ADE7978 datasheet(63/125 Pages) AD

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Data Sheet

ADE7978/ADE7933/ADE7932/ADE7923

Rev. D | Page 63 of 125

REACTIVE POWER CALCULATION

The ADE7978 can compute the total reactive power on every

phase. The calculation of total reactive power includes all funda-

mental and harmonic components of the voltages and currents.

The ADE7978 also computes the fundamental reactive power,

that is, the power determined only by the fundamental components

of the voltages and currents.

TOTAL REACTIVE POWER CALCULATION

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°.

The total reactive power is equal to

∑

∞

k I

sin(φk − γk)

(35)

where:

Vk, Ik are the rms voltage and current, respectively, of each

harmonic.

φk, γk are the phase delays of each harmonic.

This relationship is used to calculate the total reactive power in

the ADE7978 for each phase. The instantaneous reactive power

signal is generated by multiplying each harmonic of the voltage

signals by the corresponding 90° phase-shifted harmonic of the

current in each phase.

The ADE7978 stores the instantaneous total phase reactive powers

in the AVAR, BVAR, and CVAR registers (Address 0xE51B to

Address 0xE51D). The instantaneous total phase reactive powers

are expressed by

∑

∞

xVAR

sin(φk − γk) × PMAX ×

(36)

where:

VFS and IFS are the rms values of the phase voltage and current

when the ADC inputs are at full scale.

PMAX = 26,991,271, 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

any of the serial port interfaces. For more information, see

the Waveform Sampling Mode section.

FUNDAMENTAL REACTIVE POWER CALCULATION

The expression of fundamental reactive power is obtained from

Equation 35 with k = 1, as follows:

FQ = V1I1 sin(φ1 − γ1)

The ADE7978 computes the fundamental reactive power using a

proprietary algorithm that requires initialization of the network

frequency and of the nominal voltage measured in the voltage

channel. The required initialization is the same as for the

fundamental active powers and is described in the Fundamental

Active Power Calculation section.

Table 25 provides the settling time for the fundamental reactive

power measurement. The settling time is the time required for

the power to reflect the value at the input of the ADE7978.

Table 25. Settling Time for Fundamental Reactive Power

Input Signal

Settling Time (ms)

63% PMAX

375

100% PMAX

875

REACTIVE POWER GAIN CALIBRATION

The average reactive power in each phase can be scaled by ±100%

by writing to the 24-bit VAR gain register for each phase: APGAIN,

BPGAIN, or CPGAIN (Address 0x4399 to Address 0x439B). The

same registers are used to compensate the other powers computed

by the ADE7978. For more information about these registers,

see the Active Power Gain Calibration section.

REACTIVE POWER OFFSET CALIBRATION

The ADE7978 includes a 24-bit reactive power offset register for

each phase and each reactive power. The AVAROS, BVAROS,

and CVAROS registers (Address 0x439F to Address 0x43A1)

compensate offsets in the total reactive power calculations. The

AFVAROS, BFVAROS, and CFVAROS registers (Address 0x43A6

to Address 0x43A8) compensate offsets in the fundamental reactive

power calculations. These signed twos complement registers are

used to remove offsets in the reactive power calculations.

An offset can exist in the power calculation due to crosstalk

between channels on the PCB or in the chip itself. One LSB in

the reactive power offset register is equivalent to 1 LSB in the

reactive power multiplier output. With full-scale current and

voltage inputs, the LPF2 output is PMAX = 26,991,271. At

−80 dB down from full scale (active power scaled down 104

times), one LSB of the reactive power offset register represents

0.037% of PMAX.

The serial ports of the ADE7978 work with 32-, 16-, or 8-bit

words, whereas the DSP works with 28-bit words. Like the

xIGAIN registers shown in Figure 52, the 24-bit xVAROS and

xFVAROS registers are sign extended to 28 bits and padded

with four 0s for transmission as 32-bit registers.

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