ADE7758_15 datasheet(39/72 Pages) AD

39 / 72 page

Data Sheet

ADE7758

Rev. E | Page 39 of 72

When using the line cycle accumulation mode, the RSTREAD

bit (Bit 6) of the LCYCMODE register should be set to Logic 0.

APPARENT POWER CALCULATION

Apparent power is defined as the amplitude of the vector sum of

the active and reactive powers. Figure 75 shows what is typically

referred to as the power triangle.

ACTIVE POWER

APPARENT

POWER

Figure 75. Power Triangle

There are two ways to calculate apparent power: the arithmetical

approach or the vectorial method. The arithmetical approach

uses the product of the voltage rms value and current rms value

to calculate apparent power. Equation 38 describes the arithmetical

approach mathematically.

S = VRMS × IRMS

(38)

where S is the apparent power, and VRMS and IRMS are the

rms voltage and current, respectively.

The vectorial method uses the square root of the sum of the

active and reactive power, after the two are individually squared.

Equation 39 shows the calculation used in the vectorial approach.

(39)

where:

S is the apparent power.

P is the active power.

Q is the reactive power.

For a pure sinusoidal system, the two approaches should yield

the same result. The apparent energy calculation in the ADE7758

uses the arithmetical approach. However, the line cycle energy

accumulation mode in the ADE7758 enables energy accumula-

tion between active and reactive energies over a synchronous

period, thus the vectorial method can be easily implemented in

the external MCU (see the Line Cycle Active Energy

Accumulation Mode section).

Note that apparent power is always positive regardless of the

direction of the active or reactive energy flows. The rms value of

the current and voltage in each phase is multiplied to produce

the apparent power of the corresponding phase.

The output from the multiplier is then low-pass filtered to obtain

the average apparent power. The frequency response of the LPF

in the apparent power signal path is identical to that of the LPF2

used in the average active power calculation (see Figure 66).

Apparent Power Gain Calibration

Note that the average active power result from the LPF output

in each phase can be scaled by ±50% by writing to the phase’s

VAGAIN register (AVAG, BVAG, or CVAG). The VAGAIN

registers are twos complement, signed registers and have a

resolution of 0.024%/LSB. The function of the VAGAIN

registers is expressed mathematically as

⎟

⎠

⎞

⎜

⎝

⎛ +

VAGAIN

Output

LPF

Power

Apparent

Average

(40)

The output is scaled by –50% by writing 0x800 to the VAR gain

registers and increased by +50% by writing 0x7FF to them.

These registers can be used to calibrate the apparent power (or

energy) calculation in the ADE7758 for each phase.

Apparent Power Offset Calibration

Each rms measurement includes an offset compensation register

to calibrate and eliminate the dc component in the rms value

(see the Current RMS Calculation section and the Voltage

Channel RMS Calculation section). The voltage and current

rms values are then multiplied together in the apparent power

signal processing. As no additional offsets are created in the

multiplication of the rms values, there is no specific offset

compensation in the apparent power signal processing. The offset

compensation of the apparent power measurement in each phase

should be done by calibrating each individual rms measurement

(see the Calibration section).

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