Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 164

equivalent number of samples. It also means that the number of samples in one
period of fundamental component should be dividable by three. Then Eqs. 8.168a ,
b , c can be written as follows:

x 0 ð n Þ¼ 1
3

f x L1 ð n Þþ x L2 ð n Þþ x L3 ð n Þ g; ð 8 : 169a Þ

x 1 ð n Þ¼ 1
3

f x L1 ð n Þþ x L2 ð n 2N 1 = 3 Þþ x L3 ð n N 1 = 3 Þ g; ð 8 : 169b Þ

x 2 ð n Þ¼ 1
3

f x L1 ð n Þþ x L2 ð n N 1 = 3 Þþ x L3 ð n 2N 1 = 3 Þ g: ð 8 : 169c Þ

These are the simplest filters of symmetrical components. The equations are
realized in digital technique directly, as it is given above.

8.3 Summary, Conclusions and Recommendations

In this chapter the methods and specific algorithms of processing the input samples
of currents and voltages, filtered currents and voltages or their orthogonal com-
ponents into the sought criteria signals are described. All (almost all) the discussed
measurement algorithms have nonlinear character, which makes assessment of
their quality and resulting errors quite difficult. Therefore their features are sum-
marized here only partially, the other part of their assessment can be done basing
on the simulation investigations, which is presented later.
The measurement algorithms commit transformation of adequately selected
signal components into the measured variables. The basic and most popular
algorithms of protection criteria measurement apply orthogonal components of
currents and voltages. Certain specific features of measurement one can also obtain
applying algorithms with delayed orthogonal components.
As one could see, there are lots of basic methods and algorithms, and their
multitude results from a number of ways of obtaining orthogonal components,
which is described in Chap. 10 . Those methods are responsible for the resulting
algorithm features, that is their dynamics, ability of suppressing signal distortions
and noise, as well as computational complexity.
One can say that the DC (or decaying DC) component present in measured
signals (especially currents) may be a cause of significant, difficult to remove
errors of measurement. Similar conclusions may also apply for other distorting
components, depending on the algorithm at hand. It means that possible distortions
of the input signals should be appropriately minimized or eliminated before the
actual measurement algorithm is applied. Crucial are in this respect properly
selected filters or other methods of digital signal processing.
The above-described algorithms can be categorized as follows.