Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 170

to use continuous measurement to identify the fault and to estimate its inception
instant. The resulting conclusion is the following: either continuous measurement
only or mixed continuous and starting its operation at the fault instant are used in
contemporary protection systems.
From the viewpoint of final protection decision-making of importance is not
only the transient time but its trajectory as well. Monotonic, increasing or
decreasing trajectory is advantageous since then the number of wrong decisions
could significantly be minimized. These trajectories are not always monotonic and
that is why delays must sometimes be used to avoid over-/under-tripping. Deep
analysis clearly shows that transients of measurement depend on signal transient
and noise which must be removed by adequate filters, the criterion values tra-
jectory, on the other hand, depends on features of applied filters and measurement
algorithms.
Among the filters and similar digital processing methods applied one can dis-
tinguish: finite impulse response (FIR) filters, infinite impulse response (IIR) fil-
ters, Kalman filters and other signal processing (not filters), including discrete
Fourier transform, correlation and MSE methods. Standard IIR digital filters are
used in protection systems rather rarely. Disadvantages of the filters in that
application are: nonlinear phase, troubles to get orthogonal components and very
long lasting filter transient. An exception could be Kalman filter. It has short and
monotonic transient when model of the process is well defined and close to reality.
The most universal and frequently used are finite impulse filters (FIR) and similar
correlation methods. Their advantages are: sharply-defined period of transient,
linear phase and easy available orthogonal filters as well as the resulting orthog-
onal signal components. Transients of the FIR filters are analyzed below.
A FIR filter processes input signal samples according to the equation:

y ð n Þ¼ X

N 1

a ð k Þ x ð n k Þ; ð 9 : 1 Þ

k ¼ 0

where a(k) is a filter coefficients, and x is an input signal.
Such simple equation can be used and is valid in the steady state only when the
signal parameters are constant within the entire filter window (N samples).
However, when sudden change of the signal appeared within the filter window, say
at instant m (see Fig. 9.1 ), then the output signal of the filter should be expressed in
the form including samples of ''old'' and ''new'' signal:

y ð n Þ¼ X a ð k Þ x 2 ð n k Þþ X

n m N 1

a ð k Þ x 1 ð n k Þ; ð 9 : 2 Þ

k ¼ 0 k ¼ n m þ 1

which is valid for 0 n m N 1 :
When time is passing n increases the number of samples of new signal (x 2 )
observed in the filter data window also increases whereas the number of samples of
old signal (x 1 ) decreases. After N samples counted from the fault inception (change
of signal parameters), there are samples of ''new'' signal only inside the filter