Engineering, 2013, 5, 14-18 Published Online September 2013 (
Copyright © 2013 SciRes. ENG
Maintenance Scheduling of Distribution System with
Optimal Economy and Reliability
Siyuan Hong, Haifeng Li, Fengjiao Wang
School of Electrical Power, South China University of Technology, Guangzhou, China
Received June 2013
With the continuous expansion of power distribution grid, the number of distribution equipments has become larger and
larger. In order to make sure that all the equipments can operate reliably, a large amount of maintenance tasks should be
conducted. Therefore, maintenance scheduling of distribution network is an important content, which has significant
influence on reliability and economy of distribution network operation. This paper proposes a new model for mainten-
ance scheduling which considers load loss, grid active power loss and system risk a s objective functions. On this basis,
Differential Evolution algorithm is adopted to optimize equipment maintenance time and load transfer path. Finally, the
general distribution network of 33 nodes is taken for example which shows the maintenance scheduling model’s effec-
tiveness and validity.
Keywords: Maintenance Schedu ling; Multi-Objective; Differential Evolution Algo r i thm; Condition Based
1. Introduction
With the continuous development of distribution network,
maintenance scheduling of distribution equipments has
become an important work of distribution network oper-
ation dispatching. Making scientific and reasonable
maintenance plan is beneficial to enhance the reliability
of power distribution system operation. Besides, it can
improve the management level and economic benefits of
Power Supply Company.
In actual work, maintenance scheduling of distribution
network is arranged artificially, according to the expe-
rience of power department, which is checked by operat-
ing crew to make sure the stability of power distribution
system. However, this arrangement method only focuses
on the security of distribution system, while neglects the
economical efficiency. Instead of artificial scheduling,
maintenance scheduling should be an optimized process
based on scientific and effective mathematical model,
which can avoid the subjectivity and randomness of
The study of maintenance scheduling generally opti-
mizes the objective function of economic index by dif-
ferent optimization algorithms. Reference [1] introduces
an automatic scheduling method using heuristic algo-
rithm to obtain the optimal switching combination , which
considers load loss and switch operation cost as the ob-
jective functions. Reference [2] puts forward an im-
proved Genetic Algorithm (GA) using infeasible degree
to retain the good genes on infeasible solution, and
shows that the optimization procedure has less chance to
get into local convergence. On the other hand, reliability
index is also an important factor of maintenance sche-
duling. Recently, Power Supply Company has conducted
pilot application of th e Reliability Centered Maintenance
(RCM) [4], in reference [5], its optimization objective is
to lower the value of Expected Energy Not Supplied
(ENNS) and improve the power system’s reliability.
However, for the maintenance scheduling problem of
distribution system, the reliability and economy of dis-
tribution network operation should be both considered as
the optimization objective functions. This paper makes a
comprehensive analysis of objective functions, including
load loss, grid active power loss and system risk. Then,
establish a multi-objective mathematical model with the
three objective functions above. In the following, the
method of using Differential Evolution algorithm to op-
timize the maintenance scheduling is proved to be effec-
tive and feasible by the example.
2. Maintenance Scheduling Model
2.1. Multi-Objective Optimization Model
General maintenance scheduling optimization problem
will integrate several objective functions into single
one by the weighting method as follow:
Copyright © 2013 SciRes. ENG
min( )
( )0,1,2..
gx jl≤=
( )0,1,2..
zx hm= =
where x is the maintenance time vector,
is the
weight of optimize objective function i, l is the total
number of inequality constraints, m is the total number
of equality constraints.
However, weighting single objective optimization
method has the following defects:
Enough prior knowledge is required to determine
the weight of each objective function.
Only one Pareto optimal solution can be obtained in
each optimization time, which is difficult to judge
the reliability and optimality of the optimization
Each objective function has different dimension.
Considering about all these, this paper adopts mul-
ti-objective optimization model to optimize several
objective functions and requires that all objective
functions meet the condition of setting constraints,
which is shown as follow:
Min ( )(( ),( )...,( ))
()((), (),...,())0
gXgXgXgX= ≤
( ,..),
Xxx xXR= ∈
where F(X) is the optimization target vector, g(X) is the
constraint vector, X is the decision variable.
2.2. Optimization Objective Functions
The purpose of arranging maintenance scheduling is not
only to transfer load as much as possible, but to consider
the economy and reliability of distributio n network oper-
ation. Therefore, maintenance scheduling of distribution
is a combinatorial optimization problem of multi-objec-
tive and multi-constraint , which is related to the objective
functions including the following aspects:
1) Load Loss
Min( )
f PT
= ××
denotes average electricity price, N means the
assemblage of transfer nodes, Pi is the load loss, Ti is the
maintenance continuous time.
2) Grid Active Power Loss
In order to avoid the outage of distribution network
caused by equipment maintenance, we should conduct
the network load transfer and besides, choose the optimal
transfer path to reduce the grid active power loss, which
is the target of load transfer in equipment maintenance.
Min( )
= ∆
denotes the grid active power loss of transfer
path k, M denotes the assemblage of all transfer paths.
3) System Risk
Generally, maintenance scheduling optimization mod-
el requires only that transfer strategy meet the network
power flow constraint, seldom considering the problem
of load equalization. The risk value of power distribution
system is calculated as follow:
Min( )
f PR
= =
where Pj denotes the load of node j, Re is the failure rate
of main equipments on trans fe r pa t h .
The risk assessment value can be divided into three
levels as Low Risk, Medium RiskandHigh Risk,
corresponding to evaluation score 0 - 0.3, 0.3 - 0.7, 0.7 -
1.0 respectively.
The selection of power load transfer paths is closely
related to the reliability of transfer lin e. If the power load
of maintenance line is transferred to another line of low
reliability in distribution network, the failure risk of
transfer line will greatly increase, which will impact the
reliable operation of distribution network. Therefore, we
should conduct the calculation of line risk and transfer
the power load to a high reliability line as far as possible.
In this paper, combining with Condition Based Main-
tenance (CBM) conducted by Power Supply Company,
the health status of distribution equipments on transfer
path are evaluated and then, make a prediction of equip-
ment failure rate according to the health evaluation re-
sults. After that, Per-unit value of the line load is calcu-
lated based on the max line load. In the following, sys-
tem risk is calculated and the level of risk assessment is
set up according to results of risk value.
2.3. Health State and Failure Rate
Health evaluation is a comprehensive evaluation process,
which means that the electrical equipment’s health state
is evaluated by various state parameters, according to the
health state, the hidden defects of equipment are found
out in time and Power Supply Company can conduct the
maintenance to make sure that the equipment is in
healthy condition [6].
This paper adopts Fuzzy Variable Weight Analysis
method to evaluate the health degree of distribution
equipments. The method can adjust the weights of
equipments’ state parameters automatically according to
the relationship and quality of different parameters. The
procedure of distribution equipments’ health evaluation
can be described as follows:
Copyright © 2013 SciRes. ENG
iij ij
b WR
[ ]
, ,...,
B bbb=
Y cb
where Rij denotes the fuzzy evaluation score and Aij de-
notes the weight of each evaluation state parameter. B
denotes the fuzzy membership matrix of evaluation result.
Formula (8) is the weighted summation formula; cf is the
values of di f ferent evaluation indexes.
In practical evaluation, when some state parameters of
power equipments are in extremely serious statu s, w e c an
adjust the parameters’ weights by using equilibrium
coefficient. The variable weight formula is as follow:
() /
iio iio i
Wx wxwx
where Xi denotes the value of each state parameter, Wio
denotes the fixed weight of each parameter.
is the
equilibrium coefficient which values between 0 and 1.
After that, refer to the EA general formula of risk and
failure probability, the fault rate formula of equipment
health state is as follow:
Y Ke
where K denotes the proportionality coefficient and C
denotes the curvature coefficient, which are calculated
according to the statistics of equipments’ health state and
failure probability in the region.
3. Differential Evolution Algorithm
Differential Evolution (DE) algorithm is an effective and
robust method, which is used to solve the complex func-
tions with the Characteristics of Non-linear, non-differ-
rentiable and high-dimensional. At present, DE algorithm
has been widely used by the experts and scholars in dif-
ferent research field, which has become an important
branch of E v olutiona ry Algori t hm (EA).
DE algorithm adopts the s earching strategy of greed,
which means after operation process of mutation and
crossover, test individual
can become the next
generation only when its fitness is better than the original
. Otherwise,
is regarded as the next
generation. In this process, completely dominate (
) based on the concept of Pareto theory dominant is
used among the chosen operation.
In addition, another feature of DE algorithm is adopt-
ing elitism strategy to k eep the d iversity of final solutions.
The reason is that we can’t guarantee that the Pareto op-
timal solution of curre nt generation is always the opti mal
in each generation. Therefore, we u se an external storage
to store the Pareto optimal solutions which have been
found starting from the initial population and compete
the distance between the current solutions and the solu-
tions in the storage.
4. Example Analysis
This paper optimizes a maintenance schedule of the gen-
eral 33 nodes distribution network [11], which uses the
presented method in this paper. The distribution system
network is shown as the Figure 1.
Based on the method above, the maintenance week
scheduling of two lines on 33 nodes network is arranged.
The parameters of objective functions are set as Table 1.
Using Differential Evolution algorithm to opti mize the
maintenance scheduling, the parameters of Differential
Evolution algorithm are set as Table 2.
The optimization results are shown as Table 3.
In Table 3, we can see that when system risk is co nsi-
dered as objective function (Strategy 1), the grid active
power loss is more than but close to that in the situation
without considering (Strategy 2) and that, all network
loads can be transferred by contact switch operation.
Figure 1. Distribution network of 33 nodes.
Table 1. Parameters setting of objective functions.
Parameters Setting of Objective Functions Parameters Setting
Average Price The Maintenance Time Maintenance Items
Parameters Value 0.5 RMB/kWh 1 hour
Line 2 - 22
Line 10 - 11
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Table 2. Parameters setting of algorithm.
Parameters Setting of Algorithm
Parameters Setting
Parameter of Crossover Parameter of Mutation Population Size Maximum Generation
CR min CR max F0
Parameters Value 0.1 0.9 0.8 100 50
Table 3. Results of optimization.
Results of Optimization
Objective Function
Maintenance Time Contact Switch Operation Load Loss Grid Power Loss System Risk
Considering LINE RISK
(Strategy 1) Wed 8:00
Wed 14:00
Close S
Close S3S4
Open S5 0 0.0093 0.3090
Without Considering LINE RISK
(Strategy 2) Wed 8:00
Mon 8:00
Close S
Close S3S4
Open S6
0 0.0079 0.6087
However, as the table shown, the system risk (Medium
Risk) of the second strategy is much higher than the sys-
tem risk (Low Risk) of strategy 1 because the transfer
line 1 - 18 is in the state of high system risk. The failu re
rate of transfer line will greatly increase and lead to the
higher system risk if the power load is transferred to line.
Therefore, according the optimization results, line risk
degree ought to be taken into account in the load transfer
path sele c tion of ma i ntenance sche duling.
5. Conclusions
This paper establishes a multi-objective optimization
model of distribution equipments’ maintenance schedul-
ing, considering the functions of load loss, grid active
power loss and line risk. Through the analysis of distri-
bution network system of 33 nodes, conclusions are
drawn as f ollows:
1) Combining with the Condition Based Maintenance
and risk assessment of distribution network equipments,
this paper puts forward to consider system risk as opti-
mization objective function, by evaluating equipments’
health state, forecasting equipment failure rate and sys-
tem risk, in order to avoid the disadvantage of overload
2) Based on the theory of Pareto domination, a multi-
objective optimization mathematical mode l is established
according to the practical situation of maintenance sche-
duling. The diversity validation can keep the diversity of
the Pareto optimal solutions, which is an effective me-
thod of solving multi-objective problem and making
maintenance plan.
3) The optimization results of maintenance scheduling
provide a feasible maintenance scheduling and transfer
path, which greatly improve the reliability and economy
of power system’s operation and have theoretical and
practical significance.
6. Acknowledgements
This work is supported by High-tech Industrialization Key
Project in Guangdong Province (No. 2 010A010200005).
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