Digital Signal Processing Reference
In-Depth Information
on initial phase shift. Since it is unknown, the actual magnitude cannot be esti-
mated then.
Equations similar to (
9.10
) can be obtained for other algorithms of magnitude
measurement (with application of different filters, their window lengths, etc.).
Procedure of calculation of final result is either similar or identical. The steps are
following: calculation of output signals of orthogonal filters (
9.7a
,
b
) with non-
stationary coefficients (similar to (
9.9a
,
b
)), substituting them into given algorithm,
rearranging and simplifying. The calculations are sometimes complex, chosen
results are shown in Fig.
9.2
.
Transients of magnitude measurements according to algorithm with delayed
orthogonal components are shown in Fig.
9.2
b. It is seen that the set of tra-
jectories has a little bit different shape, however, one important feature is the
same as before—there is no overshoot of measured value. This virtue is extre-
mely important with the viewpoint of decision-making process in power system
protection.
Active power measurement transients are different than before (Fig.
9.2
c). Now
the transients that are non-monotonic and overshoot depending on power angle
appears. It is seen even when the phase angle is equal to p
=
2
;
i.e., when active
power steady state value is equal to zero, which may be a cause of problems during
decision-making. On the other hand advantageous is the shape of transient of
reactive power (Fig.
9.2
d). Here, the course of transient is not only monotonic but
it also does not depend on initial phase shift. This is a very important result
allowing for easier decision-making as well as for dynamical correction of pro-
tection criterion values measurement.
Transients of impedance components are shown in Fig.
9.2
e, f. It is seen now
that changes of measured values are tremendous, which is a result of measurement
algorithms being a ratio type, where the algorithm transients depend on transients
of the numerator and denominator. Here, information during transients is not
useful and one should wait until steady state is reached to avoid wrong decisions. It
could be said that during transients of impedance components measurement the
decision-making should be off.
The examples discussed before presented trajectories of measurement during
transients that were obtained with use of above algorithms under assumptions of
zero initial conditions, what is the case by starting the measurement at all or by
restarting it (reinitiating) after disturbance inception. The signals observed during
continuous measurement without filters' restarting look quite differently. Selected
exemplary results of simulations are presented in Fig.
9.3
. As one can see, the
differences are significant, however, the general picture is common: the magnitude
measurement is always monotonic, while the other criteria values may have non-
monotonic trajectory during transients. One can note even sign changes and
overshoots, especially big for resistance and reactance measurement, especially
when the signal phase changes due to disturbance are high. It is therefore to be
stressed that detailed analysis of transient behavior of the measurement algorithms
is extremely important for selection of appropriate procedures both for criteria
estimation and final protection decision-making.
Search WWH ::
Custom Search