ADE7878ACPZ datasheet(47/92 Pages) AD

47 / 92 page

ADE7878

Rev. 0 | Page 47 of 92

IRQ0 pin is set to high again by writing to the STATUS0

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

(28)

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.

REACTIVE POWER CALCULATION

The ADE7878 computes the total reactive power on every

phase. Total reactive power integrates all fundamental and

harmonic components of the voltages and currents. ADE7878

also computes the fundamental reactive power, the power

determined only by the fundamental components of the

voltages and currents.

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 gives an expression for the instantaneous reactive

power signal in an ac system when the phase of the current

channel is shifted by +90°.

∑

∞

)

(

sin(

kωt + φk)

(29)

()

∑

∞

sin

)

(

(30)

⎟

⎠

⎞

⎜

⎝

⎛

∑

∞

sin

)

(

where iʹ(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)

(31)

∑

∞

)

(

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 ]

}

(32)

The average total reactive power over an integral number of line

cycles (n) is given by the expression in Equation 33.

()

∫

∑

∞

k I

cos(

φk – γk −

)

(33)

∑

∞

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

in the ADE7878 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 ADE7878 stores the instantaneous total phase reactive

powers into the AVAR[23:0], BVAR[23:0], and CVAR[23:0]

registers. Their expression is

∑

∞

xVAR

sin(φk – γk) × PMAX ×

(34)

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, the instantaneous power computed when

the ADC inputs are at full scale and in phase.

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

various serial ports. Refer to the Waveform Sampling Mode

section for more details.

The expression of fundamental reactive power is obtained from

Equation 37 with k = 1, as follows:

FQ = V1I1 cos(φ1 – γ1)

The ADE7878 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.

ADE7878ACPZ Datasheet(PDF) 47 Page - Analog Devices

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