Decision Making in Protective Relays - Digital Signal Processing in Power System Protection and Control - page 204

Fig. 10.6 Decision space
division: a ideal situation,
b real case, c statistic
interpretation

(a)

(b)

(c)

In real life all the above conditions are rarely fulfilled in 100% situations. An
illustration of the decision space division for distinguishable and non-distin-
guishable problems is shown in Fig. 10.6 . There are cases when the decision sub-
areas corresponding to classes of events to be perceived overlap each other. It is so
for example when overloads and high impedance faults are to be distinguished.
The levels of current amplitudes in both cases are similar and proper setting of the
required threshold meets considerable difficulties.
Very helpful can be then the methods belonging to the Artificial Intelligence
family (e.g. fuzzy logic-based reasoning systems, see Chap. 11 ) or statistical
decision making procedures, one of which is presented below. Additional moti-
vation for their application in power system protection is related to the fact that the
fault (any abnormal situation) occurrence time and parameters are of probabilistic
nature; thus some of the decision tasks may and can be solved on this basis.
The statistical decision theory interprets overlapping of decision areas
corresponding to two different classes of events as overlapping of conditional
probability density functions (PDFs) of the decision vector (Fig. 10.6 c). Statistical
approach to the decision-making problem in digital protection assumes that cri-
terion values can be considered as random variables and that required conditional
statistics are known. Probabilistic nature of the decision vector is a result of
random localization of fault or such other conditions as fault resistance, fault
angle, pre-fault load, etc. [ 7 ].
With statistical approach to the decision-making problem various algorithms of
hypothesis testing can be applied. The fundamental decision theory with proba-
bilistic roots is the Bayesian approach [ 3 ]. For practical technical problems the
application of methods based on statistical hypothesis testing is proposed, where