IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 1, JANUARY 2004
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A Cost-Effective Approach of Prioritizing Distribution Maintenance Based on
System Reliability
Fangxing Li and Richard E. Brown
Abstract—This research work presents a new approach to
prioritize distribution maintenance activities based on system
reliability and cost-effectiveness. The objective of this approach
is to minimize the weighted average system reliability index
(WASRI) by ranking maintenance tasks based on their marginal
benefit-to-cost ratios, where the benefit is defined as improvement
in WASRI. Estimations of WASRI improvement are obtained
by utilizing the linear relationship between the benefit obtained
from a maintenance task and the change of failure rate of the
maintained component.
Prior work has applied RCM to distribution systems based on
marginal benefit-to-cost analysis [3]. This research work adds
rigor to this approach by incorporating failure rate models and
leveraging the linear relationship of component failure rates to
reliability indices.
The objective of this maintenance optimization approach
is to minimize the weighted average system reliability index
(WASRI) subject to cost constraints, with WASRI defined as
Index Terms—Asset management, distribution reliability, maintenance optimization, reliability indices.
(1)
where
I. INTRODUCTION
D
EREGULATION and industry restructuring are placing
utilities under increasing pressure to both improve customer reliability and decrease cost. To remain competitive,
it is critical to prioritize maintenance tasks so that the best
possible reliability is achieved with increasingly constrained
maintenance budgets.
The purpose of maintenance is to extend equipment lifetime
and/or reduce the probability of failure [1], [2]. Corrective maintenance replaces or repairs failed components, while preventive
maintenance is a proactive effort to improve the condition of an
unfailed component that may be deteriorated to some degree.
This research work addresses preventive maintenance only.
Traditional preventive maintenance policies include
time-based maintenance (TBM) and condition-based maintenance (CBM). TBM is performed at regular and scheduled
intervals, loosely based on the service history of a component
and/or the experience of service personnel. This maintenance
policy can be expensive and may not minimize the annualized
cost of equipment. CBM periodically determines the state of
equipment deterioration, and maintains equipment when the
condition falls below acceptable thresholds. CBM is generally
an improvement over TBM, but is still suboptimal since it does
not explicitly consider the probability of failure and, more
important, does not consider the consequences of failure. For
example, two identical circuit breakers with the same condition
may receive the same level of maintenance, even though one
serves customers without an alternate supply, while the other
serves customers that can be transferred to another feeder
should an interruption occur.
Reliability-centered maintenance (RCM) is an improvement
over TBM and CBM, and considers both the probability of
equipment failure and the system impact should a failure occur.
Manuscript received March 24, 2003.
The authors are with the ABB, Inc., Raleigh, NC 27606 USA (e-mail:
fangxing.li@us.abb.com).
Digital Object Identifier 10.1109/TPWRD.2003.820411
system average interruption frequency index;
system average interruption duration index;
momentary event average interruption
frequency.
The above definition of WASRI considers the three most popular reliability indices, but can be extended to include other measures of reliability provided they vary linearly with component
failure rates.
Once a utility has identified an appropriate WASRI measure
(indices and weights), its goal should be to minimize WASRI
subject to maintenance budget constraints. Approaching this optimization problem with rigor requires an analytical failure rate
and maintenance model.
II. MAINTENANCE AND COMPONENT FAILURE RATES
The failure rate of a piece of equipment can be modeled
as a function of parameters, including maintenance history.
For example, the failure rate of an overhead line may be a
strong function of construction geometry, voltage class, animal
population, animal guards, lightning activity, lightning protection, tree density, and tree trimming. Although very complex
mathematical models are possible, it is often useful to decouple
failure rate models based on factors with assumed independence [4]. For example, the failure rate of a line is the sum of
contributions from equipment-related faults, tree-related faults,
and animal-related faults. Maintenance models can then be
derived based on their impact to each factor. The feasibility
of this type of maintenance model is demonstrated by recent
work in the area of tree trimming [5], [6], where tree-related
failures are decoupled from aggregate line failures, and tree
failure are modeled as a function of years since trees were
last trimmed.
A generic maintenance model framework based on probabilistic transitions of equipment states is presented in [1] and
[2]. This model suggests that, in general, a maintenance activity
transfers the component state from a more deteriorated state to
a less deteriorated one. This state transition implies a failure
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 1, JANUARY 2004
rate reduction due to maintenance, which is compatible with the
model in [5] and [6].
For simplicity, this research work assumes that the reduction
is known. After
in failure rate for a given maintenance task
maintenance, the new failure rate is equal to the old failure rate
, subject to the new failure rate being greater or
( ) less
. This minimum failure
equal to the minimum failure rate
rate can be viewed as the failure rate associated with the initial
(no deterioration) state presented in [1] and [2].
In addition to its impact on , each maintenance task has
and form the basis for
an associated cost . Together,
the prioritization method presented in the next section. First,
is employed to identify the benefit to the
the parameter
improvement of WASRI from a maintenance task. Then, the
cost-to-benefit ratio is determined and used as the basis for
maintenance prioritization.
It should be noted that this work discusses sustained failure
rates only, but the same approach can be applied to temporary
failure rates, open circuits, and other contingency classes provided there is sufficient historical data to develop useful maintenance models.
III. COST-EFFECTIVENESS OF MAINTENANCE
The objective of this research work is to develop a methodology that can identify the combination of maintenance tasks
that achieve the best reliability within a limited financial budget.
In other words, the methodology is designed to find the most
cost-effective maintenance tasks. Here, cost is the dollar value
of maintenance tasks including hardware costs, labor costs, etc.
The benefit is the improvement of system reliability, which is
measured by WASRI.
The cost-effectiveness of a maintenance task is given by
where
failure rate of component ;
number of customers experiencing sustained interruption due to a failure of component ;
sustained interruption durations for all customers due
to a failure of component ;
sustained interruption duration for customer due to a
failure of component ,
;
number of customers experiencing temporary interruption event due to a failure of component ;
total number of customers.
Here, we consider only first-order contingencies (i.e., only
one component fails at a time). It is also assumed that a maintenance activity changes , but does not impact repair times,
switching times, or other factors that impact reliability with
,
failure rates held constant. Then, for each component ,
are constant before and after maintenance. , , and
and
can be obtained with a similar computational approach discussed in the previous work [4] to calculate SAIFI, SAIDI, and
.
With these assumptions, maintenance on a specific compoof that component. Hence,
nent will only impact the
the change of SAIFI after maintenance, which reduces the
, is given as follows:
failure rate of component by
(2)
where
change of WASRI;
cost associated with the maintenance task.
is the sum of contributions
Also, SAIFI, SAIDI, or
,
from each individual component of SAIFI, SAIDI, or
respectively. This is given as follows:
(9)
where
number of components.
Similarly, we have
(3)
(4)
(5)
(10)
contribution of SAIFI from component ;
contribution of SAIDI from component ;
contribution of
from component ;
component to be maintained.
,
, and
can be written
(11)
where
Next,
as [7]
Equations (9)–(11) show that the changes of SAIFI, SAIDI,
after a maintenance task are linearly related to the
or
change of the failure rate of the associated component. From
(9)–(11), (2) can be written as
(6)
(7)
(8)
(12)
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 1, JANUARY 2004
where
441
the component associated with the maintenance task.
Equation (12) shows that the cost-effectiveness of a maintenance task is linearly related to the change of failure rate of the
maintained component. This significantly simplifies the computation of the optimization approach.
A CBM-like ranking approach is also applied to this system
as a comparison. This approach ranks maintenance based
on component-level cost-effectiveness. That is, all candidate
maintenance tasks are ranked based on component deterioration
rather than system-level reliability. With this
approach, the WASRI of this system is reduced by 16% only.
IV. PRIORITIZING MAINTENANCE
V. CONCLUSION
The basis for maintenance optimization is to find the rankings
of all maintenance tasks based on their cost-effectiveness based
on (12). The ranking process is described as follows.
It is desirable for utilities to optimize equipment maintenance
subject to limited budgets. This work presents a prioritizing
approach to achieve this objective based on component and
system reliability modeling. This approach ranks all candidate maintenance tasks based on their impact on the system
reliability. Assuming task independence, reliability is maximized by sequentially selecting the highest ranked tasks until
either reliability targets are obtained or budget constraints are
reached.
1. Evaluate the condition of each component and the cost for the maintenance.
2. List all possible maintenance tasks.
3. Run a basic reliability assessment to
get the
,
, and
for each component
.
4. Rank the cost-effectiveness of each
maintenance task.
5. For maintenance tasks operating on the
same component, select the one with the
highest ranking and eliminate other tasks
from the list.
6. Select maintenance tasks from the
top of the ranking list until the cost
limit is reached or reliability target is
reached.
This prioritizing approach is applied to a testing utility system
with more than 4000 components and five substations. Components in the substations, such as transformers and breakers, are
recommended for maintenance. In addition, different maintenance tasks may be associated with a component. Within the
given budget limit, all tasks selected using this approach will
reduce WASRI by 28%.
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