Engineering, 2013, 5, 24-29
http://dx.doi.org/10.4236/eng.2013.59B005 Published Online September 2013 (http://www.scirp.org/journal/eng)
Load Cluster Characteristic Analysis and Modeling of
Electric Vehicles
Dan Zeng1, Ke Wang1, Yaping Li1, Xiaorui Guo1, Xiao Jiang2
1China Electric Power Research Institute, Nanjing 210003, China
2State Grid Electric Power Research Institute, Nanjing 210003, China
Received June 2013
ABSTRACT
Electric vehicle, as a clean en e rgy industry, is an important branch. Electric vehicles not only are the energy of the elec-
tric user , but also can be used as mobile and distributed energy storage unit to the grid. As a precondition of safety op-
eration for power grid, stu dies of EVs’ charging load characteristics is also the theoretical basis of intelligent sche duling
EVs charging orderly. This paper assesses the future of the electric vehicles development prospects, and secondly esta b-
lishes a charging model of a single EV. Then, considering stochastic distribution of the initial state-of-charge (SOC0)
and the arriving time of the vehicles, a clus ter model of the charging station is proposed. Meanwhile, the paper from the
types and charging mode of electric vehicles analyzes the behavior of EV. Finally, an exampl e simulation is validated.
Keywords: Electric Vehicle; Potential of Development; Charging Mode; Cluster Characteristic; Poisson Distribution
1. Introduction
Electric vehicle, as a clean energy industry, is an impor-
tant branch. Electric vehicles not only are the energy of
the electric user, but also can be used as mobile and dis-
tributed energy storage unit to the grid. Compared with
other loads, electric vehicles will not only be able to play
a better role in load shifting, but also as a system of spin-
ning reserve. However, a large number of electric ve-
hicles charging will significantly increase the disorderly
distribution system losses and damage power qua lity.
Conversely, if the charging of electric vehicles coordi-
nated control behavior, you can make disadvantages into
advantages, reduce system peak load needs, and substan-
tially reduce the negative impact.
At presen t, the load characteristic of electric cars is
still very lacking. Mos t researches are focused on the
battery charge and discharge characteristics and power
harmonics problems. The generic battery model under
considering dynamic response, the phenomenon of self-
discharge, and temperature and other factors [1-5] has
been studied a lot. The r esearc h of power harmonic fo-
cuses on the characteristics of a single charger and mod-
eling [6-11].
However, in more sophisticated smart grid system,
electric vehicles will be used as bidirectional energy
trader, in the valley of charge when grid electricity pur-
chased at low energy, to meet their own need to use; sold
at high prices when the peak load electricity or act as a
backup power supply to obtain profits. It not only can
eliminate large grid electric vehicles negative impact, but
also can be a large number of electric vehicles as a flexi-
ble load utilized to improve the system operation. This
requires a study of charging agglomeration characteris-
tics with random characteristics of large-scale electric
vehicles and the electric vehicles charging lo a d curve.
This paper assesses the future of the electric vehicles
development prospects, and secondly establishes a charg-
ing model of a single EV. Then, considering stochastic
distribution of the initial state-of-charge (SOC0) and the
arriving time of the vehicles, a cluster model of the
charging station is proposed. Meanwhile, the paper, from
the types and charging mode of electric vehicles , analyzes
the behavior of EV. Finally, an example simulation is
validated.
2. Charging Modes of Electric Vehicles
The report is expected that by 2015 the number electric
vehicles will reach 500,000, by 2020, reaching 5,000,000.
While in 2030, the electric car ownership is expected to
reach 68 million or so.
2.1. Types of Electric Vehicles
Through the analysis of China’s electric vehicle devel-
opment, as well as some provinces and cities with the
national release of the electric vehicle development plan,
it sums up the future development trend of China’s elec-

Z. DAN ET AL.
25
tric car substantially: 2010-2015, electric vehicles mainly
in buses, official cars, taxis in demonstration; 2016-2020
in the public transport system, public service vehicles to
achieve scale operation electric vehicles, privat e cars less;
2021-2030, to accelerate the development of electric cars,
the proportion has increased. Chinese main types of elec-
tric are vehicles bus e s, taxis, public ser vi c e vehicles,
private cars.
2.2. Charging Mode
Charging mo des of electric vehicles can be divided into
slow charging (Charging mode L1), normal charge
(Charging mode L2), fast charge (Charging mode L3), as
shown in Table 1.
3. The Behavior Features of the Electric
Vehicles
3.1. Behavior Characteristics o f Pure Electric
Bus
1) Driving d istan ce
According to relevant data statistics in 2012, Tianjin
buses, on average, each rou te mileag e of 19.5 km. So,
this article assumes that each single pure electr ic bus
car mileage in obedience expected value is 19.5 km
mean square error is within 5 km of normal distr ibu tion,
the speed of 25 k m/h .
2) Charg ing mode
Charg ing time of slow charging mode is longer, and
not suitable for trave l frequen tly pure elec tr ic bus; And
quick charge although greatly shorten the charging
time, it can bring gre ater impact to power grid, such as
10 minutes to finish 35 kWh batter y requ ires 210 kW
power charging. The batter y life would also be affected.
At present, Tianjin way of pure electric bus to replace
the batter y is given priority to , the change in power
inadequ ate batter y, fully charg ed b a tter y, only a f ew
minutes to complete this process.
Based on the above an alysi s, irre spe ct ive of the pure
electr ic bus battery case, assume that their way of uni-
fied use to rep lace the batter y. Ensure bus can rep lace
the batter y in time to complete, as suming that bus sta-
tion and the terminal are equipped with in power p lant,
and have enough batter ies can be replaced. According
to Shanghai, Chengdu and other cities of pure electric
bus operating experience, assu ming th at when elec tr ic
cars arrive in plant power status is lower than 30% or
not enough to complete the next single, it is necessar y
to replace th e b at ter y, rep lace th e ba tter y from charging
in plant arrangemen t. In addition, bus operation time,
place, relatively concentrated, charging can be concen-
trated in the existing park ing lot construction of charg-
ing facilities.
3) Charg ing t ime scale
Assume that pure elec tr ic bus operating time is 8:00
am to 6 PM, buses may at any time during the battery
discharg ed ba tter y is low. It is assumed that in power
station operating 24 hours a day, 24 hours a day to re-
place the batter y to charge.
3.2. Behavior Characteristics o f Private Electric
Vehicles
Unlike buses, private cars are mainly used for commut-
ing, average run twice a day, so the private car time con-
nected to the electricity grid can be divided into the day
and night in the home two hours in the company, resp ec-
tively, to consider its behavioral characteristics.
1) Driving d istan ce
A day’s t ravel journey of Private cars is between 40
km and 60 km, and supposed to work during the day and
evening work schedule are equal, then the single range
evenly distributed between 20 km and 30 km.
2) Charg ing mode
Whether parked or residence in the company parking
lot, private car longer than the time grid, generally do not
need fast charging, using slow charging or battery re-
placement approach is more reasonable choice, so here
taking private cars with a slow fast charge and replace
the battery in two ways. Slow charging for the use of
private cars, assuming their ownership in the company
parking lot and are building a sufficient number of
charging facilities, the user can always access to the grid
for charging; way to take a private car to replace the bat-
tery, and the front right Similar assumptions buses, if
their berthing places remaining in the battery status is
below 30%, or insufficient to complete the next stroke,
the user must replace the battery, replace the battery
down by the charging arrangements for power plants.
Table 1. Comparison of different charging modes of plug-in electric vehicles in China.
Charging modes Rated voltage/V Rated Current/A Application areas
L1 Single-phase 220 16 Household
2-1
L2 2-2
2-3
Single-phase 220
Three-phase 380
Three-phase 380
32
32
63 Shopping malls, Parking lots
L3 600 300 Motorway service area, Charging stations, etc.

Z. DAN ET AL.
26
3) Charg ing t ime scale
Corresponding to the private car for power mode, for
power plants can be at any time during the day down on
the replacement battery trickle charge, the situation is
similar to the pure electric bu s.
4. Charging Agglomeration Characteristics
4.1. The Simple Charging Model of Electric
Vehicle
Lithium battery is the mainstream development of elec-
tric vehicle [12,13]. This article takes lithium as the re-
search object. Battery mod e l always consists of a co n tro lled
voltage source and a constant value of resistance in series,
the description of the model equation are as foll ow s:
()
0
()
0.1( )( )
Bv t i
b
KQ KQv t
U EAeRi
Q vtQ vt
−
=−− +−
+−
(1)
0
0
( )(1)
100
t S
v tQidt=−+
∫
(2)
where
b
U
is voltage of the battery;
i
is charging cur-
rent;
Q
is the nominal capacity of the battery; R is the
battery internal resistance;
K
is the battery polarization
constant;
0
E
is the battery constant potential;
A
,
B
are the constant index of charging battery;
0
S
is initial
charged battery state;
0
SOC
is the battery remaining
power.
1) If
_maxbb
UU<
,
c
iI=
, generation into the formula
(1), (2),
b
U
can be calculated.
2) If
_maxbb
UU≥
, then
0i=
,
_maxbb
UU=
.
The battery power in th e process of charging is:
b
P Ui= −
(3)
The t wo main battery par ame t e rs are given.
n
U
is
nominal voltage of the battery (V).
Q
is battery capac-
ity (A.h). For lithium battery, according to the literature, it
can be deriv ed that:
0
1.0834
n
EU=
,
0.005645
n
K UQ=
,
0.08496
n
AU=
,
60.0619BQ=
,
0.01
n
R UQ=
.
When the battery type is not at the same time, just the
relationship in front of the coefficient is different.
For fixed nominal voltage and capacity of lithium-ion
batteries, if
0
SOC
is known, it can calculate the lithium
battery charging power curve according to the formula (1)
- (3).
Charging powe r of single electric vehicle can be con-
side red a battery charging power, described by the for-
mula (1) - (3).
4.2. Charging Load Agglomeration
Characteristics of Electric Vehicle
(1) Random distribution characteristic of EV start
charging time
Large-scale development of electric vehicles will be a
greater impact on the distribution grid. To carry out elec-
tric vehicle charging load characteristics is a prerequisite
to ensure the safe operation of the grid. It is to guide the
electric vehicle charging orderly basis. Among them, the
residential living and travel habits with regularity, which
means that residential electric car charging station load is
mor e conducive to the orderly charge control. Therefore,
the load agglomeration characteristics study more prac-
tical value.
Due to the time of arrival every elec tric vehicle charg-
ing stations is random, so this article assumes that it is a
random variable, and follow certain distribution, and the
distribution of affected by time-sharing electricity price
and residents’ daily use habits. In real life, start charging
time of the electric vehicle reaching charging stations is a
random event, when it appears in fixed average density
of the random and independent, so this incident number
in unit time can approximately obey the poisson distr ibu-
tion.
Supposing that a random process technology
{ }
,0
t
Nt≥
, indicates a count of number of random time,
process, and meeting the following three conditions:
1)
0
0N=
.
2)
t
N
is independent increment process.
3) If
0t>
,
0s≥
, then
ts s
NN
+
−
obeys the poisson
distribution. Making
ts s
kN N
+
= −
, during the time of
( ,)s tt+, the probability of random event number k is :
{ }
() , 0,1,2,
!
kt
ts s
te
PNN kk
k
λ
λ
−
+
−=== 
(4)
where
λ
is an important parameter of the poisson
process. It determines the charging starting time of elec-
tric vehicle.
(2) Rand om distribution characteristics of initial
state of battery
Charging starting state of electric vehicle
0
SOC
de-
pending on the owners charging habits is random. The
initial state of electric vehicles
0
SOC
is normally dis-
tributed
(,)N
µσ
.
µ
is the mean value, and
σ
is the
variance.
(3) Agglomeration model of EV
According to above analysis, the electric vehicle
charging load agglomeration features can be described
with the following model:
1)
[ ] ( )
12
,,~ ,
car Mstep
T
NnnnPM T
λ = =
(5)
where T is electric charging time,
step
T
is the length of
the unit time slice, M is the total number of time slice.
2) That will generate normally distributed series
0
S
,
[ ]
001 020
,,~ (,)
N
S SSSN µσ =
(6)
3) Charging load power of the ith EV can be calcu-
lated according to the initial state of charg e, according to

Z. DAN ET AL.
27
the formula (1) - (3).
Hence, the characteristics of the cluster model of the
charging station are affected by four important parame-
ters
λ
,
T
,
µ
,
σ
. Getting the four parameters, we can
simulate the corresponding lo ad concentration charac t e-
ristic of electric vehicles.
5. Simulation Analysis
(1) Simulation conditions
1) Considering the electric car’s battery life, and user
habits, etc. , it can be considered private electric vehicle
charging frequency is once per day.
2) Two cases are simulated as following
a) The first stage segments: 17:00 off work, the char g-
ing starting time is 20:00, exp e c t ed to obey the variance
of the Poisson distribution for the 10 minutes, and the
leaving time is the next day 7:00 am or 7:00 after;
b) The second stage segments: 18:00 off work, the
charging starting time is 21:00, expe cted to obey the va-
riance of the Poisson distribution for the 10 minutes, and
the leaving time is the next day 8:00 am or 8:00 after.
3) The other data
a) The type of battery is 120V/15A.
0
SOC
obeys the
normal distribution N(0 .3,0 .1 ).
b) About 20% - 30% of the private electric vehicle
needing to be charged ever y day, then, in 2015, 2020 and
2030, the number of Tianjin private electric vehicle
needing to be charged every day is 1400; 14000 and
191,250.
(2) The sim ulat ion results
The charging time of diffe ren t time periods are as
shown in Figure 1.
The pow er curves of overall load are as shown in Fig-
ure 2.
(a)
(b)

Z. DAN ET AL.
28
(c)
Figure 1. Poisson process of electric vehicle charging ti me
(a)
(b)

Z. DAN ET AL.
29
(c)
Figure 2. Load characteristic curve of electric vehicles
6. Conclusion
Charging load agglomeration features of electric vehicle
are influenced by many factors. Bas ed on simplified bat-
tery model, this paper puts forward the model of electric
vehicle load cluster based on poisson distribution, and
analyzes the four key agglomeration characteristic para-
meters. Simulation results sh o w that the proposed ag-
glomeration model of electric vehicles can reflect the
charging starting time (SOC0) and random distribution of
electric vehicles at the same time. And, charging load of
private electric cars in 2015, 2020, 2030 are forecasted.
The prediction resu lts to study the effect of future electric
vehicle loading to the power grid have a certain reference
value.
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