Energy and Power Engineering, 2013, 5, 1393-1397
doi:10.4236/epe.2013.54B264 Published Online July 2013 (http://www.scirp.org/journal/epe)
Optimal Planning of Charging Station for Phased
Electric Vehicle*
Yajing Gao, Yandong Guo
School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, China
Received March, 2013
ABSTRACT
Construction of electric vehicle charging station is the premise of the popularity of electric vehicles. In this paper, elec-
tric vehicle charging facilities planning is divided into two stages: public demonstration stage and commercial operation
stage. In public demonstration stage, This Paper applies maximal covering model into charging station location, and
then be solved by the branch and bound method. In commercial operation stage, the charging station’s service areas
division is studied based on Voronoi diagram. With the concerning technical restrains, an optimal planning method is
presented for newly-increased station positioning and service region division. The method using the most greatly air
circuit method and local dynamic characteristics of Voronoi diagram guarantees the reasonable distribution of stations.
Then charging station model of optimal load allocation is established by using M/M/c model. In the end, the correctness
and validity of the model is verified through simulation of charging station planning.
Keywords: Charging Demand; Electric Vehicle; Planning Layout; Voronoi
1. Introduction
With the deteriorating global environment and the lack of
oil resources, the society has begun to focus on the use of
electric vehicles. However, construction of electric vehi-
cle charging station is the premise of the popularity of
electric vehicles [1-3].
At present, construction of charging stations in China
is mainly for market demonstration with no clear and
reasonable layout, so establishing an effective charging
station layout and a scale setting tool have become an
urgent need at the moment. In [4], the advantages and
disadvantages of the electric vehicle charging system
have been reviewed and the external access methods of
charging stations, installed capacity and its influencing
factors are considered as a preliminary inquiry for the
planning of charging stations. In [5], the overall demand
of the charging load and planning influencing factors,
including the operating model of electric vehicles charg-
ing stations have been analyzed; principle recommenda-
tions such as planning of charging stations should meet
the radius requirements of the charging stations, traffic
density, distribution of electric vehicle charging demand
and the overall urban road planning have been made. In
[6], taking the geographical factors and the service radius
into account, a two-step screening method to identify
candidate sites for charging stations has been presented.
Combined with various sections of the electric vehicle
driving conditions and charging needs, in public demon-
stration stage maximum coverage model has been pre-
sented to strike the optimal location under funding con-
straints; in commercial operation stage, Voronoi diagram
is used to distribute demand, an optimized model is pre-
sented.
2. Analysis of Demand for Electric Vehicle
Charging
Assuming vehicle charging demand is equal the power
consumption on the section L.
V(i, k) Calculate the class-k electric vehicle electric
consumption in V(i, k) on the section L(i):
(, )()()(, )VikgkLiqik

 (1)
The power consumption of various types of electric
vehicles on the section of L (i):
1
()(, )
m
k
Vi Vik

 (2)
In the equation (1) (2): g is electricity consumption of
vehicles per kilometer constrained by vehicle type, vehi-
cle load and travel speed. This model uses the concept of
the average electricity consumption for a particular class
*This work was supported in part by the National Natural Science
Foundation of China under Grant 51177047, Fundamental Research
Funds for the Central Universi
t
ies under Grant 12MS107.

Y. J. GAO, Y. D. GUO
1394
of electric vehicles and average power consumption is a
fixed value; q (i) is the number of vehicles through a road
section in a unit time (vehicles / day). Q (i, k) is the traf-
fic volume at point I for class-k cars in a two-way traffic
flow; L (i) is the length of the road section i.
3. Charging Station Planning in Public
Demonstration Stage
The current stage of electric vehicle technology is not yet
fully mature and effective and sustainable market me-
chanism to promote the development of electric vehicles
has not yet formed. The total amount of electric vehicles
accounts for a very low proportion and electric vehicle
industry relies on government subsidies and advocacy, in
the public demonstration stage, charging facilities plan-
ning can be seen as a short-term planning.
Because of the characteristics of this stage, the initial
investment of charging stations covering all charging
needs may lead to excessive fiscal spending. As a result,
due to the limitations of the actual budget may, charging
stations may cover less demand. The model is shown as
follows:
max( )i
iI
Z
Vim

 (3)
s.t. (4) ,
i
ij
iN
mni


I
p
j
jJ
n


 (5)
,{0,1} ,
ji
nmi Ij J (6)
In the model, J is a set of candidate points of existing
gas station scalable with charging facilities and I is a set
of charging requirements. mi stands for whether charging
demand point i could receive charging services and the
value of 1 shows charging demand in point i can receive
charging service, on contrary the value is zero. Ni is a set
of candidate facility j which could cover charging de-
mand in point i and it can be expressed as i=
{j│dij
N
s
}, where d stands for distance between point i
and j and s stands for the maximum acceptable candidate
facility charge distance. The objective function of for-
mula (3) targets to covering most of the charging re-
quirements by charging facilities with the p; constraint
condition Equation (4) indicates that the number that
charging stations can be searched by charging demand
point i within a maximum acceptable service distance is
greater or equal with the value of 1; constraint formula (5)
represents the total number of facilities is limited to the
number of p. The constraint formula (6) constrains the
value of mi and nj to the value of 0 or 1.
Described by the formula (3)~(6), the charging station
planning problem is a 0-1 integer programming problem
and will be solved by the branch and bound method in
the follow.
4. Charging Station Planning in Commercial
Operation Stage
In this stage, the electric vehicle technology is assumed
basically mature and the total amount of vehicles reaches
a certain size. So in this stage, electric vehicle charging
facilities planning can be seen as a long-term planning.
4.1. Method of Alternately Positioning in
Commercial Operation Stage
In this stage, adequate charging facilities begin to be es-
tablished to meet the charging demand of electric vehicle.
Assume that electric car owners are always looking for
the nearest charging station for their services, the as-
sumption coordinates a great similarity with the Voronoi
diagram [7]. Program flow of alternately positioning in
commercial operation stage is shown in Figure 1:
Method of alternately positioning in commercial op-
eration stage is as follows:
Figure 1. Flow charts.

Y. J. GAO, Y. D. GUO 1395
1) Using charging station sites in the first stage, the
Voronoi diagram is generated. In the Voronoi diagram,
the radius of the hollow circle where the vertex in are
sorted in descending order. The center of the hollow cir-
cle of which radius is greater than the radius of the
charging stations hollow circle is set as the initial site.
2) Based on the existing sites and the new candidate
site, Voronoi diagram is regenerated to determine the
optimal service range for the new charging station. In the
service range of the new station, Use the gravity method
to determine the optimum position for the new charging
station.
3) Repeat 2) until the value of location coordinate of
the new sites is less than booking precision.
4.2. The Number of the Optimal Chargers in
Charging Station
From the current developing situation of electric vehicle
and historical data at gas stations, the following assump-
tions are made:
Per charge quantity is a fixed value Q. The arrivals of
electric vehicles are a Poisson stream of rate λ. The
charging time is a negative exponential distribution with
μ .
With the above assumptions, the charging station, as a
charging service system, is a multi service desk and finite
waiting room ( M / M / c ) system.
There are i sections in area j, V
j is the electric con-
sumption in area j:
i
j
i1
()VV

i (7)
N is the number of times of electric vehicles charge in
area i
j/NVQ (8)
Assuming vehicle charging station is open from 8 am
to 10 pm.
/14N

 (9)
The model of optimizing the quantity of chargers in
charging stations is as follow:
00
0
(1 )
min (1) 1
n
ii
n
rr
q
F
cTYN kW
r

  
 (10)
qma
LLx (11)
In (10), Fi is the cost of the charging station I, c is the
number of chargers, T is the charger cost, Yi is the annual
operating cost of the charging station i.k is the user’s
time value, it can be estimated by the user’s income in
the area. n is the depreciable life, Wq is the average wait
time. In (11), Lq is the mathematical expectation of the
number of waiting EVs, Lmax is the maximum acceptable
number of waiting EVs in station.
The problem will be solved by the LINGO in the fol-
low.
5. Example Analysis
In this paper, planning of charging stations is taken for
example: the region is a total area of 36.48 km2 which
spans 6.4 km from east to west and 5.7 km from north to
south and can be divided into 58 sections. In reality, the
type of electric vehicles differ from driving load and traf-
fic status, charge cost will also be different. However, to
simplify the problem, the example assumes that power
consumption of vehicles per kilometer is a fixed value, g
= 0.13 kWh/km. The map as well as the existing gas sta-
tion location with link numbers is shown in Figure 2.
5.1. Charging Station Planning in Public
Demonstration Stage
The region is planned to construct 5 charging stations in
the first batch and the predetermined range of the charg-
ing station is 2 km. According to the data in the Equation
(1)(2), the charging demands of different sections are
obtained. According to the charging station planning
model in public demonstration stage constrained by Equ-
ation (3)~(6), the demand is set to weight, then solve by
branch and bound method in lindo software. The max Z
is 14862 kWh and the most optimal position is shown in
Figure 3. By the optimal location, Voronoi diagram is
generated, the scope of each charging station is deter-
mined and each demand point is allocated, shown in
Figure 3.
5.2. Charging Station Planning in Commercial
Operation Stage
In Figure 3, the hollow circle radius greater than the ra-
dius of the charging stations hollow circle center are set
as the initial location. Using the existing stations with
Figure 2. City network diagram.

Y. J. GAO, Y. D. GUO
1396
new sites to generate Voronoi diagram, the scope of ser-
vices of the new station is determine, in other words,
demand is distributed again. Within the range of its ser-
vices, Use the gravity method to determine the optimum
position for the new charging station. Using the existing
stations with new optimal site to generate new Voronoi
diagram and solve the problem again with the new ser-
vice scope division of charging stations until the iterative
adjustment is less than the default precision of 0.1 km2.
The location of the new station and its service range is
shown in Figure 4. The new site is located in point 6.
5.3. The Number of the Optimal Chargers in
Charging Station
Taking into account the interests of charging stations and
users, the sum of charging stations’ service cost and cus-
tomers’ waiting fees is chosen as the objective function
for the optimal allocation of chargers.
Relevant parameters are shown in Table 1.
Using the methods described in this article, the prob-
lem has been calculated by LINGO, and then following
results have been obtained in Table 2.
Figure 3. Charging station planning in public demonstra-
tion stage.
Figure 4. Charging station planning in commercial opera-
tion stage.
Table 1. Related parameter selection.
sign Value sign Value
Q 20.8kWh g 0.13kWh/km
Lmax 20 r0 0.1
T 0.1million yuan k 25yuan/hour
Yi 0.2million yuan n 20
Table 2. The number of optimal chargers.
Station number The number of the optimal chargers
1
2
3
4
5
7
6
12
11
11
6 7
6. Conclusions
In this paper, using sections consumption to simulate
randomly charging requirements of electric vehicles is
able to provide new ideas for future research on fore-
casting electric vehicle charging load; in public demon-
stration stage, this Paper applies maximal covering
model into charging station location, and then be solved
by the branch and bound method. In commercial opera-
tion stage, using Voronoi diagram features is able to pro-
vide automatic positioning of the charging stations and
new charging Station by service area division and would
also be an attempt to solve the problem of optimized
charging station optimized planning; then charging sta-
tion model of optimal load allocation is established by
using M/M/c model. The presented models are verified to
be effectiveness through a practical example.
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