Online Multicriteria Framework for Charging Management of PHEVs

0018-9545 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2014.2320963, IEEE Transactions on Vehicular Technology

1

Abstract— Societies concerns over global warming issues and

dependency on fossil fuels have caused growing share of Plug-In

Hybrid Electric Vehicles (PHEVs) in vehicles markets. A large

penetration of PHEVs, however, would likely put higher stress on

power systems. In order to lessen the PHEVs harmful impacts on

distribution grid, this paper proposes a two-stage charging

control strategy modeled on a renewable-based energy hub. In the

first stage, a home-based charging control method is formulated

in which charging cost of PHEVs is considered as an objective.

Running this procedure by PHEVs schedulers in houses, in the

second stage of the proposed strategy, PHEVs Coordinator Agent

(PCA) applies a multi-criteria optimization framework to reach

optimal charging plans with respect to both the vehicles owners’

and system operator’s perspectives. Total losses of distribution

system, total rescheduling costs, and wind energy utilization for

PHEVs charging are those factors that are modeled in the second

stage. Once the PCA achieved optimal charging plans of PHEVs,

the imposed charging demand should be reported to energy hub

manager and optimal dispatch of the hub would be determined.

Index Terms— Charging control strategy, energy hub, plug-in

hybrid electric vehicle (PHEV), technical concerns, wind.

I. INTRODUCTION

A. Motivation and Problem Description

ATTERY vehicles in the form of either Plug-In Hybrid

Vehicles (PHEVs) or all-electric vehicles have been made

to drastically decrease the need for oil, working with alternate

sources of energy, i.e., electrical energy [1]. The presence of

PHEVs shifts energy demand for transportation targets from

crude oil to electricity [2]. As an increasing number of PHEVs

are introduced, more electrical energy is requested. Past works

have shown that current power system facilities become unable

to support all of the existing light duty vehicle fleet [3-7]. This,

however, can become worse under uncoordinated charging

scenarios. As a result, the control and management issues for

this new and growing demand of electricity arise.

B. Literature Survey

Some past works focused on the PHEVs penetration impacts

Copyright (c) 2013 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to [email protected].

M. Moeini-Aghtaie, A. Abbaspour and M. Fotuhi-Firuzabad are with the

Center of Excellence in Power System Management and Control, Department

of Electrical Engineering, Sharif University of Technology, Tehran, Iran. (e-

mails: [email protected]; [email protected]; [email protected]).

on distribution grid [3], [8-11]. The authors in [8] examine the

impacts of electric vehicles demand on a residential

distribution network applying various charging scenarios. The

PHEV presence impacts on the Belgium distribution grid

considering the traffic and driving patterns is presented in [9].

With analyzing some real scenarios, reference [9] comes to

this conclusion that integration of PHEV can deeply

deteriorates power losses and voltage deviations.

To manage the PHEVs charging load and consequently

mitigate these destructive impacts, charging control strategies

have been proposed highlighting the significance of controlled

or smart charging [5,7,12-14]. The existing charging control

schemes can be classified into two main groups, centralized

and decentralized charging strategies. The main idea of

centralized charging is to achieve optimal vehicles charging

schedules taking into account the grid technical constraints. In

this strategy, the operator decides when and at what rate every

individual vehicle should be charged [13]. Being able to reach

charging patterns with the minimum technical concerns and

facilitating the implementation of Vehicle-to-Grid (V2G) are

the main features of centralized charging scenarios.

Though, this strategy seems straightforward, achieving it in

a practical manner results in some challenges. A centralized

approach may overshadow the customers’ authority. Reaching

some implausible charging patterns in customers’ perspective

and being uncoordinated with the other home-based load

control programs can be accounted as some deficiencies

associated with the centralized charging control schemes. In

contrast, the vehicles owners directly determine their charging

patterns employing decentralized charging strategies.

Customers’ preferences and electricity tariffs are the main

factors in taking decisions for this charging management

procedure [13]. Being compatible with the customers’

requirements and also consistent with the other home-based

load control programs are the main appealing attributes of the

distributed charging strategies. However, there is no guarantee

to optimally cover technical concerns of the network by

employing this charging control method.

Although both of centralized and decentralized charging

strategies have received considerable research interest, there

are a few works in the literature that in line with requirements

of vehicles owners and system operators, covers main target of

introducing electric transportation, i.e. pollution concerns in

designing procedure of charging control framework. Among

Online Multi-Criteria Framework for Charging

Management of PHEVs

Moein Moeini-Aghtaie, Student Member, IEEE, Ali Abbaspour, and Mahmud Fotuhi-Firuzabad,

Fellow, IEEE

B



2

these valuable efforts, reference [13] proposes a decentralized

charging framework to coordinate charging demand of PHEVs

implemented based on cooperative games concept. Taking into

account the PHEVs as some cost-minimizing agents which

reacts to a commonly charging trajectory is the main basis of

this charging management approach. A decentralized charging

algorithm is also presented in [15] to fill the valleys in electric

load profile employing elasticity of electric loads. This

charging control strategy iteratively tries to solve an

optimization problem. This optimization procedure, in each

iteration, receives updated charging profiles of electric

vehicles according to control signals broadcast by the

distribution utility. Only if the rescheduling signals of utility

could be adopted by vehicles owners, there would be a

guarantee to reach optimal or near-optimal charging patterns

employing either of these charging control strategies proposed

in [13], [15]. This calls for incentive-based programs to

properly model different requirements of vehicles owners from

a charging control scheme. As truly mentioned in [16], the

selfish nature of human beings is a vital factor needs to be

considered in designing procedure of charging management

strategies. In this regard, the authors in reference [16] defines

some weighting factors in objective function of PHEV

charging selection problem aims at modeling users’

convenience in the presented optimization procedure.

In addition to the vehicles owners’ and system operators’

requirements, there are other unavoidable factors which needs

to appropriately be modeled in dealing with PHEVs and their

possible effects in power systems. Amongst, the pollution

generated by transportation sector is of great consequence in

prosperity as well as practicality of the PHEVs charging

scheduling programs. To the best of authors’ knowledge, none

of the past works presented a charging management framework

in which this key factor successfully be involved in their

optimization procedures.

C. Paper Main Targets and Contribution

To propose a comprehensive as well as efficient charging

management approach, at first we should determine the main

requirements from this control procedure in viewpoints of all

the players. These requirements can be accounted as:

Being able to consider all the technical concerns (total

losses, voltage profiles, and etc.).

Proposing a method in which different requirements of

vehicles owners can be modeled.

Designing some incentive programs for the vehicles

owners to motivate them to participate in rescheduling

programs.

Taking into account the main goal of introducing

electric vehicles, i.e. decreasing the pollution produced

by transportation sector.

To overcome the main deficiencies of these methods, this

paper introduces a two-stage framework for charging control

of PHEVs based on a combinatorial strategy. This charging

control strategy in forthcoming future vision of energy

networks is modeled by renewable-based energy hubs. In the

first stage, the desired charging schedule of each PHEV in

view point of its owner (home-based schedule) is drawn. In

this stage, the owners can, without any restrictions, set their

vehicles charging schedules taking into account other

controllable loads in their houses. The attained schedules are

then fed to an on-line multi-objective optimization framework

run by a public utility designated as PHEVs Coordinator Agent

(PCA). In this optimization framework, the PCA as a

centralized control mechanism tries to modify the desired

charging schedules based on some technical and financial

factors including total losses of distribution network, total

rescheduling costs and wind energy utilization for PHEVs

charging. The necessities of considering these three factors in

the proposed multi-objective optimization framework are

entirely investigated. Once the optimal charging patterns of the

PHEVs are achieved by PCA, their imposed electrical demand

is reported to the energy hub. Then, electrical load of feeder

and required heat load are optimally supplied by the

renewable-based energy hub. Optimization structure of the

proposed method is shown in Fig. 1. In brief, we can

summarize the main contributions of this paper as follows:

Developing a two-layer charging control strategy in which

the main requirements of all the players are properly

modeled.

Proposing a user-based optimization procedure in order to

impose no restrictions on the customers’ authorities.

Presenting a MO optimization framework to involve all

the inevitable factors in charging control programs.

Owning the abilities to be considered as an on-line

procedure.

II. ON-LINE PROCEDURE OF PHEVS CHARGING

General structure of the proposed charging management

method is shown in Fig. 2. PHEVs, PCA, and renewable-based

energy hub are the main players in this charging control

strategy. This section provides the main principles associated

with the modeling outlines of these agents.

Fig. 1. Optimization structure of the proposed charging control strategy.

.PC

Des

V

.

1PCDes

Run a MO Optimization Procedure with These Objectives:

Wind Energy Utilization for PHEVs Charging

Total Losses of Distribution Network

Total Rescheduling Costs

Charging Cost

Minimization Run by

1st PHEV Scheduler

Charging Cost

Minimization Run by

Vth PHEV Scheduler

Home-Based Charging Control Schedule

.PC

Opt

k k V

PCA Charging Control Procedure



3

Database

Energy Hub

eP

gP

Electrical

Loads

Heat

Loads

Energy Hub Agent

PHEVs Coordinator Agent

PHEVs Agent

Fig 2. General structure of the proposed charging control strategy.

A. Home-Based Charging Management Structure

In the first stage of the proposed charging control method,

we consider a fully distributed charging procedure where the

only information available to the vehicles owners is a time-

varying tariff. Here, a common time-dependent pricing

scheme, namely time of use (TOU) pricing, is considered.

Mathematic model of a three-level TOU tariff is shown in (1).

1 1

2 2

3 3

t

if t T

if t T

if t T

(1)

where, t is electricity tariff at hour t;

1 ,

2, and

3

respectively, are level of the TOU tariff at off-peak (1T ), mid-

peak (2T ), and peak (

3T ) intervals. Based on this

information, the PHEV charging scheduler in each house runs

a linear programming (LP) optimization procedure aimed to

satisfy the customer’s preference which is modeled as

willingness to pay for charging costs of PHEV. Running this

optimization problem, the charging scheduler determines time

and rate of charging. Consider that we have

, , , 1[ ,..., ,....., ]k k k

s s fk hk t k t i k t

pc pc pc k VΡC

where, kΡC ,

,k tpc and hV respectively represent charging

schedule vector of the kth

PHEV, charging level of the kth

PHEV at time t, and set of PHEVs connected to the outlet.

Also, k

st and k

ft are the plug-in time and departure time of the

kth

PHEV, respectively. The PHEVs scheduler optimization

problem can be modeled as shown below.

,

1 1

min

. .

hV T

t k t

k t

pc t

s t

(2.a)

1

.

,

kf

ks

t

Rq

k t k h

t t

pc t E k V (2.b)

max

,0 , [ , )k k

k t k h s fpc PC k V t t t (2.c)

where, .Rq

kE , max

kPC and T respectively represent the energy

required to fully charge the battery of the kth

PHEV, maximum

allowable charging level of the kth

PHEV at time t and period

of studies. A discrete-time system over T with time slots of

length t is utilized in this paper to solve the optimization

problems. Here, the time slot length of studies is considered to

be 15 min [16]. Solving this problem, desirable charging

pattern of the PHEVs ( .Des

kΡC ) at each house can be obtained.

B. PHEVs Charging Coordinator Agent

At each time step of the studies, the customers which have

returned to the houses recently (CVs), plug their PHEVs into

the outlets and notify the PHEV scheduler with their

requirements. In response, the PHEV scheduler runs the

optimization framework defined in (2). As a result, the .Des

kΡC

will be attained and reported to the PCA through wireless link.

Fig. 3 depicts the PHEVs charging status in the period of

studies. As can be traced in this figure, at time step of t the

PCA receives desirable charging patterns of CVs. It then

should decide when and at what rate the PHEVs will be

charged taking into account the vehicles owners’ constraints as

well as the technical concerns.

The PCA in taking decisions not only should consider the

desirable charging patterns of the PHEVs which have

connected to the grid either recently (CVs) or up to that time

(PVs), but also it should estimate the required charging energy

of the PHEVs which will be connected afterwards (UPVs). In

this regard, the PCA needs to fulfill the following tasks before

running the charging optimization procedure:

1- Receive some data of the CVs including

( . R ., and kDes k q

k f kt E CVsΡC ).

2- The desirable charging profile and other information

about the UPVs are modeled similar to the equivalent

day in the past week.

3- The required charging energy of various PHEVs is

updated by the PCA using (3) . .

. . Re .

. .

( )

( )

( )

Ch Rq

k k

Ch Rq c

k k k

Ch Rq

k k

E t E k CVs

E t E E k PVs

E t E k UPVs

(3)

where, .( )Ch

kE t and Re .c

kE are respectively the remained

charging energy at time i and received charging energy up to

time i.

Fig 3. PHEVs charging status in the period of studies.



4

It should be notified that any charging control strategy

which is chosen as an effective approach for on-line

applications, needs to effectively deal with these three sets of

PHEVs, i.e. PVs, CVs, UPVs in its designing procedure. As

can be seen in (3), at each time step of simulations, the PCA or

any other charging control agent has to update the required

energy of all the PHEVs based on different relations. For the

PHEVs which have connected recently, i.e. CVs, their required

energy should be considered equal to the reported amount

( . .( ) Ch Rq

k kE t E k CVs ).

For the PHEVs which have connected before, i.e. PVs, the

PCA should update their required energy for charging based

on the amount of energy they have received up to that time and

also the reported ones as their total required energy

( . . Re .( ) Ch Rq c

k k kE t E E k PVs ). However, the PCA for the

PHEVs which have not yet connected to the network needs to

use their historical data as the amount of energy which they

will require for a charging cycle ( . .( ) Ch Rq

k kE t E k UPVs ).

This procedure in treating with different PHEVs enables PCA

to accept the proposed charging control strategy as a proper

candidate for on-line application. This is the feature which has

been lost in many published works about PHEVs charging

control strategies [16].

As the essential data of PHEVs are prepared by PCA, it

should run an optimization problem to achieve optimal

charging profile of the PHEVs. Here, three criteria are

introduced as the main factors which have to be modeled in

this optimization framework.

Total Losses of Distribution Network

Increment of distribution system losses is a possible

consequence of PHEVs charging load and many past works

have been proposed to mitigate this destructive impacts of

PHEVs [7,17,18]. In addition, it has been shown that

minimizing total losses can improve voltage profile of the

distribution system [7]. Consequently, to model the technical

concerns of PHEVs charging demand, minimizing the total

losses of distribution system is proposed as the first criterion.

Aimed to evaluate total losses, we apply the method presented

in [7]. The authors in [7] have proved that maximizing load

factor approximately minimizes the system losses, that is,

,

1

1

max

min

. .

B

i t

i

Load

S

f

s t

(4.a)

min

, ,b t b tS S (4.b)

max

, ,b t b tS S (4.c)

,

1

TTot

b t b

t

S E (4.d)

where, ,b tS , min

,b tS , max

,b tS , Tot

bE and Load respectively stand for

electrical load at node b at time t, minimum allowable load at

node b at time t, maximum allowable load at node b at time t,

total energy delivered to node b over the period of studies and

average load of distribution system over the period.

Total Rescheduling Cost

The other key factor which has to be considered in a well-

organized as well as practical charging control strategy is the

vehicles owners’ requirements. As noted earlier, optimization

procedure in the PCA is forced to reschedule the .Des

kΡC aimed

to fulfill the technical concerns. Anyhow, the vehicles owners

are either reluctant to participate in rescheduling programs of

the grid or prefer to rely on their own plans. Therefore, the

PCA should propose some incentive programs to stimulate the

vehicles owners participating in corrective programs. The

prosperity of incentive programs is mainly dependent on

decision of the vehicles owners for participating in these

programs. Although, the vehicles owners determine the

effectiveness of an incentive program, the charging control

strategy has to provide the prerequisites for the customers in

freely deciding to choose an offered program based on their

concerns and priorities. None of the past works either as

centralized or decentralized approaches have modeled such

incentive programs.

In this respect, few works have been done in the literature.

This factor, however, plays a vital role in prosperity of the

charging control strategies. In this paper, aimed to reach a

practical incentive mechanism, we offer three different

alternatives for PHEVs owners based on the amount of

deviation between final charging schedule attained by the PCA

and the reported one by the vehicle owner. Total deviation of

the kth PHEV charging scheduled can be defined as:

. .

, ,

1

t T

Opt Des

k k t k t

t

Dev pc pc k V (5)

where, .

,

Opt

k tpc is the kth PHEV charging amount at time t

attained by PCA. The presented incentive-based program

covers these two important attributes as well:

It reflects different behaviors of vehicles owners in facing

with risk, i.e. being either risk-seeker or risk-averse.

These programs are comprehensive, clear, easy to

understand and also independent.

Prog A: Customers who are either risk-averse or their

preferences makes them reluctant to adopt rescheduling

programs of the PCA can choose Porg A which in view point

of the PCA means no modification should be implemented on

these charging profiles. To direct optimization procedure of

the PCA in such a way that it would impose no changes to the

desired charging schedules associated with this kind of

customers, we need to define a penalty for the PCA in which

the importance of this issue is well modeled. This penalty is

defined based on the amount of kDev , that is,

k kPen Dev CPen k Prog A (6)

where, CPen and kPen respectively are penalty cost of one

kWh energy deviation and total penalty cost of the kth PHEV.

On the other hand, those customers who are interested in



5

participating in rescheduling programs of the PCA are

categorized into two different groups. Customers who prefer a

fully-charged battery in departure time can freely choose Porg

B that guarantees providing full required charging energy.

Customers who their views about the charging process of

vehicles is financial and earning money from these programs

for them has a higher priority in compare with keeping

minimum changes to the obtained charging profiles via

charging schedulers in houses find Prog C more pleasant.

Prog B: Participating in programs of the PCA with guarantee

of providing full required charging energy of PHEVs. In this

program, the PCA pays customers a reward based on the

amount of total deviation, as shown below.

, k B k BRw Dev CRw k Prog B (7)

where, BCRw and

,k BRw respectively represent the reward of

one kWh energy deviation and total reward of the kth PHEV.

Prog C: Participating in programs of the PCA with guarantee

of providing at least 90% of the required charging energy. In

this program, PCA pays customers a reward based on the

amount of total deviation, as shown below.

, k C k CRw Dev CRw k Prog C

(8)

It is noteworthy to mention that C BCPen CRw CRw .

Consequently, the optimization procedure of the PCA tries to

adjust the charging profiles of customers who participated in

Prog B and Prog C and not the ones in Prog A. Here, a

concern may be raised about market power of the customers in

dealing with these incentive-based programs, i.e. as long

as CPen is selected much larger than BCRw and

CCRw , it

seems that customers move toward Prog A to obtain more

money. In response to this concern, we should consider that in

practical applications, values of the other objectives in PCA

viewpoint, i.e. minimizing total losses of the network and

maximizing wind energy usage for PHEVs charging

determines the allowable ranges of Total Rescheduling Cost

(TRC). Therefore, only customers who have higher priority for

their desired charging schedules decide to choose Porg A and

the others based on their real goals would be distributed

between Progs B & C.

Defining these three programs lend credence to the PCA

that customers with different goals can freely choose a

program being compatible with their charging behaviors and

requirements. As a result, another criterion which should be

minimized in the proposed optimization framework is total

costs of the rewards and penalties paid to customers.

2 minf TRC (9.a)

, ,+ +k k B k C

k k k

TRC Pen Rw RwProg A Prog B Prog C

(9.b)

Wind Energy Utilization for PHEVs Charging

Decreasing pollution generated by transportation sector can

be accounted as a main motivation for governments to adopt

the electrification projects of vehicles. Thus, in designing

procedure of charging control strategies, pollution challenge

has to be considered as a major factor. Most of the charging

control strategies proposed in the past works, however, have

discarded this vital factor. There are two possible ways for a

PHEV to generate pollution. This pollution is originated either

directly by consuming fuel burnt in combustion engine as its

driving force or indirectly by the process of electrical energy

production which is utilized to charge battery of PHEV.

Therefore, as long as electrical energy utilized to charge

batteries of PHEVs is generated by conventional units, main

goal of introducing PHEVs, i.e. lessening the pollution

generated by transportation sector cannot be satisfied and only

the pollution resource is changed from the vehicle itself to

conventional power plants.

As a result, this paper proposes a renewable-based energy

hub as the main source of satisfying various energy loads. This

energy hub allows us to provide the required energy of PHEVs

charging process via electrical energy produced by wind

turbine. The proposed energy hub structure is depicted in Fig.

4. Network-received electrical energy, wind turbine output

generation and natural gas comes from network are the input

carriers of this hub. These energy carriers would be then

converted to other forms of energies by converters in the

energy hub and finally converted energies satisfy different

loads in the output layer. Interested readers are referred to [19]

for more information about modeling procedure of the energy

hubs.

Considering wind energy utilization for PHEVs charging

can act as a leading signal for power systems in presence of

electric transportation and can not only results in higher

capacity factors for distributed generations (DGs) installed in

distribution networks, but also, guarantee lower emission

levels imposed to environment aimed to supply the required

energy for PHEVs. To properly consider this unavoidable

factor in the proposed two-stage charging control strategy, it is

modeled as the third criterion shown in (10). The wind turbine

output level at each time is a nonlinear function of the wind

speed. So, maximum levels of wind turbine output happen at

times when wind speed regimes get higher values.

Aappropriate periods of charging in wind turbine output

perspective ( sW ) are those at which have higher values than

the wind speed average will be introduced as sW .

gP

eL

hL

eP

Wind Turbine

PHEVs Charging Load

Other Electrical Load

1

Energy HubInput Layer Output layer

Converter

Transformer

CHP

Furnace

Fig 4. The proposed renewable-based energy hub.



6

3 maxf UWE (10.a)

,

1 S

V

k t

k t W

UWE pc (10.b)

As discussed heretofore, various key criteria need to be

considered in optimization framework of the PCA. To

properly deal with all these inevitable criteria, objective

function of PHEVs charging control strategy in the second

stage is defined as:

32

1 1 2 3

Base Base

fff f

TRC UWE (11.a)

1

( )T

Base w

t

UWE P t (11.b)

3

1

1j

j

(11.c)

where, ( )wP t and j represent average of the wind turbine

output at time period of t and importance factor of the ith

criterion. Value of BaseTRC can be considered as the maximum

rescheduling budget set by distribution utility. Finally,

mathematical model of the charging problem which should be

solved by the PCA can be obtained as shown in (12).

min

. .

f

s t (12.a)

1

.

, ( )

kft

Ch

k t k

t i

pc t E t k Prog C (12.b)

1

. .

,0.9 ( ) ( )

kft

Ch Ch

k k t k

t i

E t pc t E t k Prog C

(12.c)

max

,0 , [ , )k

k t k fpc PC k V t i t

(12.d)

As can be seen in (12), this mathematical modeling

procedure is a weighted-sum optimization problem which falls

into area of multi-criteria decision making (MCDM). The

generalized area of MCDM can be introduced as the body of

procedures and frameworks by which the challenge of multiple

incompatible criteria can effectively be treated as an analytical

process [20]. MCDM consists of two branches, multi-criteria

optimization and multi-criteria decision analysis (MCDA).

While MCDA is concerned with problems that have a finite

number of alternatives, multi-criteria optimization is

conducted to problems formulated within a mathematical

optimization framework, but with a stack of objectives instead

of just one. The multi-criteria optimization, itself, can be

categorized into two main approaches including priori and

posterior optimization methods [21]. In priori methods,

preferences of the objectives need to be determined taking into

account their importance in viewpoint of decision makers. In

contrast to the priori methods, in posterior methods, a set of

optimal solutions will be found based on non-dominancy

concept. The proposed multi-criteria framework for PHEVs

charging management can be distinguished in the first class of

multi-criteria optimization approach, i.e. as a priori method.

To solve a priori MO optimization problem, at first, share of

each criterion, shown in (12), needs to be determined. The

abilities of this optimization procedure in satisfying different

criteria are mainly dependent on the procedure used to set

these importance factors. Usually, the values of weighting

factors in application of weighted-sum optimization

approaches are set based on the importance of each one in

viewpoint of the decision maker. To establish a robust

optimization procedure in determining the best values for these

importance factors, we proposed an innovative algorithm

based on a fuzzy decision making method. This method can

effectively consider the decision makers’ preferences in

determining the values of importance factors. Aimed to

effectively determine the preference vector of the

aforementioned criteria of this problem, an innovative method

is proposed in this paper which will be discussed in Part C.

C. Criteria Weights in Charging Optimization Problem

Share of each criterion in optimization problem of the

PCA, shown in (11), is determined by the value of

1,2,3j j . Therefore, abilities of the PCA in satisfying

these criteria are mainly dependent on the procedure used to

set these importance factors. In the proposed method, the

decision maker (system operator) reports his imprecise goals

for each criterion which are called desirable levels. Then, the

best values of importance factors are found among a set of

results which are attained through a sensitivity analysis. The

procedure of this decision making method is as follows;

First, each importance factor is discretized into some

predefined level, i.e. 0,0.01,0.02,...,1 j=1,2,3j.

Based on different combinations of j which satisfy (11.c),

the charging optimization problem addressed in (12) should be

run and the values of three criteria, then, will be found. Taking

into account the obtained values for the criteria via this

sensitivity analysis, a rigorous monotonically declining and

continuous set, membership function (MSF), is assigned to

each criterion which denotes the fact that to what extent a

solution is approaching toward the criterion fulfillment.

Having each MSF specified, the best values of importance

factors can be reached solving optimization problem addressed

in (13) with regards to the desirable levels (μdj) selected by

decision maker. The interested readers are referred to [22] for

more information about the fuzzy decision making method. 3

1

min ( ) n [1, )j

n

dj fX Solutionset j

X (13)

III. NUMERICAL RESULTS

To verify efficiency and applicability of the proposed two-

stage charging control method, this section provides a case

study, wherein some cases with different PHEVs penetration

(11.3%, 35%, and 45%) are given special treatment.

Case I: a reference system with no PHEV.



7

Case II: a system with uncontrolled charging strategy. In

this system, the PHEVs begin charging as soon as they

return homes from their last trip.

Case III: a system with home-based charging strategy

according to method explained in section II.

Case IV: a system adopting the proposed two-stage

charging control method in which the importance factors

are 1 2 30.3, 0.4, 0.3 .

A. Test System under Study and Main Assumptions

Here, the modified IEEE 34-node test feeder is considered

as the test system whose single line diagram is depicted in Fig.

5. As a notification, Lh shown in this paper is dispersed in the

system and only for the sake of clarity, it has been shown as a

bulk thermal load. In this paper, this test system is modeled as

a residential network. The medium and low voltage levels of

this network are respectively 24.9 kV and 230 V. It is assumed

that each phase of load point is connected to two houses. Other

data about this test system can be found in [23]. The three-

level TOU tariff shown in Fig. 6 is utilized as the electric

tariffs of the energy hub at output level [24]. The understudied

energy hub owns respectively a CHP and a wind turbine with

0.3 pu and 0.1 pu capacities. Other data about the hub

converters can be found in [25]. PJM market electricity prices

in 19 July 2012 are utilized in this paper to consider variations

of electricity price at input level of the energy hub [26].

Natural gas price at input and output levels of the energy hub

are taken from [27].

Transportation surveys are proper sources of data about

driving habits and trip characteristics. National Household

Traveling Survey (NHTS) has been recently introduced as a

main reference in electric vehicles studies which can provide

essential data for these studies [28]. various information about

the PHEVs like Driving patterns, miles driven daily, the

number and types of PHEVs along with the time vehicle

plugged into the network, charging level and the time which

vehicle has to be unplugged utilized in this paper is based on

the modeling method proposed in [28].

Energy Hub

hL

eL

800

802 806 808 812 814 850

816

818

820

822

824 826

828 830 854 856

852

832

888 890

858

864

834

842

844

846

848

860 836 840

862

838

Fig 5. Single line diagram of the modified IEEE 34 node test system.

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TO

U T

arif

f (c

en

t/k

Wh

)

Time (hr) Fig 6. TOU tariff at output level of the energy hub.

B. Technical Results and Analysis

All the introduced cases (Case I-Case IV) were simulated on

the IEEE 34-node test feeder. The simulations were run on a

PC with an Intel Core Duo 2.8-GHz processor and 2 GB of

RAM. The execution time of implementing the proposed

method on the IEEE-34 node test feeder for different PHEVs

penetration, i.e. 11.3%, 35%, and 45% in Case IV respectively

took 36, 53, and 75 seconds for each time slot of the studies.

Load profiles of these cases during a typical summer day with

various penetration levels (11.3%, 35% and 45%) are

respectively depicted in Figs. 7, 8 and 9. First, we refer to

Cases I and II. As can be traced in these figures, deciding

about charging process of the PHEVs, employing Case II,

results in a higher load level and escalates the system daily

peak load compared with Case I. These conditions become

worse as the PHEVs penetration increases.

A substantial movement can be using home-based charging

strategy (Case III). As can be seen, by applying this strategy,

charging during traditional peak periods will be avoided and

done during off peak hours with low price; resulting in new

peak loads in off-peak hours (see Figs. 8 and 9). This can be

explained by different levels of TOU tariff. For each vehicle,

the PHEVs scheduler tries to find charging patterns during the

low level tariff, i.e. between 1 a.m. to 7 a.m., and consequently

all the PHEVs are simultaneously being charged at these

hours. This imposes a huge electrical load as high as the on-

peak period to the distribution system especially in high-

penetrated PHEVs scenarios. Following the results shown in

Figs. 7, 8, and 9, it can be deduced that the proposed strategy

in Case IV has efficiently distributed the required energy for

charging of various PHEVs in various times along the period

of studies which in turn prevents the new peak loads in off-

peak hours.

0

100

200

300

400

500

600

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6

To

tal E

lectr

ica

l L

oa

d (

kw

)

Time (hr)

Case I

Case II

Case III

Case IV

Fig 7. Load profiles of the various cases for 11.3% PHEVs penetration level.

0

100

200

300

400

500

600

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6

To

tal E

lectr

ica

l L

oa

d (

kw

)

Time (hr)

Case I

CaseII

Case III

Case IV

Fig 8. Load profiles of the various cases for 35% PHEVs penetration level.



8

0

100

200

300

400

500

600

700

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6

To

tal E

lectr

ica

l L

oa

d (

kw

)

Time (hr)

Case I

Case II

CaseIII

Case IV

Fig 9. Load profiles of the various cases for 45% PHEVs penetration level.

TABLE I

OPTIMAL VALUES OF DIFFERENT CRITERIA FOR CASE IV

PHEVs Pen. (%) Total losses (%) TRC* (¢) UWE (kWh)

11.3 1.56 2654 187.78

35 1.73 5883.6 688.08

45 1.89 8984.9 722.10 *: Total Rescheduling Cost **: Utilized Wind Energy

Two important points should be noted about the obtained

results shown in Figures 7, 8, and 9:

1. As can be traced from these figures, for all of the

scenarios, the proposed method effectively manages the

PHEVs charging demand and no new peak loads has

been imposed to the aggregated load of the system.

Therefore, using this two-layer charging control strategy

in high penetration scenarios of PHEVs results in valley-

filling profiles for the aggregated loads.

2. Although a valley-filling profile can be considered

optimal in viewpoint of a system operator, many other

factors can overshadows the prosperity of a charging

control strategy. As discussed earlier, as long as the

vehicles owners show no tendency to participate in

rescheduling programs, there is no guarantee to reach a

valley-filling profile. This imperative factor has been

addressed in the proposed method establishing three

incentive programs.

The other consequence assigned to the proposed method is

to gain charging patterns of the highest correlation with the

wind turbine output as the outcome. Optimal values of three

criteria considered in this strategy are presented in Table I.

Some technical parameters applying these four cases are

evaluated and presented in Table II. If uncontrolled charging is

allowed, as presented in table II, peak load of distribution

system increases. This increment overshadows total losses,

PAR and MVD indexes. Furthermore, it can be observed that

these results aggravate as the PHEVs penetration increases.

As a decentralized strategy, the PHEVs charging demand

can be pushed to off-peak hours in Case III and as a result, the

load of grid at peak hours can be remained constant. However,

in high-penetrated PHEVs scenarios, i.e. 45%, this policy

becomes unable to support the charging demand without

affecting the technical parameters of the grid.

The proposed method in Case IV can more efficiently cover

technical concerns of the grid in contrast to the other methods

in Cases II, and III. As can be seen in table II, this superiority

of the proposed method results in lower amount of total losses,

PAR and MVD for Case IV, especially in 45% PHEVs

penetration, compared with Case II and Case III.

The other concern, needs to be discussed, is scalability of

the proposed method. To discuss about this feature of the

proposed control strategy, first of all we need to know about

the amount of data which has to be transmitted over the

communication network in each run of the proposed method.

At each time step of the simulations ( t i ), the . Des

k ik CVΡC needs to be reported to the PCA through

wireless link (see Fig. 3). It means that the charging profiles of

iCVn PHEVs should be transmitted to the PCA. To put a figure

on this problem, based on the assumptions explained in Part A,

distribution of the PHEVs arrival to the houses for 35%

PHEVs penetration are presented in Fig. 10. As can be traced

in this figure, the maximum number of simultaneous arrival to

the homes is seven which is equivalent to 5.8% of all the

PHEVs. Therefore, the maximum amount of data needs to be

transmitted via communication networks has an upper bound

which is a function of PHEVs arrival time. With regards to

diversity of the customers in returning to the homes, we can be

sure that existing communication networks would be able to

support this volume of data.

TABLE II

TECHNICAL PARAMETERS OF DIFFERENT CASES

Case

I

Case II Case III Case IV

11.3% 35% 45% 11.3% 35% 45% 11.3% 35% 45%

Peak Load (kW) 454 488 562 587 454 454 547 454 454 463

Total Losses (%) 1.53 1.67 2.01 2.2 1.61 1.93 2.14 1.56 1.73 1.89

PAR* 1.52 1.57 1.68 1.71 1.47 1.37 1.59 1.46 1.35 1.33

MVD** (%) 3.86 4.07 4.63 4.87 3.96 4.32 4.51 3.91 4.06 4.17 *: Peak-to-Average **: Maximum Voltage Deviation

TABLE III

IMPORTANCE FACTORS OPTIMIZATION RESULTS

Satisfactory Levels Criteria Weights Criteria Values

µd1 µd2 µd3 ω1 ω2 ω3 Total Losses (%) UWE (kWh) TRC (¢)

0.4 0.8 0.8 0.1 0.45 0.45 2.01 699.1 5142.18

0.8 0.8 0.8 0.15 0.55 0.3 1.97 815.1 8003.6

0.6 0.6 0.4 0.1 0.4 0.5 1.97 806.9 8439.3

0.6 0.6 1 0.1 0.2 0.7 1.99 398.1 3579.1



9

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 960

1

2

3

4

5

6

7

Time Step

No

. of

PH

EV

s

Fig 10. Distribution of PHEVs home arrival time for 35% Penetration.

0

100

200

300

400

500

600

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6

To

tal E

lectr

ica

l L

oa

d (

kw

)

Time (hr)

Scenario 1

Scenario 2

Scenario 3

Fig 11. Load profiles in Case 4 with 45% PHEVs penetration level.

C. Importance Factors Setting Procedure in Case IV

Optimal values of the importance factors depend on the

values of 1,2,3di i which are selected by the decision

maker.1d to

3d respectively denote satisfactory levels for

the total losses, wind energy usage and total rescheduling cost.

With regards to technical concerns and also economic

constraints, decision maker can reasonably set these desirable

levels. For instance, if the rescheduling budget is limited to

5000¢, 3d should be selected more than 0.8. The optimized

values of importance factors are itemized in Table III.

According to these results, when 1d is increased from 0.4 to

0.8, decrement of total losses reaches to 0.04 % and the UWE

increases. These variations cause a 2861.22¢ increment in

TRC. To investigate sensitivity of the optimal charging plans

to rescheduling budget limit, the operator increases 3d from

0.4 to 1. In these new conditions, TRC has decreased to

4860.2¢ which outcomes a decrease of 408.8 kWh in UWE

together with an increment of 0.02% in total losses.

D. A Sensitivity Analysis on Rescheduling Contracts

Percentage of rescheduling contracts, i.e. Prog A, Prog B,

and Prog C in Case IV are respectively considered to be 26%,

52% and 22% which randomly distributed between various

PHEVs. To investigate the effects of these contracts on

efficiency of the proposed method, three scenarios with

different levels of PHEVs presence in these programs are

defined in Table IV. The load profiles associated with these

scenarios are depicted in Fig. 11. This figure well presents the

main differences of adopting these scenarios and provide the

decision makers with some valuable information on how to

design incentive policies for charging control issue. As shown

in this figure, once the vehicles owners shows no willingness

to participate in programs B and C (Scenario 1), it becomes

too hard for the optimization procedure to avoid simultaneity

in the optimal charging plans. As a result, new peak loads in

off-peak hours will be brought into existence.

E. Optimal Dispatch of the Renewable-Based Energy Hub

As the ( )PHEV

eL t is found. the energy hub manager should

run an optimal dispatch problem to find the share of each

energy carrier in satisfying the loads, and the dispatch factor

values. Figure 12 depicts variations in dispatch factor, the total

electrical load, and wind turbine output generation during a

24-hour simulation period. As illustrated in this figure, once

the wind turbine output generation is high (interval 12 noon to

12 midnight), dispatch factor takes lower values. The dispatch

factor values reflect differences between wind turbine output

power and the electrical load. This implies that the gas should

be guided to CHP aimed to satisfy the remained electrical

load. Obviously, due to higher cost of using network-received

electrical energy, its utilization rate increases when facing with

high level of loads which cannot be satisfied by the wind

turbine output power and CHP output.

IV. CONCLUDING REMARKS

This paper opened by addressing the main challenges which

have to be considered in an effective PHEVs charging control

method. In response, a two-stage charging control strategy was

presented in multi-carrier energy environment. The offered

method would be able to well meet the requirements of PHEVs

owners and is appreciated in handling the main technical

concerns of distribution system operator. Of the main pivotal

features of this charging strategy is involving the customers’

authorities in procedure of taking charge decisions by PCA.

Also, dealing with updated data of PHEVs at each time step of

the simulations and also modeling the UPVs based on their

historical data in optimization procedure of the PCA can

introduce this two-stage charging control strategy as an

effective one for real-time applications.

TABLE IV

DIFFERENT SCENARIOS DEFINED FOR CASE IV WITH 45% PHEV

Scenario No. Prog A (%) Prog B (%) Prog C (%)

Scenario 1 50 30 20

Scenario 2 5 70 25

Scenario 3 10 30 60

0

100

200

300

400

500

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6

Po

wer (

kw

)

Dsi

pa

tch

Fa

cto

r

Time (hr)

Electrical Load Wind Turbine Output Dispatch Factor

Fig 12. Variations of dispatch factor, wind turbine output and electrical load

during a summer day (45%).



10

The necessities of considering various factors including

total system losses, total rescheduling costs and wind energy

utilization as the main criteria of the PCA optimization

procedure were thoroughly investigated. Moreover, an

innovative decision making method was proposed to set

importance of each criterion in the optimization procedure.

The presented charging control strategy was applied on the

modified IEEE 34-node test feeder and four different charging

scenarios were introduced. The obtained results well approved

effectiveness of the proposed method. With regards to these

results, one can conclude that the proposed strategy can avoid

new peaks of charging demands without disturbing individual

convenience.

ACKNOWLEDGMENT

Financial support provided by the Iran National Science

Foundation (INSF) is appreciated.

REFERENCES

[1] A. G. Boulanger, A. C. Chu, S. Maxx, and D. L. Waltz, “Vehicle

Electrification: Status and Issues,” Proceedings of the IEEE, vol. 99, no.

6, pp. 1116-1138, June 2011.

[2] B. D. Williams and K. S. Kurani, “Commercializing light-duty plugin/

plug-out hydrogen-fuel-cell vehicles: “mobile electricity” technologies

and opportunities,” Journal of Power Sources, vol. 166, no. 2, pp. 549-

566, 2007.

[3] K. Clement-Nyns, E. Haesen, and J. Driesen, “The impact of charging

plug-in hybrid electric vehicles on a residential distribution grid,” IEEE

Trans. Power Syst., vol. 25, no. 1, pp. 371–380, 2010.

[4] M. D. Galus, and G. Andersson, “Demand Management of Grid

Connected Plug-In Hybrid Electric Vehicles (PHEV),” in Proc. 2008

IEEE Energy 2030 Conference, Nov. 2008.

[5] E. L. Karfopoulos, N. D. Hatziargyriou, “A Multi-Agent System for

Controlled Charging of a Large Population of Electric Vehicles,” IEEE

Trans. Power Syst., vol. 28, no. 2, pp. 1196-1204, May 2013.

[6] J. Lopes, F. Soares, and P. Almeida,” Integration of electric vehicles in

the electric power system,” Proceedings of the IEEE, vol. 99, no. 1,

pp.168-183, Jan. 2011.

[7] E. Sortomme, M. M. Hindi, S. D. James MacPherson and S. S. Venkata,

“Coordinated charging of plug-in hybrid electric vehicles to minimize

distribution system losses,” IEEE Trans. Smart Grid, vol. 2, no.1, pp.

198-205, March 2011.

[8] S. Shao, M. Pipattanasomporn, and S. Rahman, “Challenges of PHEV

penetration to the residential distribution network,” in Proc. 2009 IEEE

Power & Energy Society General Meeting, PES '09. IEEE, July 2009.

[9] K. Clement, E. Haesen, and J. Driesen, “The impact of charging plug-in

hybrid electric vehicles on the distribution grid,” in Proceedings 2008 -

4th IEEE BeNeLux Young Researchers Symposium in Electrical Power

Engineering, Eindhoven, The Netherlands, 2008.

[10] J. Taylor, A. Maitra, M. Alexander, D. Brooks, and M. Duvall,

“Evaluation of the impact of plug-in electric vehicle loading on

distribution system operations,” in Proc. of IEEE Power Energy Society

General Canada, July 2009.

[11] L. Pieltain Fe Cossent, C. M.

Domingo, and P. “Assessment of the Impact of Plug-in Electric

Vehicles on Distribution Networks” IEEE Trans. Power Systems, vol.

26, no. 1, pp. 206-213, Feb. 2011.

[12] Q. D. Van, J. H. Bae, J. D. Lee, and S. J. Lee, “Monitoring of Power

Allocation in Centralized Electric Vehicle Charging Spot System,”

Journal of Energy Procedia, vol. 17, pp. 1542-1549, 2012.

[13] Z. Ma, D. S. Callaway, and I. A. Hiskens, “Decentralized charging

control of large populations of plug-in electric vehicles," IEEE Trans.

on Control Systems Technology, vol. 21, no. 1, pp. 67-78, Jan. 2013.

[14] C. Ahn, C. T. Li, H. Peng, “Decentralized charging algorithm for

electrified vehicles connected to smart grid,” American Control Conf.

(ACC), pp.3924-3929, June-July 2011.

[15] L. Gan, U. Topcu, and S. Low, “Optimal Decentralized Protocol for

Electric Vehicle Charging,” IEEE Trans. Power Systems, vol. 28, no. 2,

pp. 940-951, May 2013.

[16] C. K. Wen, J. C. Chen, J. H. Teng, and P. Ting, “Decentralized Plug-in

Electric Vehicle Charging Selection Algorithm in Power Systems,”

IEEE Trans. Smart Grid, vol. 3, no. 4, pp.1779-1789, Dec. 2012.

[17] K. Clement, E. Haesen, and J. Driesen, “Coordinated charging of

multiple plug-in hybrid electric vehicles in residential distribution

grids,” in Proc. Power Syst. Conf. Expo., 2009, pp. 1–7.

[18] K. Clement-Nyns, E. Haesen, and J. Driesen, “The impact of charging

plug-in hybrid electric vehicles on a residential distribution grid,” IEEE

Trans. Power Syst., vol. 25, no. 1, pp. 371–380, 2010.

[19] M. Moeini-Aghtaie, A. Abbaspour, M. Fotuhi-Firuzabad, and E.

Hajipour, “A Decomposed Solution to Multiple-Energy Carriers

Optimal Power Flow,” IEEE Trans. Power Syst., vol. 29, no. 2, pp. 707-

716, March 2014.

[20] M. Ehrgott, Multicriteria Optimization, Springer, 2005.

[21] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms.

New York: Wiley, 2003.

[22] M. Moeini-Aghtaie, A. Abbaspour, and M. Fotuhi-Firuzabad,

“Incorporating large-scale distant wind farms in probabilistic

transmission expansion planning—Part I: Theory and algorithm,” IEEE

Trans. Power Systems, vol. 27, no. 3, pp. 1585-1593, 2012.

[23] Radial Test Feeders - IEEE Distribution System Analysis

Subcommittee; [Online]. Available:

http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html.

[24] Baltimore gas and electric three-level summer’s tariffs, Available:

http://www.bge.com/waystosave/residential/resprogramsresources/pages

/time-of-use-pricing.aspx.

[25] M. Moeini-Aghtaie, P. Dehghanian, M. Fotuhi-Firuzabad, and A.

Abbaspour, “Multiagent Genetic Algorithm: An Online Probabilistic

View on Economic Dispatch of Energy Hubs Constrained by Wind

Availability,” To appear in the IEEE Trans. Sustainable Energy, 2013.

[26] [Online]. Available: http://www.pjm.com/markets-and-

operations/energy/day-ahead/lmpda.aspx.

[27] [Online]. Available:

http://www.eia.gov/dnav/ng/ng_pri_rescom_dcu_smd_m.html.

[28] S. Shafiee, M. Fotuhi-Firuzabad and M. Rastegar, “Investigating the

impacts of plug-in hybrid electric vehicles on power distribution

systems,” IEEE Trans. Smart Grid, vol. 4, no. 3, pp. 1351-1360, Sept.

2013.

Moein Moeini-Aghtaie (S’11) received the B.Sc. and

M.Sc. degrees (Hons.) in Electrical Engineering from

Shahid Bahonar University of Kerman and Sharif

University of Technology in 2008 and 2010, respectively.

He is currently working toward the Ph.D. degree at Sharif

University of Technology.

Ali Abbaspour received B.Sc. and M.Sc. degrees in

Electrical Engineering from Amir Kabir University of

Technology and Tehran University respectively and Ph.D.

Degree in Electrical Engineering from the Massachusetts

Institute of Technology (MIT), USA. Presently he is an

associate professor in the Department of Electrical

Engineering, Sharif University of Technology, Tehran, Iran.

Mahmud Fotuhi-Firuzabad (F’14) received the B.Sc. and

M.Sc. degrees in electrical engineering from Sharif

University of Technology and Tehran University in 1986

and 1989, respectively, and the M.Sc. and Ph.D. degrees in

electrical engineering from the University of Saskatchewan,

Saskatoon, SK, Canada, in 1993 and 1997, respectively.

Currently, he is a Professor and Head of the Department of

Electrical Engineering, Sharif University of Technology, Tehran, Iran.

http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html

http://www.bge.com/waystosave/residential/resprogramsresources/pages/time-of-use-pricing.aspx

http://www.bge.com/waystosave/residential/resprogramsresources/pages/time-of-use-pricing.aspx

http://www.pjm.com/markets-and-operations/energy/day-ahead/lmpda.aspx

http://www.pjm.com/markets-and-operations/energy/day-ahead/lmpda.aspx

http://www.eia.gov/dnav/ng/ng_pri_rescom_dcu_smd_m.html

Documents

Online Multicriteria Framework for Charging Management of PHEVs