Power distribution systems does in general have several states of functionality (e.g. severalload points that can function separately), which makes it reasonable to model them as multistatesystems 38, i.e. systems that allow for several levels of function of for exampleavailability. The component reliability importance indices presented in subchapter 3.1 arebased on systems that are binary, i.
e. either functioning or not (two states). This is an approachwhich proves ambiguous for networks with for example more than one load point, as forexample shown in paper III, Table 3. One component might be crucial from the perspective ofone load point while virtually unnecessary from another load point’s perspective. This calls foran approach that takes the whole network’s reliability performance into account in onemeasure and relates this measure to the individual component. The concept of the developedindices is to utilize customer interruption costs as a measure of system reliability performance.
Component reliability importance indices for power systems is identified as a topic ofincreasing interest to the research community. This can be seen in that most of the publicationsin the topic are relatively new (see references for this chapter). The increased interest isprobably explained by the reregulation of the electricity market, resulting in a higher interest ingood payoff of maintenance actions, and in increased possibilities to perform advancedreliability calculations.This chapter starts with a brief introduction to general component reliability importanceindices, followed by a survey on what has been done in this specific topic for power systems.The chapter continues with a more detailed presentation of the indices developed within thePhD project.
The chapter ends by outlining an approach to component reliability importanceindices for transmission systems. 203.1 Traditional component reliability importance indicesThis subchapter contains a short description of some of the most referred component reliabilityimportance indices, followed by a brief discussion on their potential use in transmission anddistribution systems.3.1.1 Birnbaum’s reliability importanceBirnbaum’s measure of component importance is a partial derivative of system reliability withrespect to individual component failure rate 47.
It can also be argued that this is a sensitivityanalysis of system reliability with respect to component reliability. This index gives anindication of how system reliability will change with changes in component reliability.iBi ph I t?? = ( ) ( ) p (3.1)where h is the system reliability depending on all component reliabilities p (and systemstructure) and pi component i’s reliability.
A drawback with this method is that the studiedcomponent’s reliability does not affect the importance index (for the specific component).Another issue regarding this index is that it cannot be used in order to predict the effect ofseveral changes at the same time, i.e. reliability changes in several components at a time 56.
This is, however, a drawback shared with most component reliability importance indices.3.1.2 Birnbaum’s structural importanceBirnbaum’s structural importance does not take any reliability into account, and hence it can bestated that this method is truly deterministic. The method defines component importance as thecomponent’s number of occurrences in critical paths, normalized by the total number of systemstates.Definition of structural importance in accordance with 47 and 57:I?(i) = ??(i) / 2n-1 (3.
2)where ??(i) is the number of critical path vectors for component i and 2n-1 is the total ofpossible state vectors. In other words; the number of critical paths a component is involved inis proportional to its importance. The structural importance can be calculated from Birnbaum’sreliability importance by setting all component reliabilities to ½ 47
