ADE7758ARWRL datasheet(30/68 Pages) AD

30 / 68 page

ADE7758

Rev. A | Page 30 of 68

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. The expression below shows how the gain adjustment

is related to the contents of the voltage gain register.

⎟

⎠

⎞

⎜

⎝

⎛ +

VRMSGAIN

Gain

without

Values

RMS

Nominal

VRMS

Content

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

the ADC output is scaled up by 50%.

0x7FF = 2047d, 2047/212 = 0.5

Similarly, 0x800 = –2047d (signed twos complement) and 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 5 gives an expression for the instantaneous

power signal in an ac system.

()

( t

VRMS

sin

)

(3)

()

( )t

IRMS

sin

(4)

where VRMS = rms voltage, IRMS = rms current.

( )

VRMS

IRMS

–

VRMS

(t)

cos

(5)

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

given by the expression in Equation 6.

()

IRMS

VRMS

∫

(6)

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 5, 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 64 shows this process. The active power of each

phase accumulates in the corresponding 16-bit watt-hour

each active energy register can be changed depending on the

accumulation mode setting (see Table 17).

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 64. Active Power Calculation

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

response (Figure 65), 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 65. Frequency Response of the LPF Used

to Filter Instantaneous Power in Each Phase

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