ADE7754_15 datasheet(23/44 Pages) AD

23 / 44 page

REV. 0

ADE7754

–23–

Thus the

IRQ line can also be used to signal the end of a cali-

bration. Equation 14 is derived from Equations 8 and 12.

VI dt

ftdt

()

–

cos

= ∫

+ 



























()

∫

(14)

where n is an integer and T is the line cycle period. Since the

sinusoidal component is integrated over an integer number of

line cycles, its value is always zero.

Therefore,

VI dt

()

∫

(15)

VInT

()

(16)

The total active power calculated by the ADE7754 in the line

accumulation mode depends on the configuration of the

WATMOD bits in the WATMode register. Each term of the

formula can be disabled or enabled by the LWATSEL bits of

the WATMode register. The different configurations are

described in Table III.

Table III. Total Line Active Energy Calculation

WATMOD LWATSEL0

LWATSEL1 LWATSEL2

0VA

IA*

+ VB

IB*

+ VC

IC*

1VA

(IA*– IB*)+ 0

+ VC

(IC*– IB*)

2VA

(IA*– IB*)+ 0

+ VC

IC*

Note that IA*, IB*, and IC* represent the current channels

samples after APGAIN correction and high-pass filtering.

The line active energy accumulation uses the same signal path

as the active energy accumulation; however, the LSB size of the

two registers is different. If the line active energy register and

active energy register are accumulated at the same time, the line

active energy register will be four times bigger than the active

energy register.

The LAENERGY register is also used to accumulate the reac-

tive energy by setting to Logic 1 Bit 5 of the WAVMode register

(Address 0Ch). See the Reactive Power Calculation section.

When this bit is set to 1, the accumulation of the active energy

over half line cycles in the LAENERGY register is disabled and

is done instead in the LVAENERGY register. Because the

LVAENERGY register is an unsigned value, the accumulation

of the active energy in the LVAENERGY register is unsigned in

this mode. The reactive energy is then accumulated in the

LAENERGY register. See Figure 33. In this mode (reactive en-

ergy), selecting the phases accumulated in the LAENERGY

and LVAENERGY registers is done by the LWATSEL selec-

tion bits of the WATTMode register.

In normal mode, Bit 5 of the WAVMODE register equals 0,

and the type of active power summation in the LAENERGY

selected by Bit 2 of the gain register.

In the mode where the active powers are accumulated in the

LVAENERGY register, and Bit 5 of the WAVMODE register

equals 1, note that the sum of several active powers is always

done ignoring the sign of the active powers. This is due to the

unsigned nature of the LVAENERGY register which does not

allow signed addition.

REACTIVE POWER CALCULATION

Reactive power is defined as the product of the voltage and

current waveforms when one of this signals is phase shifted by

90º at each frequency. It is defined mathematically in the IEEE

Standards Dictionary 100 as

Reactive Power

sin

=×

()

∞

where Vn and In are the voltage and current rms values of the n

harmonics of the line frequency, respectively, and n is the

phase difference between the voltage and current nth harmon-

ics. The resulting waveform is called the instantaneous reactive

power signal (VAR).

Equation 19 gives an expression for the instantaneous reactive

power signal in an ac system without harmonics when the phase

of the current channel is shifted by –90º.

()

sin(

)

=−

ωϕ

(17)

t i t

()

sin(

) '( )

sin

− ∏









ωω

(18)

VAR t

v t

i t

VAR t

V I

()

'( )

()

sin(

)

sin(

)

=×

1 1

ϕω

(19)

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

given in Equation 20.

VAR

VAR t dt

V I

∫

()

sin( )

(20)

where T is the line cycle period.

VAR is referred to as the reactive power. Note that the reactive

power is equal to the dc component of the instantaneous reactive

power signal VAR(t) in Equation 19. This is the relationship

used to calculate reactive power in the ADE7754 for each phase.

The instantaneous reactive power signal VAR(t) is generated by

multiplying the current and voltage signals in each phase. In this

case, the phase of the current channel is shifted by –89º. The dc

component of the instantaneous reactive power signal in each

phase (A, B, and C) is then extracted by a low-pass filter to

obtain the reactive power information on each phase. In a

polyphase system, the total reactive power is simply the sum of

the reactive power in all active phases. The different solutions

available to process the total reactive power from the individual

calculation are discussed in the following section.

Figure 32 shows the signal processing in each phase for the

reactive power calculation in the ADE7754.

Since the phase shift applied on the current channel is not –90º

as it should be ideally, the reactive power calculation done in

the ADE7754 cannot be used directly for the reactive power

calculation. Consequently, using the ADE7754 reactive power

measurement only to get the sign of the reactive power is rec-

ommended. The reactive power can be processed using the

power triangle method.

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