ADE7753ARS datasheet(34/60 Pages) AD

34 / 60 page

ADE7753

Rev. C | Page 34 of 60

90°. The resulting waveform is called the instantaneous reactive

power signal. Equation 25 gives an expression for the instanta-

neous reactive power signal in an ac system when the phase of

the current channel is shifted by +90°.

The average reactive power over an integral number of lines (n)

is given in Equation 26.

v(t) =

)

sin(

ωt

(23)

∫

)

sin(

)

(

(26)

i(t) =

)

sin(

⎟

⎠

⎞

⎜

⎝

⎛

′

sin

)

(

(24)

where:

T is the line cycle period.

RP is referred to as the reactive power.

Note that the reactive power is equal to the dc component of the

instantaneous reactive power signal Rp(t) in Equation 25. This

is the relationship used to calculate reactive power in the

ADE7753. The instantaneous reactive power signal Rp(t) is

generated by multiplying Channel 1 and Channel 2. In this case,

the phase of Channel 1 is shifted by +90°. The dc component of

the instantaneous reactive power signal is then extracted by a

low-pass filter in order to obtain the reactive power informa-

tion. Figure 71 shows the signal processing in the reactive

power calculation in the ADE7753.

where:

θ is the phase difference between the voltage and current

channel.

V is the rms voltage.

I is the rms current.

Rp(t) = v(t) × i’(t)

(25)

Rp(t) = VI sin (θ) + VI sin(2ωt + θ)

ZERO-CROSSING

DETECTION

MULTIPLIER

LVARENERGY [23:0]

ACCUMULATE REACTIVE

ENERGY IN INTERNAL

THE LVARENERGY REGISTER

AT THE END OF LINECYC HALF

LINE CYCLES

INSTANTANEOUS REACTIVE

POWER SIGNAL (Rp(t))

02875-0-070

LPF1

FROM

CHANNEL 2

ADC

LINECYC [15:0]

LPF2

CALIBRATION

CONTROL

90 DEGREE

PHASE SHIFT

Figure 71. Reactive Power Signal Processing

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