International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

doi: 10.14355/ijes.2014.0402.02

www.ijesci.org

Optimal Reliability-based Placement of

Plug-In Electric Vehicles in Smart
Distribution Network
Mohammadhadi Amini1, Arif I. Sarwat*2
Department of Electrical and Computer Engineering, Florida International University, 10555 W. Flagler St., Miami,
FL 33174, USA
mamin006@fiu.edu; *2asarwat@fiu.edu

Abstract
Distributed renewable resources are one of the major
technological inclinations that play a pivotal role in the
future green power system. In this context, high penetration
of Plug-In Electric Vehicles (PIEVs) may bring many
challenges for the smart grid. PIEVs unscheduled utilization
will cause technical issues for both generation side and
demand side. High penetration of PIEVs may lead to
reliability deterioration of smart distribution network. In this
paper, firstly a PIEV owner behavior model is introduced.
The output of this model is the hourly demand of PIEVs per
day. Secondly, a comprehensive reliability-based objective
function is proposed to allocate these modeled PIEVs in
smart distribution network. Finally, IEEE RBTS bus 2 is used
for implementing allocation algorithm utilizing both genetic
algorithm and particle swarm optimization.
Keywords
Plug-In Electric Vehicle (PIEV); Reliability-based Objective
Function; Smart Distribution Network; Heuristic Optimization

Introduction
Regarding the ever increasing demand for power
generation and limits on current resources only one
suggestion can be practical and economical, that is to
take advantage of distributed renewable resources
(DRRs) and to cut down on reliance on fossil fuels in
order to have a more environmental-friendly power
grid. Hydroelectric, wind power and photovoltaic in
comparison with coal, have shown to have great
potentials since they can be near to the place of energy
demand. Therefore, these sort of energy resources will
require a lot of modern equipment. As standard of life
continues to rise, so have consumer expectations and
demands for power reliability.Considering the great
extent of the grid application of old methods of direct
and continuous supervision by staff is not anymore
feasible and more optimized solutions should be
thought of [1]. In the beginning of the 21st century this

concern led to a great movement smart grid (SG) was

one of its outcomes.
Smart grid will gradually lead to the development and
upgrading of the whole power grid, including electric
power generating, transmission, distribution and
supplying, that creates a more secure, energy-saving,
environmental protection, and economic power
systems [2-3]. Figure 1 demonstrates the role of PIEVs
as distributed resources in the smart grid framework.
Figure 1 shows the schematic view of the industry
drivers of Smart Grid as mentioned in [4]. As shown in
this figure the new face of Smart Grid include (a)
emphasis on environmental protection, including
variable generation (wind, solar, etc.), demand
response, and distributed generation, (b) the drive for
better asset utilization, including operating closer to
the knee of the curve while maintaining reliable
system operation, and (c) the need for enhanced
customer choice[4].

FIG. 1A NOVEL PARADIGMFOR SMART GRID [4]

Another concept which appears in Smart Grid

environment is smart home. Gelling depicts the smart
home with control center and energy management
system as fig 4. In this home, several mentioned
elements of the Smart Grid such as AMI, DG and
electric vehicle are considered [5][6].

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International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

is defined. This function is based on four variables:

electricity price, fuel price, charging rate (fast or slow)
and charging control (controlled or uncontrolled). This
function is shown in (1)[11]:

F j=
(t , p j , y ) FCE j (t , p j ) + FCF j (t , y )
+ FFSPj (t ) + FCUPj ( j )

FIG. 2 FUTURE HOMES, ENABLING SMART GRID

TECHNOLOGIES [5]

As figure 2 shows, Plug-In Electric Vehicles (PIEVs)

are inevitable part of future power system, especially
in smart homes. They can serve as storages like the
flexible loads [7].
If the EV can inject the stored power to the grid, it is
referred to as V2G [8]. Fig.2 depicts a gradual raise in
the amount of EVs and the impact of controlled and
uncontrolled charging curve at the peak load [9-10].
As shown in this figure, uncontrolled charging
deteriorates load curve.

(1)

where "t" represents different times of day, "y" is an

interval in which fuel prices are understood to be fixed
and pj represents time intervals each of which of two
hour duration, as defined by (2):

pj =
[2 j , 2 + 2 j ]

; j {0,1,...,11}

(2)

FCE j , FCFj , FFSPj and FCUPj show the electricity price,

fuel price, fast charging penetration and controlled
charging penetration, respectively.
According to the survey of 30 PHEV owners and curve
fitting on each of the four factors, coefficients

b t , c t
i

and

d t
i

a t

were extracted.

In order to compare different scenarios and

investigating the effect of electricity price on EV
customers' behavior this paper defined a customer
acceptance index (CAI ) [11]. This index is shown in
the following equation:
11

CAI =

FIG.3 FORECASTING THE PEAK INCREASING DUE TO

CONTROLLED AND UNCONTROLLED CHARGING [9]

The rest of this paper is arranged as follows: In the

next section, PIEV's customer behaviormodeling is
introduced. This model is based on PIEV users' survey.
Then, problem formulation is addressed in terms of
defining a reliability-based objective function. Next
section, is devoted to the optimization methodology.
This section will introduce two approaches for optimal
allocation of PIEVs. Case study is discussed after
introducing two optimization methods and the last
section, concludes the paper.
PIEV Owners Behavior Modelling
There is a comprehensive model which introduced in
[11]. For the modeling purpose, an acceptance function

44

2 j +2

j =0 t =2 j

F j (t , p j , y )dt ]

(3)

24

This model is adaptive for customer behavior

prediction. Nevertheless, another model should be
introduced to evaluate the parking lots charging
demand. As the main objective of this paper is
reliability evaluation, only the charging rate is counted
as variable in this model. Figure 5 demonstrates the
charging rate effect on this model output.
TABLE CHARGING RATES IN A PROPORTION OF BATTERY CAPACITY

Charging Mode

Charging Rate

Slow Charging

0.1 BCAP/hour

Quick Charging

0.3 BCAP/hour

Fast Charging

1.0 BCAP/hour

Problem Formulation
In this part, two methods are utilized to allocate the
PIEVs in the smart distribution network. Firstly, a
reliability-based objective function is introduced for

International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

the optimization purpose. The proposed objective

function can be shaped based on various purposes.
The input of proposed objective function is the output
of probabilistic PIEV model which is discussed in
section II. Furthermore, the characteristic of the smart
distribution network which is used for the simulation
purposes is another input of optimization process.
Objective function of PIEVs placement in a feeder is
subject to improve power distribution system
reliability satisfying some constraints. Two influential
reliability indices are used in order to evaluate the
distribution network's reliability; The Customer
Average Interruption Duration Index (CAIDI) which is
commonly used by power utilities in order to consider
the average outage duration that is expectable for
customer to experience, and energy not supplied (ENS)
are considered [12].
The proposed objective function (OF) illustrated in the
following equation, indicates composite reliability
index through weighted aggregation of these two
indices [13]:

OF = (CAIDI

CAIDI
ENS
) + ( ENS
)

CAIDI T
ENS T

(4)

Where OF is a composite reliability index and

coefficient x > 0 indicates the weight for
corresponding reliability index and subscript T
indicates the target value of each index. These
coefficients are considered to be the same value 0.5,
and the objective value of CAIDI and ENS are
considered 1.5 hours (based on IEEE Standard 13661998 this index's value is about 1.36 for the North
American utilities) and 47, respectively. In the
proposed optimization framework, technical issues of
power distribution network such as power
consumption of PIEVs and voltage constraints are
considered.
Optimization Using Particle Swarm
Optimization and Genetic Algorithm
In order to optimize the proposed objective function
there are various population-based heuristic methods
include genetic algorithms, evolutionary computation,
and particle swarm optimization (PSO). Prior research
using the genetic-algorithm (GA) and simulatedannealing (SA) techniques has provided effective
optimal designs for various apparatuses and systems
[14][20]. In this paper the optimization is obtained
utilizing both GA and PSO so that the comparison
between results from these two optimization methods
leads to more accuracy in placement process.

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Because of the discrete nature of allocation process, it

has numbers of local minimums. To optimize this type
of objective function, heuristic algorithms may be
effective. In this paper genetic algorithm (GA) is used
to minimize the proposed objective function
containing two high-flying reliability indices [13]. In
this paper fitness function of genetic algorithm and
objective function considered to be the same. The
chromosomes include binary numbers which
determine the number of buses that PIEV groups
should be connected to the smart distribution network
at them. Candidate load points in the test system are
just residential and commercial buses and the number
of candidate load points does not exceed 24-1, each
chromosome for PIEV bus number is five bits so the
population size is five. Other GA parameters, cross
over fraction, mutation probability and population
size set 0.65, 0.18 and 50 respectively [15]. The
reliability-based objective function optimization is
shown in Figure 4.
Particle swarm optimization (PSO) algorithm is
introduced by Kennedy and Elberhart [16-18],
supposed to be a optimization method based on the
social behavior of flocks of birds. Optimization starts
by generating random positions for particles. In order
to avoid defined articles from leaving search space at
the first iteration, these randomly-generated positions
should be zero or a small value. Based on (5) and (6)
standard version of PSO algorithm starts by generating
random positions for the particles, within an
initialization region. Velocities are usually initialized
within that region, but they can also be initialized to
zero or to small random values to prevent particles
from leaving the search space during the first iterations.
During the main loop of the algorithm, the velocities
and positions of the particles are iteratively updated
until a stopping criterion is met. The update rules are
shown in (5) and (6).

V i k +1 =
wV i k + C 1rand 1 + ( Pbest ik X ik
+ C 2 rand 2 (Gbest ik X ik
+1
X ik=
X ik + Vi k +1

(5)
(6)

whereXi = [Xi1, Xi2 ,...., Xid] and Vi = [Vi1, Vi2,...., Vid] in are
the position and velocity of the ith particle. Let Pbesti =
[Xi1pbest, Xi2pbest,.,Xidpbest] and Gbest = [X1gbest, X2gbest,.....,
Xdgbest] be the best position of particle i and its neighbors
best position so far respectively. The key attractive
feature of PSO is its simplicity as it involves only two
models (5) and (6).

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International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

=
max

(max min ) iter

itermax

(7)

PIEV Owners Behavior

Modeling Considering
Specific Charging Rates and
Various Number of Vehicles

Initial population
random generation

[10]. In order to evaluate the proposed algorithm, it is

tested on distribution system for RBTS [19][21]. This
radial test system consists of four feeders with four
types of customers,
residential, commercial,
government/institutions and small user that
commercial and residential ones were considered as
candidates for EVs' parking placement. The test
system is shown in Figure 6. As a result, first and
second feeders are connected as maneuver points with
normally open switches. In addition, third and fourth
feeders are also connected in the same way. The
candidate buses do not include the exclusive industrial
customers.

OF calcuation

Printing
Results

Yes

Termination
Criteria
No

Selection

Cross over

FIG. 6 DISTRIBUTION SYSTEM FOR RBTS BUS 2 [19]

Mutation

FIG. 4 OBJECTIVE FUNCTION OPTIMIZATION UTILIZINTG

GENETIC ALGORITHM

Simulation Results
Four scenarios are defined to
effectiveness of the proposed method.

evaluate

the

Scenario 1
In this scenario the slow charging method was
considered. 1000 PIEVs considered to be allocated in
five buses.
Scenario 2

FIG. 5 COMPARING FAST AND SLOW CHARGING METHOD[10]

In this scenario the fast charging method was

considered. 1000 PIEVs considered to be allocated in
five buses. The goal of defining this scenario is to
evaluate the effect of charging rate on the proposed
objective function and optimal placement of PIEVs.

Case Study

Scenario 3

Firstly, as it is mentioned in figure 5 the effect of

charging rate is evaluated based on the PIEV model

In this scenario the slow charging method was

considered. 1500 PIEVs considered to be allocated in

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International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

five buses.
Scenario 4
In this scenario the fast charging method was
considered. 1500 PIEVs considered to be allocated in
five buses. This scenario is defined to achieve a
sensitivity analysis on charging rate effect on the value
of proposed objective function.
Table II shows the results of optimization with GA
and PSO. As the results shown, when the charging
rate starts increasing, the OF value will reduce. For
instance, the value of OF for fast charging is less than
that of Slow and quick charging, considering the same
number of PIEVs. Furthermore, a comparison between
results of first and thirds scenario illustrates that when
the number of PIEVs increased, OF value increased
and this means the reliability will deteriorate by
increasing PIEV number. Therefore, although the
optimal allocation of PIEVs considering reliability
indices improves reliability deterioration, high
penetration of PIEVs reduce the level of reliability and
in order to maintain an acceptable level of reliability,
other smart equipments should be utilized at same
time.
Figure 7 represents the value of proposed objective
function using GA and PSO for introduced scenarios.

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As results of this figure shows, particle swarm

optimization is preferable for the reliability-based
allocation of PIEVs and utilizing this optimization
method leads to better reliability improvement.
Conclusion and Future Work
In this paper, a novel reliability-based placement of
PIEVs utilizing two well-known heuristic optimization
methods, GA and PSO, is introduced. The proposed
method prevents future distribution network, called
smart
distribution
network,
from
reliability
deterioration after high penetration of PIEVs. Key
feature of this approach is to consider two influential
reliability indices simultaneously by defining a
specific objective function. The case study results
conclude that it is not feasible to connect PIEVs to
industrial load points.
For the validation purpose, the proposed method has
been implemented on distribution system for RBTS
bus 2. The results of simulations show the high
correlation of PIEV optimal location with charging
method as well as total number of PIEVs (PIEV
penetration). This paper analyzed the technical aspects
of PIEV placement, including reliability features of
distribution network. Future studied can concentrate
on economical optimization of PIEVs' high penetration.

TABLE SIMULATION RESULTS

Scenario number

Charging Method

Total EVs

OF value (GA)

OF value (PSO)

WITHOUT EV
1
2
3
4
5
6

SLOW
FAST
SLOW
FAST
QUICK
QUICK

1000
1000
1500
1500
1000
1500

1.05512
1.09134
1.06742
1.11397
1.09981
1.08136
1.10072

1.05512
1.08134
1.0731
1.11237
1.0878
1.08093
1.09900

PIEVs' optimum
location
1, 8, 10-11, 18
2, 12, 16, 18-19
1,6-7,17-18
2, 10, 12, 15, 19
1, 7, 16, 18-19
1, 6, 15, 17, 19

FIG.7 OPTIMAL VALUE OF PROPOSED OBJECTIVE FUNCTION USING GA AND PSO

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International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

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MohammadhadiAminiwas
born
in
Shahreza. He received the B.S. and M.Sc.
degree in electrical engineering from Sharif
University
of
Technology
and
TarbiatModares University in 2011 and
2013, respectively. He is currently working

International Journal of Energy Science (IJES) Volume 4 Issue 2, April 2014

toward the Ph.D. in electrical engineering at Florida

International University. He has published more than 25
papers in Smart Grid Implementation field. His research
interests include Smart Grid reliability assessment, real-time
load estimation, smart grid mathematical modeling,plug-in
electric vehicles, power system optimization and power
system state estimation.

Arif I. Sarwatreceived his M.S. degree in

electrical and computer engineering from
University of Florida, Gainesville. In 2010
Dr. Sarwat received his Ph.D. degree in
electrical engineering from the University
of South Florida. He worked in the
industry(SIEMENS)
for nine years
executing many critical projects. Before joining Florida

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International University as Assistant Professor, he was

Assistant Professor of Electrical Engineering at the
University at Buffalo, the State University of New York
(SUNY) and the Deputy Director of the Power Center for
Utility Explorations. He is co-developer of the DOE funded
Gateway to Power (G2P) Project along with FPL/NextEra
company. His significant work in energy storage, microgrid
and DSM is demonstrated by Sustainable Electric Energy
Delivery Systems in Florida. He is also co-principle
investigator in the study of reliability & predictability of
high penetration renewable resources power plants (DOE)
funded Sunshine State Solar Grid Initiative (SUNGRIN). His
research areas are Smart Grids, High Penetration Renewable
Systems, Power System Reliability, Large Scale Distributed
Generation Integration, Large Scale Data Analysis,
Distributed Power Systems, and Demand Side Management.

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