ADE7166 datasheet(59/148 Pages) AD

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Preliminary Technical Data

ADE75xx/ADE71xx

Rev. PrE | Page 59 of 148

REACTIVE POWER CALCULATION15

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 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°.

v(t) =

)

sin(

ωt

(23)

i(t) =

)

sin(

⎟

⎠

⎞

⎜

⎝

⎛

′

sin

)

(

(24)

where:

θ is the phase difference between the voltage and current

channel.

V is the rms voltage.

I is the rms current.

q(t) = v(t) × i’(t)

(25)

q(t) = VI sin (θ) + VI sin

)

(

ωt

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

is given in Equation 26.

∫

)

sin(

)

(

(26)

where:

T is the line cycle period.

q is referred to as the reactive power.

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

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

the relationship used to calculate reactive power in the

ADE75XX/ADE71XX. The instantaneous reactive power signal

q(t) is generated by multiplying Voltage and Current channels.

In this case, the phase of Current channel 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 information – see Figure 45.

In addition, the phase shifting filter has a non-unity magnitude

response. Because the phase-shift filter has a large attenuation at

high frequency, the reactive power is primarily for the

calculation at line frequency. The effect of harmonics is largely

ignored in the reactive power calculation. Note that because of

the magnitude characteristic of the phase shifting filter, the

weight of the reactive power is slightly different from the active

power calculation – see Energy register scaling.

15 This function is not available in ADE7566 and ADE7166products

The frequency response of the LPF in the reactive signal path is

identical to that of the LPF2 used in the average active power

calculation. Since LPF2 does not have an ideal “brick wall”

frequency response—see Figure 38, the reactive power signal

has some ripple due to the instantaneous reactive 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 reactive power signal is integrated to

calculate energy—see the Reactive Power Calculation section.

The reactive power signal can be read from the waveform

the WFSM bit in the Interrupt Enable Register 3 SFR

(MIRQENH, 0xDB). Like the current and voltage channels

waveform sampling modes, the waveform date is available at

sample rates of 27.9 kSPS, 14 kSPS, 7 kSPS, or

3.5 kSPS.

Reactive gain automatic compenstation

The ADE75XX/ADE71XX reactive power calculation has a

20dB/decade attenuation over frequency. In order to attenuate

this effect for the line frequency, the ADE75XX/ADE71XX has

a dynamic compensation of the line frequency to maintain a

constant gain over the fundamental line frequency between 45

and 65Hz. However, this automatic compensation can be

disabled by setting bit 7 of the NLMODE register (0x0E).

Reactive power gain calibration

Figure 45 shows the signal processing chain for the reactive

power calculation in the ADE75XX/ADE71XX. As explained,

the reactive power is calculated by low-pass filtering the

instantaneous reactive power signal. Note that when reading the

waveform samples from the output of LPF2, the gain of the

reactive energy can be adjusted by using the multiplier and var

gain register (VARGAIN[11:0]). The gain is adjusted by writing

a twos complement 12-bit word to the var gain register.

Equation 11 shows how the gain adjustment is related to the

contents of the watt gain register:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎭

⎬

⎫

⎩

⎨

⎧ +

VARGAIN

Power

active

VARGAIN

Output

(11)

The resolution of the VARGAIN register is the same as the

WGAIN register – see Active power gain calibration section.

VARGAIN can be used to calibrate the reactive power (or

energy) calculation in the ADE75XX/ADE71XX.

Reactive power offset calibration

The ADE75XX/ADE71XX also incorporates a reactive power

offset register (VAROS[15:0]). This is a signed twos

complement 16-bit register that can be used to remove offsets in

the reactive power calculation—see Figure 45. An offset could

exist in the reactive power calculation due to crosstalk between

channels on the PCB or in the IC itself. The offset calibration

allows the contents of the reactive power register to be

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