Maintenance Scheduling of Distribution System with Optimal Economy and Reliability

doi:10.4236/eng.2013.59B003

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Engineering, 2013, 5, 14-18

http://dx.doi.org/10.4236/eng.2013.59B003 Published Online September 2013 (http://www.scirp.org/journal/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

Email: [email protected]

Received June 2013

ABSTRACT

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

Maintenance

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

maintenance.

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:

S. Y. HONG ET AL.

min( )

∑

..st

( )0,1,2..

gx jl≤=

(1)

( )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

results.

• 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 ( )(( ),( )...,( ))

FXf XfXfX

∈

..st

()((), (),...,())0

gXgXgXgX= ≤

{ }

( ()0R XgX= ≤

(2)

( ,..),

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

∈

= ××

∑

(3)

where

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( )

∈

= ∆

∑

(4)

where

P∆

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:

311

Min( )

f PR

= =

∑∑

(5)

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 Risk” and “High 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:

S. Y. HONG ET AL.

iij ij

b WR

=∑

(6)

[ ]

, ,...,

B bbb=

(7)

Y cb

=∑

(8)

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

−−

=∑

(9)

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

(10)

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

individual

. 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

S. Y. HONG ET AL.

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

operation.

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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