ADE7953 datasheet(28/68 Pages) AD

28 / 68 page

ADE7953

Data Sheet

Rev. A | Page 28 of 68

REACTIVE POWER CALCULATION

Reactive power is defined as the product of the voltage and

current waveforms when one of these signals is phase shifted

by 90°. The resulting waveform is called the instantaneous

reactive power signal.

Equation 16 provides an expression for the instantaneous

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

current channel is shifted by +90°.

RP(t) = V(t) × I’(t)

(16)

RP(t) = VI × sin(θ) + VI × sin(2ωt + θ)

(17)

)

sin(

ωt

V(t)

(18)

)

sin(

ωt

I(t)

(19)

I’(t) =

⎟

⎠

⎞

⎜

⎝

⎛

sin

ωt

(20)

where:

V is the rms voltage.

I is the rms current.

θ is the phase difference between the voltage and current channel.

The average reactive power over an integral number of line

cycles (n) is given by the expression in Equation 21.

∫

)

sin(

)

(

(21)

where:

RP is the reactive power.

T is the line cycle period.

The reactive power is equal to the dc component of the

instantaneous reactive power signal (RP(t) in Equation 16).

This relationship is used to calculate reactive power in the

ADE7953. The signal chain for the reactive power and energy

calculations in the ADE7953 is shown in Figure 51.

The instantaneous reactive power signal RP(t) is generated by

multiplying the current signal and the voltage signal. Simulta-

neous calculations are performed using Current Channel A and

Current Channel B. The multiplication is performed over the full

1.23 kHz bandwidth and results in a reactive power measurement

that includes all harmonics included in this range.

The ADE7953 reactive power measurement is stable over the

full frequency range. The dc component of the instantaneous

reactive power signal is then extracted by a low-pass filter to

obtain the reactive power information.

The frequency response of the LPFs in the reactive power signal

paths is identical to the frequency response of the LPFs used in

the active power calculation. Because the LPF does not have an

ideal “brick wall” frequency response, the reactive power signal

has some ripple associated with it. 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 reactive

power signal is integrated to compute the reactive energy (see

the Reactive Energy Calculation section).

The ADE7953 computes the reactive power simultaneously

on Current Channel A and Current Channel B and stores the

resulting measurements in the AVAR (Address 0x214 and

Address 0x314) and BVAR (Address 0x215 and Address 0x315)

registers, respectively. With full-scale inputs, the expected

reading in the AVAR and BVAR registers is approximately

4862401 LSBs (decimal).

The reactive power registers are updated at a rate of 6.99 kHz

and can be read using the waveform sampling mode (see the

Instantaneous Powers and Waveform Sampling section).

SIGN OF REACTIVE POWER CALCULATION

The reactive power measurement in the ADE7953 is a signed

calculation. If the current waveform is leading the voltage wave-

form, the reactive power is negative. Negative reactive power

indicates a capacitive load. If the current waveform is lagging

the voltage waveform, the reactive power is positive. Positive

reactive power indicates an inductive load. The ACCMODE

indication bits that show the sign of the reactive power of

Current Channel A (VARSIGN_A) and Current Channel B

(VARSIGN_B). See the Sign Indication section for more

information.

CURRENT

CHANNEL

A OR B

xVAROS

VOLTAGE

CHANNEL

INTERNAL

ACCUMULATION

FIXED INTERNAL

THRESHOLD

REACTIVE

POWER

SIGNAL

RENERGYx

REACTIVE

POWER

ALGORITHM

xVARGAIN

Figure 51. Reactive Energy Signal Chain

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