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ADE7754
? ? nT
VI
? × ∫ cos ( ) dt
E ( t ) = ∫ VI dt – ? 2 π f t
(14)
?
?
? f ?
0
0
1 + ? ?
?
?
Σ V n n n )
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.
? ?
? ?
nT
2
? ? 8 ? ?
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,
nT
E ( t ) = ∫ VI dt + 0 (15)
0
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 = n = 1 × I × sin ( ?
where V n and I n are the voltage and current rms values of the n th
harmonics of the line frequency, respectively, and n is the
phase difference between the voltage and current nth harmon-
E ( t ) = VInT
(16)
ics. The resulting waveform is called the instantaneous reactive
power signal (VAR).
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
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.
formula can be disabled or enabled by the LWATSEL bits of
the WATMode register. The different configurations are
v ( t ) = 2 V 1 sin( ω t ? ? 1 )
(17)
i ( t ) = 2 I 1 1 sin ? ω t ?
sin( ω t ) i '( t ) = 2 I
∏ ?
2 ?
described in Table III.
Table III. Total Line Active Energy Calculation
?
?
?
(18)
WATMOD LWATSEL0
0 V A I A *
LWATSEL1 LWATSEL2
+ V B I B * + V C I C *
VAR ( t ) = v ( t ) × i '( t )
VAR ( t ) = V 1 I 1 sin( ? 1 ) + V 1 I 1 sin( 2 ω t + ? 1 )
(19)
1
2
V A
V A
(I A * – I B * ) + 0
(I A * – I B * ) + 0
+ V C
+ V C
(I C * – I B * )
I C *
The average power over an integral number of line cycles (n) is
given in Equation 20.
I sin( ?
∫ VAR ( t ) dt = V 1 1 1 )
Note that I A * , I B * , and I C * represent the current channels
samples after APGAIN correction and high-pass filtering.
VAR =
1 nT
nT 0
(20)
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
register (sum of absolute active power or arithmetic sum) is
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
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.
REV. 0
–23 –
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