ADE7756AN-REF datasheet(21/32 Pages) AD

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ADE7756

–21–

ACTIVE POWER CALCULATION

Electrical power is defined as the rate of energy flow from source to

load. It is given by the product of the voltage and current wave-

forms. The resulting waveform is called the instantaneous power

signal and it is equal to the rate of energy flow at every instant of

time. The unit of power is the watt or joules/sec. Equation 3

gives an expression for the instantaneous power signal in an

ac system.

( )

sin(

)

= 2

(1)

( )

sin(

)

= 2

(2)

where

V = rms voltage,

I = rms current.

i t

p t

()

( )

–

cos (

)

=×

(3)

The average power over an integral number of line cycles (n) is

given by the expression in Equation 4.

p t dt

∫

()

(4)

where

T is the line cycle period.

and

P is referred to as the Active or Real Power.

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

instantaneous power signal p(t) in Equation 3 , i.e., VI. This is

the relationship used to calculate active power in the ADE7756.

The instantaneous power signal p(t) is generated by multiplying

the current and voltage signals. The dc component of the instan-

taneous power signal is then extracted by LPF2 (Low-Pass Filter)

to obtain the active power information. This process is graphi-

cally illustrated in Figure 26. Since LPF2 does not have an ideal

“brick wall” frequency response—see Figure 27—the Active

Power signal will have some ripple due to the instantaneous

power signal. This ripple is sinusoidal and has a frequency equal

to twice the line frequency. Since the ripple is sinusoidal in

nature it will be removed when the Active Power signal is inte-

grated to calculate Energy—see Energy Calculation section.

VOLTAGE

CURRENT

INSTANTANEOUS

POWER SIGNAL

ACTIVE REAL POWER

SIGNAL = V

00000h

1999Ah

V. I.

CCCDh

p(t) = V

1 – V

COS(2 t)

I(t) =

SIN( t)

V(t) =

SIN( t)

Figure 26. Active Power Calculation

Figure 28 shows the signal processing chain for the Active

Power calculation in the ADE7756. As explained, the Active

Power is calculated by low-pass filtering the instantaneous

power signal.

FREQUENCY – Hz

–24

–20

100

–12

–16

–8

–4

Figure 27. Frequency Response of LPF2

CCCDh

00h

HPF

LPF2

MULTIPLIER

INSTANTANEOUS POWER SIGNAL

p(t) = –40%FS TO +40%FS

ACTIVE POWER

SIGNAL – P

CURRENT SIGNAL – I(t)

VOLTAGE SIGNAL – V(t)

1999Ah

Figure 28. Active Power Signal Processing

Shown in Figure 29 is the maximum code (Hexadecimal) out-

put range for the Active Power signal (LPF2). Note that the

output range changes, depending on the contents of the Active

Power Gain register—see Channel 1 ADC section. The mini-

mum output range is given when the Active Power Gain register

contents are equal to 800h, and the maximum range is given

by writing 7FFh to the Active Power Gain register. This can

be used to calibrate the Active Power (or Energy) calculation

in the ADE7756.

00000h

+20% FS

–20% FS

+30% FS

+10% FS

–10% FS

–30% FS

CCCDh

F3333h

000h

7FFh

800h

CHANNEL 1 (ACTIVE POWER)

CALIBRATION RANGE

POSITIVE

POWER

6666h

F999Ah

1999Ah

E6666h

APGAIN[11:0]

NEGATIVE

POWER

Figure 29. Active Power Calculation Output Range

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