Journal of Power and Energy Engineering, 2014, 2, 457-462
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2014.24061
How to cite this paper: Zhang, C., et al. (2014) Optimal Resources Dispatching Technology of Distribution Network Rush-
Repairing. Journal of Power and Energy Engineering, 2, 457-462. http://dx.doi.o rg/10.4236/jpee.2014.24061
Optimal Resources Dispatching Technology
of Distribution Network Rush-Repairing
Chao Zhang, Xinhe Chen, Xing Xiong, Jing Zhou, Wenbin Zhang
State Grid Electric Power Research Institute, Beijing, China
Received Dec emb er 2013
Abstract
Confronted with the r equi rement of higher efficiency and higher quality of distribution network
fault rush-repair, the subject addressed in this paper is the optimal resource dispatching issue of
the distribution network rush-repair when single resource center cannot meet the emergent re-
source demands. A multi-resource and multi-center dispatching model is established with the ob-
jective of “the shortest repair start-time” and “the least number of the repair centers”. The optimal
and worst solutions of each objective are both obtained, and a “proximity degree method” is used
to calculate the optimal resource dispatching plan. The feasibility of the proposed algorithm is il-
lustrated by an example of a distribution network fault. The proposed method provides a practical
technique for efficiency improvement of fault rush-repair work of distribution network, and thus
mostly abbreviates power recovery time and improves the management level of the distribution
network.
Keywords
Distribution Network; Rush-Repairing; Multi-Objective and Multi-Resource Dispatching; Proximity
Degree Method
1. Introduction
The power recovery efficiency of the power grid depends on the matching degree between the damage of the
power grid and the rush-repair capability. The rush-repair capability of the power gird depends on the repair re-
source reserves, field circumstance and the dispatching capability. The resource reserves are fundamental to the
rush-repair work. And the resources dispatching technology is critical for the fast recovery to meet with the re-
quir ement of the distribution network fault rush-repair [1]-[5].
When the power grid is facing with the continuous or extensive attack, such as severe weather or geological
disaster, rush-repair crew will be very busy and the repairing resource might not be able to meet with the emer-
gency resource demands.
In a rush-repair work, when the repair resources are insufficient in local resource center, the decision-maker
relies on his previous experience to command. It might be very difficult for them to make an optimal decision
under the condition that there are various kinds of resource demands form distributed resource centers, which

C. Zhang et al.
458
implies that it is hard to make an optimal decision. Besides, there is not evaluation criterion for the decision
made by the commander until the rush-repair work is done. In this paper, a reasonable evaluation criterion and
corresponding techniques for the decision making are studied to figure out the optimal resource dispatching
plan.
2. Modelling for Resource Dispatching
2.1. The Resource Dispatching Process
When a power outage event happen in the power grid, the rush repairing command center analyzes the outage
cause based on the information from DSCADA, electricity usage data acquisition system, 95,598 customer ser-
vice system, and etc.. According to the fault analysis, the command center recognizes the needed type and
amount of the repair resources and then sends dispatching order to the resource centers. The dispatching process
is shown in Figure 1.
2.2. Resource Dispatching Modelling
Sufficient repair resources are the fundamental requirement for the distribution network rush-repairing. In a
rush-repair work, there will be n involved resource centers, which are notated as
12
,,
n
AA A…,
. Meanwhile, there
will be m (m > 1) types of repair resources needed in fault location A. The types of resources are notated as
12 m
,,XX X…,
, and the amount needed for every resource is
12
,,
m
xx x…,
, respectively.
ij
x
and
'
ij
x
is as-
sumed to be the resource reserve and supplying amount of the jth type of resource from the ith resource center, in
which
1in≤≤
,
1jm≤≤
and
1
n
ij j
i
xx
=
≥
∑
. The delivery time from
i
A
to A is
i
t
(
0
i
t>
), assuming
12
t
n
tt≤≤≤
…
. The optimal resource dispatching plan implies that the start-time of the rush-repairing work is
shortest and the number of involved resource centers is minimized.
Ass uming the optimal plan is
ϕ
, which is specified as
12
={ ,,}
m
ϕ ϕϕϕ …,
(1)
where,
()()( ) { }
112 2k k
ddd dd d
'' '
,, ,,, ,
j jjj
Ax AxAx ϕ =
represents the rush-repairing plan for the jth resource.
If the selected resource center
12
,,
k
dd d…,
from all of n centers satisfy the demand of the jth resource, we
have
'
1
dj
i
k
j
i
xx
=
=
∑
, (
1, 2,,jm=…
) (2)
where,
d2
1
'' '
dd
,,
jk
jj
xx x…，
are the supplying amount of the jth resource from the selected resource centers, sep-
arately. The set of all the dispatching plans is Ω .
Outage
Outage
Resource demands met ?
Resource demands met ?
Y
N
Resource
dispatching from
available centers
Resource
dispatching from
available centers
Check the available resources
in the centers near the fault
Check the available resources
in the centers near the fault
Resource dispatching command
Resource dispatching command
Rush-repairing ends
Rush-repairing ends
Fault Analyzing
Fault Analyzing
Resource dispatching
in the center
Resource dispatching
in the center
Figure 1. Rush-repair process.

C. Zhang et al.
459
Definition 1: The number of the selected resource centers is
()
N ϕ
and the start-time of the rush-repair
work is
( )
T ϕ
, which implies that all the needed repair resources arrive at the fault location in
( )
T ϕ
with
their demand satisfied. Thus,
()max( )
i
Tt ϕ =
,
12
,,
k
i ddd=…,
(3)
The objective of the resource dispatching is to minimize the start-time of the rush-repair work and the number
of the resource centers involved. That is
min( ())
min(( ))
.
T
N
st
ϕ
ϕ
ϕ




∈Ω 
(4)
The Equation (4) is a multi-target decision-making problem which can be solved by the technique of order
preference by similarity to ideal solution. Therefore, the positive distance and the negative distance to the ideal
solution can be worked out from the two following objective functions.
min( ( ))
.
T
st
ϕ
ϕ


∈Ω 
(5)
min(( ))
.
N
st
ϕ
ϕ


∈Ω 
(6)
Assume
ϕϕ
′′ ′′
，
is the best and worst solution of the Equation (5), separately. And
ϕϕ
′′
，
is the best and
worst solution of the Equation (6), separately. The proximity degree between a dispatching plan
v
ϕ
and the
best solution can be expressed as:
12
() ()
() ()
vvv
NT
RNT
ϕϕ
ωω
ϕϕ
′ ′′
= +
(7)
Similarly, the proximity degree between the plan
v
ϕ
and the worst solution can be expressed as:
12
() ()
() ()
vv
v
NT
rNT
ϕϕ
ωω
ϕϕ
= +
′ ′′
(8)
In the Equation (8),
1
ω
and
2
ω
are the weight of “the number of the resource center” and “the start-time of
the rush-repair work”, separately, and
12
1 ωω +=
. The specific value can be obtained by specialists. In this pa-
per, both of them are 0.5. The relative proximity degree between the plan
v
ϕ
and the ideal solution can be ex-
pressed as follows:
v
vvv
R
Rr
ε =+
，
01
v
ε ≤≤
(9)
Therefore, the multi-objective decision-making problem can be translated to the proximity degree problem
between the suggested solution and the ideal solution. The solution which obtains the maximal proximity degree
v
ε
is optimal [6].
3. The Solution to the Resource Dispatching Problem
( ) ()
", "NN ϕϕ
and
( ) ( )
", "TT ϕϕ
should be solved firstly for the Equations (7)-(9).
3.1. The Solution to the
( ) ( )
,TT"" ϕϕ
The resource centers involved should be near enough to make sure that the start-time of the rush-repair work is
as earlier as possible.
Assume the resource centers
12
,,
n
AA A…,
are ranked by the delivery time to the fault location from shortest
to longest.
If
1
00
jj
qq
pj jpj
pp
xx x
−
= =
<≤
∑∑
,

C. Zhang et al.
460
where
0
0
j
x=
, the optimal dispatching plan for the jth resource with the objective of the shortest delivery time
can be expressed as:
1
11220
( ,),(,),(,)
j
j
q
jjjq jpj
p
AxAxA xx ϕ
−
=
′=− ∑
…，
(10)
Thus,
j
q
t
which is the delivery time of the jth resource from the resource center Aqj to the fault location, is the
shortest delivery time for the jth resource.
Similarly, the shortest delivery time for the other resources can be obtained. And the best solution to the Equ-
ation (5) is
{ }
12
,,
m
ϕ ϕϕϕ
′ ′′′
=…,
.
Therefore
12
()max( ,,,)
m
qq q
Ttt t ϕ
′′ =
(11)
And
( )()n T Tt ϕϕ
′′ ≤≤
(12)
Notice that the longest delivery time is
n
t
, that is:
( ")=
n
Tt ϕ
(13)
3.2. The Solution to the
() ( )
,NN '' ϕϕ
Similar to Section 3.1, assume the resource centers
12
,,
n
AA A…,
are ranked by the resource reserve of the jth
resource from least to most.
The optimal dispatching plan for the jth resource with the objective of the least number of the involved re-
source centers can be expressed as:
11 22
1
1
(,),(,), ,(,)
j
pj
j
p
jk kjkkjkjkj
i
AxAxA xx ϕ
−
=


= −



∑
…
(14)
where,
j
p
is least number of the involved resource centers for the jth resource.
Therefore, the least number of the involved resource centers of the rush-repair work is
max1 2
max( ,,)
m
Npp p =
(15)
And for every dispatching plan
ϕ
,
max
()NNn ϕ ≤≤
(16)
3.3. The Solution to the Dispatching Problem
In the resource dispatching optimization problem, not only the number of the involved resource centers is con-
sidered to be as small as possible, but also the start-time of the rush-repair work should be as early as possible.
Therefore, the dispatching plan whose relative proximity degree
v
ε
is the biggest is taken as the optimal solu-
tion.
The calculation steps of the
v
ε
are as follows:
Step 1: Work out
max
N
,
( ) ( )
", "TT ϕϕ
;
Step 2: Let the set R = {
12
,,
n
AA A…，
} be the group of the repair centers,
max
nN
′=
and the serial number
y = 0;
Step 3: Select combinations of
n′
centers from the set R. If there is not a combination feasible, go to step 9;
Step 4: Let y = y + 1, Select the combination
v
ϕ
whose start-time
()
v
T ϕ
is shortest from all of the availa-
ble feasible combinations;
Step 5: Let
'
()
v
Nn ϕ =
, and if y = 1, let
'
() ()
v
NN ϕϕ =
and
'
()Nn ϕ =
;
Step 6: According to the Equation (7) and (8), calculate the proximity degree of between
v
ϕ
and the ideal
solution;
Step 7: Obtain the
y
ε
by Equation (9), and figure out the dispatching plan
*
y
ϕ
;

C. Zhang et al.
461
Step 8: Modify the set R by deleting the repair centers whose start-time
i
t
is longer than
()
v
T ϕ
;
Step 9: Let
1 nn
′′
= +
;
Step 10: If the length of the set R is larger than
' n
, go to step 3; or else, go to step 11;
Step 11: Compare the obtained
y
ε
, and the largest one is optimal
The flow chart of the algorithm is shown in Figure 2.
4. Case Study
In this study case, the distribution power grid was affected by storm. Based on GIS technology, the rush-repair-
ing center confirmed that the fault location is A. The dispatching plan of the required repair resources should be
optimized to ensure the efficient of the rush-repair work.
In this rush-repairing, 32*insulator (XPW-7)\25*pole (18 m) and 36*Cross Arm (1 meter) are required.
There are eight available resource centers near fault location A, and their resource reserves are shown in Ta-
ble 1.
The weights
1
ω
and
2
ω
are set to be 0.5. As is shown in Table 2, the biggest relative proximity degree is
0.6364 (y = 3). Therefore, the third dispatching plan whose start-time is 15 minutes is the optimal one.
The delivery time for every center is 10, 12, 14, 15, 20, 22, 25 and 30 minutes, separately.
Follow the algorithm proposed in this paper, the calculation results are shown in Table 2.
The details of the optimal plan are shown in Table 3.
Let
According to (7) and (8), calculate the
proximity degree of the solution to the
best solution and the worst solution.
Work out
Let be the group of the repair
centers , and let y=0, and
Select the combinations of n’ centers from R
Is there a combination
feasible ?
Is the length of the
set R larger than
Modify the set R by deleting the repair centers
whose start-time is larger than
' '1nn= +
Y
N
Y
Let
And if y==1, let
N
y
ε
According to (9), calculate the optimal index ,
and figure out the dispatching plan .
y
ε
*
y
ϕ
max
nN
′=
Let y=y+1, and select the
combination whose start-
time is shortest
max
,( ),( )NTT ϕϕ
′′ ′′
() ()
()
v
NN
Nn
ϕϕ
ϕ
′=

′=

v
ϕ
()
v
T ϕ
()
v
N n ϕ =′
i
t
()
v
T ϕ
'n
{ }
12
,, n R AAA=
i
A
Compare the obtained , and
the maximum one is optimal
v
ϕ
End
End
Figure 2. The flow chart of the resource dispatching.

C. Zhang et al.
462
Table 1. The resource reserves.
Resou r ce
1
A
2
A
3
A
4
A
5
A
6
A
7
A
8
A
Insulator 12 5 10 9 9 6 24 7
Pole 10 8 4 12 4 15 10 5
Cross Arm 12 16 5 7 9 12 20 14
Table 2. Calculation results.
y
R
y
N′
y
φ
n′
t
y
ε
1 A1, A2, A3, A4, A5, A6, A7, A8 unfeasible 2
2 A1, A2, A3, A4, A5, A6, A7, A8 A1, A2, A7 (A1, 12), (A2, 5), (A7,15) (A1, 10), (A2, 8), (A7,7)
(A1, 12), (A2, 16), (A7, 8) 3 25 0.5697
3 A1, A2, A3, A4, A5, A6 A1, A2, A3, A4 (A1, 12), (A2, 5), (A3, 10), (A4, 5) (A1, 10), (A2, 8), (A3, 4), (A4, 3)
(A1, 12), (A2, 16), (A3, 2), (A4, 6) 4 15 0.6364
4
When the quantities of elements are
smaller than n', the calculation ends. 5
Table 3. The optimal resource dispatching plan.
Resou r ce A1 A2 A3 A4
Insulator (XPW-7) 12 5 10 5
Pole (18 m) 10 8 4 3
Cross Arm (1 m) 12 16 5 6
5. Conclusion
In this paper, the optimal resource dispatching issue of the distribution network rush-repair is studied. The dis-
patching model is established first with the objective of “the shortest repair start-time” and “the least number of
the repair centers”. And a “proximity degree method” is used to calculate the optimal resource dispatching plan.
The feasibility of the proposed algorithm is illustrated by an example of a distribution network fault. The pro-
posed method provides a practical technique for efficiency improvement of fault rush-repair work of distribution
network, and thus mostly abbreviates power recovery time and improves the management level of the distribu-
tion network.
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