Power for this chapter). The increased interest is

Power distribution systems does in general have several states of functionality (e.g. several
load points that can function separately), which makes it reasonable to model them as multistate
systems 38, i.e. systems that allow for several levels of function of for example
availability. The component reliability importance indices presented in subchapter 3.1 are
based on systems that are binary, i.e. either functioning or not (two states). This is an approach
which proves ambiguous for networks with for example more than one load point, as for
example shown in paper III, Table 3. One component might be crucial from the perspective of
one load point while virtually unnecessary from another load point’s perspective. This calls for
an approach that takes the whole network’s reliability performance into account in one
measure and relates this measure to the individual component. The concept of the developed
indices 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 of
increasing interest to the research community. This can be seen in that most of the publications
in the topic are relatively new (see references for this chapter). The increased interest is
probably explained by the reregulation of the electricity market, resulting in a higher interest in
good payoff of maintenance actions, and in increased possibilities to perform advanced
reliability calculations.
This chapter starts with a brief introduction to general component reliability importance
indices, 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 the
PhD project. The chapter ends by outlining an approach to component reliability importance
indices for transmission systems.
3.1 Traditional component reliability importance indices
This subchapter contains a short description of some of the most referred component reliability
importance indices, followed by a brief discussion on their potential use in transmission and
distribution systems.
3.1.1 Birnbaum’s reliability importance
Birnbaum’s measure of component importance is a partial derivative of system reliability with
respect to individual component failure rate 47. It can also be argued that this is a sensitivity
analysis of system reliability with respect to component reliability. This index gives an
indication of how system reliability will change with changes in component reliability.
i p
h I t
? = ( ) ( ) p (3.1)
where h is the system reliability depending on all component reliabilities p (and system
structure) and pi component i’s reliability. A drawback with this method is that the studied
component’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 of
several 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 importance
Birnbaum’s structural importance does not take any reliability into account, and hence it can be
stated that this method is truly deterministic. The method defines component importance as the
component’s number of occurrences in critical paths, normalized by the total number of system
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 of
possible state vectors. In other words; the number of critical paths a component is involved in
is proportional to its importance. The structural importance can be calculated from Birnbaum’s
reliability importance by setting all component reliabilities to ½ 47


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