EFFECT OF BATTERY STORAGE TECHNOLOGY ON THE CONSTRUCTION OF
ELECTRIC VEHICLE CHARGING STATIONS
By
Navwant Thakur

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Construction Management - Master of Science
2017

ABSTRACT
EFFECT OF BATTERY STORAGE TECHNOLOGY ON THE CONSTRUCTION OF
ELECTRIC VEHICLE CHARGING STATIONS
By
Navwant Thakur
Battery storage has become a critical component of electric vehicle (EV) charging infrastructure.
However, whether and how battery storage may serve a crucial role in enabling fast-charging
stations (FCSs) to fulfill customer demand and provide a profit for charging station operators is
unclear. This thesis provides a better understanding of how to construct FCSs with integrated
battery storage systems. The work is threefold. First, an in-depth literature review discusses EVs,
details the types of charging stations and standards, and evaluates battery technologies. The review
indicates that lithium-ion batteries are most promising for charging station applications followed
by lead-acid and vanadium-redox batteries. Second, processes and considerations for installation
of an FCS and battery storage unit are conducted. The results provide a cost estimation for various
configurations of FCSs and battery storage costs based on battery size, type, and vendor. Third, a
discrete event simulation (DES) model is developed to evaluate battery storage costs and
characteristics for a network of FCSs in Southeast Michigan. The simulation finds that when
considering network costs (i.e., the cost of setting up a new distribution line), no exchange of
energy occurs and each of the FCSs requires more than one battery. When network costs are not
considered, less exchange of energy occurs, and two-thirds of the FCSs require a battery. For this
network, lithium-ion batteries cost the most whereas zinc-air batteries cost the least. Owing to high
network costs, a highly condensed FCS network would provide higher benefit and result in lower
total cost through battery units connected to a microgrid. This model is useful to stakeholders in
this area (e.g., charging station operators, battery manufacturers, and vendors) to evaluate the
battery costs and characteristics that fit their FCS network best.

This thesis is dedicated to my parents, who have nurtured me into what I am.
To my sister, who inspired me to learn.
To all my friends, who have constantly supported and been with me through all times.

iii

ACKNOWLEDGEMENTS

I would like to thank Dr. Dong Zhao, my thesis committee chair, for his guidance and support
through the entire thesis process.

I am thankful to Dr. Michael Thomas and Dr. Mohamed El-Gafy for the guidance and feedback
they have provided for this study.

I am grateful to serve as a research assistant for the collaborative battery storage project of
Consumers Energy and Michigan State University. I would like to thank the research team from
MSU involved in this project. The work completed through this project has contributed immensely
to my thesis.

I would like to express my gratitude to the faculty and staff of Construction Management, School
of Planning Design and Construction for instilling the invaluable knowledge for building my career
within this industry.

Finally, I express my gratitude to my family and friends for providing me with unfailing support
and continuous encouragement throughout my years of study as well as through the process of
researching and writing this thesis. This accomplishment would not have been possible without
them. Thank you.

iv

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................................ vii
LIST OF FIGURES ....................................................................................................................... ix
KEY TO ABBREVIATIONS ......................................................................................................... x
Chapter 1 Introduction ................................................................................................................... 1
1.1

Background ...................................................................................................................... 1

1.2

Need statement ................................................................................................................. 3

1.3

Problem statement ............................................................................................................ 5

1.4

Research objectives .......................................................................................................... 6

1.5

Methodology .................................................................................................................... 7

1.5.1

Research plan and strategy........................................................................................ 7

1.5.2

Methods for objective 1 ............................................................................................ 8

1.5.3

Methods for objective 2 ............................................................................................ 9

1.5.4

Methods for objective 3 .......................................................................................... 11

Chapter 2 Literature review ......................................................................................................... 14
2.1

EVs ................................................................................................................................. 14

2.2

EV charging.................................................................................................................... 15

2.3

DC fast-charging standards ............................................................................................ 17

2.4

Battery technologies ....................................................................................................... 17

2.5

FCSs and battery technologies ....................................................................................... 23

2.6

Microgrid........................................................................................................................ 25

2.7

Summary ........................................................................................................................ 26

Chapter 3 Construction of a FCS and battery storage................................................................... 27
3.1

Installation process of a FCS.......................................................................................... 27

3.1.1

Site requirements .................................................................................................... 28

3.1.2

Installation preparation ........................................................................................... 30

3.1.3

Installation and inspection ...................................................................................... 31

3.1.4

Responsibility matrix .............................................................................................. 33

3.1.5

Applicable codes and standards .............................................................................. 33

v

3.1.6

Signage .................................................................................................................... 35

3.2

FCS costs ........................................................................................................................ 36

3.3

Battery storage installation process ................................................................................ 40

3.4

Battery storage costs....................................................................................................... 44

3.4.1

Various cost metrics ................................................................................................ 45

3.4.2

Vendor costs............................................................................................................ 47

3.5

Summary ........................................................................................................................ 48

Chapter 4 A FCS network with battery storage to meet energy demand: DES modeling ............ 50
4.1

Introduction and objective.............................................................................................. 50

4.2

Model description and assumptions ............................................................................... 50

4.2.1

Assumptions............................................................................................................ 51

4.2.2

DES diagram ........................................................................................................... 54

4.2.3

Study area................................................................................................................ 55

4.2.4

Functioning of model #1 ......................................................................................... 58

4.2.5

Functioning of model #2 ......................................................................................... 61

4.3

Results ............................................................................................................................ 66

4.4

Summary ........................................................................................................................ 72

Chapter 5 Conclusion.................................................................................................................... 73
5.1

Findings .......................................................................................................................... 73

5.2

Contribution ................................................................................................................... 74

5.3

Limitations ..................................................................................................................... 75

5.4

Future work .................................................................................................................... 75

APPENDICES .............................................................................................................................. 76
Appendix A. Construction process of a charging station ......................................................... 77
Appendix B. Phases and actions for a battery storage project .................................................. 82
Appendix C. Cost calculations for battery storage ................................................................... 83
Appendix D. DES modeling codes ........................................................................................... 86
BIBLIOGRAPHY ......................................................................................................................... 93

vi

LIST OF TABLES

Table 2.1 Performance comparison of various battery technologies ............................................ 18
Table 3.1 Control categories in FCS installation .......................................................................... 27
Table 3.2 Mechanism categories in FCS installation.................................................................... 27
Table 3.3 Responsibility matrix of various stakeholders for FCS installations ............................ 33
Table 3.4 SAE standards for charging station .............................................................................. 34
Table 3.5 NEC standards for charging station .............................................................................. 35
Table 3.6 Charging station configurations .................................................................................... 38
Table 3.7 Costs for option 1.......................................................................................................... 39
Table 3.8 Costs for option 2.......................................................................................................... 39
Table 3.9 Costs of a DCFC under different configurations .......................................................... 40
Table 3.10 Control categories in battery system installation ........................................................ 40
Table 3.11 Mechanism categories in battery system installation ................................................. 41
Table 3.12 Applicable codes and standard bodies for battery projects......................................... 44
Table 3.13 Cost comparison of various battery technologies ....................................................... 45
Table 3.14 Storage system cost details…… ................................................................................. 46
Table 3.15 Summary of battery costs provided by vendors.......................................................... 47
Table 4.1 Information on 15 FCSs used in simulation ................................................................. 56
Table 4.2 Inputs used in model ..................................................................................................... 63
Table 4.3 Battery costs used in model .......................................................................................... 64
Table 4.4 Construction cost for battery installation ...................................................................... 64
Table 4.5 Model results for each battery type considering network costs .................................... 66

vii

Table 4.6 Model results for each battery type without network costs .......................................... 66
Table 4.7 Difference in results for each battery type with and without network costs................. 67

viii

LIST OF FIGURES

Figure 1.1 Research plan flowchart for each study phase .............................................................. 8
Figure 1.2 Basic IDEF0 block consisting of function box and arrows ......................................... 11
Figure 3.1 IDEF0 diagram of a FCS installation process ............................................................. 28
Figure 3.2 Signage for EV charging stations ................................................................................ 36
Figure 3.3 Costs of DC fast charger installation ........................................................................... 38
Figure 3.4 IDEF0 diagram of battery storage installation process ............................................... 41
Figure 4.1 Conceptual diagram of model #2 ................................................................................ 54
Figure 4.2 Energy exchange decision rule within the microgrid in model #1 .............................. 55
Figure 4.3 Map of all DCFCs in Michigan ................................................................................... 57
Figure 4.4 Map of 15 FCSs used in simulation ............................................................................ 58
Figure 4.5 Graph of total gap vs. number of batteries for given inputs ........................................ 60
Figure 4.6 Screenshot of python interface showing the code for model #1 ................................. 61
Figure 4.7 Screenshot of input interface for model #2 ................................................................. 62
Figure 4.8 Screenshot of model #2 running with computing status ............................................. 63
Figure 4.9 3D graphs for battery types considering network costs............................................... 67
Figure 4.10 3D graphs for battery types without considering network costs ............................... 69

ix

KEY TO ABBREVIATIONS

AESC

Alternative Energy Systems Consulting

BEV

Battery Electric Vehicle

CCS

Combined Charging Standard

CHAdeMO

Charge de Move

DES

Discrete Event Simulation

DCFC

DC Fast Charger

DOE

Department of Energy

EV

Electric Vehicle

EPRI

Electric Power Research Institute

EVCS

EV Charging Station

EVSE

EV Supply Equipment

FCS

Fast-Charging Station

HEV

Hybrid Electric Vehicle

NEC

National Electric Code

PHEV

Plug-in HEV

SAE

Society of Automotive Engineers

UL

Underwriters Laboratories

x

Chapter 1
Introduction

1.1 Background
Owing to the exhaustion of fuels used for transportation and increased environmental awareness,
many countries have been electrifying their transportation system. The transportation sector
contributes roughly 27 percent of total U.S. greenhouse gas (GHG) emissions and 63 percent of
petroleum consumption (United States Environmental Protection Agency, 2012). Electric vehicles
(EVs) can reduce current dependence on fossil fuels as well as emissions (Institute for Energy
Research, 2013). By doing so for the personal vehicle fleet in the United States, EVs may alleviate
national and global concerns about energy security and climate change (Office of the Press
Secretary, 2009). The U.S. government has pledged $22 million in funding to accelerate the
development of plug-in EVs (National Labs, 2016). According to the Electric Drive Transportation
Association, EV sales in the United States jumped by 37% in 2016 with total sales of 159,139
vehicles (Association, 2016). EVs include hybrid EVs (HEVs), plug-in hybrid EVs (PHEVs), and
battery EVs (BEVs). In addition, greater adoption of EVs may help address climate change and
bring energy savings (Chandler, 2016).

As an increased number of EVs enter the market, the buildout of proper charging infrastructure
has become critical. An EV charging station supplies electricity for the recharging of PHEVs and
BEVs. The distance that an EV can travel is as critical as whether a facility for refueling exists
when battery power dwindles (McDonald, 2016). Currently, three types of EV charging stations
exist: Level 1 (Residential), Level 2 (Public), and Level 3 (DC Fast). As of 2015, approximately
70% of all public EV charging outlets are of the Level 2 type, 21.5% are Level 1, and 8.5% are

1

Level 3 (Flores, 2016). The literature review (Section 2.2) details charging station types Levels 1,
2, and 3. Despite being the least-adopted charger type, Level 3 charging stations, often termed fastcharging stations (FCSs), can charge a PHEV battery up to 80% within minutes. Residential
charging stations enable drivers to charge in their homes, but drivers prefer to charge quickly and
conveniently on the road to avoid range anxiety (Detwiler, 2014). Among the various types of
charging stations, FCSs are particularly required to boost EV sales.

There are many concerns about the strain that FCSs exert on the power grid owing to their large
load and short charging time. The extent of this impact depends on the EV penetration rate,
charging requirements, and time of day the EV is charged at the FCS. Nevertheless, deploying
large-scale FCSs may lead to grid instability (Bayram et al., 2013). Various studies have been
conducted to examine the future impact of EV charging on the electrical grid. A study by Schneider
(2008) finds that for a 240V rapid-charging station, storage devices are necessary for any level of
penetration. The simulation results in Lin (2010) show that the high penetration of PHEV charging
from the grid increase the feeder and fault currents. A DC FCS quickly charges a battery in minutes
but requires a huge amount of power. In some situations, peak power demand from the grid may
become so high that the contracted maximum power from the grid may not be sufficient for a
charging station to serve all EVs at the charging station (Aziz, 2016). A functioning FCS must be
able to cater to peak load demands and maintain a steady power supply throughout the day. This
can be established by using battery storage technology to support the power demands of a charging
station. Equipping FCSs with energy storage devices can reduce the impact of EV charging on the
electric grid (Bashiri & Bahadori, 2016).

2

Utility-scale battery storage technologies and applications are becoming an integral part of a
national strategy to modernize the nation’s electric system to meet future energy demand; integrate
increasingly disparate renewable energy facilities; address climate change issues; and enhance
overall reliability, safety, and security (Akhil, 2015). In this study, battery technology implies the
types of batteries available on the market and studied in this report. By improving the operational
capabilities of the grid, energy storage can play an important role in contributing to system
reliability and emergency preparedness with backup power, potentially lowering costs and
reducing infrastructure investments. The U.S. Department of Energy has indicated that electric
utilities have a diverse suite of energy storage technologies available for consideration, including
pumped hydro, compressed air energy storage, various types of batteries, flywheels, and
electrochemical capacitors. Potential storage applications include energy management, backup
power, load-leveling, frequency regulation, voltage support, and grid stabilization (U.S.
Department of Energy, 2013). Energy storage can be deployed at different stages of the electric
power system: generation, transmission, distribution, and consumption. Storage plays a role at the
consumer level by allowing consumers to store energy when excess capacity (or low-cost
electricity) is available, and the stored energy is used when capacity is limited (or electricity is
costly; Carnegie, 2013). Battery storage can become a buffer to abate the adverse effects of the
charging station on the grid and may be realized in coordination with FCSs.

1.2 Need statement
As EVs gain traction, energy storage is becoming a necessary infrastructure component (John,
2015). However, it is still unclear whether and how battery storage can serve a crucial role in
enabling FCSs to fulfill customer demand and seem a profitable investment to charging station

3

operators. With several battery storage technology options available in the market and each
claiming to be competitive in terms of safety, cost, and technical performance, determining the
most-appropriate technology for a particular application is critical. Many factors are involved in
assessing the optimal sizing of storage as well as which charging station locations are suitable for
deployment. An increased need then exists for tools and analysis that evaluate the financial benefits
and projected cost of a battery storage project under a given scenario (DiOrio, 2015).

Little research has addressed the construction of battery storage technology on a network of FCSs.
Deng (2016) presented a method for creating high-power fast-charging batteries controllable using
two energy storage units. His study addresses only the energy regulation problem. Rogge (2015)
conducted an analysis on real-world bus network data in Germany and explained the tradeoff
between battery capacity and charging power. His study does not consider the economic
implications of employing energy storage units for that network. Ding (2015) proposed a mixedinteger non-linear programming formulation to extract the monetary value of energy storage used
in coordination with an FCS but did not extend this study to a real-time network of FCSs. Bashiri
and Bahadori (2016) present an FCS with a flywheel energy storage system to meet demand
charge, improve and develop the load profile, and minimize the operational costs of an FCS.
Although the authors use a lifecycle cost analysis approach to compare different storage systems,
operational costs using fast chargers were not discussed. The work of Momtazpour (2014)
demonstrates a systematic data-mining methodology that can be used to identify locations for
placing charging and storage infrastructure. However, several measures were not considered, such
as battery life, energy storage, and an economic analysis. Therefore, the construction process and
economics of battery storage and FCSs have not been analyzed in most studies.

4

1.3 Problem statement
Problem 1: The effect of battery storage technology on the construction of individual EV FCSs
is unclear.
The economic implications of grid-scale energy storage technologies are obscure for power grid
operators, storage manufacturers, and regulators (Zakeri, 2014). From a utility standpoint,
investigating whether a battery storage system would be cheaper than upgrading the electric grid
to accommodate FCSs is critical. The step-by-step process of battery storage and FCS installation
as well as the roles of relevant stakeholders is not clearly defined (Schroeder, 2012). Different
studies (ZhuD, 2013; Bradbury, 2014; Evans, 2013) have suggested that a lack of adequate
information regarding the installation process and economies of utility scale of energy storage
systems at the distribution or consumer level are major barriers to widespread use of these
technologies.

Thus, a meticulous techno-economic analysis is required with updated cost data and a holistic
installation process framework for use of these technologies with respect to FCSs.

Problem 2: The effect of battery storage technology on the construction of EV FCSs in a
microgrid network is unknown.
The energy savings and financial benefit of adopting battery technology to support an operating
network of EV charging stations are unclear. With charging network operators rapidly installing
hundreds of DC fast chargers on their open network, understanding whether battery storage
deployed at certain stations can benefit the entire network is vital (PlugShare, 2017). Installing

5

storage at every FCS may not be necessary, as the utilization rates of each station vary. Hence, to
assess viability, a detailed study must be conducted to estimate the changes in cost and power
supply using battery storage in a network of FCSs.

1.4 Research objectives
The long-term goal of this research is to facilitate the adoption of EVs by better equipping charging
stations to meet customer needs. Using battery storage as a buffer, customers are provided highpower charging that allows them to recharge an EV in a limited timeframe (Sbordonea, 2014),
reducing range anxiety. This research evaluates battery systems to meet future needs for FCS
applications. This study aids electric utilities, charging station network operators, battery
manufacturers, and vendors to provide insights into the financial risks and benefits as well as
potential energy savings when using energy storage for a network of fast chargers.

Objective 1: To provide a better understanding of battery technology and its associations with
FCSs for EVs.
This objective addresses Problem 1 as follows:
(A) To review and evaluate the present state of battery-sourced storage technologies, storage
systems, and applications, manufacturers, and vendors of battery systems for FCSs of EVs.
(B) To analyze and compare different battery systems’ performance, cost, and siting
considerations, including an assessment of potential safety, environmental, and financial
impacts.

6

Objective 2: To identify the construction cost and process of an FCS that includes battery
storage.
This objective address Problem 1 through the following specific aims:
(A) Identify and prepare a list of project actions prior to construction as well as during
construction and installation phase of an FCS and battery storage system.
(B) Identify the costs for installation of FCSs, cost metrics used for battery storage, and battery
storage costs.

Objective 3: To determine the optimal battery storage system for supporting a given network of
FCSs.
In this study, battery storage system configuration means the size, number, and type of battery
storage units.
This objective address Problem 2 through the following specific aims:
(A) Evaluate the energy supply in a network of FCSs assisted by the battery storage system
through discrete event simulation (DES).
(B) Identify the size and optimum number of battery storage system units that minimize the
cost of the entire system and reduce energy load on the grid.

1.5 Methodology
1.5.1

Research plan and strategy

This study was divided into three phases. The first phase provides a general overview of electric
charging stations and battery storage technologies, examining their pros and cons and determining
the best technologies for use with an FCS. The second phase lists project activities and cost

7

information for the installation of an FCS and a battery storage system, using cost reports and
installation guides from various charging-station network operators and battery companies. The
third phase models the energy supply in a network of battery assisted FCSs using a case study of
the greater Detroit area in Michigan. A DES model has been implemented in Python to identify
the optimum configuration of battery units that result in the lowest energy supply cost. Figure 1.1
shows the research plan for each phase.

Figure 1.1 Research plan flowchart for each study phase

1.5.2

Methods for objective 1

An extensive literature review was conducted to provide a better understanding of EV charging
and battery storage technology. The literature review comprised journal articles, reports,

8

conference proceedings, and websites over 2010–2016 in the areas of electrical engineering,
energy fuels, transportation science, and technology. This phase included the following reviews:
(A) Types of EVs, charging station types, and charging station standards, including their
advantages and disadvantages.
(B) Existing and near-term battery storage technologies and their associations with FCSs. This
includes a discussion of the different battery types (e.g., lithium ion, lead acid, and vanadium
redox) used in utility scale applications:
(1) A comparison of various battery types based on lifecycle, temperature effects, and number
of past projects.
(2) Feasibility of utilizing each battery type for charging station applications, such as peak
shaving and backup power.
(3) The safety of each battery type and environmental impacts, including siting, operation, and
end-of-life disposal.

1.5.3

Methods for objective 2

Construction of FCS & Battery Storage
This study phase reviewed the installation process and costs of FCS and battery storage
construction. A qualitative analysis of the literature sources included review of recent installation
guides, handbooks, technical reports, and cost reports published by charging station operators and
installers, U.S. Department of Energy, Electric Power Research Institute, battery manufacturers
and installers, and the Clean Energy Council.
1. Installation process

9

(A) Present the decision-making and process flow of installing FCS and battery storage using
the IDEF0 diagram. IDEF0 is explained in Section 2.7.1.
(B) Based on the literature review, outline site considerations for deployment, activities prior,
during, and post installation, applicable codes, and standards governing installation
processes.
2. Costs of FCS and battery technologies
(A) Provide cost estimates for different configurations of FCSs based on literature sources.
(B) Compare costs of various battery technologies discussed in Chapter 1 based on literature
sources. Define the cost metrics used for evaluating the costs of battery storage.
(C) Compare the cost of battery systems provided by vendors using a cost survey conducted by
Michigan State University and Consumers Energy on distribution-scale battery storage.

Function modeling: In systems engineering, a function model is a structured graph for
representing activities, processes, and operations in a defined context (Zhao et al., 2016). The
function model provides a visual platform to accommodate process information and uncover
associated mechanisms and constraints. Furthermore, this model supports collaboration and
project team communication during the design and construction stages.

IDEF0 diagram: The IDEF0 diagram is a function-modeling tool (Grover and Kettinger, 2000)
for creating a flow diagram comprising function boxes and arrows. Fig. 1.2 shows a basic IDEF
block, in which the function box represents a decision-making process and the arrows represent
movements and directions (inputs/outputs and controls/mechanisms, respectively). Typically,
input arrows face the function box from the left and indicate the origin of the decision; output

10

arrows face out of the box from the right and indicate the decision made; control arrows face the
box from the top and represent an internal or external constraint; and mechanism arrows point
outward from the bottom and represent supporting resources (Zhao et al., 2016). A decisionmaking chain diagram is formed by connecting a certain number of IDEF0 blocks. This diagram
allows researchers to visualize decision-making chains and discover critical decision constraints.

Figure 1.2 Basic IDEF0 block consisting of function box and arrows

1.5.4

Methods for objective 3

In this phase, a DES model of an FCS was created in Python 2.7.13 by varying energy demand
using different battery units. See Section 2.8 for a description on DES. The installation cost range
of each battery type and vendor (see Chapter 3) were used as model inputs, and the model
parameters (i.e., location and power output) are based qualitatively on the network of fast chargers
near Detroit. To address the FCS energy gap, battery units are introduced that can supply energy
to nearby FCSs and exchange stored energy. The model evaluates the optimal configuration of
battery units required to meet the energy gap of the network at minimum cost by simulating these
network structures for different battery sizes, types, and exchange ranges.

11

Discrete event simulation: DES models a system as a chronological sequence of events where
each event can be defined as an instant in which a significant state change occurs in the system
(Robinson, 2004). DES has been used to tackle a wide range of problems, including project
planning (Rizk and Wales, 1997; Lee and Arditi, 2006), optimization of construction operations
(Hassan and Gruber, 2008; Zhang et al., 2006), resource allocation (Martinez et al., 2001), and
strategic construction management (Han et al., 2011). The fundamental components of DES are
as follows:
(A) Entities – Entities are items that flow through the simulation (Caro, 2005). In the model in
Chapter 4, FCSs are entities.
(B) Events – Events are another major element of a DES. These are broadly defined as anything
that can happen during the simulation (Caro, 2005). In Model #1 implemented in this study,
the addition of each battery unit marks an event in the simulation.
(C) Time – Another major component of a DES is time. The simulation clock tracks the passage
of time (Caro, 2005).
(D) Resources – A major element for economic evaluation is handling of resources, which are
incorporated directly into a DES. An entity may consume a resource, and this consumption
involves a defined number of resource units (Caro, 2005). In the model in this study, energy
units are resources.

Implementation of DES: Most of the steps in a DES are common to all modeling approaches.
First, formulate the problem and include the simulation goals (Caro, 2005). For a DES, processing
the events is the most crucial step. This is best done using a general-purpose programming
language such as Fortran or Python, where the software conducts the simulation by applying the

12

given logic to each entity. The model is run until the system stabilizes to a steady state or a prespecified condition.

Monte carlo simulation: In a Monte Carlo simulation, each simulation run generates random
numbers that determine whether an event occurs. Scikit-monaco is a library for Monte Carlo
integration in Python. In this study, scikit-monaco version 0.2.1 is used for inputting the cost values
of a range based on a lognormal distribution. In contrast to a normal distribution that can take both
positive and negative values, a lognormal distribution is commonly used for distribution of
financial assets (e.g., prices), as they cannot be negative (Zucchi, 2014).

13

Chapter 2
Literature review

2.1 EVs
EVs refers to the broad category of vehicles that use electricity as a portion of their energy to drive
the vehicle. The types of EVs on the market are as follows:
Hybrid EVs (HEVs) combine an internal combustion engine propulsion system with an electric
propulsion system, and they do not plug into an electricity source. HEVs transfer the energy
created through braking into electricity, which is stored in a battery. The electricity then helps the
engine achieve maximum fuel efficiency and minimize operating costs (Energy, 2015). HEVs are
thus completely dependent on gasoline or diesel coupled with regenerative braking.

Plug-in HEVs (PHEVs) utilize both electricity and gasoline to power the vehicle. They mostly run
on a battery that is recharged by plugging into the power grid (Energy, 2015). They operate on
electricity for a limited range and switch to a traditional engine for an extended range. They are
referred to as ‘extended-range EVs’ and typically have a mileage range of 30–40 miles on battery
(Corporation, 2016).

Battery EVs (BEVs) are propelled by electricity stored in a battery and used by an electric motor
without an internal combustion engine. They are charged by plugging into an electricity source,
typically the power grid. BEVs require a large DC motor and a large battery pack. They are also
called ‘pure EVs’ and typically have a range of 100–200 miles (Corporation E. , 2016).

14

2.2 EV charging
EV charging is generally performed at three current and voltage levels: AC Level 1, AC Level 2,
and Level 3 DC charging (Shuhui Li K. B., 2014). Batteries in EVs must be periodically recharged
from the power grid at home or at a charging station. According to the US Department of Energy,
the United States now has between 6,000 and 7,000 electric charging stations, of which the
majority (more than 5,000) are privately owned. Moreover, nearly 80% of all existing charging
stations are Level 2.
AC Level 1 charging uses a standard 120-V, 15A, or 20A circuit, has a maximum charging power
of 1.44kW, and requires 8 to 14 hours to fully charge a vehicle (Yu Nie, 2013). Most PEVs come
with a Level 1 cordset. Level 1 charging stations can be wall mounted or pedestal mounted at
parking spots. Depending on the EV battery type, battery size, and charging control, this station
adds approximately 2–5 miles of range per hour of charging time. Level 1 charging typically
requires a long charging time and is intended to be used at home or where the vehicle can sit for
an extended period. The advantages of such charging are low installation costs and low impact on
electric utility peak-demand charges.
AC Level 2 charging uses a 208V (typical in commercial applications) to 240-V (typical in
residential applications), single-phase outlet, provides 40A of current, has a maximum charging
power of 10kW, and can fully charge a vehicle in 4 to 6 hours (Ghamami, 2016). In addition to the
charging equipment of a Level 1 charging station, a dedicated 20–80A must be installed.
Depending on the battery type, circuit capacity, and charging control, this type adds 10–20 miles
of range per hour of charging time (Smith, 2015). The advantages of such charging are that the
charge time is significantly faster than Level 1 and that a variety of manufacturers provide
differentiated products for distinct markets and requirements (Vermont Energy Investment Co.,

15

2014). The disadvantages of such charging are that installation costs are higher than Level 1 and
that costs are highly variable depending on equipment and installation issues.
Level 3 DC charging is also called fast charging. It uses 480-V, up to 400-A, three-phase electrical
service for fast charging of EVs in minutes instead of hours. These chargers enable rapid charging
and are normally located at public fueling stations and sites along heavy traffic corridors. They
typically add 50–70 miles of range in approximately 20 minutes, and an 80% charge can be
provided in 30 minutes or less for most EVs. As Level 3 chargers operate with high voltage, they
are generally much more expensive to build and are available only at commercial charging stations
(Morrow, 2008). Level 3 is the most practical for installation in public commercial areas, and it
enables greater integration of EVs into the market because of quick charging. Fast charging attracts
EV users as it replicates the ease of conventional refueling and attracts potential operators because
it promises interesting business options (Andreas Schroeder, 2012). According to ABB, a leading
power and automation technology company, the market for charging infrastructure solutions is
worth $1 billion in 2017 and will be approximately $4 billion by 2020. There are currently nearly
2,200 high-speed chargers in the United States (McDonald, 2016). The prime advantage of Level
3 charging is that charge time is drastically reduced. The disadvantages are that equipment and
installation costs are very high depending on onsite power availability, and fast charging may strain
the grid or incur high ‘demand charges’ for pulling power off the grid at peak times (Gartner,
2012). DC FCSs are intended for locations where vehicles are parked (primarily near major roads)
for short periods of approximately 30 minutes, such as service stations, fast-food restaurants, cafĂŠs,
and some urban parking areas.

16

2.3 DC fast-charging standards
Charge de Move (CHAdeMO), Combined Charging Standard (CCS or SAE Combo), and the Tesla
Super Charger are the three charging standards in use in the United States.
CHAdeMO: In 2010, Toyota, Nissan, and Mitsubishi partnered to establish the CHAdeMO quickcharge standard (McDonald, 2016). The maximum charging power specified by the CHAdeMO
standard is 62 kW. CHAdeMO ports do not support AC charging, and cars must have two charging
ports: one for AC Level 2, the other for CHAdeMO (Herron, 2014). CHAdeMO is compatible
with Nissan, Mitsubishi, and Kia.
Combined Charging System (CCS): CCS is built on the existing J1772 Level 2 charge standard
to allow for all three charging speeds from a single port. CCS chargers improved several of the
practicality and cost issues associated with CHAdeMO while allowing for a higher potential rate
of charge. Although existing CCS chargers typically run at the same speeds as CHAdeMO, the
standard allows for a theoretical maximum of 350 kW through the port—more than twice as fast
as a Tesla Supercharger (McDonald, 2016). CCS is compatible with BMW, Volkswagen,
Chevrolet, and all upcoming electric cars in the United States.
Tesla Supercharger: The Tesla Supercharger system is rated at 120kW. Tesla also sells an addon adapter to enable Tesla owners to charge their vehicle using CHAdeMO or J1772 standards.
As of 2017, there are currently 828 Supercharger stations and 5,339 Superchargers in use (Tesla,
2017).

2.4 Battery technologies
There exist many battery technologies with applications in utility power production and
distribution, such as lithium ion, sodium sulfur, lead acid, vanadium redox flow, nickel cadmium,

17

nickel metal hydride, sodium nickel chloride, zinc air, zinc bromine, and iron-chromium (Akhil et
al., 2015). The emerging development of battery technology in recent years has presented new
possibilities with applications in electric utility transmission and distribution, renewable energy,
smart grids, and EVs. Installing energy storage also provides capacity for additional EV charging
without expensive utility upgrades.
Table 2.1 provides a comparison of performance attributes of the various battery technologies later
detailed.
Table 2.1 Performance comparison of various battery technologies
Battery Storage
Type
Lithium-ion

Discharge Duration

Size

10 min – 9h 21 min 1 kW – 48 MW

Nominal
Voltage

Number of
Cycles

Number of
Projects
≤ 1 MW

3.7 V

~5,000

430

Sodium-sulfur

6h – 8h

400 kW – 50
MW

2.1 V

500–10,000

14

Lead-acid

50s – 9h 36 mins

2 kW – 36 MW

2.0 V

~1,500

72

Vanadium redox
flow

16 min – 20h

5 kW – 20 MW

1.6 V

~10,000

48

Nickel-cadmium

5 min – 15 min

3 MW – 27
MW

1.2 V

~500–3,000

0

15 min

300 kW

1.2 V

~600–1,200

1

42 min – 5h

20 kW – 5 MW

2.6 V

~1,000

24

Zinc-bromine

2h – 6h

3 kW – 25 MW

1.8 V

> 2,000

32

Zinc-air

2h – 48h

250 kW – 10
MW

1.65 V

~5,000

0

Iron-chromium

4h

250 kW

1.18 V

> 5,000

0

Nickel metal
hydride
Sodium-nickelchloride

Lithium-ion battery: Lithium-ion (Li-ion) batteries were first commercialized in the early 1990s
and have become one of the most-preferred storage technologies in many applications owing to
their high energy density, high voltage ratings, high efficiency, low self-discharge, lack of cell

18

‘memory,’ and fast response (Puget Sound Energy, 2015). Moreover, Li-ion batteries do not need
to be discharged completely (Oswal M., 2010).
However, Li-ion batteries have some disadvantages, such as short cycle life, high cost, heat
management issues, and narrow operating temperatures (International Electrotechnical
Commission, 2011). More than 300 energy storage projects with Li-ion batteries are currently in
operation worldwide. Li-ion batteries can adapt to a range of power and energy ratings, and the
rated power of the operational projects varies from 1 kW to 48 MW. Li-ion batteries are mostly
used in projects with rated power below 5 MW. Li-ion batteries have several subtypes based on
cathode material, including lithium manganese oxide (LMO), lithium iron phosphate (LFP),
lithium nickel cobalt aluminum (NCA), lithium titanate (LTO) and lithium nickel manganese
cobalt (NMC).
Sodium sulfur battery: Sodium-sulfur (NaS) battery technology was first invented in the 1960s
by Ford Motor Company, and the first mega-watt-class system of NaS batteries in the United States
was installed in 2006. After decades of development and support by companies like NGK
Insulators, Ltd., and Tokyo Electric Power Co. (TEPCO) and its utilities, there are approximately
30 operational NaS projects worldwide (U.S. Department of Energy, 2016). According to the DOE
Global Energy Storage database, most utility-scale operational projects have rated power greater
than 1 MW (varying from 100 kW to 50 MW), and the duration at rated power is between 3 to 8
hours. NaS batteries are projected to have a calendar life of 15 years (DOE-EPRI 2013 Energy
Storage Handbook).
The advantages of NaS batteries are long discharge period (approximately 6 to 7.2 hours),
relatively high energy densities, fast response, and commercial maturity. Moreover, the NaS
battery uses inexpensive, non-toxic materials and is thus highly recyclable (Gonzales et al., 2012;

19

Kawakami et al., 2010). One drawback of the NaS battery is that the internal heating unit uses the
battery’s own stored energy and thus reduces battery performance. Another downside is the risk
of fire and that the system must be protected from water and oxidizing atmospheres.
Lead-acid battery: Lead-acid (LA) batteries have been commonly used in many applications,
including stationary and mobile ones (IEC, 2011). Stationary LA batteries are more efficient than
starter batteries but cost more. Two main types of LA batteries exist, that is, carbon LA
technologies and advanced LA technologies (Sandia, 2007). The service life of a LA battery is
typically in the 6- to 15-year range and has a cycle life of 1,500 cycles and a discharge depth of
80%. Moreover, the efficiency of LA batteries is within the 80 to 90% range. LA advantages
include fast recharge rates, simple charging technology, long cycle life in deep-discharge
applications, favorable cost/performance ratio, and little maintenance (IEC, 2011; Sandia, 2007;
Axion, 2016). LA batteries have high commercial maturity and relatively low disposal cost, total
installed cost, and relocation cost (Sandia, 2007). More than 70 LA projects exist globally, most
having rated power less than 1 MW.
Vanadium redox flow battery: Vanadium redox flow batteries (VRFB) are a relatively mature
type of flow battery being used in various stationary applications. The power of flow batteries is
defined by the size and design of the electrochemical cell, whereas the energy depends on the size
of the tanks (IEC, 2011). These batteries are inherently safe, with no thermal runaway. The
electrolyte is aqueous and non-flammable, and they are environmentally friendly and recyclable.
Furthermore, the electrolyte is reusable and provides an emission-free energy supply. These
batteries have high energy efficiency, short response time, long cycle life, independently tunable
power rating and energy capacity, and consistently stable performance (Cunha, 2014). The DOE

20

Global Energy Storage database indicates that more than 30 operational VRFB projects exist
worldwide, most with rated power less than 1 MW.
Nickel cadmium battery: Nickel cadmium (Ni-Cd) and nickel metal hydride (NiMH) batteries
are the two main members of the nickel-based battery family.
Ni-Cd batteries have been commercially used since 1915 and are therefore a relatively mature
technology, but few grid-scale deployments exist. This type of battery performs well even at low
temperatures (in the -20 °C to -40 °C range). Nickel-based batteries have higher power density,
slightly greater energy density, and a higher number of cycles than LA batteries do (IEC, 2011).
Ni-Cd batteries also pose several disadvantages. For example, cadmium is prohibited for customer
use because it is very toxic and dangerous to the environment.
Nickel metal hydride battery: NiMH batteries were developed as an alternative for NiCd because
of the toxicity of cadmium. Although NiMH batteries share almost all the advantages of NiCd
batteries, the maximal nominal capacity is still 10 times less than that of NiCd and LA (IEC, 2011).
Furthermore, they charge slower than NiCd and cannot withstand very low operating temperatures
(Puget Sound Energy, 2015). At present, only one operational NiCd project exists (in Japan) with
300 kW rated power.
Sodium nickel chloride battery: Sodium nickel chloride (NaNiCl) batteries are also known as
zero-emission battery research activities (ZEBRA). Like NaS batteries, they are high-temperature
(HT) batteries, but they use nickel chloride instead of sulfur for the positive electrode. According
to the DOE Global Energy Storage database, approximately 20 operational ZEBRA projects exist
globally and approximately 10 are announced or under construction. Most of the utility-scale
operational projects are from 20 kW to 5MW, and the duration at rated power is between 42
minutes to 5 hours.

21

Some advantages of NaNiCl over NAS chemistry include overcharge and discharge tolerance,
potentially better safety characteristics, and higher cell voltage. Other beneficial features of
ZEBRA are its low environmental impact owing to fully recyclable materials as well as its fast
response, long cycle life, tolerance of short circuits, constant performance and cycle life in harsh
operating environments, high energy density (five times higher than LA), and scalability. This
battery type has been shown to have relatively low intrinsic risks during normal operation. Sodium
nickel technology is maintenance-free and has zero ambient emissions. However, ZEBRA units
have limited utility grid application, and, therefore, the technology is currently used in the
transportation and military equipment industries and in limited grid-scale applications in North
America (Chen et al., 2009; IEC, 2011; Dustman, 2004).
Zinc bromine battery: Zinc-bromine batteries (ZBBs) are a promising and emerging technology.
This battery is still in early stages of field deployment and demonstration trials for utility
applications. According to the DOE Energy Storage database, 10 projects are operational and 10
are contracted or under construction. The rated power is not very high as most projects are below
500 kW, but the duration at rated power is relatively long, from 2 to 6 hours. The features of a
conventional battery and flow battery are combined, and, thus, higher power and energy densities
are allowed than in other types of flow batteries. Furthermore, ZBBs have long estimated lifetimes
(20 years), because the active materials themselves do not degrade and the lifetime is not strongly
dependent on the number of cycles or the depth of discharge but on the number of hours of
operation (DOE-EPRI 2013 Energy Storage Handbook). Other advantages of ZBBs include long
cycle lives, operational AC-to-AC efficiencies of approximately 65%, 100% depth of discharge,

22

ambient temperature range, and no shelf life. One disadvantage of ZBBs is that it contains
potentially contaminating materials.
Zinc-air battery: This type of battery offers low material cost and high specific energy. This
technology is far more stable and less dangerous than other battery technologies and has up to
three times the energy density of Li-ion, the most-competitive battery technology. Moreover, zincair batteries are very environmentally friendly because they do not produce potentially toxic or
explosive gases and contain no toxic or environmentally dangerous components. A downside of
zinc-air batteries is that they are sensitive to extreme temperatures and humid conditions. These
batteries are still in early stages of utility applications, and no zinc-air projects are currently
operational but two contracts for such projects exist in California.
Iron-chromium battery: This battery is still in the R&D stage and only one demo project has
been conducted. Iron-chromium batteries are safer than integrated cell storage architectures (e.g.,
LA, NaS, and Li-ion) owing to the separation of power and energy. They are also environmentally
benign because the utilized iron and chromium species have low toxicity.

2.5 FCSs and battery technologies
A major challenge for public charging stations is reducing charging time. This can be addressed
by increasing the rate of power transfer through energy storage units (e.g., batteries; Sbordonea,
2014). As discussed in the previous section, many types of batteries are available for an FCS. By
improving the operational capabilities of the FCS, battery storage can contribute to system
reliability and emergency preparedness with backup power, potentially lowering costs and
reducing infrastructure investments (Akhil et al., 2015). In addition to supporting DC fast charging,
battery systems are used to sell power back to the grid. As mentioned in Joos and Freige (2010),

23

battery storage should satisfy the following performance criteria to maximize charging station
efficiency:
(A) Dynamic device: Because the charging station operates for only 20 minutes (short duration),
the storage devices must be able to charge and discharge in that period.
(B) High-power density: Because of the previous requirement, devices must also have high power
density to deliver a large amount of power for a short period.
(C) High efficiency: The charging station must achieve maximum efficiency. This last criterion
depends on the converters and storage devices, which are the main station components.
Therefore, considering highly efficient energy storage and conversion is required.
(D) Environmentally friendly: The device must have no or negligible adverse effects on the
environment.
A battery storage system used in conjunction with a FCS operates in the following modes (Aziz,
2016):
1. Battery discharge mode: The battery discharges its electricity in assisting the system. EV
charging is performed using electricity from both the grid and the battery. This mode is applied in
fast charging of multiple EVs, especially when electricity prices are high. The power balance
equation for this mode is shown in Eq. 1.
P (grid) + P (batt) = P (fc) + P (loss)

(1)

where P (grid) is the electricity from the grid, P (batt) is electricity charged/discharged from battery,
P (fc) is electricity for EV quick charging, and P (loss) is electricity loss.
2. Battery charging mode: When a surplus of electricity from the grid exists, the demand for
charging is low and the price of electricity is reduced. The power balance function for this mode
is shown in Eq. 2.

24

P(grid) – P(batt) = P(fc) + P(loss)

(2)

3. Battery idle mode: The battery can be in idle mode when the power capacity from the grid is
sufficient to cover quick charging of EVs or the battery is empty owing to continuous charging of
multiple EVs. The power balance function for this mode is shown in Eq. 3.
P(grid) = P(fc) + P(loss)

(3)

2.6 Microgrid
A microgrid is a small-scale power grid that can operate independently or in conjunction with the
area’s main electric grid (Rouse, 2015). Microgrids can be intended as backup power or to support
the main power grid during periods of heavy demand. Microgrids incorporate renewable power
using multiple energy sources like distributed generators, batteries, or solar panels (Microgrid
Institute, 2014). A microgrid is a locally controlled system and can function both connected to the
traditional grid or as an electrical island. According to Berkeley Lab (2015), there are two major
types of microgrids: customer microgrids (wholly on one site, akin to a traditional utility customer)
and milligrids (involving a legacy regulated grid segment). Military bases, hospitals,
municipalities, data centers, and business parks are all developing microgrids. Microgrids tend to
be owned by private or government entities; some utilities have also constructed microgrids.

The operation of microgrids offers distinct advantages to customers and utilities: improved energy
efficiency, minimization of overall energy consumption, reduced environmental effects, supply
reliability improvements, network operational benefits (e.g., loss reduction, congestion relief,
voltage control, and security of supply), and cost-efficient electricity infrastructure replacement
(Berkeley Lab, 2015). Microgrids may offer new revenue streams to utilities because they make
the grid more efficient. However, costs exist for building new infrastructure, and new microgrids

25

may adversely impact customer rates (U.S. Department of Energy, 2014). According to Stadler et.
al. (2015), significant economic returns can be achieved by the deployment of microgrids in
applications ranging from residential to commercial and large industrial.

2.7 Summary
Battery storage systems enable FCSs to meet power demand. For supporting a DC fast charger,
battery systems with less than 100kW power that can run for at least 4 hours are required
(depending on the load profiles of the charging station). Existing research suggests that Li-ion
batteries currently provide the best safety, cost, and technical performance for small-sized power
distribution applications, and LA and VFRB are also competitive in these areas. These three
technologies are relatively mature and scalable, and operational and safety solutions have already
been developed. They have the highest number of projects installed with less than 1 MW power.
Furthermore, for the technologies, the number of installations is increasing, large availability of
suppliers ensures that future installations are cost-competitive and that support remains available,
and service and cycle life are competitive with other technologies.

26

Chapter 3
Construction of a FCS and battery storage

3.1 Installation process of a FCS
As an increasing number of consumers purchase PEVs, the demand for electrical charging stations
will increase. Contractors will therefore receive more requests to install charging stations in both
new construction and existing homes, retail outlets, corporate campuses, and parking decks.
Electrical inspectors will also be challenged by this evolving technology as requests for approvals
increase and the installation scope varies (Advanced Energy Co., 2011). Understanding the
processes involved in the installation of a DC FCS are then vital.
Fig. 3.1 shows a flowchart (IDEF0 diagram) depicting the processes involved in the installation of
a FCS. Tables 3.1 and 3.2 summarize the five predefined control categories and the five predefined
mechanism categories for function modeling, respectively.

Table 3.1 Control categories in FCS installation
Identifier
C1
C2
C3
C4

Control
(constraint)
Assessment
Approvals
Regulations
Efficiency

Description
Engineering calculations, service upgrade assessment, site plan
Permit and estimate approval
Standards and requirements
Adequate qualified resources

Table 3.2 Mechanism categories in FCS installation
Identifier
M1
M2
M3

Mechanism
(resource)
Space
Funding
Professionalism

Description
Parking, facilities, and electric service availability at site
Government/utility incentives
Licensed contractor/expertise, skills, good judgement

27

Table 3.2 (cont’d)
M4
M5

Time
Collaboration

Schedule
Communication and coordination with third parties

C 3 (R E G U L A T IO N S )
C 1 (A S S E S M E N T )

S ELE C T
TY P E

C 2 (A P R O V A L S )

C 4 (E F F IC IE N C Y )

C H O O S E S IT E
L O C A T IO N

O F FC S
C ON TA C T
U T IL IT Y A N D
L O C A L P E R M IT
O F F IC E
IN ST A L L A T IO N
P R E P A R A T IO N

IN S T A L L A T IO N

IN S P E C T IO N

M 1 (SP A C E )

M 2 (F U N D IN G )

WORK
C O M P LE TED

M 5 (C O L L A B O R A T IO N )

M 4 (T IM E )

M 3 (PR O F E S SIO N A L ISM )

Figure 3.1 IDEF0 diagram of a FCS installation process

The following sections describe each stage of the installation process in detail, including the
steps contractors should follow.
3.1.1

Site requirements

The site for an FCS must be safe, accessible, convenient, and reliable. The site should contain a
type and mix of charging stations that maximize usefulness (Alternative Energy Systems
Consulting, Dec 2015) and meet the following minimum requirements to satisfy the needs of the

28

EV client and infrastructure goals (Alternative Energy Systems Consulting, Dec 2015) &
(Advanced Energy, 2013):
(A) Location: The host site should be within urban areas, preferably within a one-mile radius from
a highway interchange. The location must be cleared and accessible during winter and not be
used as a snow dump or hinder snow-clearing operations. It should be visible to encourage its
use by EV drivers.
(B) Parking: It should have adequately lit, appropriate paved parking and reasonable ingress/egress
points.
(C) New construction: From an electrical and accessibility standpoint, it is simpler (but not always
preferable) to design a new DC FCS than retrofit an existing location.
(D) Facilities: Host sites should ideally have 24-hour access to well-maintained restrooms.
Preferred sites should have internet connectivity capabilities to facilitate communications
between the EV supply equipment (EVSE) and EV and serve as the medium for integrating
the EVSE with utility smart-grid systems. Moreover, sites that offer products and ancillary
services while charging, such as snacks, vending machines, fast food, shopping, and
restaurants, are preferred.
(E) Safety: The site should have dusk-to-dawn area lighting and have a reasonable level of activity.
The site must also have shelter for inclement weather.
(F) Electric power: Access to existing 480-V three-phase power nearby is preferable. The local
grid must have adequate capacity to serve the site and all chargers.
An FCS usually requires a concrete base, and its installation is like that of street-side locations. In
choosing a location for this type of station, the following factors must be considered (Hydro
Quebec, 2015):

29

(A) Station configuration
(B) Locations of any underground lines and tanks
(C) Distance from the street (i.e., the charging cable must never extend over the sidewalk)
(D) Required excavation work
(E) Proximity of the distribution panel
(F) Planning of any underground conduits and excavation work
(G) Coordination with excavation consultants before starting work
(H) Contractor expertise (must have appropriate licenses)
(I) Possibility of installing a concrete base
Appendix A provides a general overview of the installation process in different phases and a
contractor checklist for surveying FCSs (Advanced Energy Co., 2011).
3.1.2

Installation preparation

Following the initial site visit, the contractor should prepare for installation. Complete the
following checklist (Advanced Energy Co., 2011):
(A) Submit price quote to customer and get approval. Ensure that total installation cost, including
utility upgrades and all other work, is understood by the customer.
(B) Order equipment including selected charging station(s).
(C) If necessary, perform and stamp engineering calculations. Contact local permit department for
questions regarding the need for load calculations.
(D) Complete site plan modification along with necessary diagrams (typically required for parking
lots, decks, and on-street parking).
(E) Perform service upgrade and/or new service assessment if required.

30

(F) Fill out permit application along with site plan modification, load calculations, and any other
information deemed necessary by the local permitting department.
(G) Ensure permit is approved.
(H) Schedule the plan (i.e., contact all stakeholder parties and schedule work).
(I) Hire additional contractors for boring, concrete, paving, or other surface restoration work.
(J) Utility work: utility markings, service upgrades, new service, and meter pull.
(K) Utility marking of existing power lines, gas lines, and other infrastructure should be conducted
prior to installation. Utilize “Call Miss Dig” services.
3.1.3

Installation and inspection

The process remains similar despite that installation varies based on type of site and number of
stations installed (Advanced Energy Co., 2011):
(A) Post permit at site in visible location.
(B) Conduct any excavations of materials required to run a conduit and/or wiring and install a
charging station. Typical excavation actions include the removal of drywall, insulation, pavers,
and concrete or pavement as well as hand digging, trenching, boring, and drilling.
(C) Run the conduit from the power source to the station location. For charging stations rated more
than 60 amp, a separate disconnect must be installed (NEC 625.23) when running the conduit.
Some customers may desire a separate disconnect for stations rated below 60 amp, and this
disconnect should be visible from the charging station.
(D) Schedule an initial rough electrical inspection after the conduit has been run and prior to
connecting equipment and running wires. If the installation does not pass inspection, the
contractor should correct any items discussed by the inspector and schedule a second rough
inspection prior to moving on to the next step.

31

(E) Pull the wires. Charging stations require two hot lines (a neutral and a ground), and as charging
equipment is considered a continuous load, conductors should be sized to support 125 percent
of the rated equipment load (NEC 625.21).
(F) Prepare the mounting surface according to the charging station manufacturer’s instructions.
Floor mounts typically require a concrete foundation that allow the conductors to enter through
the base of the charging station and the appropriate installation of J-bolts should be based on
the station base plate. For wall/pole/ceiling mounts, brackets may need to be installed to mount
the charging equipment.
(G) Mount the charging station(s), and ensure that equipment is level and mounted in accordance
with manufacturer instructions.
(H) Install any necessary protective bollard(s) and/or wheel stop(s).
(I) Install any required electrical panels or sub-panels.
(J) Perform utility work such as service upgrades, new service, and new meter installations. The
utility may also pull a meter to allow for the charging station wires to be connected to a panel.
(K) Finish electrical wiring.
(L) Perform finishing work.
(M) Replace drywall.
(N) Bury conduit and conductors.
(O) Fill and compact as needed.
(P) Replace walking surfaces—concrete, asphalt, and pavers.
(Q) Perform final inspection. If required, the inspector should examine the wiring, connections,
mounting and finish work, and ensure that the charging station is safe for operation in its given
location.

32

(R) If possible, the contractor should verify that the charging station functions properly.
3.1.4

Responsibility matrix

Table 3.3 shows the stakeholders responsible for each process during FCS installation.

Table 3.3 Responsibility matrix of various stakeholders for FCS installations
Step
1

2
3
4
5
6
7
8
9
10

11
12
13
14

3.1.5

Action
Approve installation of charging station:
(1) Workplace, retail, public lots/decks
(2) On-street parking, residential owner (obtain permit
and reserve parking space)
(3) On-street parking, non-residential owner

Person responsible

Select charging level and number of charging stations
Select charging station(s)
Select parking space(s)
Select power source
Estimate installation costs
Create site plan and determine whether electrical
upgrades are necessary
Approve/accept estimate
File permit application
Complete electrical upgrade, if required:
(1) Panel upgrade/new panel
(2) Service upgrade/new service
(3) New meter
Restore power
Conduct installation
Perform inspection
Verify performance

Owner
Owner
Owner
Owner/utility
Contractor
Contractor/utility

(1) Parking spot owner
(2) Residential owner
(3) Right-of-way owner

Owner/contractor
Contractor
Utility
(1) Contractor
(2) Utility
(3) Utility
Utility
Contractor
Inspector
Contractor

Applicable codes and standards

These general EV charging station (EVCS) installation standards relate to electrical code and
workmanship requirements, equipment, determination of proper electrical load, physical

33

installation, post-installation equipment use and maintenance, and communications (California
Energy Commission, 2016). The National Electrical Contractors Association (NECA) publishes
the National Electrical Installation Standards (NEIS) to define a minimum baseline of quality and
workmanship for installing electrical products and systems. The NEIS code for EVCS is NECA
413-2012, Standard for Installing and Maintaining Electric Vehicle Supply Equipment. NECA 413
includes guidance on the EVSE, the installation process, ongoing maintenance, and
communications. NECA 413 also recommends that all work should be performed in accordance
with established requirements for electrical safety.
Society of automotive engineers and national electrical code standards
The Society of Automotive Engineers (SAE) has developed standards for energy transfer and a
common cord set to ensure common standards for vehicle charging. These standards ensure that
all PEVs have a common charging ‘plug,’ that is, that any PEV can plug into any charging station.
The two main standards are SAE J1772 and SAE J2293, which reference other SAE, National
Electrical Code (NEC), and Underwriters Laboratories (UL) standards or codes.

Table 3.4 SAE standards for charging stations
SAE standards for charging stations
Standard Description
J1772

Electrical and mechanical aspects of the cord set; references UL for safety and shock
protection as well as the NEC for the cord and couple.

J2293

Standard for the EV energy transfer system. This encompasses the system for
transferring energy from the charging station to the car.

J2293-1

Functionality requirements and system architecture

J2293-2

Communication requirements and network architecture

34

Table 3.5 NEC standards for charging stations
NEC standards for charging stations
Standard
Description
NEC 110.11

Deteriorating Agents

NEC 110.28

Enclosure Types

NEC 110.26

Electrical Equipment Spacing

NEC 110.26 (A)(2)

Width of Working Space

NEC 110.27(B)

Guarding of Live Parts – Prevent Physical Damage

NEC 210.70(A)(2)

Lighting Outlets Required – Dwelling Units – Additional Locations

NEC 300.4

Protection [of conductors] Against Physical Damage

NEC 334.15

Exposed Work [requirements for nonmetallic-sheathed cable]

NEC 334.30

Securing and supporting nonmetallic-sheathed cable

NEC 625.1–625.5

General (Scope, Definitions, Other Articles, Voltage, Listed/Labeled)

NEC 625.9 (A–F)

Wiring Methods (EV Coupler)

NEC 625.13–625.19

Equipment Construction

NEC 625.21–625.26

Control and Protection

NEC 626.28–625.30

EV Supply Equipment Locations

3.1.6

Signage

Although many EV users locate EVCS locations through their smart phones or onboard navigation
systems, clear roadside signage for EVSEs is critical (Vermont Energy Investment Co., 2014). In
the United States, the Federal Highway Administration developed a pictogram that represents a
charging station (see Figure 3.2) used in public parking areas equipped with charging stations. In
addition, supplemental plaques denoting the level of charging below the main sign may also be
added to inform drivers of the limitations.

35

Figure 3.2 Signage for EV charging stations

3.2 FCS costs
EVSE installation costs vary widely depending on site characteristics and the quantity and type of
EVSE being installed. Like any product, price is influenced by the degree of competition amongst
EVSE vendors and the ability of vendors to achieve economies of scale in service delivery. As
EVSEs become more prevalent, equipment prices and installation costs decrease (particularly for
Level 3 charging equipment) (Vermont Energy Investment Co., 2014).

Although past EVSE installations provide a wide range of information on costs for future
installations, cost estimates for a specific site can only be determined by contacting the utility,
EVSE manufacturers, and EVSE installers who can conduct a site assessment.
The following installation costs exist for an FCS (Hydro Quebec, 2015), (Vermont Energy
Investment Co., 2014):
(A) Purchase price of the charging station and associated equipment
(B) Power connection to the electric grid, including purchase and installation of electrical
equipment (e.g., conduits, conductors, transformers, protective devices, switching equipment,
cabinet, and grounding)
(C) Civil engineering work (e.g., mounting, excavation, and concrete bases)

36

(D) Charging station installation
(E) Protective devices (e.g., bollards and wheel stops)
(F) Signage, parking lot lines, and stripes
(G) Lighting
Different sources provide varying estimates for DC fast charger (DCFC) installation costs. A DC
FCS can have multiple DCFC. According to a study by American Council for an Energy-Efficient
Economy titled “Plug-in EV Challenges and Opportunities,” installation costs for a DCFC range
from $20,000 to $50,000. Installation cost estimates obtained from experienced installers such as
Green Power Technologies and Peck Electric indicate that the equipment cost varies from $15,000
to $60,000 and the installation cost varies from $10,000 to $25,000. Thus, total costs are between
$25,000 and $85,000, where the lower cost range is for sites that used existing electrical services.
DCFCs proposed in remote areas may require additional costs if the site lacks access to threephase power: the cost of introducing three-phase power to a new location is costly (approximately
$15,000 to $30,000 per mile) or more, depending on the utility company performing the work and
the number of customers served. Permit costs are not a significant factor impacting commercial
installation costs (Alexander, 2014). The DC FCS installation costs presented in Fig. 3.3 are based
on single-port products available in 2014 and 2015.

37

Figure 3.3 Costs of DC fast charger installation

Table 3.6 presents two charging station configuration options, as recommended by Alternative
Energy Systems Consulting (AESC).
Table 3.6 Charging station configurations
Equipment
Level 2 charger (single port)
Level 2 charger (dual port)
Dual-protocol DCFC

Option 1 quantity
1
0
1

Option 2 quantity
0
1
2

Tables 3.7 and 3.8 break down the costs for these two DCFC installation options. The costs used
to determine the limits for Options 1 and 2 represent the maximum expected costs of installation
and equipment for each option, but specific site conditions may result in significant deviations
from estimated costs. Price ranges were determined using a combination of interviews with
industry experts (Alternative Energy Systems Consulting, Dec 2015). The dual-protocol DCFC is
configured with both a CHAdeMO and SAE Combo (CCS) connector; however, because only one
protocol can be used at a time, it effectively becomes a single-port unit. A Level 2 charger is

38

desirable because it significantly increases the functionality of the charging station with little added
cost and serves as a backup in case all DCFCs are in use. This option also allows the station to
serve local drivers.
Table 3.7 Costs for option 1
Costs for Option 1
Description
Site work (e.g., demolition, concrete, mounting, signs)
General electrical work (e.g., wire and conduit)
New 300kVA transformer
Extend utility service
Level 2 charger (single port)
Dual-protocol DCFC

Units
1
1
1
1
1
1

Typical cost
per unit
$10,000
$3,000
$32,500
$17,500
$7,500
$35,000

Total cost
$10,000
$3,000
$32,500
$17,500
$7,500
$35,000

Subtotal

$98,000

10% contingency

$10,550

Total

$108,550

Table 3.8 Costs for option 2
Costs for Option 2
Description
Site work (e.g., demolition, concrete, mounting, signs)
General electrical work (e.g., wire and conduit)
New 500kVA transformer
Extend utility service
Level 2 charger (dual port)
Dual-protocol DCFC

Units
1
1
1
1
1
2

Typical cost
per unit
$15,000
$3,000
$40,000
$17,500
$10,000
$35,000

Total cost
$15,000
$3,000
$40,000
$17,500
$10,000
$70,000

Subtotal

$155,500

10% contingency

$15,550

Total

$171,050

39

Based on the costs for each activity/item specified in these tables, more DCFC installation
configurations can be created depending on whether an additional Level 2 charger, an electrical
upgrade (new transformer), or extended utility service are required. Table 3.9 lists total costs for
such configurations.
Table 3.9 Costs of a DCFC under different configurations
Step

1
2
3
4
5
6

Dualprotocol
DCFC
Yes
Yes
Yes
Yes
Yes
Yes

Cost of a DCFC under different configurations
Level 2
Level 2
Extend
Electrical
charger
charger (dual
utility
upgrade
(single port)
port)
service
No
No
No
No
No
No
No
Yes
No
No
Yes
No
No
No
Yes
Yes
Yes
No
Yes
Yes
No
Yes
Yes
Yes

Total cost
$58,550
$76,050
$91,050
$108,550
$116,050
$171,050

3.3 Battery storage installation process
The introduction of new storage equipment solutions has led to the emergence of grid-connected
battery storage installation. Fig. 3.4 shows a flowchart (IDEF0 diagram) depicting the processes
involved in installation of a battery storage unit. Tables 3.10 and 3.11 summarize the five
predefined control categories and the four predefined mechanism categories for function modeling,
respectively.
Table 3.10 Control categories in battery system installation
Identifier
C1
C2
C3
C4

Control (constraint)
Assessment
Approvals
Regulations
Time

Description
Site visit and evaluation
Building permission and permission to connect to local grid
Standards and requirements
Delivery at customer site and installation schedule

40

Table 3.11 Mechanism categories in battery system installation
Identifier
M1
M2
M3
M4

Mechanism
(resource)
Space
Professionalism
Collaboration
Materials

Description
Environment, temperature, foundation, electric power
Licensed contractor
Communication with other parties
Construction of foundation/concrete plate and resources
C 3 (R E G U L A T IO N S )

C 1 (A S SE SM E N T )

C 2 (A P PR O V A L S)

S ELE C T
B A TT ER Y
TY P E A ND

C 4 (T IM E )

S IT E L O C A T IO N /
P R E P A R A T IO N

S IZ E
A PP R O V A L S
FOR
IN S T A L L A T IO N

IN ST A L L A T IO N
PR E PA R A T IO N

IN ST A L L A T IO N

T E ST IN G
M 1 (S PA C E )

P ER F OR M A NC E
V E R IFIE D

M 3 (M A T E R IA L S)

M 2 (P R O F E S S IO N A L IS M )

M 4 (C O L L A B O R A T IO N )

Figure 3.4 IDEF0 diagram of battery storage installation process

Appendix B lists different phases and actions in each phase of a battery storage project. The
following step-by-step process for installing a battery storage unit at any given site is as follows:
1. Location/site preparation requirements:
When planning the battery system space requirements, consider the following issues (Enersys,
2016), (Clean Energy Council, 2016):

41

(A) Space—Maintain proper spacing between cells/batteries to provide thermal management and
ensure proper fit of hardware connections. Proper accessibility to the installation area must be
provided.
(B) Environment—Must be a clean, cool, and dry place.
(C) Temperature—Installing the unit where ambient temperature is within operating range is
recommended, as higher temperatures reduce operating life and lower temperatures reduce
battery performance.
(D) Ventilation—Adequate ventilation must be provided.
(E) Codes—Building codes and fire codes may require a spill-containment system for battery
installations.
(F) Foundation—The foundation must support the weight of the battery as well as any auxiliary
equipment. Foundation documents and execution planning for a standard soil are usually
delivered in advance to the installation, and the specific thickness of the concrete plate must
be defined with respect to the properties of the installation area.
2. Electrical power connection
3. Communication interfaces
4. Grounding and lighting protection: A proper grounding connection compatible with local
standards must be provided at the installation site. Inspection for electrical code compliance must
be performed through a locally certified and approved electrician.
5. Installation approval: All necessary approvals, including building permission and permission to
connect to the local grid, should be obtained prior to installation.
6. Commissioning process: The commissioning process covers three main phases (Sandia National
Laboratories, 2016):

42

I Pre-installation measures
(A) Building and construction permission
(B) Permission for electrical connection
(C) Definition of contact people for IT systems integration, electrical installation, and facility
management
(D) Installation timeframe approval
(E) Construction of foundation, concrete plating, and electrical connection points
(F) Foundation specifications approval
(G) Delivery at customer site
II Installation measures
(A) Unload with a crane
(B) Place the energy unit at final position (on concrete plate)
(C) Maintain electrical ground connection
(D) Receive approval for ground connection
(E) Place the power unit
(F) Connect the battery to the grid
(G) Connect the communication devices
(H) Maintain fluid and electrical connections
(I) Conduct a safety test
III Power-up
(A) Conduct a system test
(B) Switch system on
(C) Charge to 100% charge level

43

(D) Discharge to 0% charge level
(E) Charge to 30% charge level
Project timeline: Smaller storage systems (in the 1 MW–5 MW range) have been commissioned
in less than 2 years from initial concept to commission (Akhil et al., 2015). Storage systems in
the 50kW–150kW, which is the optimal range for an FCS, may be installed in the field and
brought online within months after reaching the project site.
Applicable codes and standards: The increased interest in battery storage solutions has led
various code- and standard-making bodies to expand their regulations and align local municipal
building and electrical codes to the National Electric Code (Centorbi, 2017). Typically, storage
systems are governed by the National Electrical Safety Code. A sampling of relevant codes and
standards for a utility-based, advanced LA battery project is shown in Table 3.12:
Table 3.12 Applicable codes and standard bodies for battery projects
ANSI
IEEE
NEC
NEMA
NESCÂŽ
NFPA
OSHA
UL

American National Standards Institute
Institute of Electrical and Electronics Engineers
National Electrical Code
National Electrical Manufacturers Association
National Electrical Safety CodeÂŽ
National Fire Protection Association
Occupational Safety and Health Administration
Underwriters Laboratories

Project developers should be aware of all applicable national and local codes, local
interpretations of codes, and code overlaps or gray areas where codes conflict or do not exist.

3.4 Battery storage costs
Storage system costs involve two components, power and energy. The power cost component is
the cost of the power conditioning system and its auxiliaries that determine the kW or MW

44

capability of the system and can be described in $/kW, whereas the energy component is the cost
of the battery. For a given system, the total cost is the sum of these components. We focus on only
the energy component in this study. This total cost is specific to system size and is (mostly) not
linearly scalable.
Table 3.13 Cost comparison of various battery technologies
Battery Storage Technology

Power Cost ($/KW)

Energy Cost ($/KWh)

Lithium-ion (all)

$1,800–$4,100

$800–$2,500

Sodium-sulfur

$3,200–$4,000

$400–$900

Lead-acid

$2,000–$4,600

$500–$1,700

Vanadium-redox

$3,000–$3,300

$500–$1,500

Sodium-nickel-chloride

$2,900–$4,000

$700–$1,200

Zinc-bromine

$1,670–$2,015

$300–$1,600

Zinc-air

$1,440–$1,700

$300–$600

Iron-chromium

$1,200–$1,600

$200–$600

3.4.1

Various cost metrics

For battery storage, considering costs to install (in $/kW), present value of lifecycle costs (LCC;
in $/kW and $/kWh), and levelized cost of energy (in $/MWh) is also critical. The values of these
costs are taken from storage system cost details for distribution and transmission in the DOE/EPRI
Electricity Storage Handbook. The cost to install includes all equipment, delivery, installation, and
interconnection costs, but does not include land costs, permitting, and project planning costs. The
present value of LCC includes costs to install and all ongoing fixed and variable operating costs

45

over the useful life of the project. The levelized cost of energy includes LCC and rate of return
based on financing assumptions. This metric is often used to compare the cost to deliver energy
among a variety of technologies and regions (DOE-EPRI 2013 Energy Storage Handbook). Table
3.14 details storage system costs for transmission and distribution.

Table 3.14 Storage system cost details

Battery
storage
technology

Syste
m size
(MW)

Syste
m
storag
e (Hr)

Lithium-ion

1–10

1–6

Sodiumsulfur

1–100

6–7

Lead-acid

1–100

3–4

4–10

3.5–5

1–2

4–5

1–100

2–5

Zinc-air

1–3

6–6.5

Ironchromium

1–70

4–5

Vanadium
redox
Sodiumnickelchloride
Zincbromine

Installe
d cost
($/kW)

Installe
d cost
($/kWh
)

1,400–
6,000
3,100–
3,700
2,500–
5,800
3,300–
4,000

1,000–
2,100
500–
600
500–
2,500
800–
1,100

Present
value
of
lifecycl
e Costs
($/kW)
2,000–
13,000
5,500–
7,000
4,500–
11,000
6,000–
7,500

Present
value
of
lifecycl
e costs
($kWh)
2,200–
4,000
500–
1,000
500–
4,000
1,500–
2,000

Leveliz
ed cost
of
energy
($/MW
h)
700–
1,300
250–
300
270–
1,300
400–
600

2,900–
5,600

700–
1,200

5,000–
10,000

1,200–
2,500

350–
650

1,600–
3,000
2,000–
2,200
1,500–
1,800

300–
1,600
200–
300
300–
500

3,000–
6,000
3,500–
4,000
2,800–
3,500

500–
3,000
500–
1,000
1,000–
1,300

120–
850
180–
220
200–
280

Levelize
d cost of
capacity
($/kWyr)
250–
1,500
650–720
500–
1,250
680–800
550–
1,200
300–680
400–450
320–400

The following energy storage system costs are critical to understanding the economics of energy
storage. Appendix C provides a list of nomenclature and formulae for each cost category.
1. Total capital cost (TCC)—Also known as total plant cost, TCC evaluates all costs that should
be covered for the purchase, installation, and delivery of an EES unit, including costs of PCS,
energy storage-related costs, and balance-of-power (BOP) costs (Zakeri, 2015).

46

2. BOP cost—BOP costs include costs for project engineering, grid connection interfaces, and
integration facilities (e.g. transformers), construction management (including cost of land and
accessibility), and other services and assets required that are not included in the scope of PCS
and storage-related costs (Zakeri, 2015).
3. LCC—LCC encompasses fixed and variable operation and maintenance (O&M) expenses as
well as replacement, disposal and recycling costs, and TCC (Zakeri, 2015).
4. Levelized cost of energy (LCOE)—This represents the revenue for delivered energy required
to cover all fixed and variable LCCs and provides the target rate of return based on financing
assumptions and ownership types (Akhil et al., 2015).
3.4.2

Vendor costs

For a pilot battery project for Consumers Energy, Michigan State University surveyed various
vendors via questionnaire. The responses received from the vendors for their battery product
offering costs are shown in Table 3.15 (Thomas et al., 2016a, 2016b):
Table 3.15 Summary of battery costs provided by vendors
Vendors

Price Range ($/kWh)

ABB
NEC
S&C
Gildemeister
Doosan Gridtech
Greensmith

600–1,000
480–790
758–860
675–775
800–1,000
700–750

This cost includes only the purchase price of the battery system; that is, installation, site
development, and project management costs are considered separately depending on the size of
the system, site conditions, and requirements. Project estimates are more detailed and based on

47

site-specific conditions and use cases. Site-specific requirements such as shipping, labor,
engineering studies, interconnection, and permitting should be added to the cost of the battery
system to obtain total project cost.

3.5 Summary
The construction processes of FCSs and battery storage are similar. The construction cost of an
FCS typically lies in the $58,000–$171,000 range depending on whether the FCS requires an
additional Level 2 charger, electric upgrades, or extended utility service. Smaller battery storage
units in the 50kW to 150kW range may be appropriate for supporting an FCS, but battery storage
of this magnitude might not be cost-effective unless it is connected to a microgrid of FCSs.

The actual costs of a storage system depend on many factors, and the assumptions and means for
calculating some of the values are subjective and continue to be debated even among subject
experts. Costs of energy storage systems depend not only on the type of technology but also on the
planned operation and hours of storage required. Calculating the present LCC value allows for an
equal-value comparison of the benefits. Given that there are many performance dimensions for a
battery storage technology, a direct cost comparison is typically not appropriate. A more useful
approach would be to identify the applications that a utility needs to serve and then identify the
appropriate battery storage technology for that application. Then, cost for each candidate battery
technology can be estimated based on use over its lifetime, which varies by application.

Moreover, as battery storage costs depend on several parameters, identifying and establishing
parameters such as battery size, type, and hours of use is critical. In this study, DES is used to

48

calculate costs associated with battery storage units appropriate for supporting a network of FCSs
during peak hours.

49

Chapter 4
A FCS network with battery storage to meet energy demand: DES modeling

4.1 Introduction and objective
There often exists a gap between energy supplied by the electric grid and expected demand for an
FCS during peak hours (Negarestani, 2016). EV users may have to wait and charge for longer as
they receive less energy from the charging station even when the charging station is capable of
supplying energy up to its maximum rated value. Of great interest to charging station operators
and electric utilities is how FCSs with reduced energy supply use stored energy from a battery to
access electrical energy that helps bridge the gap. Thus, analyzing how a condensed network of
FCSs maintains required energy using supply from multiple battery storage units is of interest.

In this chapter, a model of FCSs with varying supply and demand gaps was qualitatively built
based on a network of 15 FCSs located in Southeast Michigan. The model evaluates the optimal
configuration of battery units required to meet the network energy gap by simulating network
structures and comparing the results. The model delivers insights into how battery characteristics
such as size, battery type, number of battery units, and exchange range radius address this gap.
The model aims to lower the cost of supplied energy for the entire network while fully supplying
energy demanded by all FCSs using the supplemental battery units.

4.2 Model description and assumptions
DES is the process of codifying the behavior of a complex system as an ordered sequence of welldefined events. Nance (1993) described DES as a mathematical and logical model of a physical

50

system that has changes at precise points in simulated time. In this study, Model #1 was
implemented as a DES (i.e., in Model #1, the number of battery units consecutively marks a change
of state in the system), whereas Model #2 was implemented as an optimization problem using a
Monte Carlo simulation. Because events in a DES are bootstrapped, the simulation designer must
decide when the simulation ends (e.g., when a statistical measure reaches a particular value;
Albrecht, 2010). The simulations of Model 1 in this study stop when the energy gap of the entire
system reaches zero. The models were implemented in Python 2.7.13, and Python-generated
functions are used to model the active components. A Monte Carlo package known as scikitmonaco was used to lognormally distribute the cost range inputs in Model #2. In contrast to a
normal distribution that can take both positive and negative values, a lognormal distribution is
commonly used for distribution of financial assets (e.g., prices), which cannot be negative (Zucchi,
2014). Figure 4.1 provides a conceptualization of the function of Model #2.
4.2.1

Assumptions

1. All FCSs are connected to the electric grid as part of the distribution network, which supplies
limited energy.
2. The demand for each FCS is considered constant during peak hours, which is equal to the power
rating (maximum capacity) of that FCS.
3. The gap in supply and demand exists only during peak hours (i.e., for 4 hours). During this 4hour period, this gap is addressed by battery units charging from the grid at a low level of power
at off-peak hours or when the battery is not in use. This assumption is based on the study by
ChargePoint (2016), that is, the peak hours of DCFCs are between 1 and 5 PM. These peaks arise
because drivers who started long trips early in the day start to deplete their batteries, people need

51

to charge rapidly while running errands around town, or because of those deciding to charge on
their way home from work.
4. The cost ($) of energy supply depends on the following:
(A) Network costs, that is, construction of a new overhead distribution line may be required so
energy from a battery can be supplied to other FCSs. A utility would not build this unless there
is a positive business case, but the relatively low level of EV market penetration means that
this is unlikely.
(B) Installation costs of the battery by battery type.
(C) Construction cost of the battery, including land cost, permitting, and project development cost.
5. A battery storage unit with surplus energy can provide energy to a nearby FCS if it is inside the
exchange range specified in the model. In this study, the exchange range is the radial distance
outward from the battery storage unit. In an energy exchange, the battery first provides a full supply
of energy to fulfill the energy gap of the FCS it is positioned at. Then, if any energy remains, it
supports other FCSs within the exchange range. During the exchange, if a battery unit can choose
between two other FCSs that are both in need of energy, it prefers the one closer to it. Figure 4.1
demonstrates the decision rules governing the exchange of energy in Models #1 and #2.
6. A microgrid is proposed within an established distribution system. Here, an FCS network is
considered a microgrid. Each FCS draws power from the distribution network, and batteries are
charged during off-peak hours to supply energy during peak hours. An FCS with excess capacity
can sell power to the utility at on-peak rates or receive a credit that other FCSs within the microgrid
can use. However, it might not make financial sense to construct a separate transmission system.
The test microgrid falls within the service territory of DTE (utility serving Southeast Michigan),
implying that the FCSs are already connected and can exchange energy. Without the utility already

52

connecting these FCSs, a microgrid would prove costly; therefore, keeping a microgrid within the
service area is recommended.

53

4.2.2

DES diagram

S TA R T

A S S IG N

A S SIG N E N E R G Y

SE L E C T

IN S T A L L A T IO N

L O C A T IO N T O
E AC H F C S

GA P VA LU E T O

B A TTE R Y

C OS T R A N GE

E A C H FC S

T YP E

D AT A

M O N TE C A R LO P AC K A GE
S E L E C T 1 0 ,0 0 0
IN S T A L L A T IO N C O S T
P O IN TS

n = 1 , 2 , 3 ............... 1 5
A S S IG N B A T T E R Y
S IZ E
(1 1 0 0 )kW W IT H
IN C R E M E N T O F 1 kW

A SS IG N S H A R IN G
R A D IU S
. - .
(0 0 0 1 0 0 ) U N IT S W ITH
.
IN C R E M E N T O F 0 0 1 U N IT

M O DE L #1
CA LCU LA TE
NUMB ER OF
B A TT E R Y T HA T
M E ET E NE R GY
GAP

C O M PU T E C O S T S

V IS U A L IS E R E SU L T S

G EN ER A TE 3D G R AP H
EN D

TO T A L C O S T V / S B A T T E R Y
S I Z E V /S S H A R I N G R A D I U S

D E T E C T O PT IM A L O P T IO N

EV A LU AT E
IN ST A L L A T IO N C O S T

L O W E ST T O T A L C O ST
B A TT E R Y S IZ E
N U M B E R O F B A T T E R IE S

EV AL UA TE
C O N S T R U C T IO N C O S T

S H A R IN G R A D IU S
EV AL UA TE NE TW O R K
COST

Figure 4.1 Conceptual diagram of model #2

54

FCS
A SS IG N

ST A R T

A T T R IB U T E S:
L O C A T IO N

ID E N T IFY F C S

A S S IG N B A T T E R Y W IT H

W IT H M A X IM U M

S IZ E A N D SH A R IN G

EN ER G Y GA P

R A D IU S T O F C S

E NE R GY G AP

S U P P L Y R E M A IN IN G
E N E R G Y IN B A T T E R Y

YES

G AP = 0

IS O T H E R F C S W IT H IN

YES

IS S IZ E > = G A P ?

S H A R IN G R A D IU S?

TO O TH ER F C S

NO
NO
D E T E R M IN E
EN D

IS R E M A IN IN G
E N E R G Y > = G A P?

YE S

R E A S S IG N

NE W G AP

GAP = 0 OF
O TH ER F C S

NO

D E T E R M IN E

R E A S SI G N

N EW G A P

Figure 4.2 Energy exchange decision rule within the microgrid in model #1

4.2.3

Study area

Each FCS has two attributes, its location and a fixed demand–supply energy gap. The coordinates
(i.e., the latitude and longitude values) are known for all 15 FCSs in Southeast Michigan. For the
demand–supply gap, it is assumed that every FCS has a constant demand equal to the maximum
rated power of that FCS. The supply range for each FCS is obtained from comments (online) by
EV owners using those FCSs (PlugShare, 2017). The energy gap is calculated by taking the

55

difference in demand and minimum supply for the FCSs. The following table summarizes the
characteristics of the FCS network in Southeast Michigan on which the model is based.
Table 4.1 Information on 15 FCSs used in simulation
Statio
n#

1

2

3

4

5

Station
Name &
City
Dunkin
Donuts –
Sterling
Heights
Dunkin
Donuts –
Ferndale
Dunkin
Donuts –
Dearborn
Heights
Dunkin
Donuts –
Woodhave
n
Nissan
Technical
Center –
Farmingto
n Hills

7

USA 2 Go
– Novi
Dunkin
Donuts –
Plymouth

8

AAA –
Canton

6

EV
network

1

eVgo
Network

1

eVgo
Network

Chademo &
J1772comb
o
Chademo &
J1772comb
o

1

eVgo
Network

1

eVgo
Network

1

ChargePoin
t Network

1

eVgo
Network

1

eVgo
Network

1

eVgo
Network

1

eVgo
Network

1

eVgo
Network

10

DD –
Belleville
Tim
Hortons –
Howell

11

USA 2 Go
– Howell

1

eVgo
Network

12

AAA –
Brighton

1

eVgo
Network

9

EV
connector
types

Outlet
s

Latitud
e

Longitud
e

Deman
d

Suppl
y

Ga
p

42.58

-83.03

44

24–35

20

42.45

-83.13

44

35

9

Chademo &
J1772comb
o

42.27

-83.27

44

37

7

Chademo &
J1772comb
o

42.14

-83.22

44

33

11

42.49

-83.42

50

27–41

23

42.49

-83.51

44

28–37

16

42.36

-83.43

44

30–38

14

42.32

-83.48

44

28–31

16

42.22

-83.48

44

31–36

13

42.62

-83.87

44

33–40

11

42.58

-83.88

44

25

19

42.54

-83.78

44

26–36

18

Chademo
Chademo &
J1772comb
o
Chademo &
J1772comb
o
Chademo &
J1772comb
o
Chademo &
J1772comb
o
Chademo &
J1772comb
o
Chademo &
J1772comb
o
Chademo &
J1772comb
o

56

Table 4.1 (cont’d)

14

NISSAN –
Ann Arbor
Meijer,
Tesla –
Ann Arbor

15

Shell –
Ann Arbor

13

1

Charge
Point
Network

Chademo

42.28

-83.80

50

26–41

24

8

Tesla

Tesla

42.23

-83.76

120

70–93

50

1

eVgo
Network

Chademo &
J1772combo

42.24

-83.73

44

34–
36.5

10

Figure 4.3 Map of all DCFCs in Michigan

57

Figure 4.4 Map of 15 FCSs used in simulation

4.2.4

Functioning of model #1

First, respective coordinates and energy gaps are assigned to all 15 FCSs. The model requests
battery size and exchange range as user inputs. After providing the inputs, the specified battery
units are introduced to each FCS to reduce the energy gap until the total energy gap of all charging
stations is reduced to zero. A battery that is assigned to the FCSs and closes the energy gap checks
whether other FCSs exist within the exchange range specified. To exchange energy, the battery
first supplies its energy to the FCS it is positioned at. If the battery is then left with surplus power,
it supplies the remaining energy to meet the energy gap of the FCS nearest to it within the exchange
range. The next battery is that positioned at the FCS with the second-highest energy gap, and so
on. This model then outputs the number of batteries required for a given battery size and exchange
range. Appendix D provides the code for this model, and Fig. 4.6 shows a screenshot of the Python
58

interface. For example, when battery units of size 30kW and exchange range of 0.2 units are input
into the system, the following depicts the functioning of the model as output with each incremental
battery unit until the energy gap is fully addressed:
Enter battery supply unit value: 30 kW
Enter exchange range: 0.2 units
1. At ID: 14, Gap = 50. New Gap = 20. Total batteries used: 1.
2. At ID: 13, Gap = 24. New Gap = 0. Exchange from ID: 13 to ID: 14, Energy units = 6 with
new Gap at Station 14 = 14. Total batteries used: 2.
3. At ID: 5, Gap = 23. New Gap = 0. Exchange from ID: 5 to ID: 6, Energy units = 7 with new
Gap at Station 6 = 9. Total Number of Battery Consumed: 3.
4. At ID: 1, Gap = 20. New Gap = 0. Exchange from ID: 1 to ID: 2, Energy units = 9 with new
Gap at Station 2 = 0. Total batteries used: 4
5. At ID: 11, Gap = 19. New Gap = 0. Exchange from ID: 11 to ID: 10, Energy units = 11 with
new Gap at Station 10 = 0. Total batteries used: 5
6. At ID: 12, Gap = 18. New Gap = 0. Total batteries used: 6
7. At ID: 8, Gap = 16. New Gap = 0. Exchange from ID: 8 to ID: 7, Energy units = 14 with new
Gap at Station 7 = 0. Total Number batteries used: 7
8. At ID: 14, Gap = 14. New Gap = 0. Exchange from ID: 14 to ID: 15, Energy units = 10 with
new Gap at Station 15 = 0. Total batteries used: 8
9. At ID: 9, Gap = 13. New Gap = 0. Total batteries used: 9
10. At ID: 4, Gap = 11. New Gap = 0. Exchange from ID: 4 to ID: 3, Energy units = 7 with new
Gap at Station 3 = 0. Total batteries used: 10
11. At ID: 6, Gap = 9. New Gap = 0. Total batteries used: 11

59

Total surplus energy remaining in batteries = 69

Figure 4.5 Graph of total gap vs. number of batteries for given inputs

Hence, for a battery size of 30kW with a share radius of 0.2 units, 11 batteries are required to
reduce the system gap to zero.

60

Figure 4.6 Screenshot of python interface showing the code for model #1

4.2.5

Functioning of model #2

This model is a revised version of the previous model. It additionally considers installation and
construction costs of the battery systems (Table 4.3) as well as the cost of setting up a new
distribution line (network cost) to enable the exchange of energy from batteries. Table 4.2 shows
the inputs used in this model, which was implemented in Python using the scikit-monaco library
for Monte Carlo integrations. The installation cost range of various battery types is shown in Table
3.14, and construction and network costs are fixed for all battery types. The model asks the user
to input the battery type. Based on the battery type selected, the installation cost range of that
battery is chosen and converted into a lognormal distribution. Next, the model calculates total costs
61

and selects 10,000 total cost values from the lognormal distribution. The model varies battery size
from 1kW to 100kW in increments of 1kW and share radius from 0.00 to 1 in increments of 0.01
units. This generates 100x100x10,000 input points. For all input points, the model calculates the
number of batteries required, battery size, and exchange range that result in the lowest energy
supply cost. The model is run twice for each battery type, first considering network costs and
second without network costs. In the first case (i.e., considering network costs), new distribution
lines are constructed within the existing microgrid. In the second case (i.e., no network costs), all
batteries and FCSs are connected to the microgrid within the existing distribution system.
Appendix D provides the code for this model. Figures 4.7 and 4.8 show the input interface and the
running model, respectively.

Figure 4.7 Screenshot of input interface for model #2

62

Figure 4.8 Screenshot of model #2 running with computing status

Table 4.2 Inputs used in model
Input Category
Battery
FCS
Network

Inputs
Battery type cost
Battery size
Location
Demand gap
Exchange range
New distribution line cost

63

Input values
Table 4.3
(1–100) kW
(x, y) coordinates
constant (kW)
(0.00–1) unit distance
$ 8,325,000 per unit distance

Table 4.3 Battery costs used in model
Battery type

Installation cost ($/kWh) (range)

Construction cost ($) (fixed)

Lithium-ion
Lead-acid
Vanadium redox
Sodium-sulfur
Sodium-nickel-chloride
Zinc-bromine
Zinc-air
Iron-chromium

1,000–2,100
500–2,500
800–1,100
500–600
700–1,200
300–1,600
200–300
300–500

20,000 per installation
20,000 per installation
20,000 per installation
20,000 per installation
20,000 per installation
20,000 per installation
20,000 per installation
20,000 per installation

Table 4.4 provides the breakdown of construction-related costs for site preparation, project
management, and general conditions for building of a 20'x20' concrete pad for battery installation.
This table does not include costs related to the battery storage system itself.

Table 4.4 Construction cost for battery installation
Cost type
Building permit
Survey
Professional surveyor
Engineering testing
Soil test
Sitework
Clearing and grubbing (for an approx. area of 400 sqft)
Excavation and compaction
Grading
Site layout
Concrete pad (20' x 20')
Formwork
Reinforcement
Labor (1 foreman, 1 finisher, 1 carpenter)
Concrete
Rental equipment (compactor, spreader, finisher)
Curing
Project management costs
Project engineer (for 5 days)
64

Quantity

Unit

Cost ($)
2,500

1

lump sum

2,000
1,500

400
400
400

sqft
sqft
sqft

7

cy

1

lump sum

250
500
100
400
200
300
1,800
840
800
0
1,800

Table 4.4 (cont’d)
Temp. fencing
Temp. power supply
Temp. water supply
Temp. toilets
Dumpster
Safety and first aid
Safety signs
Fire protection
First aid supplies

1,000
1,500
500
1,000
400
200
1,000
500
Total cost ($) 19,090

The total cost of energy supply considered in the model is as follows:
1. Installation cost: The installation costs were taken from Table 3.14 and are in kW/h. The
battery system is assumed to run for a 4-hour duration.
The total cost of installation = (Installation cost x battery size x 4 x number of units)

(4)

2. Construction cost: A cost of $20,000 for the installation of each battery unit is assumed
irrespective of the battery size. Although the installation cost varies based on the size of the
battery, battery size is below 100kW; thus, installation costs are consistent. This estimated
value is detailed in Table 4.4.
Total construction cost = ($20,000 x number of units)

(5)

3. Network cost: According to McCarthy (2011), building a new overhead distribution line costs
an average of $166,500 per mile. In the model, 1 mile is equivalent to 0.02 units of distance,
bringing network costs to $8,325,000 per unit distance if no local grid/distribution exists for
the network and it is not located in an urban area.
Network cost = ($8,325,000 x exchange range)

Total cost of energy supply = Installation cost + Construction cost + Network cost
65

(6)

(7)

4.3 Results
Table 4.5 shows the results for the model considering network costs, and Table 4.6 indicates the
results without considering network costs. Table 4.7 shows a comparison table indicating the
difference in results between the two cases.

Table 4.5 Model results for each battery type considering network costs
Total cost
Battery type
($)
Lithium-ion
5,295,019
Lead-acid
4,569,688
Vanadium redox
3,740,124
Sodium-sulfur
2,504,760
Sodium-nickel-chloride
3,655,281
Zinc-bromine
3,114,688
Zinc-air
1,380,862
Iron-chromium
1,880,297

Battery size
(kW)
7
10
10
12
11
13
20
14

Exchange range
(units)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

Number of
batteries
45
33
33
29
31
27
20
26

Table 4.6 Model results for each battery type without network costs
Battery type

Total cost
($)
Lithium-ion
4,218,274
Lead-acid
3,548,833
Vanadium redox
2,889,329
Sodium-sulfur
1,786,008
Sodium-nickel-chloride 2,784,694
Zinc-bromine
2,323,296
Zinc-air
877,810
Iron-chromium
1,295,707

Battery size
(kW)
22
29
29
29
29
29
53
29

66

Exchange
range (units)
0.81
0.67
0.36
0.36
0.73
0.95
0.98
0.5

Number of
batteries
13
10
10
10
10
10
6
10

Table 4.7 Difference in results for each battery type with and without network costs
Battery type
Lithium-ion
Lead-acid
Vanadium redox
Sodium sulfur
Sodium-nickel-chloride
Zinc-bromine
Zinc-air
Iron-chromium

Total cost ($)
Battery size (kW) Number of batteries
Diff.
% Diff. Diff.
% Diff.
Diff.
% Diff.
-1,076,745 -20.34
15
0.68
-32
-0.71
-1,020,855 -22.34
19
0.66
-23
-0.70
-850,795 -22.75
19
0.66
-23
-0.70
-718,752 -28.70
17
0.59
-19
-0.66
-870,587 -23.82
18
0.62
-21
-0.68
-791,392 -25.41
16
0.55
-17
-0.63
-503,052 -36.43
33
0.62
-14
-0.70
-584,590 -31.09
15
0.52
-16
-0.62

The following total cost vs. battery size vs. exchange range graphs are obtained for each battery
type. Figure 4.9 shows this comparison considering network costs, and Figure 4.10 does so without
considering network costs.

Figure 4.9 3D graphs for battery types considering network costs

67

Figure 4.9 (cont’d)

68

Figure 4.10 3D graphs for battery types without considering network costs
69

Figure 4.10 (cont’d)

1. Considering network costs: Li-ion batteries have the highest cost, whereas zinc-air batteries
have the lowest cost. This is because li-ion batteries are the most expensive to install and zincair batteries are the least expensive. For all battery types, the exchange range for the lowest
total cost is 0.00 units, indicating that no exchange of battery energy occurs. This is because
the construction cost of the utility network is much higher than that of battery storage. In this
case, total cost is dependent only on construction and installation costs. The battery size varies
from 7–20 kW: Li-ion is the smallest (7 kW) and zinc-air is the largest (20 kW). Similarly, the
number of batteries used vary from 20–45: the most being li-ion (45 batteries) and the least
zinc-air (20 batteries). This indicates that to operate effectively, each of the 15 FCSs requires
at least one battery. Total construction cost is dependent on the number of batteries, and total
installation cost is dependent on battery size, battery type, and number of batteries. Therefore,
to achieve the lowest cost required to meet the energy gap of all charging stations using highcost batteries such as li-ion, smaller batteries are used in higher quantities. For low-cost

70

batteries (e.g., zinc-air batteries), larger batteries are used in lower quantities to achieve the
same results.

2. Without considering network costs: When the exchange of energy occurs without network
costs, the highest total costs are for li-ion batteries and the lowest total costs are for zinc-air
batteries, as in the previous case. For all battery types, the observed exchange range is less than
0.1 units (i.e., 5 miles). This indicates that to achieve less total costs, energy exchange is viable
only within a 5-mile radius. Most batteries in this model choose a 29 Kw battery, which is
smaller than expected given that the exchange of energy takes place without network costs.
However, zinc-air has a large battery (53 Kw), a high exchange range (0.98 units), and a low
number of batteries (6). This indicates that as the installation costs decrease for a specific
battery type, its battery size increases, the exchange of energy increases, and fewer batteries
are required to meet the energy gap at the lowest total cost. The number of batteries used
remains consistent at 10 batteries except for li-ion (13) and zinc-air (6). This indicates that
among the 15 FCSs, at least two-thirds would require a battery.

3. Comparison table: The pattern of each battery type remains consistent whether network costs
are considered.

71

4.4 Summary
This chapter describes the study area, functioning, assumptions, and results of a DES model.
Battery units are introduced to address the supply and demand energy gap of a network of FCSs
in Southeast Michigan with the goal of achieving a zero gap in stored energy. Here, FCSs within
a battery’s exchange range can receive that battery’s remaining energy; in this manner, the energy
gap of the entire FCS network can be met by fewer batteries and better battery utilization. The gap
in energy and the locations of the FCSs are known, and the model identifies the battery size and
exchange range that results in lowest total cost for each battery type.

When the model is run for each battery type considering network costs, no exchange of energy
from the battery takes place for any battery type. For smaller battery sizes, more than one battery
is required for each FCS to meet the network energy gap. When the model is run without
considering network costs, exchange of energy takes place for all battery types, and less (and
larger) batteries are required. These results indicate that a condensed network of FCSs that is
energy deficient from the grid can benefit from battery units that supply stored energy during peak
hours and recharged during off-peak hours. Such a model can be applied to any network to
determine the battery size, number of units, and exchange range that results in the lowest-cost
investment to achieve an energy gap of zero. Based on the total cost, the best battery type for the
given network can be chosen. These findings may be useful for FCS operators, who can contract
with players in the battery space and identify the size and number of batteries most suitable for
their network at the lowest cost.

72

Chapter 5
Conclusion

5.1 Findings
This study found that battery storage can be used in coordination with FCSs to support the energy
demands of a FCS during peak hours. Batteries act as buffer storage for energy: excess capacity is
sold during on-peak hours and charging occurs during non-peak hours. Li-ion batteries (followed
by LA and VRFB) are chiefly recommended for these projects as they are the most appropriate for
charging-station applications. These batteries show the best safety, cost, and technical performance
for small-sized power distribution applications and are relatively mature, scalable, and have
existing operational and safety solutions. This recommendation was made based on the literature
review and comparative analysis of various battery technologies but does not consider the results
from Chapter 4.

The construction processes of FCSs and of battery storage are similar. The construction cost of a
FCS typically varies from $58,000–$171,000 depending on whether the FCS requires an additional
Level 2 charger, an electric upgrade, or extended utility service. Smaller battery storage (i.e., 50kW
to 150Kw) may be appropriate for supporting an FCS, but battery storage of that magnitude may
not be cost-effective unless connected to an FCS microgrid. The costs of energy storage depend
on many factors such as the type of technology, battery size, hours of operation, and vendors.
Identifying the application and battery storage parameters to establish costs is critical. Here, as a
case study, a DES model is used to calculate the cost and characteristics of battery storage for a
FCS network in Southeast Michigan.

73

The DES model results indicate that less exchange of energy from battery units occurs for the FCS
network even when no network costs exist. At least two-thirds of the FCSs require a battery,
indicating that every FCS may need a battery to support itself. When network costs are considered,
each of the 15 FCSs requires at least two batteries to meet the energy demand at lowest total cost,
and no exchange of energy takes place. Li-ion batteries exhibit the highest cost, whereas zinc-air
batteries cost the least. Owing to the high cost of setting up a new distribution line, a highly
condensed discrete microgrids of FCSs would benefit more from exchange of energy between
battery units to neighboring FCSs.

5.2 Contribution
This study provides information on EV charging, particularly fast charging, and the role of battery
technology to support its power supply. From the literature review, a general understanding of
types of EVs, charging types, and charging standards is obtained that is useful in the subsequent
chapters of this study. Through a comparative analysis of performance attributes of present battery
types, the most-suitable potential battery technologies to be used in coordination with a FCS are
recommended. The following chapter reviews the entire FCS and battery storage system
installation process. It provides insights into the responsibilities, considerations, measures, and
standards owners and contractors must adhere to for successful installations of such systems. Cost
values for various configurations of fast chargers are estimated. Then, battery system costs are
provided in addition to the relation to battery size and type most useful to stakeholders. In the final
chapter, an FCS model is created and the simulation study helps identify the battery size and
exchange range that meets the required energy supply and minimum cost of supplied energy for

74

the entire system. The simulation can be extended to any condensed network of FCSs to evaluate
battery storage characteristics most fit for the network that address the gap in energy demanded.

5.3 Limitations
The study limitations include data constraints, scope, and assumptions. In this study, cost values
for charging stations and batteries used were based on literature sources and information provided
by vendors. These values may not exactly match prevailing industry standards, but they offer
possible pre-construction phase estimates. Once the scope and requirements of such projects are
defined, more precise cost values over different installation phases can be easily obtained from
charging station network operators/suppliers as well as battery manufacturers/vendors. This study
also does not consider technical aspects of using batteries along with FCSs. The simulation model
is based on many assumptions. It would be more useful to have realistic values of energy supply
and demand as well as the costs of exchanging energy through batteries for a FCS network.

5.4 Future work
Future work can conduct a detailed cost comparison of FCSs between network operators or
suppliers. A more feasible approach would be to conduct a site visit of a battery powered FCS
installation and note the associated costs. The simulation model should be applied to a condensed
network of fast chargers, where energy exchange from battery storage may be more feasible and
economical. An LCC analysis can also be performed for battery and FCS to evaluate the
operational costs.

75

APPENDICES

76

Appendix A. Construction process of a charging station

The following information provides a general overview of the installation process, and is broken
down into three phases:

Phase 1: Pre-work – contractor (Checklist)
Site information
Address: An address must be available in order to obtain a permit in most areas. If an address does
not exist for the parking area, the building address for the supporting parking site may be used in
many areas. In some cases where a dedicated meter is installed, a new address may need to be
applied for. The local permitting entity should be contacted for questions regarding addressing.
Does Customer have ownership of the site in which charging station(s) will be installed? Yes/No
If NO - Does the customer have necessary approval to install charging station(s) at site? Yes/No
If YES - The customer should have authorization form available upon site visit and/or be
willing to sign forms claiming permission to install charging station(s) at the site.
If NO - The customer will need to obtain approval from site owner.
Intended use
In order to ensure proper technology selection and charging station placement, it is important to
understand the intended use of the charging station(s). The intended use should be one or more of
the following:
Personal

Fleet

Employee

Customer

Visitor

Customer decisions
The customer will make a number of decisions regarding the installation. All decisions should be
reviewed to ensure requirements will be met and to avoid potential problems. Remaining decisions
should be finalized following the initial on-site portion of this process.
Charging Station Make _________________________
Model __________________________________________
From this information, the contractor can determine important information regarding the charging
station including the following:
77

Mounting Type: Bollard

Wall-Mount

Pole-Mount

Ceiling-Mount

Vehicle charging
Number of Vehicle Charging Connectors per Charging Station ______________
Communications Requirements: Ethernet Cellular
Physical

Dimensions:

Height___________

Wi-Fi

Other____________

Width____________

Depth_____________

Base Dimensions (for bollard units) ___________ Cord Length______________
Number of charging stations to be installed: _____________ It is important to understand whether
this number refers to number of stations or the number of cord sets (which references the number
of vehicles that can be served simultaneously).
Have specific parking spaces been selected? Yes

No

Yes

No

Has a power source been selected?

If Yes – Does the customer have ownership of the power source? Yes

No

If Yes - The customer must provide proof of approval and/ or be willing to sign documentation
claiming necessary approval.
If No - Does the customer have approval to use the power source? Yes

No

Approval must be gained prior to installation.
If No - The contractor will need to aid in this decision during the on-site portion of this process.

Phase 2: Pre-work – customer
After gathering initial information from the customer, it is important to suggest actions the
customer can take in order to save time during the installation process.
Contact utility
The customer should contact their local utility to inform them vehicle charging infrastructure will
be installed at the site. The customer should ask their utility the following questions: Are there any
incentives or different rate structures that may save the customer cost in installation or ongoing
electricity cost? What is the size of the electrical service to the site? The utility may be able to
provide knowledge as to the likelihood of needing a service upgrade based on the existing service
and the intended number of charging stations. If there has been a determined need for a service
upgrade or a new meter, an appointment should be made with a utility planner to visit the site.
When possible, this should be coordinated with the contractor.

78

Contact local permit office
Different jurisdictions may have slightly different requirements or processes regarding the
permitting, installation and inspection of charging stations. The contractor should contact the
permitting office with jurisdiction over the installation site to identify specific requirements.
Requirements of interest are listed below.
Concealment - While uncommon, certain municipalities may require charging stations are
concealed with a hedge, fence or other object.
Engineering calculations - Municipalities may require load calculations to be performed and/or
stamped by a licensed engineer. This can vary based on the location and number of charging
stations to be installed. If engineering calculations are required, the contractor should coordinate
the assessment time with the visit of a utility planner (if deemed necessary), the initial contractor
visit and the customer’s schedule. If these cannot be coordinated, each visit should be encouraged
to happen as quickly as possible and all information should be reported to the contractor.
Phase 3: On-site evaluation
Once the necessary information is gathered and appointments are coordinated, the contractor will
visit the site. The first site visit will answer any additional questions and resolve any decisions yet
to be made. The charging station selected will influence the site selection and vice versa. If the
customer has selected both the charging station and the site in advance, it will be important to
check the National Electrical Code is adhered to and potential problems are avoided.
Whether a charging station has already been selected or still needs to be selected, contractors
should ensure the charging station meets the following guidelines:

Surveying fast charging stations
Contractors are encouraged to use the following checklists for surveying charging station
locations. Select appropriate parking spaces based on the following criteria:
•

Visibility: Locations more visible to drivers and pedestrians, are less likely to be vandalized.

•

Proximity to building entrance: Particularly important in locations where vehicle charging is
viewed as an incentive, such as retail locations and places of work.

•

Proximity to power source: Selecting spaces close to an existing transformer or panel with
sufficient electrical capacity will save cost.
79

•

Avoidance of existing infrastructure and landscaping: Installing charging stations close to
existing infrastructure or trees can cause damage which may result in higher costs, potential
hazards and other undesirable outcomes.

•

Length of parking spaces: If there is a difference in length of parking spaces in a parking deck,
longer parking spaces will allow for greater room to fit a charging station while maintaining
usability and limiting the risk of vehicle impact. It is important the installation of a charging
station does not shorten parking spaces to below minimum local zoning requirements.

•

Width of parking spaces: Wider parking spaces decrease the risk of a cord set being damaged
if it lies to the side of PEV, connected or otherwise. Additionally, wider spaces provided space
for proper operation of the charging station and plugging the PEV in should the charge port be
located in the side of the vehicle.

•

Lighting: A well-lit parking space may reduce the risk of tripping and damage to the charging
station from vehicle impact or vandalism. Additionally, it may aid in the operation of the
charging station, including plugging the vehicle in.

Survey the charging station at the particular parking space(s)
•

Consider available space on floors, walls and ceiling.

•

If a charging station mounting type has been selected, eliminate types of location that do not
match (i.e.: ceiling-mount units may not work on walls). Ensure installation does not conflict
with vehicle’s ability to park within the space and to adequately use the charging station and
plug in the vehicle.

•

If a charging station has been selected or a particular model is desired note the number of cord
sets per charging station. The charging station should be placed to provide direct access to each
parking space without a cord being draped across another space and without blocking walking
paths.

Ensure remaining locations best meet guidelines for a parking lot as follows:
•

Lighting

Requirement: Lighting in parking lots is typically governed by local zoning codes. Review local
codes to ensure compliance.
Recommendation: Ensure lighting is functional and discuss the addition of a separate lighting
circuit if lighting levels are determined to be insufficient. Lighting levels are recommended to be
two foot candles or higher.
80

•

Connector height

Requirement: Connector will be mounted at a height between 24˝ and 48˝ from the ground (NEC
625.29).
Recommendation: Connector should be mounted at a height between 36˝ and 48˝ from the ground.
•

Enclosure height

Requirement: None
Recommendation: For wall/pole-mount stations, the enclosure should be installed at a height above
36˝. Greater heights are typically recommended, provided the connector can be mounted below
48˝.
•

Space around enclosure

Requirements: Sufficient space will exist around electrical equipment for safe operation and
maintenance (NEC 110.26). A space 30˝ wide or the width of the charging station, whichever is
greater, should be maintained to a depth of 3´ from the front of the enclosure without physical
obstruction, at a height of 6´ 6˝.
•

Tripping hazard mitigation

Requirement: None
Recommendation: Charging stations should be placed as to minimize the intersection of cords with
typical walking paths. Stations mounted at greater heights and equipped with cord management
technologies may further reduce this risk.
•

Physical damage prevention

Requirement: Equipment operating above 50 volts will be protected against accidental physical
damage (NEC 110.27).
Recommendation: When possible, placement of the charging station out of the line of vehicle
travel is advised. Protective bollards can offer significant protection where there is sufficient space.
Wheel stops may be beneficial in areas where bollards are not feasible.

81

Appendix B. Phases and actions for a battery storage project

Actions in different phases of a battery storage project:

1. Planning and analysis phase
This phase includes four areas of investigation:
•

Battery system analysis - A detailed analysis of each battery technology based on
considerations of feasibility, cost, power capacity, environmental and safety concerns should
be carried out. Determining use cases is the next step in the process and identifying the
battery storage technology most appropriate for that application.

•

Circuit analysis - Circuits that would benefit from battery storage systems should be
identified, located, and tested.

•

Financial analysis - Costs of battery scale (dollars per kW/kWh), converting existing
transformers to battery storage, life cycle costs, site development and construction, and
potential return on investment, all these costs should be analyzed.

•

Vendor analysis – Identification of battery manufacturers, integrators and suppliers to have
an idea of the product offerings, typical cost, system features etc.

2. Contracting phase
The contracting phase consists of four general actions, creating a short list of vendors for battery
technologies, application, and systems; determining the type of contract; developing a project
solicitation; and reviewing proposals and awarding the contract.
3. Construction and testing phase
Once the previous steps are completed, including the circuit analysis and selection of contractors,
the project would commence with the procurement of financing, site analysis and engineering,
and obtaining the necessary building permits. Significant interaction with local communities
would include public information dissemination, permit application including assessments of
environmental impacts, noise, and land use compatibility; public hearings; and so on before site
preparation and construction would begin. Pre-operation testing would follow installation of the
battery system.

82

Appendix C. Cost calculations for battery storage

Calculations for cost of battery storage

Nomenclature
CBOP Cost of balance of plant ($/kW)
Ccap

Total capital costs per unit of power rating ($/kW)

Ccap;a Annualized value of total capital costs($/kW-yr)
CDR

Disposal and recycling costs ($/kW)

CDR,a Annualized disposal and recycling costs($/kW‐yr)
CFOM,a Fixed operational and maintenance costs($/kW‐yr)
CLCC,a Annualized life cycle costs($/kW‐yr)
CO&M,a Annualized operational and maintenance costs($/kW‐yr)
CPCS Cost of power conversion system ($/kW)
CR

Replacement costs ($/kWh)

CR,a Annualized replacement costs($/kW‐yr)
Cstor Cost of storage section (€/kWh)
CVOM Variable operational and maintenance costs (€/kWh)
Ein
Eout

Input energy in one cycle (kWh)
Output energy in one cycle (kWh)

h

Discharge time(hr)

i

Interest rate (_)

n

Number of discharge cycles per year

r

Number of replacements

t

Replacement period(yr)

T

Lifetime (yr)

Ρsys Overall efficiency of storage system(%) =

𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜
𝐸𝐸𝑖𝑖𝑖𝑖

83

(kWh/kWh)

(8)

Total capital cost (TCC) calculation
TCC can be calculated per unit of output power rating, presented as (Ccap) in the following
equation. While CPCS, CBOP, and Cstor represent unitary costs of PCS, BOP, and storage
compartment ($/kWh), respectively, ‘h’ is the charging/discharging time. (Behnam Zakeri,
Electrical energy storage systems: A comparative life cycle cost analysis, 2015)
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐶𝐶𝑃𝑃𝑃𝑃𝑃𝑃 + 𝐶𝐶𝐵𝐵𝐵𝐵𝐵𝐵 + 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ×ℎ($/kW)

(9)

Ccap can be interchangeably presented per unit of power rating or storage capacity ($/kWh). Cost
per kWh per cycle offers a better indicator for the cost evaluation of EES systems, as it also
accounts for the lifecycle numbers of EES (Chen H, 2009).
Life cycle cost (LCC) calculation
LCC is an important indicator to evaluate and compare different EES systems. LCC can be
presented in levelized annual costs ($/kW yr), which is the yearly payment that the operator
should maintain for all services of EES, including repayment of the loan and upfront of the
capital costs. LCC calculations can be performed, first, by annualizing TCC (Ccap), presented by
(Ccap,a) in Eq. (3). Based on the present value of money the capital recovery factor (CRF) is
calculated by applying Eq. (4), subject to the interest rate (i) during the lifetime (T). (Behnam
Zakeri, Electrical energy storage systems: A comparative life cycle cost analysis, 2015)
𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐,𝑎𝑎 = 𝑇𝑇𝑇𝑇𝑇𝑇 ×𝐶𝐶𝐶𝐶𝐶𝐶

($/kW – yr)

(10)

𝑖𝑖(1+𝑖𝑖)𝑇𝑇

𝐶𝐶𝐶𝐶𝐶𝐶 = (1+𝑖𝑖)𝑇𝑇 −1

(11)

Total annual O&M costs (CO&M,a) can be expressed by adding annualized costs of fixed O&M
(CFOM,a), and variable O&M (CVOM) multiplied by yearly operating hours, as presented in Eq.
(5).
𝐶𝐶𝑂𝑂&𝑀𝑀,𝑎𝑎 = 𝐶𝐶𝐹𝐹𝐹𝐹𝐹𝐹,𝑎𝑎 + 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉 ×𝑛𝑛 ×ℎ ($/kW-yr)

(12)

To accommodate the replacement costs for replaceable EES systems, e.g. batteries, the future
cost of replacement (CR) in $/kWh and replacement period (t) in years should be known.
Annualized replacement costs (CR,a) can be calculated by using Eq. (6), given the number of
replacements (r) during the application lifetime.
𝐶𝐶𝑅𝑅,𝑎𝑎 = 𝐶𝐶𝐶𝐶𝐶𝐶 × ∑𝑟𝑟𝑘𝑘=1(1 + 𝑖𝑖)−𝑘𝑘𝑘𝑘 ×

𝐶𝐶𝑅𝑅 ×ℎ
𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠

($/kW-yr)

84

(13)

Disposal and recycling costs (CDR) are other cost items that are usually neglected in the LCC
analysis of EES in the literature. Annualized disposal and recycling costs (CDR,a) can be
calculated by applying interest rate(i) and lifetime of the plant(T), as explained in Eq. (7).
𝐶𝐶𝐷𝐷𝐷𝐷,𝑎𝑎 = 𝐶𝐶𝐷𝐷𝐷𝐷 ×

𝑖𝑖

(1+𝑖𝑖)𝑇𝑇 −1

($/kW-yr)

(14)

The annualized LCC costs (ALCC) of EES systems, presented by CLCC,a in Eq. (8), is determined
by stacking the previously discussed cost items.
𝐶𝐶𝐿𝐿𝐿𝐿𝐿𝐿,𝑎𝑎 = 𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐,𝑎𝑎 + 𝐶𝐶𝑂𝑂&𝑀𝑀,𝑎𝑎 + 𝐶𝐶𝑅𝑅,𝑎𝑎 + 𝐶𝐶𝐷𝐷𝐷𝐷,𝑎𝑎

($/kW-yr)

(15)

Levelized cost of energy (LCOE) calculation
The levelized cost of electricity (LCOE) delivered by EES systems can be then calculated by
applying Eq. (9), knowing the annual operating hours of the system in question. (Zakeri, 2015)
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 =

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴

𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

=

𝐶𝐶𝐿𝐿𝐿𝐿𝐿𝐿,𝑎𝑎
𝑛𝑛×ℎ

($/kWh)

(16)

Levelized cost of storage (LCOS) calculation
If the cost of charging electricity would be deducted from the LCOE delivered by EES, the net
levelized cost of storage (LCOS) itself can be realized (Eq. (10)). (Zakeri, 2015)
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = 𝐿𝐿𝐶𝐶𝑂𝑂𝑂𝑂 −

𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑜𝑜𝑜𝑜 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸

($/kWh)

85

(17)

Appendix D. DES modeling codes

Code for model #1
from matplotlib import pyplot as plt
import operator
nStations=15
coords = {
1:(42.58160019,
-83.03096771),
2:(42.45776749,
-83.13323975),
3:(42.27840424,
-83.2700882),
4:(42.14104462,
-83.22714233),
5:(42.4941234, -83.4256796),
6:(42.49123764,
-83.51441956),
7:(42.3601265, -83.43258667),
8:(42.32044601,
-83.48866272),
9:(42.22281265,
-83.48566437),
10:(42.628,
-83.874),
11:(42.58,
-83.88),
12:(42.54561996,-83.78999329),
13:(42.2843526,
-83.8084963),
14:(42.2397874, -83.7668615),
15:(42.24443817,-83.7388382)
}
delta = {
1:20,
2:9,
3:7,
4:11,
5:23,
6:16,
7:14,
8:16,
9:13,
10:11,
11:19,
12:18,
13:24,
14:50,
15:10
}
supply = input("Enter battery supply unit value: ")
86

threshold = input("Enter stopping threshold: ")
radius = input("Enter exchange range: ")
count=1
maxDelta=0
deltaLevels = []
wastage=0
while(1):
sorted_delta = sorted(delta.items(),
key=operator.itemgetter(1), reverse=True)
deltaLevels.append(sum(delta.values()))
unit=sorted_delta[0]
stationID = unit[0]
print "ID: " + str(stationID) + ", Gap = " +
str(delta[stationID])
demand = delta[stationID]
if(demand>threshold):
print "Battery Consumed : " + str(count)
extraSupply=0
if(supply>demand):
delta[stationID] = 0
extraSupply = supply-demand
else:
delta[stationID] = demand-supply
print "ID: " + str(stationID) + ", New Gap = " +
str(delta[stationID])
if(extraSupply>0):
locA = coords[stationID];
distFromLocA={}
for n,p in coords.iteritems():
locB = p;
dist = pow(pow((locA[0]locB[0]),2)+pow((locA[1]-locB[1]),2),0.5)
distFromLocA[n]=dist
sorted_dist = sorted(distFromLocA.items(),
key=operator.itemgetter(1))

87

for n,dist in sorted_dist:
if n!=stationID and delta[n]>0 and
extraSupply>0 and dist<=radius :
demand = delta[n]
if(extraSupply>demand):
delta[n] = 0
extraSupply = extraSupply - demand
print "Exchange from " +
str(stationID) + " to " + str(n) + " amount = " + str(demand) +
" still remaining: " + str(extraSupply)
else:
delta[n]= demand-extraSupply
print "Exchange from " +
str(stationID) + " to " + str(n) + " all amount = " +
str(extraSupply) + " with updated Gap at Station " + str(n) + "
= " + str(delta[n])
extraSupply=0
if(extraSupply>0):
wastage=wastage+extraSupply
count=count+1
else:
break
print "Total Surplus Energy Remaining in Batteries = " +
str(wastage)
x = range(len(deltaLevels))
plt.plot(x,deltaLevels)
plt.ylabel('Total Gap')
plt.xlabel('Num. of Batteries Consumed')
plt.show()

Code for model #2

import math
import numpy
from matplotlib import pyplot as plt
import operator
from mpl_toolkits.mplot3d import Axes3D
from skmonaco import mcquad
from skmonaco import mcimport
from numpy.random import normal,lognormal
88

print 'Enter the Battery Type:'
print ' 1. Li-Ion\n 2. Lead Acid\n 3. Vanadium Redox\n 4.
Sodium-sulfur\n 5. Sodium-nickel-chloride\n 6. Zinc-bromine\n 7.
Zinc-air\n 8. Iron-chromium\n'
opt = input()
if(opt==1):
xl=[1000.]
xu=[2100.]
elif(opt==2):
xl=[500.]
xu=[2500.]
elif(opt==3):
xl=[800.]
xu=[1100.]
elif(opt==4):
xl=[500.]
xu=[600.]
elif(opt==5):
xl=[700.]
xu=[1200.]
elif(opt==6):
xl=[300.]
xu=[1600.]
elif(opt==7):
xl=[200.]
xu=[300.]
elif(opt==8):
xl=[300.]
xu=[500.]

mean= (xl[0]+xu[0])/2
print mean
threshold = 0
costArray=numpy.zeros((101,101))
totalcost = 10000000000000
for supply in numpy.linspace(1, 100, 100):
print supply
for radius in numpy.linspace(0.00, 1, 101):
nStations=15
coords = {
89

1:(42.58160019, -83.03096771),
2:(42.45776749, -83.13323975),
3:(42.27840424, -83.2700882),
4:(42.14104462, -83.22714233),
5:(42.4941234,
-83.4256796),
6:(42.49123764, -83.51441956),
7:(42.3601265,
-83.43258667),
8:(42.32044601, -83.48866272),
9:(42.22281265, -83.48566437),
10:(42.628,
-83.874),
11:(42.58,
-83.88),
12:(42.54561996,-83.78999329),
13:(42.2843526, -83.8084963),
14:(42.2397874, -83.7668615),
15:(42.24443817,-83.7388382)
}
delta = {
1:20,
2:9,
3:7,
4:11,
5:23,
6:16,
7:14,
8:16,
9:13,
10:11,
11:19,
12:18,
13:24,
14:50,
15:10
}
count=1
maxDelta=0
deltaLevels = []
wastage=0
while(1):
sorted_delta = sorted(delta.items(),
key=operator.itemgetter(1), reverse=True)
deltaLevels.append(sum(delta.values()))
unit=sorted_delta[0]
90

stationID = unit[0]
demand = delta[stationID]
if(demand>threshold):
extraSupply=0
if(supply>demand):
delta[stationID] = 0
extraSupply = supply-demand
else:
delta[stationID] = demand-supply
if(extraSupply>0):
locA = coords[stationID];
distFromLocA={}
for n,p in coords.iteritems():
locB = p;
dist = pow(pow((locA[0]locB[0]),2)+pow((locA[1]-locB[1]),2),0.5)
distFromLocA[n]=dist
sorted_dist = sorted(distFromLocA.items(),
key=operator.itemgetter(1))
for n,dist in sorted_dist:
if n!=stationID and delta[n]>0 and
extraSupply>0 and dist<=radius :
demand = delta[n]
if(extraSupply>demand):
delta[n] = 0
extraSupply = extraSupply demand
if(extraSupply>0):
wastage=wastage+extraSupply
count=count+1
else:
break
c = lambda supplycost: (0 * radius) +
(((supplycost*mean)+xl[0]) * supply * count * 4) + (20000 *
count)
cost,error =
mcimport(c,npoints=100,distribution=lognormal)

91

costArray[int(supply)][int(radius*100)]=cost
if(cost<totalcost):
totalcost = cost
batteryUnit = supply
batteryCount = count
radiusFinal = radius
print 'total cost = ' + str(totalcost)
print 'battery unit = ' + str(batteryUnit)
print 'battery cost range ' + str(xl[0]) + ' to ' +
str(xu[0])
print 'num of batteries= ' + str(batteryCount)
print 'radius final = ' + str(radiusFinal)
print "Total Wastage = " + str(wastage)
print ""
print
print
print
print

'total cost = ' + str(totalcost)
'battery unit = ' + str(batteryUnit)
'num of batteries= ' + str(batteryCount)
'radius final = ' + str(radiusFinal)

nx, ny = 101,101
x = range(nx)
y = range(ny)
hf = plt.figure()
ha = hf.add_subplot(111,projection='3d')
X,Y = numpy.meshgrid(x,y)
ha.plot_surface(X,Y,costArray)
ha.set_xlabel("exchange range")
ha.set_ylabel("battery size")
ha.set_zlabel("Total cost")
plt.show()

92

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93

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