Decision Making in Protective Relays - Digital Signal Processing in Power System Protection and Control - page 207

set of possible ones for given decision problem, a value of distance D between both
PDFs may be used, defined as [ 7 ]

D 1 ¼ X

p

2 ½ f ð x i j H 0 Þ f ð x i j H 1 Þ ð 10 : 7 Þ

i ¼ 1

or

D 2 ¼ sup
d i 2 D X
i ¼ 1 ; ... ; p

½ F ð x i j H 0 Þ F ð x i j H 1 Þ ; ð 10 : 8 Þ

where:
D X range of possible values of the decision random variable X,

f, F probability density and distribution functions for both hypotheses,

p number of intervals of discretized range D X :

The best results of probabilistic decision making will be achieved for decision
variable with highest value of distance D.
The application of the SPRT algorithm for fault detection and fault type
identification [ 10 ] may serve as an example how the probabilistic technique can be
used for decision making. The block scheme of proposed fault detection and
classification algorithm is shown in Fig. 10.8 . A set of SPRT units supplemented
with additional logic is proposed to realize both detection and classification of fault
events. Three simultaneously operating SPRT blocks (SPRT1-SPRT3) are applied
in each phase to indicate which of them are involved in a fault (SPRT equipped
with PDFs referring to normal operation state and fault conditions). The fourth
SPRT block (SPRT4) discriminates whether a ground fault occurred (PDFs for
ground and isolated faults).
The Logic and Control Unit (LCU) realizes:

• determination of the fault instant and type (on basis of the four SPRT blocks
outputs),
• coordination of SPRT blocks operation (commands to block and restart the
sequential testing procedures),
• on-line correction of SPRT parameters (setting the time instant in blocks
remaining in testing transient state).

The proposed algorithm operates as follows. In normal operation state, when
none of the testing blocks indicates a fault, all the SPRT units work independently
one from another. Their operation is automatically restarted after a decision of
unfaulty condition was taken. If one of the testing blocks indicates a fault in
corresponding phase (e.g. in phase L1), the LCU is activated. If any of SPRT
blocks remains in transient interval of testing, the LCU prevents restarting of those
SPRTs which have already completed their work. This allows avoiding problems
with convergence of the method in cases when particular SPRT blocks issue their
decisions with some delay (not synchronously). For those which are in operation a