Energy and Power Engineering, 2013, 5, 1404-1409
doi:10.4236/epe.2013.54B266 Published Online July 2013 (
Optimal Siting of Electric Vehicle Charging Stations
Based on Voronoi Diagram and FAHP Method
Zheci Tang, Chunlin Guo, Pengxin Hou, Yubo Fan
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,
North China Electric Power University, Beijing, China
Received March, 2013
The electric vehicle charging station should be allocated based on traffic density, geographical distribution and other
factors, and Voronoi diagram is adopted to set the service area of charging station. In combination with the actu al situa-
tion of site selection of electric vehicle charging station, the comprehensive benefits index system is established. There
are numerous factors influencing the site selection, among which there are uncertainty and fuzziness. The comprehen-
sive evaluation method based on the fuzzy analysis and Analytical Hierarchy Process (AHP) is used to evaluate the
comprehensive benefits in the site selection of electric vehicle charging stations, with the consultation of experts. This
paper contributes to the best selection of comprehensive benefits and provides the reference for the decision-making of
building the electric vehicle charging station. Actual examples show that the method proposed is effective.
Keywords: Electric Vehicles; Charging Station; Voronoi Diagram; Fuzzy-AHP; Optimal Siting
1. Introduction
With the growing problem of global fossil energy crisis
and environmental degradation, all countries turn their
attention to the development and application of new en-
ergy currently so that exploration and research of large-
scale electric vehicles has become a hot spot. Meantime,
Markets around the world have a greater demand for
family cars with economic development and the im-
provement of people’s income levels, which has certain
positive significance in improv ing residents' trav el modes
and the development of th e automobile industry, but also
has a negative impact on energy security and environ-
mental protection. Construction of electric vehicle charg-
ing station is a prerequisite for the popularity of electric
vehicles while improving the efficiency of energy supply
network is one of the necessary conditions for electric
vehicles widely used [1, 2].
2. Basic Description of the Voronoi Diagram
The Voronoi diagram on the plane is the result of each
vertex Pi(i = 1, 2, …, n) in the point set P expanding
outward at the same speed until they meet each other.
These outmost points form open area, each of the re-
maining points forms a convex polygon. The Voronoi
diagram plays an important role in solving a dis-
tance-related geometry object problem, and has been
widely applied in many areas related to the geometric
information [3], especially in geospatial facility location
Suppose that 12
{, ,},3
 is a point
set in the Euclidean p lane, these points are different from
each other, that is to say
,,, {1,2,,
ij n
PPijijI n},
 (, )
represents the Euclidean distance between Pi and Pj
Suppose there is a point x on the plane, then area
() {|(,)(,
VxEdxpdxp ),
1, 2,,,}jnj i
is called Voronoi polygon, remembered as V(pi). V pol-
ygon of each point comes together to form V diagram of
the closest point. Figure 1 shows V polygon generated
by given points P1, P2, …, P9.
3. Fuzzy-AHP Model
The site selection of electric vehicle charging station is a
complex multi-factor system and its content of the evalu-
ation is multifaceted. A comprehensive evaluation about
the main factors affecting the location and its indicators
would be carried out in order to select the optimal pro-
gram from many other site options. In the current evalua-
tion methods, the fuzzy comprehensive evaluation
*This work is supported by: National High Technology R&D Program
of China (863Program) (2012AA050804), Key Project of the National
Research Program of China (2011BAG02B14), National High Tech-
nology R&D Program of China (863 Program) (2011AA05A109).
Copyright © 2013 SciRes. EPE
Z. C. TANG ET AL. 1405
method and the Analytic Hierarchy Process are often
Figure 1. Voronoi diagram example.
used to evaluate the qualitative indicators. The fuzzy
comprehensive evaluation method measures fuzzy dif-
ferences with strict figures languages and utilizes mem-
bership function to divide its boundaries. But, establish-
ment of the weight of fuzzy comprehensive evaluation
often relies on the judgment of experts’ subjective ex-
perience inevitably. Analytic Hierarchy Process (AHP) is
a combination of qualitative and quantitative, expresses
and processes the subjective judgment of persons with
number forms, which would not only fully reflect the
fuzziness of the evaluation index and the evaluation pro-
cess, but also eliminate the one-sidedness of the subjec-
tive judgment so that the results of the evaluation could
be more objective and credible. Therefore, this paper
combines the advantages of these two methods, deter-
mines the weights of the sub-targets and indexes by AHP,
evaluates the comprehensive benefits of the site selection
of electric vehicle charging station by Fuzzy- AHP and
provides the reference for the optimal decision-making of
the site selection [4, 5].
Fuzzy-AHP is a comprehensive evaluation model that
applies AHP and fuzzy comprehensive evaluation to the
establishment of comprehensive evaluation model in
fuzzy layer, gives play to the advantages of these two
methods, takes full account of the various factors affect-
ing the evaluation system, and combines the qualitative
and quantitative analysis[6].
3.1. Determine the Weights of Each Evaluation
Index by AHP
Analytic hierarchy process (AHP) was introduced by
Professor T. L. Saaty, an American operations researcher,
in the 1970. The basic principle of AHP is:
Through the analysis of factors and correlation of
complicated system, make the problem methodical and
hierarchical in order to objectively build a multi-level
analysis structure model. Compare the various elements
of each level pairwise, by introducing 1~9 ratio scaling
method (Table 1) to construct the judgment matrix.
Through calculating the biggest eigenvalues and corre-
sponding eigenvectors of judgment matrix, getting im-
portance orders of elements of all levels for a certain
element, the weight vector is established. Finally, a com-
prehensive judgment is made. As follows are the main
1) According to Table 1, construct comparison matrix
pairwise, i.e., judgment matrix:
()(, 1,2,,)
ijn n
ij n
where 1, 1/
ii ijji
2) Multiply the elements of each row of the judgment
matrix A, and find the nth root of the results respectively,
3) Normalize i
W to achieve Wi.
4) Calculate the maximum eigenvalues and their cor-
responding eigenvectors.
(, ,,)
max 1()/
5) Consistency check
a) Calculate the consistency index
()/(CInn 1)
 (6)
b) According to Table 2, find the average random
consistency index RI corresponding to CI.
Table 1. 1~9 ratio scaling.
Criteria scale Definition
1 X and Y are equally important
3 X is a little important than Y
5 X is obviously important than Y
7 X is strongly important than y
9 X is absolutely important than Y
2,4,6,8 Its important degree between the above
two adjacent judgment value
Table 2. The average random consistency index RI of the
judgment matrix.
n123 4 5 6 7 8 9
RI 000.580.901.12 1.24 1.32 1.411.45
Copyright © 2013 SciRes. EPE
c) Calculate consistency proportion
The judgment matrix A passes the consistency check
When CR < 0.1, otherwise, it is required to re-construct,
until the consistency proportion meets the requirements.
3.2. Main Steps of the Fuzzy-AHP Model
1) The establishment of the factors set of comprehen-
sive evaluation, , reflects the main
indicators of the evaluation object (first grade indexes),
which is also affected by the sub-indicators (secondary
,,, (1,2,,)
Uuu uik (7)
12 1
nnn nn
2) Determine the weight distribution set of secondary
indexes according to the result of AHP.
,,, (1,2,,
Wwwwik (9)
3) Determine the weight distribution set of first grade
indexes according to the result of AHP.
AA A (10)
4) In combination with the actual situation of site se-
lection of electric vehicle charging station, select the
evaluation set to form a judgment collection
In this model, n = 4, the judgment collection is
= {better, good, general, poor}
5) Evaluate secondary indexes by several experts’
voting to reach evaluation matrix Ri.
11 121314
21 222324
ii ii
nn nn
6) Figure out the total evaluation matrix B.
a) Calculate the evaluation vector Bi of every first
grade index Ui.
BWRi k (12)
b) The total evaluation matrix B is
(, ,, )
BBB B (13)
7) Obtain the total objective evaluation vector C.
CAB (14)
8) Figure out the comprehensive benefits of site selec-
tion of electric vehicle charging station after the total
objective evaluation vector C is ready, which depends on
maximum memb ership d egree l aw.
4. Example of the Optimal Decision of the
Site Selection of Electric Vehicle
Charging Station
4.1. Use the Voronoi Diagram to
Differentiate Areas
Assuming a city as the planning area of electric vehicle
charging station network, According to the city's traffic
density distribution and regional distribution, several
center points are selected. The Voronoi diagram is used
to differentiate areas, in which a charging station is build,
to finish the earlier work for charging station location.
The center point is not necessarily the optimal charging
station location. The optimal siting of charging station is
optimized by using the Fuzzy-AHP model [7, 8].
4.2. Establishment of Evaluation Index System
for Electric Vehicle Charging Station
Reviewing the related literature material and the princi-
ple of comprehensive evaluation index system, the com-
prehensive evaluation index system is established for
electric vehicle charging station location, in considera-
tion of traffic factors, economic factors, and social fac-
tors and influencing factors. Lane crossing number, road
conditions and main roads are considered in the area of
transportation; Total cost of construction investment,
operation and maintenance, and cost of wear and tear are
considered in. economic aspects. Social aspects include
local government’s opinions, construction conditions,
technical conditions and resource distribution. Effects
include environmental impact, power grid safety and
people life, and so forth. An evaluation index system for
electric vehicle charging station location is shown in
Figure 2.
Figure 2. Comprehensive evaluation index system of the site
selection of thermal power plant.
Copyright © 2013 SciRes. EPE
Z. C. TANG ET AL. 1407
4.3. Determine the Weights of Each Evaluation
Index by AHP
4.3.1. Establish Index Sets
Four first grade indexes and thirteen secondary indexes
in Figure 2 are established to evaluate the comprehen-
sive benefits of the site selection of electric vehicle
charging station. Then, comprehensive evaluation index
set U includes four first grade indexes, i.e.
12 3 4
The first grade indexes set is
, and thirteen secondary indexes are
111 12132212223
331 3233 344414243
,, ,,,,
,,, ,,,
4.3.2. Determine the Weights of Each Evaluation
Reviewing a large number of the existing date, in con-
sideration of the actual situation of electric vehicle
charging station location, each level of judgment matrix
based on Table 1 is established in order to calculate the
weight of each index and have a consistency check [9].
Traffic factors are taken for example.
1) Construct judgment matrix of
U1 u11 u12 u13
u11 1 1/3 1/5
u12 3 1 1/4
u13 5 4 1
2) Multiply the elements of each row of the judgment
matrix, and find the 3th root of the results respectively.
So, 11 1213
0.41, 0.91, 2.71.WWW
3) Normalize 1i
W to achieve
11 12 13
0.10, 0.23,0.67WWW
4) Calculate the maximum eigenvalues and their cor-
responding eigenvectors. i.e.
max 1
() /=3.0863
5) Consistency check
a) Calculate the consistency index
() / (1)0.0432CIn n
 
b) According Table 2, RI=0.58, CR=CI/RI=0.074<0.1,
the assignment of the judgment matrix constructed is
reasonable. Similarly, the judgment matrixes about
221 2223331 323334
4414243 1234
,, ,,,,
,, ,,,,
as follows:
u22 u23 U3 u31 u32 u33 u34
U2 u21
u21 1 5 5 u31 1 1/4 1/41/2
u22 1/51 1/2 u32 4 1 1 3
u23 1/52 1 u33 4 1 1 4
u34 2 1/3 1/41
U4 u41 u42 u43 U U1 U2 U3 U4
u41 1 1/5 1/3 U1 1 1/3 1/21/3
u42 5 1 4 U2 3 1 1/21/4
u43 3 1/4 1 U3 2 2 1 1/2
4 3 4 2 1
Finally, the result is:
4.4. Construct a Fuzzy Evaluation Matrix
esult is
esult in Table 3, by calculating the
Evaluate each index by ten experts’ voting, the r
shown in Table 3.
According the r
embership degree of each index corresponding evalua-
tion sets, the fuzzy evaluation matrix are:
0.2 0.4 0.400.3 0.4
0.2 0.1
0.10.6 0.2 0.10.3 0.30.2 0.2
0.4 0.4 0.200.4
0.3 0.50.1 0.4 0.2
0.2 0.50.2
0.4 0.3 0.300.2 0.3 0.3 0.2
0.1 0.4 0.3 0.2
 
 
 
1(0.10,0.23,0 .67)W
The weight set is established
by AHP, further, comn vector about
traffic is prehensive evaluatio
, cSimilarly, accordingompre-
hensive evaluation vecto
r about traffic is
According comehensive
ev pr
aluation vec
tor about traffic is
According comprehensive evalua-
tion vector ab
out traffic is
The general goal of the evaluation matrix is obtained
from the B1, B2, B3 and B4.i.e.
Copyright © 2013 SciRes. EPE
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s of experts’ voting to the index of the site selection of charging stations.
Table 3. Result
evaluation grade
First grade indexes Secondary indexes weight
better poor good general
Transportation Lan e crossing numbers u11 0.10 2 4 4 0
U10.11 Road conditions u12 0.23 1 6 2 1
Main roads u13 0.67 4 4 2 0
Economy struction investment u21
Society ns u31
Ef ct
Total cost of con0.71 3 4 2 1
U20.17 Cost of operation and maintenance u22 0.11 3 3 2 2
Cost of wear and tear u23 0.18 4 2 3 1
Local government’s opinio0.08 3 5 1 1
U30.25 Construction conditions u32 0.38 2 5 2 1
Technical conditions u33 0.41 4 3 3 0
Resource distribution u34 0.13 1 4 3 2
feEnvironmental impact u41 0.10 1 3 4 2
U40.47 Power grid safety u42 0.67 4 4 1 1
People life u43 0.23 2 3 3 2
4.5. The Comprehensive Benefit Evaluation of
eight se
5. Conclusions
iagram is used to divide the zone, in
combining AHP and fuzzy com-
fore, the evaluation results are more objective and credi-
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0.32 0.35 0.220.11
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Electric Vehicle Charging Stations Location
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the Fuzzy-AHP model.
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of electric vehicle charging station location, the organic
combination of the qualitative and quantitative analysis
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