Energy Consumption Model and Charging Station Placement for

Electric Vehicles

Zonggen Yi and Peter H. Bauer

Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, U.S.A.

Keywords:

Electric Vehicle(EV), Energy Consumption Model, Charging Station Placement, Reachable Range Estima-

tion, Energy Constraint, Google Maps Api.

Abstract:

A detailed energy consumption model is introduced for electric vehicles (EVs), that takes into account all

tractive effort components, regenerative braking, and parasitic power users. Based on this model a software

tool for EV reachable range estimation (EVRE) is developed and implemented. This software tool uses real

driving distances and elevation data from Google Maps and can therefore much more accurate predict the

reachable range of a given EV than the typical Euclidean distance models. Furthermore, an optimization

model for the placement of charging stations to maximize the number of reachable households under energy

constraints is established using EVRE. These results are illustrated by a number of examples involving the

cities of New York City, Boulder Colorado, and South Bend, Indiana. The developed methodology can eas-

ily incorporate additional constraints such as popular destinations, preferred parking, driver habits, available

power infrastructure, etc. to initially reduce the search space for optimal charging station placement.

1 INTRODUCTION

Advances in battery technology have already put a

signiﬁcant number of electric vehicles on the road

(Dickerman and Harrison, 2010). Innovative tech-

nologies to reduce manufacturing costs and increase

battery capacity are needed to make such vehicles

more appealing to the public. Allowing EV users to

reach charging stations conveniently is crucial for the

popularization of electric vehicles.

For accurately predicting and simulating vehicle

range, an accurate energy consumption model based

on the tractive effort is needed. Simpliﬁed EV power

train models were developed for new and existing pro-

duction vehicles(Hayes et al., 2011). An energy usage

model based on tractive effort has been constructed

for electrically powered utility vehicles traveling a

route with signiﬁcant elevation variations(Prins et al.,

2012). In our energy consumption model, a more

detailed tractive effort model is provided. The driv-

ing distances and elevation data for routes on Google

Maps are used in an infrastructure model for in-

creased accuracy.

The problem of charging station placement has

been investigated by many researchers. A maxi-

mal coverage model to optimize the demand covered

within an acceptable level of service has been investi-

gated in (Frade et al., 2011). An optimization model

was developed to maximize total ﬂeet-wide charging

levels for the location of a public EV charging in-

frastructure (Xi et al., 2013). In (Ge et al., 2011),

a grid partition method has been investigated for lo-

cating, sizing and service area division of the charg-

ing stations. A two-step clustering process was pro-

posed in (Ip et al., 2010) for optimizing the alloca-

tion of fast charging stations. A coordinated clus-

tering algorithms was programmed for mapping the

charging infrastructures in (Momtazpour et al., 2012).

(Andrews et al., 2013) studied how EV would per-

form in meeting the driving needs of vehicle owners

and then proposed an optimization model based on

a user charging model to ﬁnd locations for charging

stations. In (Lam et al., 2013), the electric vehicle

charging station placement problem was formulated

to minimize the total construction cost subject to the

constraints for the charging station coverage and the

convenience of the drivers for EV charging. The NP-

hardness property of the problem was studied and an

efﬁcient greedy algorithm to tackle this problem was

proposed. In (Wang et al., 2013) a location model

of charging stations is established based on electric-

ity consumption along the roads among cities. Fur-

thermore a quantitative model of charging stations

was presented based on the conversion of oil sales

150

Yi Z. and H. Bauer P..

Energy Consumption Model and Charging Station Placement for Electric Vehicles.

DOI: 10.5220/0004859601500156

In Proceedings of the 3rd International Conference on Smart Grids and Green IT Systems (SMARTGREENS-2014), pages 150-156

ISBN: 978-989-758-025-3

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

in a certain area. Driving patterns have been widely

used to optimize the charging station placement. An

agent-based decision support system was presented

for identifying patterns in residential EV ownership

and driving activities to enable strategic deployment

of new charging infrastructure(Sweda and Klabjan,

2011). An improved charging station location solu-

tion was developed by providing behavioral models

to predict when and where vehicles are likely to be

parked (Chen et al., 2013). An optimization model

based on driving patterns was proposed to ﬁnd loca-

tions for charging stations needed to support EV us-

age (John et al., ). Another important method is based

on the Voronoi diagram. In(Koyanagi and Yokoyama,

2010) and (Koyanagi et al., 2001), the candidates of

charging facilities for EVs were analyzed by using

Voronoi diagrams for the equilibrium arrangement in

Musashino city. In (Feng et al., 2012), a weighted

Voronoi diagram was used for the research of locat-

ing, sizing and service area division of the charging

stations. The problem with Voronoi diagrams is that

Euclidean distance is used instead of the real driving

distance.

The placement of charging stations can be ap-

proached from a number of different angles, that may

for example include the energy deﬁcit of EVs, the

available power infrastructure, popular parking loca-

tions and stay times, minimizing overall energy, min-

imizing congestion, etc. We address the problem of

optimal charging station placement from the view-

point of reaching the most customers or households,

i.e. something a private charging station owner would

typically consider. On the other hand, this problem is

also of interest for municipalities, power companies,

and federal agencies such as the environmental pro-

tection agency and the department of transportation.

The developed concept can easily be used in conjunc-

tion with the other above mentioned criteria, if the

placement methods based on these criteria can nar-

row down the number of possible locations for charg-

ing station placement a priori. Therefore, these crite-

ria would be used in form of location constraints. In

this paper, the optimization problem for charging sta-

tion placement is investigated based on an EV energy

consumption model including driving distance and el-

evation. Given an energy bound, the corresponding

reachable contures in Google Maps for different pos-

sible charging station centers are determined. Maxi-

mizing the number of households in this range is dis-

cussed subsequently.

This paper is organized as follows. In Section 2,

the energy model for EVs is presented. In Section 3,

an optimization model for charging station placement

is provided. The simulation results are discussed in

Section 4. Conclusions are provided in Section 5.

2 ENERGY MODELS FOR

ELECTRIC VEHICLES

In this section we will introduce a detailed energy

consumption model that has two main components: a

tractive effort model with air drag, rolling resistance,

acceleration, and hill climbing components, and a

lumped loss model for the mechanical and electric

powertrain, that is described by individual efﬁcien-

cies of powertrain components. Together, both com-

ponents provide a fairly accurate description of the

energy usage of an EV in almost any driving situa-

tion.

The air drag power component is modeled by:

air

(t) =

ρC

ds(t)

)

(1)

where A is frontal cross sectional area, ρ the den-

sity of air, C

is the drag coefﬁcient, s(t) is the driving

distance,

ds(t)

is the corresponding velocity at time t.

The rolling resistance power component is mod-

eled by:

roll

(t) = f

ds(t)

(2)

where f

is the coefﬁcient of rolling resistance, M

is the mass of the EV, g is the gravitational accelera-

tion, which is 9.81 m/s

The hill climbing power component is given by:

hill

(t) = Mg

dh(t)

(3)

where h(t) is the elevation at t,

dh(t)

is the vertical

velocity component.

The acceleration power component is given by:

(t) = M

s(t)

ds(t)

(4)

where

s(t)

is the acceleration at time t.

The efﬁciencies of battery, power converter, e-

motor controller, e-motor and mechanical powertrain

are denoted by η

bat

, η

conv

, η

contr

, η

respec-

tively.

Therefore, the overall propulsion power balance

equation can be written as:

bat

(t)η

bat

conv

contr

= P

air

(t) + P

roll

(t) + P

hill

(t) + P

(t)

(5)

EnergyConsumptionModelandChargingStationPlacementforElectricVehicles

151

Now denoting parasitic power losses at the battery

(lights, heater, stereo, etc.) as P

para

, we obtain:

bat

(t) − P

para

(t))η

bat

conv

contr

= P

air

(t) + P

roll

(t) + P

hill

(t) + P

(t)

(6)

In the case of regenerative braking we need to

reverse the powerﬂow and hence use the following

modiﬁcation of the above equation:

bat

(t) −P

para

(t)

= (P

air

(t) +P

roll

(t) +P

hill

(t) +P

(t))η

bat

conv

contr

(7)

with η

bat

, η

conv

, η

contr

, η

being the efﬁcien-

cies of the respective components for reversed power-

ﬂow.

3 OPTIMIZATION FOR

CHARGING STATION

PLACEMENT

The optimal placement of charging stations has been

intensely researched and many methods have been de-

veloped((Xi et al., 2013),(Chen et al., 2013),(Feng

et al., 2012),(Frade et al., 2011),(Sweda and Klab-

jan, 2011),(Koyanagi and Yokoyama, 2010)). This

method is based on the energy consumption model of

electric vehicles. We focus on maximizing the reach-

able households with a given battery energy bound.

Given this constraint, the reachable range can be de-

rived on Google Maps. To get the amount of covered

population in the reachable range, the population dis-

tribution for the considered area must be known. A

reasonable way is to divide the city by ZIP code zones

and then use the population in each ZIP code area.

Suppose there are N possible positions

X = {x

,...,x

} for charging station placement.

There are M ZIP code zones Y = {y

,...,y

}. The

model for a ZIP code zone is y

= (ycp

,ypop

where ycp

is the center position of y

and ypop

is the population number of y

. For each possible

position x

, function Range(x

bound

) is used to get

its reachable range R

, where E

bound

is the energy

bound constraint. This range can be obtained by

the software tool EVRE, which is implemented

based on Google Maps Javascript API. Deﬁne

= (Z pos

,Z pop

) as the kth ZIP code zone

covered by range R

, where Z pos

is the center

position and Z pop

is the population number. Then

we can get the following optimization model for

maximizing reachable households.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Time(s)

Velocity(mph)

Figure 1: FTP-75 Driving Cycle.

Maximize

∑

Z pop

subject to x

∈ X = {x

,...,x

}

∈ Y = {y

,...,y

}

= Range(x

, E

bound

)

= {Z

∈ Y and Z pos

∈ R

}

i = 1,...,N; j = 1, . . . , M; 1 ≤ k ≤ M

(8)

Model (8) is easy to implement, but only the cen-

ter position is used to represent the whole ZIP code

zone, which may cause errors when the center lies

near the boundary of the range. To obtain a more ac-

curate, implementable and computable optimization

model, each ZIP code zone can be further divided into

subareas.

4 SIMULATION RESULTS

4.1 Reachable Range Estimation

The electric vehicle reachable range estima-

tion(EVRE) software tool is implemented based on

the Google Maps API (Google, ) by applying the

energy model we constructed.

To estimate the reachable range, the driving dis-

tance, elevation data and velocity information are

needed. The driving distance and elevation data along

the route between two positions on Google Maps can

be obtained directly using the corresponding APIs.

FTP-75 driving cycle in Figure 1 is used to mimic the

driving velocity for EVs in the urban area, which are a

series of tests deﬁned by the US Environmental Pro-

tection Agency (EPA). It consists of starting with a

cold engine and making 23 stops over a period of 31

minutes for an average speed of 20 mph and with a

top speed of 56 mph. The average velocity derived

from the driving distance and duration information is

used for the suburban area. With this data, the energy

consumption can be calculated by applying the energy

model.

Given the energy constraint, the reachable range

is represented by a polygon and a breadth-ﬁrst search

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152

method is used to estimate it by determining its ver-

tices. In each search step, a set of positions on one cir-

cle serves as the possible origins and the charging sta-

tion position is the destination. Each pair (origin and

destination) has its corresponding energy consump-

tion value. Comparing them with the energy con-

straint is done to judge whether these positions can be

the vertices of the reachable range polygon. Differ-

ent radii of the circles for these possible positions are

used in different steps. Once all the vertices are found,

the searching process is complete and the reachable

range is determined.

Tesla Model S is selected as the electric vehicle

prototype. Its mass is 2108 kg, frontal area is 2 m

drag coefﬁcient is 0.24, rolling resistance coefﬁcient

is 0.01, battery capacity is 85 kWh and nominal range

is 265 mile.

Boulder, Co and New York City are selected as the

example areas. These two cities have different ter-

rains. Boulder is a small city with many mountains

on the westside with drastic elevation changes. New

York City is a metropolis with a complicated street

system and less elevation changes. Since our model

considers the real driving distance and elevation, the

reachable range is expected to be totally different.

Given the battery energy bound 2 kWh, the reach-

able range (charging station is marked as the center

and serves as destination) in Figure 2 is derived using

EVRE. Both of the ranges are unsymmetric, because

different driving directions have different routes and

elevation in both cities. Figure 2 shows that the reach-

able range in Boulder is much larger than in New York

City. There are at least two reasons for it. First, the

driving direction is from positions outside of the city

center. In Boulder, there are many downhill routes,

which casuses the EVs to have a larger driving range,

because the EV’s regenerative braking plays a dom-

inant roll. While in New York City, there is less

potential energy reused with little elevation change.

Second, New York City’s complicated street system

makes the EV’s velocity more like the FTP-75 cy-

cle. There are many accelerations and decelerations,

which will be a large energy cost. Hence, under the

same energy bound constraint, the reachable range in

New York is much smaller than in Boulder.

Figure 2 also shows the comparison results with

the Euclidean model. The Euclidean model is typi-

cally calculated using the following method.

Range

Capacity

265mile

85kW h

= 3.12mile/kWh

Two concentric circles are set in Fig. 2, one with

radius 3.12 miles, the other with radius 6.24 miles

for a energy bound of 2 kWh. The reachable range

Figure 2: Top:Reachable range estimation(2kWh)in Boul-

der Bottom:Reachable range estimation(2kWh)in New

York.

derived from EVRE is signiﬁcantly different from

the range created by the Euclidean model. Because

driving distance and elevation data are considered,

our model and software can provide a more accurate

range for EVs than the Euclidean model.

The intersection area is shown in Figure 3, the

red coverage is obtained by traveling from the subur-

ban area to the charging station center in the city; the

blue coverage is obtained by traveling in the opposite

direction. The elevation is changed when the route

direction is reversed, which makes the energy con-

sumption unsymmetric with regard to direction, espe-

cially in Boulder. There are many other factors that

change, for example, the route choice(there are many

one-ways in New York.) Hence we can get two differ-

ent coverage areas. From Figure 3, we can see that the

difference in Boulder is much larger than that in New

York. This shows the elevation change is responsible

for the energy consumption difference when reversing

the driving direction. The intersection for these two

coverage areas is where EVs can commute between

its position and the charging station by using up to 2

kWh energy. The intersection area should be the real

coverage range for the corresponding charging station

EnergyConsumptionModelandChargingStationPlacementforElectricVehicles

153

Figure 3: Top:Intersection Area in Boulder(2kWh) Bottom:

Intersection Area in New York(2kWh).

considered by the EV owner.

Figure 4 shows the results with different energy

radii for these two cities. Each coverage area repre-

sents a reachable range with the given amount of en-

ergy. Three kinds of energy radii are considered: 2

kWh, 3 kWh and 4 kWh. Figure 4 shows that these

coverage areas are no longer concentric circles, they

become irregular and the resulting polygons are not

similar for the different energy levels.

4.2 Charging Station Placement for

South Bend

South Bend, IN, a midsize city in the US, is selected

as a showcase area. As stated in the optimization

model (8) , to model the population distribution, the

area can be divided according to ZIP codes. There

are 13 ZIP codes in South Bend area, which means

M = 13. Table 1 includes the ZIP codes and their

corresponding population information. For possible

charging station positions, ﬁve possible places are se-

lected as examples, which means N = 5. They are

listed in Table 2. We need to choose one for these ﬁve

possible positions to maximize the reachable popula-

Figure 4: Top: Energy radius in Boulder, Bottom: En-

ergy radius in New York (Green: 2kWh, Blue: 3kWh, Red:

4kWh).

tion.

Table 1: Population Distribution in South Bend.

Y ZIP Code Population

46544 30695

46545 28445

46556 7424

46601 8460

46613 11526

46614 27041

46615 16905

46616 6431

46617 11644

46619 22489

46628 25319

46635 4172

46637 13829

With these ZIP codes and their population infor-

mation, EVRE is used to calculate the covered popu-

lation for each possible position. The energy bound

bound

for the reachable range is 2 kWh. Figure 5

shows the coverage of two possible charging station

positions, one is the Century Center and the other is

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Table 2: Charging Station Placement in South Bend.

X Possible Position Covered Population

Century Center 187719

University of Notre Dame 97310

McKinley Town Center 125702

University Park Mall 62434

South Bend Airport 74225

Figure 5: Coverage Range in South Bend, IN. Top: Univer-

sity Park Mall, Bottom: Century Center

the University Park Mall. The Blue markers are the

centers of the covered ZIP code zones, and the green

markers are the charging station positions. From Fig-

ure 5, we can see that they have different reachable

ranges and will cover different ZIP code zones. After

we know the covered ZIP code zones, we can calcu-

late the corresponding covered population. The cov-

ered population is listed in Table 2.

From the results in Table 2, we can see that Cen-

tury Center has the largest covered population, which

means that under this gain function and the 2 kWh

battery energy bound constraint, it is the best position

to place the charging station among these ﬁve possible

positions.

5 CONCLUSION

In this paper, a detailed energy consumption model

for EVs has been introduced. It includes a vehicle

as well as an infrastructure model aided by Google

Maps. The combination of these two models allows

to predict vehicle driving range in any geographic lo-

cation supported by google maps. A software tool

(EVRE) was developed that accurately predicts this

driving range from a speciﬁed starting point or to a

speciﬁed destination. In a second step, this software

tool was used to solve the problem of optimally plac-

ing charging stations, with the goal to reach the max-

imum number of households. EVRE allows to solve

this problem efﬁciently. In addition, the developed

concept allows to perform other types of charging sta-

tion optimizations and can take a number of practical

constraints into account. In fact constraints such as

power infrastucture, popular parking destinations, en-

ergy constraints, etc. can easily be incorporated to

narrow down the initial search space for candidate lo-

cations of charging stations.

ACKNOWLEDGEMENTS

We acknowledge gratefully the support of NSF grant

# 1239224.

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