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ADE7763

Rev. A | Page 25 of 56

FREQUENCY (Hz)

0.4

0.3

0.2

0.1

0.0

–0.1

–0.2

–0.3

–0.4

Figure 52. Combined Gain Response of HPF and Phase Compensation

ACTIVE POWER CALCULATION

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

the load. It is defined as the product of the voltage and current

waveforms. The resulting waveform is called the instantaneous

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

time. The unit of power is the watt or joules/s. Equation 9 gives

an expression for the instantaneous power signal in an ac system.

)

sin(ω

)

(

(7)

)

sin(ω

)

(

(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.

∫

)

(

(10)

where:

T is the line cycle period.

P is 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 ADE7763.

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 illustrated

in Figure 53.

INSTANTANEOUS

POWER SIGNAL

p(t) = v

× i-v × i × cos(2ωt)

ACTIVE REAL POWER

SIGNAL = v

× i

0x19 999A

0xC CCCD

0x0 0000

CURRENT

i(t) = 2

× i × sin(ωt)

VOLTAGE

v(t) = 2

× v × sin(ωt)

Figure 53. Active Power Calculation

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

response (see Figure 54), 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

Figure 54. Frequency Response of LPF2

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