Digital Signal Processing Reference
In-Depth Information
n
=
0
u
(
n
)
Q
(
n
)
=
T
(
n
)
Q
Q
Algorithm
Q
1
1
T
(
n
)
i
(
n
)
n
=
N
4
1
u
(
n
)
P
(
n
)
=
T
(
n
)
P
P
Algorithm
Q
1
1
T
(
n
)
π
i
(
n
)
−
n
=
N
4
1
i
(
n
)
I
2
1
(
n
)
=
T
(
n
)
I
2
I
2
Algorithm
Q
1
T
(
n
)
π
−
Fig. 9.5
Block scheme of P, Q and I measurement with correction
Q
;
ð
n
þ
1
Þ
2
sin
2
ð
nX
1
Þ
sin
2
ð
X
1
Þ
Q
1
ð
n
Þ¼
1
N
1
ð
9
:
16
Þ
which can be written in a shorter form:
Q
1
ð
n
Þ¼
T
ð
n
Þ
Q
:
ð
9
:
17
Þ
Knowing time instant n and function T(n) the steady state value Q
1
T
ð
n
Þ
Q
1
ð
n
Þ
Q
¼
ð
9
:
18
Þ
can be calculated much earlier, at the very beginning, shortly after fault inception.
Since algorithms of measurement of reactive power only have unique, phase
independent transient response there appears a problem of dynamical correction of
the remaining criterion values. The simplest solution of the problem is application
of p
=
2 delay of current signal (equivalent number of delay samples). Then an
algorithm of reactive power measurement becomes an algorithm of active power
since sin
½
u
U
ð
u
I
p
=
2
Þ ¼
cos
ð
u
U
u
I
Þ:
The block scheme of active power
measurement with correction is presented in Fig.
9.5
. Realization of zero initial
conditions requires starting the algorithm after the time needed to realize the
current signal delay. In the simplest case it means the number of samples equiv-
alent to a quarter of period of the fundamental frequency component. It is also
possible to use the methods of orthogonalization by single or double delay. They
also provide the same delay, however, here additional speed-up measurement is
obtained since delayed current is given as early as after one or two samples.
It is also evident that the same algorithm (of active power) can be used to
measure magnitudes of voltages and currents.
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