ADE7759ARS datasheet(21/32 Pages) AD

21 / 32 page

REV. 0

ADE7759

–21–

INSTANTANEOUS

POWER SIGNAL

p(t) = V

I – V

cos(2 t)

ACTIVE REAL POWER

SIGNAL = V

1999Ah

CCCDh

00000h

CURRENT

i(t) = 2

sin( t)

VOLTAGE

v(t) = 2

sin( t)

Figure 32. Active Power Calculation

FREQUENCY – Hz

–24

–20

100

–12

–16

–8

–4

Figure 33. Frequency Response of LPF2

Figure 34 shows the signal processing chain for the Active Power

calculation in the ADE7759. As explained, the Active Power is

calculated by low pass filtering the instantaneous power signal.

LPF2

CCCDh

1999Ah

00h

INSTANTANEOUS POWER SIGNAL – p(t)

–40% TO +40% FS

ACTIVE POWER

SIGNAL – P

CURRENT SIGNAL – i(t)

HPF

VOLTAGE SIGNAL – v(t)

MULTIPLIER

Figure 34. Active Power Signal Processing

Shown in Figure 35 is the maximum code (hexadecimal) output

range for the Active Power signal (LPF2) when the digital inte-

grator is disabled. Note that when the integrator is enabled, the

output range changes depending on the input signal frequency.

Furthermore, the output range can also be changed by the Active

Power Gain register—see Channel 1 ADC section. The minimum

output range is given when the Active Power Gain register con-

tents 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 ADE7759.

+30% FS

+20% FS

+10% FS

–10% FS

–20% FS

–30% FS

13333h

CCCDh

6666h

F999Ah

F3333h

ECCCDh

00000h

POSITIVE

POWER

NEGATIVE

POWER

000h

7FFh

800h

{APGAIN [11:0]}

CHANNEL 1 (ACTIVE POWER)

CALIBRATION RANGE

Figure 35. Active Power Calculation Output Range

ENERGY CALCULATION

As stated earlier, power is defined as the rate of energy flow.

This relationship can be expressed mathematically as:

(5)

Where P = Power and E = Energy

Conversely, Energy is given as the integral of Power:

Pdt

=∫

(6)

The AD7759 achieves the integration of the Active Power signal

by continuously accumulating the Active Power signal in the 40-

bit Active Energy register (ASENERGY[39:0]). This discrete

time accumulation or summation is equivalent to integration in

continuous time. Equation 7 expresses this relationship.

P t dt

Lim

p nT

=∫

∑













→

∞

()

(

)

(7)

Where n is the discrete time sample number and T is the sample period.

The discrete time sample period (T) for the accumulation regis-

ter in the ADE7759 is 1.1

µs (4/CLKIN). As well as calculating

the Energy, this integration removes any sinusodial components

which may be in the Active Power signal.

Figure 36 shows a graphical representation of this discrete time

integration or accumulation. The Active Power signal in the

Waveform register is continuously added to the Active Energy

energy will be subtracted from the Active Energy contents.

As shown in Figure 36, the Active Power signal is accumulated

in a 40-bit signed register (AENERGY[39:0]). The Active

Power signal can be read from the Waveform register by setting

MODE[14:13] = 0, 0 and setting the WSMP bit (Bit 3) in the

Interrupt Enable register to 1. Like Channel 1 and Channel 2

waveform sampling modes, the waveform data is available at

sample rates of 27.9 kSPS, 14 kSPS, 7 kSPS, or 3.5 kSPS—see

Figure 24. Figure 37 shows this energy accumulation for full-

scale signals (sinusodial) on analog inputs. The three curves

displayed illustrate the minimum period of time it takes the

energy register to roll over when the Active Power Gain register

contents are 7FFh, 000h, and 800h. The Active Power Gain

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