Digital Signal Processing Reference
In-Depth Information
(a)
(b)
1
1
I
md
I
m
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
10
20
30
40
0
10
20
30
40
n
n
(c)
(d)
0.5
P
Q
0.3
0.4
0.25
0.2
0.15
0.3
0.1
0.05
0.2
0
-0.05
0.1
-0.1
0
40
0
10
20
30
40
0
10
20
30
n
n
(e)
(f)
3
2
R
X
2.5
1.5
2
1
1.5
0.5
1
0
0.5
-0.5
0
-1
-0.5
-1.5
-1
-2
0
10
20
30
40
0
10
20
30
40
n
n
Fig. 9.2 Transient response of the measurement algorithms for zero initial conditions:
a, b measurement of current magnitude, c, d active and reactive power, e, f impedance
components; algorithms: (
8.37
), (
8.41
), (
8.46a
,
b
), (
8.48
), (
8.64
), (
8.65
)
in Fig.
9.2
a. It is seen that steady state is reached after the time equivalent to filter
window, in this case after N
1
equal to 20 samples (here and in many other cases the
sampling frequency was assumed 1000 Hz, which means that sampling period is
equal to 1 ms). At instant equal to half filter window and for time greater than filter
window length one observes that they have values independent of the initial phase
shift. At other instants during transients measured values are different, depending
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