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ADE7752B
Example 2
f 1 to 7 = 0 . 56 Hz , SCF = S0 = S1 = 1
In this example, the ADE7752B is connected to a 3-phase,
3-wire delta service as shown in Figure 17. The total active
energy calculation processed in the ADE7752B can be
expressed as
Total Active Power = ( V A – V C ) × I A + ( V B – V C ) × I B
V AN = V BN = I A = I B = I C = 500 m V peak ac =
0 . 5
V rms
2
V CN = I C = 0
V REF = 2 . 4 V nominal reference value
(19)
where:
V A , V B , and V C represent the voltage on Phase A, Phase B, and
Phase C, respectively.
I A and I B represent the current on Phase A and Phase B,
Note that if the on-chip reference is used, actual output
frequencies can vary from device to device due to a reference
tolerance of ±8%.
× = 0 . 133 Hz
respectively.
With respect to the voltage and current inputs in Equation 7
Freq = 2 ×
6 . 313 × 0 . 5 × 0 . 5 × 0 . 56
2 × 2 × 2 . 4 2
3
2
(20)
P = ? 2 × V A × cos ( ω l t ) ? 2 × V C × cos ? ? ω l t +
? ? ×
? 2 × V B × cos ? ω l t +
? ? v 2 × V C × cos ? ω l t +
? ? ×
2 × I B × cos ? ? ω l t +
2 π ?
?
3 ?
and Equation 8, the total active power (P) is
P = ( V A ? V C ) ( I AP ? I AN ) + ( V B ? V C ) × ( I BP ? I BN )
2 × I A × cos ( ω l t ) +
? ? 2 π ? ? 4 π ? ?
? ? 3 ? ? 3 ? ?
?
? ? 3 ? ?
? 4 π ? ?
Table 6 shows a complete listing of all maximum output
frequencies when using all three channel inputs.
Table 6. Maximum Output Frequency on F1 and F2
SCF S1 S0 Maximum Frequency for AC Inputs (Hz)
0 0 0 0.92
1 0 1 1.84
0 0 1 0.46
1 0 1 1.84
0 1 0 2.09
1 1 0 0.46
For simplification, assume that ΦA = ΦB = ΦC = 0 and
(15)
0
1
1
1
1
1
0.23
0.23
V A = V B = V C = V . The preceding equation becomes
FREQUENCY OUTPUT CF
P = 2 × V × I A × sin ? ?
? × cos ( ω l t ) +
? × sin ? ω l t +
2 × V × I B × sin ? ? ? ? × sin ( ω l t + π ) × cos ? ? ω l t +
π 2 π ?
?
3 ?
? 3 ?
P = V AN A × ? sin ? ?
? 2 π ? ? 2 π ? ?
V BN B × ? sin ? ? ? ? + sin ? ? 2 ω l t +
× I
? ?
P then becomes
× I ? + sin ? 2 ω l t + ? ? +
where:
? ? 3 ? ? 3 ? ?
? π π ? ?
? ? 3 ? ? 3 ? ?
? 3 ? ? 3 ?
2 π ? ? 2 π ?
?
(16)
(17)
The pulse output calibration frequency (CF) is intended for use
during calibration. The output pulse rate on CF can be up to
64× the pulse rate on F1 and F2. Table 7 shows how the two
frequencies are related, depending on the states of the logic
inputs S0, S1, and SCF. Because of its relatively high pulse rate,
the frequency at this logic output is proportional to the instantane-
ous active power. As is the case with F1 and F2, the frequency is
derived from the output of the low-pass filter after multiplication.
However, because the output frequency is high, this active
power information is accumulated over a much shorter time.
Thus, less averaging is carried out in the digital-to-frequency
conversion. The CF output is much more responsive to power
V AN = V × sin(2π/3)
V BN = V × sin(π/3)
As the LPF on each channel eliminates the 2ω l component of
the equation, the active power measured by the ADE7752B is
fluctuations with much less averaging of the active power signal
(see Figure 11).
Table 7. Maximum Output Frequency on CF
SCF S1 S0 f 1 to 7 (Hz) CF Maximum for AC Signals (Hz)
× I A × + V BN × I B ×
P = V AN
3
2
3
2
(18)
0
1
0
0
0
0
2.24
4.49
16 × F1, F2 = 14.76
8 × F1, F2 = 14.76
If full-scale ac voltage of ±500 mV peak is applied to the voltage
channels and current channels, the expected output frequency
is calculated as follows:
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1.12
4.49
5.09
1.12
0.56
0.56
32 × F1, F2 = 14.76
16 × F1, F2 = 29.51
160 × F1, F2 = 334
16 × F1, F2 = 7.38
32 × F1, F2 = 7.38
16 × F1, F2 = 3.69
Rev. 0 | Page 21 of 24
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