Digital Signal Processing Reference
In-Depth Information
(b3)
application
of
orthogonal
of
3
=
4-cycle
orthogonal
filters
and
the
algorithms (
8.97
-
8.99
).
(c)
measurement time B20 ms (full cycle of the fundamental frequency):
(c1)
application of full-cycle sin, cos filters and algorithms (
8.97
-
8.99
),
(c2)
full-cycle averaging algorithms (
8.122
), (
8.123
), m = 2; the reactance
value can be obtained from calculated resistance and impedance.
(d)
measurement time B25 ms:
(d1)
application of one full-cycle filter (20 ms, sine, cosine or other) for
current and voltage, plus 5 ms delay for orthogonalization, (
8.104
-
8.106
),
(d2)
application of a pair of half-cycle orthogonal filters for current and
voltage and then algorithms (
8.66
)to(
8.68
)with1
=
4-cycle delay,
(d3)
application of a pair of orthogonal filters with 5
=
4-cycle window
(different gain coefficients) and algorithms (
8.94
-
8.96
).
Selection of particular version should take into consideration all important
requirements and constraints, e.g., expected frequency spectra of input signals,
computational burden, frequency features of applied filters, etc. The frequency
responses of various filters with windows from 1
=
2- to 5
=
4-cycle are presented in
Fig.
8.7
. One can see that the most favorable filtration of disturbing components in
case of assumed measurement time 15 ms is obtained for the case (c), i.e., for the
filter of longest possible window. However, this algorithm is the most complex one
since it requires four filters, and additionally—their gains cannot be cancelled. A
very simple algorithm is obtained when only one filter with 10 ms data window is
applied; filter gains can now be cancelled, which leads to very simple measure-
ment equations. Similar discussion can be done for all remaining permissible
(assumed) measurement times.
The required orthogonal components needed in particular versions of algo-
rithms can be obtained in the ways as considered in Example 8.9, according to
block schemes from Fig.
8.6
. It is essential to perform orthogonalization of both
current and voltage signals with the same algorithm, which creates possibility of
obtaining very simple measurement equations.
Since the algorithms for magnitude and power measurement have already been
illustrated with numerous examples, below chosen variants only as applied for
resistance measurement are presented.
Case (a2)—measurement time 10 ms (N
¼
10 for assumed sampling fre-
quency). Orthogonal components of voltage signals can be calculated from:
u
F1C
ð
n
Þ¼
X
9
u
1
ð
n
k
Þ
cos
½
0
:
1p
ð
4
:
5
k
Þ;
k
¼
0
u
F1S
ð
n
Þ¼
X
9
u
1
ð
n
k
Þ
sin
½
0
:
1p
ð
4
:
5
k
Þ;
k
¼
0
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