ1)

The ADE7880 computes the fundamental reactive power using

a proprietary algorithm that requires some initialization

function of the frequency of the network and its nominal

voltage measured in the voltage channel. These initializations

are introduced in the Active Power Calculation section and are

common for both fundamental active and reactive powers.

The ADE7880 stores the instantaneous fundamental phase

reactive powers into the AFVAR, BFVAR, and CFVAR registers.

Their equation is

xFVAR

sin(φ1 – γ1) × PMAX ×

(35)

where:

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

the ADC inputs are at full scale.

PMAX = 27,059,678, the instantaneous power computed when

the ADC inputs are at full scale and in phase.

The xFVAR waveform registers are not mapped with an address

in the register space and can be accessed only through HSDC

port in the waveform sampling mode (see Waveform Sampling

Mode section for details). Fundamental reactive power

information is also available through the harmonic calculations

of the ADE7880 (see Harmonics Calculations section for details).

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