ADE7753ARSRL datasheet(28/60 Pages) AD

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ADE7753

Rev. C | Page 28 of 60

FREQUENCY (Hz)

0.4

0.3

0.2

0.1

0.0

–0.1

–0.2

–0.3

–0.4

02875-0-059

Figure 60. Combined Gain Response of the HPF and Phase Compensation

ACTIVE POWER CALCULATION

Power is defined as the rate of energy flow from source to load.

It is defined as the product of the voltage and current wave-

forms. The resulting waveform is called the instantaneous

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

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

Equation 9 gives an expression for the instantaneous power

signal in an ac system.

v(t) =

)

sin(

(7)

i(t) =

)

sin(

(8)

where:

V is the rms voltage.

I is the rms current.

)

(

)

(

)

(

)

cos(

)

(

−

(9)

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

given by the expression in Equation 10.

P =

∫

nT 0

)

(

(10)

where:

T is the line cycle period.

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 8, i.e., VI. This is

the relationship used to calculate active power in the ADE7753.

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

the current and voltage signals. The dc component of the

instantaneous power signal is then extracted by LPF2 (low-pass

filter) to obtain the active power information. This process is

illustrated in Figure 61.

INSTANTANEOUS

POWER SIGNAL

p(t) = v

×i-v×i×cos(2ωt)

ACTIVE REAL POWER

SIGNAL = v

× i

0x19999A

0xCCCCD

0x00000

CURRENT

i(t) = 2

×i×sin(ωt)

VOLTAGE

v(t) = 2

×v×sin(ωt)

02875-0-060

Figure 61. Active Power Calculation

Since LPF2 does not have an ideal “brick wall” frequency

response—see Figure 62, the active power signal has some

ripple due to the instantaneous 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 active power signal is integrated to calculate energy—see the

Energy Calculation section.

FREQUENCY (Hz)

–24

–20

100

–12

–16

–8

–4

02875-0-061

Figure 62. Frequency Response of LPF2

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