ADE7953ACPZ datasheet(24/68 Pages) AD

24 / 68 page

ADE7953

Data Sheet

Rev. A | Page 24 of 68

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 every

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

)

sin(

ωt

V(t)

(3)

)

sin(

ωt

I(t)

(4)

where:

is the rms voltage.

is the rms current.

P(t)

= V(t) × I(t)

(5)

P(t)

= VI − VI × cos(2ωt)

(6)

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

is given by the expression in Equation 7.

∫

)

(

(7)

where:

P is the active or real power.

T is the line cycle period.

The active power is equal to the dc component of the instanta-

neous power signal (P(t) in Equation 5). The active power is

therefore equal to VI. This relationship is used to calculate active

power in the ADE7953. Figure 44 illustrates this concept.

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

ACTIVE POWER SIGNAL:

VRMS × IRMS

P(t) = VRMS × IRMS – VRMS × IRMS × cos(2ωt)

VRMS

IRMS

0x0 0000

I(t) = √2 × IRMS × sin(ωt)

V(t) = √2× VRMS × sin(ωt)

Figure 44. Active Power Calculation

The signal chain for the active power and energy calculations in

the ADE7953 is shown in Figure 45. 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. Because LFP2 does not have an ideal “brick

wall” frequency response, the active power signal has some

ripple associated with it. 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 compute the active energy (see the Active

Energy Calculation section).

The ADE7953 computes the active power simultaneously on

Current Channel A and Current Channel B and stores the

resulting measurements in the AWATT (Address 0x212 and

Address 0x312) and BWATT (Address 0x213 and Address 0x313)

registers, respectively. With full-scale inputs, the expected

reading in the AWATT and BWATT registers is approximately

4862401 LSBs (decimal).

The active power measurements are taken over a bandwidth of

1.23 kHz and include the effects of any harmonics within that

range. The active power registers are updated at a rate of 6.99 kHz

and can be read using the waveform sampling mode (see the

Instantaneous Powers and Waveform Sampling section).

SIGN OF ACTIVE POWER CALCULATION

The active power measurement in the ADE7953 is a signed

calculation. If the phase differential between the current and

voltage waveforms is more than 90°, the power is negative.

Negative power indicates that energy is being injected back

into the grid. The ACCMODE register (Address 0x201 and

Address 0x301) includes two sign indication bits that show the

sign of the active power of Current Channel A (APSIGN_A)

and Current Channel B (APSIGN_B). See the Sign Indication

section for more information.

VGAIN

CURRENT

CHANNEL

A OR B

VOLTAGE

CHANNEL

HPF

xIGAIN

DIGITAL

INTEGRATOR

HPF

xWATTOS

PHCALx

INTERNAL

ACCUMULATION

FIXED INTERNAL

THRESHOLD

ACTIVE POWER

SIGNAL

AENERGYx

LPF2

xWGAIN

Figure 45. Active Energy Signal Chain

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