ADE7758_15 datasheet(30/72 Pages) AD

30 / 72 page

ADE7758

Data Sheet

Rev. E | Page 30 of 72

Voltage RMS Gain Adjust

The ADC gain in each phase of the voltage channel can be

adjusted for the rms calculation by using the voltage rms gain

registers (AVRMSGAIN, BVRMSGAIN, and CVRMSGAIN).

The gain of the voltage waveforms before LPF1 is adjusted by

writing twos complement, 12-bit words to the voltage rms gain

registers. Equation 11 shows how the gain adjustment is related

to the contents of the voltage gain register.











 





VRMSGAIN

Gain

Without

Values

RMS

Nominal

VRMS

Content

(11)

For example, when 0x7FF is written to the voltage gain register,

the RMS value is scaled up by 50%.

0x7FF = 2047d

2047/212 = 0.5

Similarly, when 0x800, which equals –2047d (signed twos

complement), is written the ADC output is scaled by –50%.

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 waveforms. 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 14 gives an expression for the instantaneous

power signal in an ac system.

(t) = √2 × VRMS × sin(ωt)

(12)

(t) = √2 × IRMS × sin(ωt)

(13)

where VRMS = rms voltage and IRMS = rms current.

(t) = v(t) × i(t)

(t) = IRMS × VRMS − IRMS × VRMS × cos(2ωt)

(14)

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

given by the expression in Equation 15.



IRMS

VRMS







(15)

where:

is the line cycle period.

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 14, that is, VRMS × IRMS. This is the

relationship used to calculate the active power in the ADE7758

for each phase.

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

the current and voltage signals in each phase. The dc component

of the instantaneous power signal in each phase (A, B, and C) is

then extracted by LPF2 (the low-pass filter) to obtain the

average active power information on each phase. Figure 65

shows this process. The active power of each phase accumulates

in the corresponding 16-bit watt-hour register (AWATTHR,

BWATTHR, or CWATTHR). The input to each active energy

setting (see Table 22).

INSTANTANEOUS

POWER SIGNAL

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

ACTIVE REAL POWER

SIGNAL = VRMS × IRMS

0x19999A

VRMS × IRMS

0xCCCCD

0x00000

CURRENT

i(t) = 2 × IRMS × sin(ωt)

VOLTAGE

v(t) = 2 × VRMS × sin(ωt)

Figure 65. Active Power Calculation

Because LPF2 does not have an ideal brick wall frequency

response (see Figure 66), 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 over time to calculate the

energy.

–4

–8

–12

–16

–20

–24

FREQUENCY (Hz)

100

Figure 66. Frequency Response of the LPF Used

to Filter Instantaneous Power in Each Phase

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