ADE7763ARSRL datasheet(31/56 Pages) AD

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ADE7763

Rev. A | Page 31 of 56

APPARENT POWER CALCULATION

The apparent power is the maximum power that can be

delivered to a load. Vrms and Irms are the effective voltage and

current delivered to the load; the apparent power (AP) is

defined as Vrms × Irms. The angle θ between the active power and

the apparent power generally represents the phase shift due to

nonresistive loads. For single-phase applications, θ represents

the angle between the voltage and the current signals—see

Figure 63. Equation 24 gives an expression of the instantaneous

power signal in an ac system with a phase shift.

REACTIVE

POWER

APPARENT POWER

ACTIVE POWER

Figure 63. Power Triangle

()

sin(

)

rms

()

sin(

)

rms

ω θ

(23)

)

(

)

(

)

(

)

cos(

)

cos(

)

(

−

rms

(24)

The apparent power is defined as Vrms × Irms. This expression is

independent from the phase angle between the current and

the voltage.

Figure 64 illustrates the signal processing in each phase for the

calculation of the apparent power in the ADE7763.

VRMS

IRMS

0xA D055

APPARENT POWER

SIGNAL (P)

CURRENT RMS SIGNAL – i(t)

VOLTAGE RMS SIGNAL– v(t)

MULTIPLIER

0x00

0x1C 82B3

0x00

0x17 D338

VAGAIN

Figure 64. Apparent Power Signal Processing

The gain of the apparent energy can be adjusted by using the

multiplier and VAGAIN register (VAGAIN[11:0]). The gain is

adjusted by writing a twos complement, 12-bit word to the

VAGAIN register. Equation 25 shows how the gain adjustment

is related to the contents of the VAGAIN register.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎭

⎬

⎫

⎩

⎨

⎧ +

VAGAIN

Power

Apparent

OutputVAGA

(25)

For example, when 0x7FF is written to the VAGAIN register, the

power output is scaled up by 50%. 0x7FF = 2047d, 2047/212 = 0.5.

Similarly, 0x800 = –2047d (signed, twos complement) and power

output is scaled by –50%. Each LSB represents 0.0244% of the

power output. The apparent power is calculated with the current

and voltage rms values obtained in the rms blocks of the

ADE7763. Figure 65 shows the maximum code (hexadecimal)

output range of the apparent power signal. Note that the output

range changes depending on the contents of the apparent power

gain registers. The minimum output range is given when the

apparent power gain register content is equal to 0x800; the

maximum range is given by writing 0x7FF to the apparent

power gain register. This can be used to calibrate the apparent

power (or energy) calculation in the ADE7763.

0x10 3880

0xA D055

0x5 682B

0x0 0000

0x000

0x7FF

0x800

{VAGAIN[11:0]}

APPARENT POWER 100% FS

APPARENT POWER 150% FS

APPARENT POWER 50% FS

APPARENT POWER

CALIBRATION RANGE,

VOLTAGE AND CURRENT

CHANNEL INPUTS: 0.5V/GAIN

Figure 65. Apparent Power Calculation Output Range

Apparent Power Offset Calibration

Each rms measurement includes an offset compensation

value—see the Channel 1 RMS Calculation and Channel 2 RMS

Calculation sections. The Channel 1 and Channel 2 rms values

are then multiplied together in the apparent power signal

processing. Because 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 is

done by calibrating each individual rms measurement.

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