Protection System Reliability Modeling: Unreadiness Probability and Mean Duration of Undetected Faults

A reliability model of a system and its associated protection system is described. The protection system detects the presence of faults and isolates the faulted equipment so as to prevent damage and minimize the effect of the faulted equipment on the operation of the rest of the system. If the protection system does not respond and the faulted component is not disconnected, a backup protection system comes into operation. The backup operation isolates a larger segment and disturbs the system more than if the designated protection system had responded appropriately. An example is the protective relay systems for electric power transmission and distribution systems. A measure of system unreadiness is defined and suitable expressions are derived for this index and the mean duration of undetected faults. The unreadiness probability is sensitive not only to the failure rate of the protection system but also to the failure rate of the system, the pdf of interval between inspections and its mean value. The unreadiness probability estimated from a given system cannot be used for another system having a similar protection system. The protection system failure rate can, however, be used to obtain the unreadiness probability.