S. Y. HONG ET AL.
Copyright © 2013 SciRes. ENG
(1)
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:
12
Min ( )(( ),( )...,( ))
k
XR
FXf XfXfX
∈
=
12
()((), (),...,())0
m
gXgXgXgX= ≤
(2)
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
(3)
where
λ
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.
(4)
where
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:
(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: