Charith_Tammineedi_Thesis.pdf

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The Pennsylvania State University

The Graduate School

MODELING BATTERY-ULTRACAPACITOR HYBRID SYSTEMS FOR SOLAR

AND WIND APPLICATIONS

A Thesis in

Energy and Mineral Engineering

by

Charith Tammineedi

2011 Charith Tammineedi

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2011


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The thesis of Charith Tammineedi was reviewed and approved∗ by the following:

Jeffrey R. S. BrownsonAssistant Professor of Energy and Mineral EngineeringThesis Advisor

Ramakrishnan RajagopalanResearch Associate of Materials Research Institute

Susan W. StewartResearch Associate of Aerospace Engineering and Architectural Engineering

Yaw D. YeboahProfessor of Energy and Mineral Engineering

Head of the Department of Energy and Mineral Engineering

∗Signatures are on file in the Graduate School.


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Abstract

The purpose of this study was to quantify the improvement in the performance of a battery with

the addition of an ultracapacitor as an auxillary energy storage device for solar and wind applica-tions. The improvement in performance was demonstrated through simulation and modeling. Aceraolo battery model and a third order ultracapacitor ladder model were implemented in Mat-lab/Simulink. Sample battery load cycles for solar and wind applications have been obtainedfrom literature and the corresponding C-rates were quantified. The C-rate for the solar loadcycle was found to be 0.3C and 0.2C for the wind load cycle. The performance of the battery-ultracapacitor system was checked for the sample solar and wind load cycles and compared withthe performance of the battery system without an ultracapacitor. A reduction of 50.5% in bat-tery RMS currents was found for the solar load cycle and 60.9% for the wind load cycle. Thisreduction in battery RMS currents was found to be directly proportional to the ultracapacitorcontribution. Given the low C-rates for the sample load cycles it was deduced that the additionof an ultracapacitor will not significantly improve the battery life to justify the high initial costs.

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Table of Contents

List of Figures v

List of Tables vii

List of Symbols viii

Acknowledgments x

Chapter 1Literature Review 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Lead Acid Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Lead Acid Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1.1 Discharge Process . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1.2 Charge Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Lead Acid Battery Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.1 Operating Conditions of Batteries in Solar PV systems . . . . . . . . . . . 91.3.2 Battery Aging in PV systems . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.2.1 Sulfation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2.2 Acid Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Ultracapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.2 Principle of operation - Simple Double Layer capacitor . . . . . . . . . . . 131.4.3 Classification and materials used . . . . . . . . . . . . . . . . . . . . . . . 14

1.4.3.1 Double Layer Capacitors . . . . . . . . . . . . . . . . . . . . . . 141.4.3.2 Capacitors utilizing pseudo-capacitance . . . . . . . . . . . . . . 151.4.3.3 Hybrid (Asymmetric) Capacitors . . . . . . . . . . . . . . . . . . 15

1.4.4 Ultracapacitor Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.5 Ultracapacitor Cost considerations . . . . . . . . . . . . . . . . . . . . . . 171.5 Ultracapacitor Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.5.1 Classical Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . 171.5.2 Transmission Line Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.5.3 Justification for using Third Order UC Model . . . . . . . . . . . . . . . . 18

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Chapter 2Modeling Battery-ultracapaitor hybrid system 202.1 Lead Acid Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.1.1 Ceraolo Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.1.1.1 Battery Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1.1.2 State of Charge(SOC) and Depth of Charge(DOC) . . . . . . . . 222.1.1.3 Extracted Charge . . . . . . . . . . . . . . . . . . . . . . . . . . 222.1.1.4 Main Branch Voltage (Em) . . . . . . . . . . . . . . . . . . . . . 222.1.1.5 Main Branch Resistance (R1) . . . . . . . . . . . . . . . . . . . . 232.1.1.6 Main Branch Capacitance (C 1) . . . . . . . . . . . . . . . . . . . 232.1.1.7 Terminal Resistance (R0) . . . . . . . . . . . . . . . . . . . . . . 232.1.1.8 Main branch Resistance (R2) . . . . . . . . . . . . . . . . . . . . 232.1.1.9 Parasitic branch Current (I p) . . . . . . . . . . . . . . . . . . . . 242.1.1.10 Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Component development in Simscape . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.0.11 Third Order Ultracapacitor Modeling . . . . . . . . . . . . . . . 25

2.3 Energy Storage System Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.1 Battery Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.2 Ultracapacitor Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Chapter 3Results and Discussion 303.1 Battery Modeling results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Solar Load Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Battery response without ultracapacitor . . . . . . . . . . . . . . . . . . 313.2.2 Battery response with ultracapacitor . . . . . . . . . . . . . . . . . . . . . 333.2.3 Ultracapacitor Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Wind Load cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Battery response without ultracapacitor . . . . . . . . . . . . . . . . . . 363.3.2 Battery response with ultracapacitor . . . . . . . . . . . . . . . . . . . . . 373.3.3 Ultracapacitor Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Impact of DC-DC converter block . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Initial System costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Chapter 4Conclusions 46

Appendix AModel Implementation In Matlab 48A.1 Battery and Ultracapacitor Models . . . . . . . . . . . . . . . . . . . . . . . . . . 48A.2 Storage System Costs: Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Bibliography 52

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List of Figures

1.1 Ragone Plot - Lead Acid Battery . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Ragone Plot - Energy Storage options . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Characteristic Output of Large scale Wind systems[1] . . . . . . . . . . . . . . . 41.4 Characteristic Output of Large scale Solar systems[2] . . . . . . . . . . . . . . . . 41.5 Solubility curve for lead sulfate in sulphuric acid[3]. . . . . . . . . . . . . . . . . . 6

1.6 Thevenin Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.7 Non-Linear Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.8 Battery Currents in units of I 10 for European Conditions[4]. . . . . . . . . . . . . 101.9 State of Charge for different Classes of operating conditions[4]. . . . . . . . . . . 101.10 Maxwell BOOSTCAP ultracapacitors . . . . . . . . . . . . . . . . . . . . . . . . 121.11 U ltracapacitor[5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.12 Classical equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . . 181.13 Ladder Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.14 Comparison of accuracy of various orders[6] . . . . . . . . . . . . . . . . . . . . . 191.15 Working Order of Ultracapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1 Lead-acid Battery equivalent electric model . . . . . . . . . . . . . . . . . . . . . 212.2 Battery Stack building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Third Order Ultracapacitor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4 Ultracapacitor Order Reduction Methodlogy . . . . . . . . . . . . . . . . . . . . . 27

3.1 Measured vs Modeled Voltage (V) . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 Solar Load cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Solar C-Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Solar Load cycle:Battery Performance w/o ultracapacitor . . . . . . . . . . . . . 343.5 Solar Load cycle: Battery Performance with Ultracapacitor . . . . . . . . . . . . 353.6 Solar Load cycle: Ultracapacitor Performance . . . . . . . . . . . . . . . . . . . . 363.7 Solar Load cycle: Battery-Ultracapacitor currents . . . . . . . . . . . . . . . . . . 373.8 Wind Load cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.9 Wind C-Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.10 Wind Load cycle: Battery Performance w/o ultracapacitor . . . . . . . . . . . . 40

3.11 Wind Load cycle: Battery Performance with ultracapacitor . . . . . . . . . . . . 413.12 Wind Load cycle: Ultracapacitor Performance . . . . . . . . . . . . . . . . . . . . 413.13 Wind Load cycle: Battery-Ultracapacitor currents . . . . . . . . . . . . . . . . . 423.14 Solar Load cycle: Impact of DC-DC converter . . . . . . . . . . . . . . . . . . . . 433.15 Solar Load cycle:Battery Current Histogram w/o ultracapacitor . . . . . . . . . . 443.16 Solar Load cycle:Battery Current Histogram with ultracapacitor . . . . . . . . . 44

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3.17 Wind Load cycle: Battery Current Histogram w/o ultracapacitor . . . . . . . . . 453.18 Wind Load cycle: Battery Current Histogram with ultracapacitor . . . . . . . . . 45

A.1 Battery Model in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49A.2 Ultracapacitor Model in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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List of Tables

1.1 Classes of battery operating conditions . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Comparison battery and ultracapacitor characteristics[7] . . . . . . . . . . . . . . 131.3 Classification of Ultracapacitors[8] . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Performance Characteristics of Ultracapacitor technologies[8] . . . . . . . . . . . 141.5 The specific capacitance of selected electrode materials[8] . . . . . . . . . . . . . 16

2.1 Ceraolo Model Parameters[9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Model Parameters of Maxwell 100F . . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Scaled Ultracapacitor Model Parameters . . . . . . . . . . . . . . . . . . . . . . 28

3.1 Battery and Ultracapacitor Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Energy Storage System Specifications . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Solar Load Cycle: Energy Storage System Performance . . . . . . . . . . . . . . 363.4 Energy Storage System Specifications: WInd . . . . . . . . . . . . . . . . . . . . 383.5 Wind Load Cycle: Energy Storage System Performance . . . . . . . . . . . . . . 39

A.1 Energy Storage System Costs: Wind . . . . . . . . . . . . . . . . . . . . . . . . . 51A.2 Energy Storage System Costs: Solar . . . . . . . . . . . . . . . . . . . . . . . . . 51

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List of Symbols

Letters

θf Electrolyte freezing temperature

Q ChargeC Capacitanceθ Electrolyte Temperature I avg Mean Discharge current(A)E m Main branch voltageE m0,K E constants for a batteryR1 Main branch resistanceR10 Emperical constantR0 Terminal resistanceA0,R00 Constants for a batteryR2 Main branch resistanceR20,A21 and A22 Empirical constants for a batteryI p Current loss in the parasitic branch

V PN Voltage at parasitic branchG p0 ConstantV p0 ConstantAP Constantθa Ambient Temperature P s Internal Heat generation (W)C θ Thermal Capacitance (

J oC

)N Scaling Ratio (oC )Rknew New Resistance (Ω)N s Cells in seriesN p Cells in parallel∆V Voltage drop

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Abbreviations & Acronyms

PV Photovoltaic

CEC Classical Equivalent CircuitHEV Hybrid Electric VehicleEV Electric VehicleEDLC Electric Double Layer CapacitorRMS Root Mean SquareESR Equivalent Series ResistanceEPR Equivalent Parallel ResistanceSOC State of ChargeDOC Depth of ChargeDoD Depth of Discharge

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Acknowledgments

I would like to first thank my advisor Dr. Jeffery Brownson for giving me this opportunity andintroducing me to the beautiful world of solar energy. I would like to thank Dr. Ramakrish-nan Rajagopalan for his valuable guidance throughout the course of this project and Dr. SusanStewart for her valuable input.

I would also like to thank Luke Witmer and Ramprasad Chandrasekharan for their consider-able help in various aspects of this project.

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Dedication

For my parents to whom I will forever be in debt for their constant love and support.

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Chapter1

Literature Review

1.1 Introduction

The rapid deployment of stand-alone renewable energy systems such as wind and solar is limited

by high life cycle costs. One main contributor to the high life cost is the battery bank which

is used to store electricity generated from intermittent systems such as wind and solar. Energy

Storage is an integral part of renewable energy systems such as wind and solar due to their

intermittent nature. However this very intermittent nature of their output causes the battery to

operate at conditions that it was not designed for. They often operate at deep-discharged and

overcharged states and the continuous exposure to rapid charge/discharge profiles degrades the

battery performance and reduces its lifetime[3, 10, 11]. The reduced battery lifetimes lead tofrequent replacement thereby increasing the overall life cycle costs. Shown in Figure 1.1 is the

Ragone the plot of the lead acid battery. It can be seen that the as the power demand increases

the battery energy capacity decreases due to which the batteries need to be oversized for high

power applications. This can be a problem for space constrained applications and additionally

for high discharge rates (>18C) the battery lifetime is also reduced significantly[3].

It can be seen from Figure 1.2 that ultracapacitors have much higher than power densities

and have the potential to complement traditional battery systems[12]. This configuration is

mainly being considered by the automotive industry for HEV and EV applications because of

the potential reduction in the size/volume of the overall energy storage system. The usage of

ultracapacitors also decreases the current loads on battery systems thereby potentially improvingbattery lifetimes. It is this because of these advantages, that makes it worth investigating the

battery-ultracapacitor configuration in the context of PV and wind systems.

Previous studies have shown that a simple parallel combination of battery and ultracapacitor

leads to improved energy storage system performance [13, 14]. It has been shown theoritically

that peak power of the energy storage system can be enhanced, internal losses be reduced and

discharge life of the battery be extended with the usage of ultracapacitors[13]. Experimental


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Figure 1.1. Ragone Plot - Lead Acid Battery

Figure 1.2. Ragone Plot - Energy Storage options


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studies on battery-ultracapacitor hybrid systems have been conducted and demonstrated im-

proved performance[14]. Battery-ultracapacitor hybrid have first been explored as an alternative

to batteries subjected to pulsed loads in digital communication applications[15]. Studies have

demonstrated that ultracapacitors are a good fit with fuel cell systems which have poor dynamic

response [14, 16, 17, 18]. Battery-ultracapacitor hybrid systems are being explored as an alterna-

tive to traditional battery systems by the automotive community due to potential size reduction

and potential improvement in battery lifetime due reduction in battery RMS values[18, 19].

Ultracapacitors are also being considered for use in renewable energy applications especially

wind[20, 21, 22]. For PV applications some studies have directly integrated the ultracapacitors

to the PV systems for improving efficiency and reliability[23, 24]. The characterization studies

of large scale PV and wind output have revealed that ultracapacitors can share the load during

high frequency power fluctuations and other high energy density devices can provide fill in power

over lower frequencies as shown in Figure 1.3 and Figure 1.4 [1, 2].

1.2 Lead Acid Batteries

Renewable Energy Systems like Solar and Wind are intermittent in nature. For stand-alone

applications they often require energy storage systems to provide the fill in power. Batteries

have been traditionally used to provide the fill-in power for solar and wind systems

The Lead Acid Battery is one of the widely used electrochemical energy storage systems. This

can be attributed to its chemical and physical properties that makes it an efficient system and

suitable for a variety of applications. A few of these properties are given below.

The reactants are solids of low solubility which causes a stable voltage and higly reversible

reactions

Both electrodes contain only lead and lead compounds as active material that do not require

conducting additives

It has a high cell voltage of 2V

Lead Acid technology is cheaper than most technologies and is the primary reason for being

widely used in renewable systems where larger storage capacities are required.

1.2.1 Lead Acid Chemistry

The reaction inside the lead acid battery consists of several steps before the actual charge transfer.

The slowest step is what determines the overall rate of the reaction. It is thus essential to

understand the individual steps to understand the overall response of the lead-acid battery and

also the subsequent aging mechanisms at high discharge rates. The overall reaction of the lead-

acid battery can be given by,


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Figure 1.3. Characteristic Output of Large scale Wind systems[1]

Figure 1.4. Characteristic Output of Large scale Solar systems[2]


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Pb + PbO2 + 2 H2SO4 −−→ 2 PbSO4 + 2 H2O

where Pb and PbO2 are the reactants and PbSO4 is the product of the cell reaction. Lead sulfate

is formed as a product at both electrodes since lead is the basic element in both the electrodes.

1.2.1.1 Discharge Process

Reaction at Negative Electrode: During the discharge process the Pb atoms of the negative

electrode are converted to Pb 2+ ions. This reaction can only take place on conductive sites i.e

on fresh lead. Therefore the rate of this reaction is dependent on the surface area of the fresh

lead available.

Pb −−→ Pb 2+ + 2 e –

Given the concentration ranges of H2SO4 in the battery it would have already dissociatedinto H+ and HSO –4 . Only about 1 percent of the H2SO4 molecules dissociate into 2 H

+ and

SO –4 [25]. The Pb2+ then reacts with HSO –4 to form PbSO4 (Lead Sulfate) which is termed the

Deposition process.

Pb 2+ + HSO –4 −−→ PbSO4 + H+

This reaction is function of the both Pb 2+ and sulfuric acid concentrations. The solubility of

lead sulfate reaches a maximum value at 10% concentration of the acid and it only decreases with

further increase in concentration of the acid as shown in the figure1.5. So the overall discharge

reaction now becomes,

Pb + H+ + HSO –4 −−→ PbSO4 + 2 H+ + 2 e –

Reaction at Positive Electrode:

PbO2 + HSO –4 + 3 H

+ + 2 e+ −−→ PbSO4 + 2 H2O

It can be seen that at higher concentrations of sulfuric acid formation of lead sulfate is

faster. It would be ideal if the formation of this lead sulfate is uniform throughout the negative

electrode but this is not the case in reality as the concentration of the acid in the interior of

the electrode decreases and so does the formation of lead sulfate in these areas. The formation

of lead sulfate is higher at the electrode electrolyte interface due to the higher concentration of

sulfuric acid in these areas. The penetration of lead sulfate through the electrode is a function of

surface area, paste density and discharge rates. For the same paste density and surface area the

penetration becomes solely the function of the discharge rate. At lower discharge rates(


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Figure 1.5. Solubility curve for lead sulfate in sulphuric acid[3].

the electrode.For high rates of discharge the supersaturation level Pb 2+ is high and so is its

dissolution rate. This leads to a much faster formation of lead sulfate. The transport of HSO –4

cannot keep up with lead sulfate production so the interior quickly runs out of HSO –4 ions and

the replenishment is not allowed to happen. Now the formation of lead sulfate is mainly in the

outer regions of the electrode leading to non-uniform distribution of lead sulfate.

1.2.1.2 Charge Process

The charge process consists of the dissolution of PbSO4 to Pb2+ and SO 2 –4 followed by the

subsequent deposition of Pb 2+ to Pb.

PbSO4 −−→ Pb2+ + SO 2 –4

H+ + SO 2 –4 −−→ HSO –4

Pb 2+ + 2 e – −−→ Pb


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The overall charge process of the negative electrode is given by,

PbSO4 + 2 e – + H+ −−→ Pb + HSO –4

During the charging process the electrons flow through the grid metal to the active sites as

the electrical resistance of the grid metal is smaller than that of discharged material. Along

with the deposition of Pb there is also the competing reaction of hydrogen evolution.Now for

the charging process after the battery has been discharged at low discharge rates,the relative

density of sulfuric acid is more due to more utilization of active material. It can be seen from

Figure 1.5 that at low concentration of acid the dissociation of PbSO 4 to Pb2+ and SO 2 –4 takes

place easily. The subsequent deposition of Pb 2+ to Pb is not impeded and can take place before

the evolution of hydrogen. On the other hand when the battery is discharged at high rates

the relative density of acid is higher which plays a key role during subsequent charging. The

rate of dissociation of PbSO4 is slow. The subsequent lower concentration of Pb

2+

impedes thedeposition of lead which decreases the active material available for the next discharge cycle. The

evolution of hydrogen starts earlier than expected. The lead sulfate keeps accumulating after

every cycle and eventually completely cuts off access to the active material thereby leading to

battery failure due to sulfation.


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1.3 Lead Acid Battery Models

Batteries in general exhibit complex, non-linear behavior as they are electrochemical systems

that store and release energy through oxidation and reduction reactions. There exist modelsthat are based on the electrochemistry of the system [26][27] and also Equivalent circuit models

that consist of capacitors and resistances used to represent the charge storing capacity of the

battery and the resistance to the flow of charge respectively[28][29]. The most commonly used

electrochemical model is the Shepherds model[26]. The shepherds model is used in several forms

with modifications made to suite specific battery types. The simplest of the equivalent circuit

models for batteries is the Thevenin Battery Model [28].

Figure 1.6. Thevenin Battery Model

As shown in the figure it consists of a no-load voltage source, internal resistance R, a capacitor

C with a resistance R0 in parallel to it. The values of the various components remain constant

throughout the simulation which is why this model is not very accurate. In reality the values of

the components are a function of several battery conditions like State of Charge(SOC), Battery

Storage Capacity, Rate of Discharge and Temperature[30].

Figure 1.7. Non-Linear Battery Model


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A non-linear Electrical Model consists of components whose values vary non-linearly.The

functional forms that model the non-linearity of the individual components can be determined

empirically . Two such models were found in literature, the Salameh Model [30] and the Ceraolo

Model [9, 31]. For the purpose of this study the equivalent circuit model approach was selected

due to its compatibility with the chosen simulation environment, Simscape. The Ceraolo model,

a rate-dependent third order model was selected because of its well documented validation work,

accuracy and ease of implementation within the Matlab/Simulink environment. The implemented

battery model is shown in Appendix A.

1.3.1 Operating Conditions of Batteries in Solar PV systems

It is essential to understand the typical operating conditions of batteries in stand-alone systems

to be able to design them properly. Additionally most of the aging processes are a function of

these operating conditions and a good understanding is necessary to optimize battery life. Thefollowing classification has been made based on an intensive study of 30 stand-alone PV systems

(under European conditions) that use batteries by the authors of [32, 4].

Table 1.1. Classes of battery operating conditions

System Indicators Class 1 Class 2 Class 3 Class 4

Solar Fraction 100% 70-90 % 50% < 50%Days of Autonomy 3-10 3-5 1-3 1Currents small small medium highCapacity throughput 10-25 30-80 100-150 150-200

Based on the operating conditions they are divided into four classes. Where Class 1 is a

system without a back up diesel generator and is designed to be highly reliable. Class 2, 3

and 4 are hybrid systems with increasing capacities of diesel power back-up. It can be seen

in Figure 1.8 that for class 1 battery the normalized discharge rates are not very high and for

classes 2, 3 the normalized discharge rates are relatively higher. For class 4, where battery size

is relatively smaller, the normalized discharge currents are higher than classes 2 and 3. Due

to the availability of diesel generator back-up, the days of autonomy for the battery for classes

2,3 and 4 do not have to be very high. As a result the smaller sized batteries are subjected to

relatively larger number of charge/discharge cycles. Similarly it can be seen from Figure 1.9 that

the battery depth of discharge is higher for classes 2 and 4. The class 3 battery has however

been designed to operate at much higher states of charge even though the rates of discharge are

similar to classes 2 and 3. From the capacity throughput values (defined as ratio of Ampere-hour

discharged from the battery to the nominal capacity of the battery) it can be seen that the

number of charge/discharge cycles is increasing progressively from class 1 to class 4 with class 4

battery being subjected to the most number of cycles (>1200 cycles). Given the lower discharge

rates of class 1 and class 2 batteries, it can be theorized that they will not be facing the same


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10

Figure 1.8. Battery Currents in units of I 10 for European Conditions[4].

Figure 1.9. State of Charge for different Classes of operating conditions[4].


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11

aging problems as the batteries of class 3 and 4 which have higher discharge rates.

1.3.2 Battery Aging in PV systems

1.3.2.1 Sulfation

As elaborated in the sections above during the discharge process of a lead-acid battery lead sulfate

is formed (PbSO4) is formed and during the subsequent charging process it gets dissociated into

Pb 2+ and SO 2 –4 . However in reality the complete dissociation of lead sulfate never happens[11].

The remaining lead sulfate represents the loss in capacity for the immediate discharge cycle. As

the number of cycles increases the lead sulfate that could not be dissolved keeps accumulating

and the capacity loss keeps on increasing until the battery completely fails. The rate of dissolu-

tion of lead sulfate is directly proportional to its surface area. Hence it is essential to maximize

the surface area of the lead sulfate during its formation. At high discharge rates the lead sulfate

does not penetrate throughout the electrode but is formed preferentially on the areas closer to

the free electrolyte. As a result the overall surface area of the lead sulfate formed is reduced.

The size of the lead sulfate crystals also plays an important role in the dissolution of lead sulfate.

For a given volume of lead sulfate formed, a large number of small sulfate crystals has a larger

surface area than a fewer number of large sulfate crystals. Hence it is essential to keep the size

of the sulfate crystals small. This can be done under high supersaturation of the electrolyte with

Pb2+ ions. This occurs only at the beginning of a discharge after a complete charging when

lead sulfate has been completely dissolved. With this as the background it has been proposed

that after complete charging of the battery, if it is discharged under high discharge rates for a

few seconds (such that the high supersaturation P b2+ ions takes place), a large number of small

crystals could be generated[10]. For more detailed explanation of this phenomena please refer

the following references[10, 33, 34]

1.3.2.2 Acid Stratification

In lead-acid batteries the concentration of the sulfuric is not uniform. These exists a gradient

with the upper part of the electrode being exposed more diluted sulfuric and lower part being

exposed to more concentrated sulfuric acid. Due to this the active material in the upper part of

the electrode is only partially utilized and it is overstressed in lower part of the electrode. Acid

Stratification in itself is not an aging process but accelerates active material disintegration in thelower parts of the positive electrode and sulfation in the lower parts of the negative electrode[10,

25]. This is a serious issue in stationary applications like stand-alone systems. Forced agitation

is used to partially solve the problem however the usage of immobilized electrolyte has proven to

be more effective.


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12

1.4 Ultracapacitors

1.4.1 History

The ultracapacitor also known as a supercapacitor or electric double layer capacitor are large

capacitance devices, with capacitances upto of several thousand farads. The first patent for

a capacitor based on high surface area carbon dates back to 1957 [35]. In 1969 the SOHIO

Corporation made the first attempt to commercialize ultracapacitors [36].

Figure 1.10. Maxwell BOOSTCAP

ultracapacitors

However it was not until the nineties that the interest in ultracapacitors was renewed in

the context of hybrid electric vehicles. An ever increasing power requirement for automotive

applications have rendered the standard battery design obsolete leading to the design of pulsed

batteries and battery-ultracapacitor hybrid systems for high power applications[18, 19]. However

with the increasing penetration of renewable energy technologies that require energy storage, the

usage of ultracapacitors in these systems has also been investigated by few authors[24, 22].

Ultracapacitors are high power density devices. It can be seen from the Figure 1.2 that

ultracapacitors fills the gap between batteries and conventional capacitors in terms of specific

energy and specific power and due to this it lends itself very well as a complementary device to

the battery. By combining ultracapacitors with batteries, which are typically low power devices,

the battery performance can be improved in terms of the power density. Additionally they have

high cycle life which makes them attractive for high power applications.


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13

Table 1.2. Comparison battery and ultracapacitor characteristics[7]

Available Performance Lead Acid Battery Ultracapacitor

Energy Density (Wh/Kg) 10-100 1-10Power Density(W/Kg) 500000Efficiency 0.7 - 0.85 0.85-0.98Discharge Time 0.3-3 hrs 0.3 - 30sCharge Time 1-5 hrs 0.3-30s

Figure 1.11. Ultracapacitor[5]

1.4.2 Principle of operation - Simple Double Layer capacitor

The storage of electric charge and energy in an ultracapacitor is electrostatic i.e non-faradaic. An

electrode when immersed in an electrolyte results in the formation of an electrochemical double

layer at the solid/electrolyte interface. Ultracapacitors store the electric energy in this electro-

chemical double layer also known as the Helmholtz Layer. The double layer capacitance is about

16-50 µF/cm2

[37] for an electrode in concentrated electrolyte solution and the correspondingelectric field in the electrochemical double layer is very high and assumes values of up to 106

V/cm [38]. In order to achieve a higher capacitance the electrode surface area is increased by

using porous electrodes with an extremely large internal effective surface(1000 to 2000m2/g)[37].

A single cell of an ultracapacitor (shown in figure 1.11) consists of two electrodes immersed in

an electrolyte. The electrodes in the system are separated by a porous separator containing the


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14

same electrolyte. The energy stored in an ultracapacitor is given by,

E = CV 2

2

(1.1)

where Q is the energy stored, C is the capacitance and V is the voltage. However the calculation

of capacitance for an ultracapacitor is very complex. For an ideal double-layer capacitor there

should not be any faradaic reactions between the electrode and electrolyte. The capacitance for

such a capacitor is independent of the voltage.

Another mode of storage has also been utilized by the ultracapacitors that involves faradaic

reactions. Capacitance in such cases is termed pseudo-capacitance. Charge transferred in such

cases is voltage dependent subsequently leading the capacitance to also be voltage dependent.

1.4.3 Classification and materials used

Based on mode of storage they can be classified into double layer capacitors, pseudo-capacitance

based Capacitors and hybrid ultracapacitors.

Table 1.3. Classification of Ultracapacitors[8]

Technology type Electrode materials Energy storage mechanisms

Electric double-layer Activated carbon Charge SeparationAdvanced carbon Graphite carbon Charge transfer or intercalationAdvanced carbon Nanotube forest Charge separationPseudo-capacitive Metal oxides Redox charge transferHybrid Carbon/metal oxide Double-layer/ charge transfer

Hybrid Carbon/lead oxide Double-layer/faradaic

Table 1.4. Performance Characteristics of Ultracapacitor technologies[8]

Eelctrode Materials Energy density Wh/kg Cell voltages Power density kW/kg

Activated carbon 5-7 2.5-3 1-3Graphite carbon 8-12 3-3.5 1-2Nanotube forest - 2.5-3 -Carbon/lead oxide 10-12 1.5-2.2 1-2Metal oxides 10-15 2-3.5 1-2Carbon/metal oxide 10-15 2-3.3 1-2

1.4.3.1 Double Layer Capacitors

This is the most commercialized of the several ultracapacitor technologies and is termed electric

double layer capacitor(EDLC). In the Double Layer Capacitor the energy is stored in the dou-


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ble layer formed at the electrode/electrolyte interface. Carbon is mainly used as the electrode

material for this type of ultracapacitor[39, 40]. The reasons for using carbon as the electrode

material are i.) Low Cost ii.) High Surface area iii.) Availability and iv.) Established elec-

trode production technologies. For carbon electrodes the energy stored is mainly capacitive with

a minor contribution from pseudo-capacitance.For carbon electrodes both aqueous and organic

electrolytes can be used with each configuration having its own advantage. A higher cell voltage

can be obtained using an organic electrolyte(typically 2.7V) and thereby a higher energy density

as energy stored is CV 2/2 . But the organic electrolytes have higher specific resistances thereby

decreasing the maximum usable power. On the other hand the aqueous electrolytes typically

limit the cell voltage to 1V. However they have higher conductances thereby leading to higher

power densities and additionally the aqueous electrolytes cost less. The measured specific capac-

itances as shown in Table 1.5 for carbon materials are in the range of 75-175 F/g for aqueous

electrolytes and 40-100 F/g for organic electrolytes. This disparity can be attributed to the

larger sized ions present in the organic electrolytes. The cell voltage is mainly dependent on the

breakdown voltage of the electrolyte. For the aqueous electrolyte the cell voltage is around 1V

and for the organic electrolytes it is 2.7V[8].

1.4.3.2 Capacitors utilizing pseudo-capacitance

For capacitors based on pseudo-capacitance there exists a faradaic reaction between the elec-

trode and the electrolyte. In other words the ions in the double-layer are transferred to the

surface. The charge transferred is voltage dependent therefore the capacitance of the system

also becomes voltage-dependent. Three types of electrochemical processes have been utilized for

storing charge. They are Surface Adsorption of ions from electrolyte, redox reactions involvingions from the electrolyte, and the doping and undoping of active conducting polymer material

in the electrode[8]. The main advantage is that they have much higher energy densities than

the double layer ultracapacitors. This technology is mainly in the research phase and is not

commercially available[41].

1.4.3.3 Hybrid (Asymmetric) Capacitors

This category of devices use carbon as one of the electrodes and the other electrode utilizes either

a pseudocapacitance material or a faradaic material like that used in a battery and hence the

term assymetric capacitors. Hybrid Capacitors employ materials like nickel oxide and lead oxide

as the material in positive electrode and carbon cloth for negative electrodes. The dischargetimes are in the range of 10-20 min, the peak power densities are aound 300W/kg and the energy

densities are projected to be in the range of 10-20Wh/kg. The performance characteristics are

closer to that of battery’s than the ultracapacitor’s.


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Chapter2

Modeling Battery-ultracapaitor

hybrid system

As mentioned before the approach taken to test the compatibility of battery-ultracapacitor sys-

tems was to develop a system scale model of the energy storage system which will then be then

subjected varying load profiles that represent a renewable energy load requirement. So each

component of the energy storage system, i.e. the battery and the ultracapacitor system were

modeled and tested separately and then integrated to form the energy storage system that is the

subject of study.

2.1 Lead Acid Battery Model

2.1.1 Ceraolo Battery Model

The Ceraolo Battery Model is a third order model. It is essentially an electric equivalent model

in which the individual parameters of each electric component are determined empirically. The

Ceraolo Model interpolates the battery behavior as seen from the terminals and does not model

individual parts of the battery i.e. electrodes, electrode/electrolyte interface, electrolyte etc.

Shown below is the generic electrical equivalent schematic of the Ceraolo Model.

It can be seen that the network has two main branches the main branch which is composed

of several R-C blocks and the parasitic branch. The parasitic branch models the irreversibleparasitic reactions like the water electrolysis that draw current but do not participate in the

main reaction. The complexity of the main branch can be increased by adding more R-C blocks

depending on the type of application. The type of application is characterized by the speed of

evolution of the electric quantities. However for most applications it is sufficient to include only

one R-C block and still obtain good accuracy.


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Figure 2.1. Lead-acid Battery equivalent electric model

2.1.1.1 Battery Capacity

The first and most important step is to accurately model the battery capacity. The battery

capacity is not a constant and is strongly dependent on the discharge current I and the electrolyte

temperature θ . At fixed discharge currents I the variation of capacity is given by

C (I, θ)I,θ=const = C 0(I )(1 + θ

−θf ) (2.1)

where, θf is the electrolyte freezing temperature and can be assumed to be -40 and C 0(I ) is a

function of discharge current I and is equal to the battery capacity at 0

. From experimentalresults C 0(I ) was determined emperically to be,

C 0(I ) = K cC 0∗

1 + (K c − 1)( I I ∗

)δ (2.2)

K c and δ are emperical coefficients that are constant for a given battery and a reference current

I ∗. Eq.(2.3) gives accurate results for a wide range of currents around I ∗ and its value is unique

for a given battery application. Now by combining Eq. 2.1 and 2.3 we have,

C (I, θ) =K cC 0∗(1 +

θ−θf

)

1 + (K c − 1)( I I ∗

)δ (2.3)

Eq. 2.1 and 2.3 are valid when electrolyte temperature and discharge current are constant.

For transient currents the Ceraolo Model postulates that they are still valid given that instead

of the actual current I a filtered value of this current I avg is used so that C (I, θ) now becomes

C (I avg, θ). The value of I avg is equated to the value of the current flowing in the resistor(R1)

in the main branch. This hypothesis has been experimentally confirmed by the authors of the

model.


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2.1.1.2 State of Charge(SOC) and Depth of Charge(DOC)

In the Ceraolo Model the values of individual circuit elements need to be identified for different

States of Charge (SOC). The State of Charge (SOC) of a battery is the ratio of the capacityremaining in the battery to the maximum capacity of the battery at a given temperature. Depth

of Discharge (DOC) is the ratio of the capacity remaining in the battery to the maximum capacity

of the battery with reference to the actual discharge regime. In other words State of Charge (SOC)

is a measure of the fraction of charge remaining in the battery and the Depth of Charge (DOC)

is a measure of usable fraction of charge remaining in the battery.

SOC = 1 −Qe

C (0, θ) (2.4)

DOC = 1 −Qe

C (I avg, θ)

(2.5)

Where,

SOC State of Charge

DOC Depth of Charge

Qe Charge of battery (A− secs)

C Battery Capacity (A− secs)

θ Electrolyte Temperature(oC )

I avg Mean Discharge current(A)

2.1.1.3 Extracted Charge

Qe is the extracted charge from the battery and can be calculated by integrating the current that

is flowing in and out of the battery.

Qe(t) = Qe−initial +

t0

−I m(τ )dτ (2.6)

Where,

Qe−initial Charge extracted initially

I m Main branch current(A)

τ Integration time variable

t time

2.1.1.4 Main Branch Voltage (Em)

Em is the open circuit voltage of a battery cell. It can be seen that it is a function of

temperature(θ) and state of charge(SOC) of the cell.

E m = E m0 −K E (273 + θ)(1− SOC ) (2.7)


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Where,

E m Main branch voltage

E m0,K E constants for a battery

2.1.1.5 Main Branch Resistance (R1)

The resistance R1 varies with the depth of discharge(DOC) of the battery. It can be seen that

the resistance increases exponentially as the DOC decreases.

R1 = −R10ln(DOC ) (2.8)

Where,

R1 Main branch resistance

R10 Emperical constant

2.1.1.6 Main Branch Capacitance (C 1)

The main branch capacitance C 1 is given by

C 1 = τ 1R1

(2.9)

Where,

C 1 Main branch capacitance

τ 1 Main branch time constant(secs)

2.1.1.7 Terminal Resistance (R0)

The resistance R0 is the resistance observed at the battery terminals. It is assumed to be constant

at all temperatures[ASSUMPTION] but is a function of State of Charge(SOC).

R0 = R00[1 + A0(1− SOC )] (2.10)

Where,

R0 Terminal resistance

A0,R00 Constants for a battery.

2.1.1.8 Main branch Resistance (R2)

It can be seen that the resistance R2 increases with the increase in state of charge(SOC) and

is also dependent on the discharge rate. The resistance becomes significant during the charging

and becomes relatively insignificant during discharging.

R2 = R20exp[A21(1− SOC )]

1 + exp (A22I m)I ∗

)(2.11)


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Where,

R2 Main branch resistance

R20,A21 and A22 Empirical constants for a battery

2.1.1.9 Parasitic branch Current (I p)

Parasitic branch currentI p is the current lost during the charging of a battery. The behavior of

the parasitic branch is strongly non-linear and the empirical equation matches the Tafel gassing

-current relationship. It is imortant to note that R2 = 0 and I P = 0 during the discharge. Hence

R2 and the whole parasitic branch can be omitted from the model while simulating the discharge

alone.

I p = V PN G p0exp(V PN V p0

+ AP (1 −θ

θf )) (2.12)

Where,

I p Current loss in the parasitic branch

V PN Voltage at parasitic branch

G p0 constant

V p0 constant

AP constant

2.1.1.10 Thermal Model

A thermal model of the battery is required to compute the Electrolyte temperature. In reality the

temperature of the electrolyte is not uniform but to avoid additional complexity the electrolytetemperature is assumed to be uniform throughout the battery. By developing a heat balance we

have,

C θdθ

dt =

θ − θaRθ

+ P s (2.13)

P s is the internal heat generation in the R0 and R2 components

P s = I 2mR2 + (I m − I p)

2R0 (2.14)

The electrolyte temperature can now be computed by

θ(t) = θinit + t0

(P s −

(θ−θa)

RθC θ )dt (2.15)

Where,

θ Electrolyte Temperature (oC )

θa Ambient Temperature (oC )

P s Internal Heat generation(W)

C θ Thermal Capacitance ( J oC

)


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Table 2.1. Ceraolo Model Parameters[9]

Parameters Symbol Value

Parameters refering to the battery capacity

I ∗

49AK c 1.18ε 1.29

C 0∗ 261.6 Ahθf -40 δ 1.40

Parameters refering to main branch of the circuit

τ 1 5000 sK E 0.580e−

3 V/ R00 2.0 mΩA0 -0.30A21 -8.0E m0 2.135 VR10 0.7 mΩ

R20 15 mΩA22 -8.45

Parameters refering to parasitic reaction branch

E p 1.95 VG p0 2 pSV p0 2.0 mΩA p 2

Parameters refering to the thermal model C θ 15 Wh

Rθ 0.2 /W

2.2 Component development in Simscape

The Ceraolo model was used to develop a 2V lead acid battery cell in Simulink. The batterycell was developed to enable modular building of the battery stack. The battery can be sized for

voltage and capacity by adding cells in series and parallel respectively as shown in Figure 2.2.

2.2.0.11 Third Order Ultracapacitor Modeling

The model order reduction and parameter scaling methodology as described in [6] was used for

this study. In order to reduce the order of the Ultracapacitor model the RC branches are merely

subtracted from the circuit and the resistances and capacitances of the removed RC brances

are added to the last RC branch of the new circuit as shown in Figure 2.4. For example, to

reduce from the 5-order to the 4-order, the 4th order capacitor value in the 4-order network is

substituted by the C4+C5 value in the five-order circuit. The inductance is ignored for orders

lower than the 5-order.

A Maxwell 100F utracapacitor has been employed for this study and the model parameters for

this ultracapacitor are given in Table 3.1. The ultracapacitor bank has been sized based on the

100F Maxwell ultracapacitor and the scaling of the parameters is done to accurately characterize

the behavior of the ultracapacitor bank. The scaling methodology is described by the Eq.


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Figure 2.2. Battery Stack building

Figure 2.3. Third Order Ultracapacitor Model

N = C total

100 ; Rknew =

RkN

; C knew = C kN ; (2.16)

Where,

N Scaling Ratio (oC )

Rk Resistance (Ω)

Rknew New Resistance (Ω)

C k Capacitance (F )

C knew New Capacitance (F )


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Figure 2.4. Ultracapacitor Order Reduction Methodlogy

Table 2.2. Model Parameters of Maxwell 100F

R1 0.02961Ω C1 31.7 F

R2 0.00494Ω C2 53.2 F

R3 0.00147Ω C3 18.9 F

R4 0.00170Ω C4 2.05 F

R5 0.00662Ω C5 0.02 F

2.3 Energy Storage System Sizing

2.3.1 Battery Sizing

The lead acid battery has been sized for various fractions of ultracapacitor contribution including

the case with no ultracapacitors. For the case without the ultracapacitors the battery has been

sized to meet the peak current demand over the discharge period and for the cases with the

ultracapacitor, the battery has been sized to meet the average current demand for the discharge

period. The same procedure has been followed for both solar and wind systems.


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29

parallel.

2.4 Simulation Environment

The system scale simulation was developed in Matlab/Simulink environment. The Battery and

the ultracapacitor components were developed in simulink and then integrated in Simscape.

Modeling of the electrical circuit containing the battery-ultracapacitor hybrid system along with

the solar and wind loads was done using the Simscape tool in Simulink. Simscape is a Matlab

based tool that enables the users to model Electrical and Mechanical systems as physical networks.

Components corresponding to physical elements such as pumps, motors, and op-amps, are joined

by lines corresponding to the physical connections that transmit power. Simscape technology

automatically constructs equations that characterize the behavior of the system.


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Chapter3

Results and Discussion

3.1 Battery Modeling results

Before the integration of the battery-ultracapacitor hybrid system it is essential to check the

performance of individual components to ensure proper functioning of the overall system. Hence

the results of the Ceraolo battery model are compared with measured battery performance data

reported by the author of the Ceraolo model[9]. The battery parameters used for the model

are given in Table 2.1. A discharge current of 63A was applied for 7.2 hours (25920s) and then

0A for the remaining period. The battery voltage drops as expected during the discharge and

returns to open circuit voltage value when no current is drawn. It was noted that the model

over predicts the voltage during discharge and underpredicts during no load condition. It wasobserved that the modeled battery voltage takes approximately 1s to reach its no load voltage.

Due to this behavior a high error percentage (22.1%) was observed for the first timestep. For

most of the simulation period the error percentage is less than 1. The error percentage increased

to a maximum of 3.9% as the battery got further discharged which can be attributed to the

extended linear region of the modeled voltage profile.

Table 3.1. Battery and Ultracapacitor Sizing

System Battery w/o UC (Ah) Battery w/ UC (Ah) UC (F)

Solar 40 19.6 7212Wind 170 83.4 18030


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Figure 3.2. Solar Load cycle

seen that the power requirement for the solar load cycle is not high. The System specfications

are given in Table 3.4. Results of a 12V 40Ah battery without an ultracapacitor subjected to thesolar load cycle are shown in Figure 3.4. The battery voltage, current and state of charge were

obtained for the solar load cycle.

Table 3.2. Energy Storage System Specifications

System Parameters w/o Ultracapacitor with Ultracapacitor

Battery Pack Voltage(V) 12.5 12.5Battery Capacity (Ah) 40 19.4Discharge Period(h) 3.5 3.5UC cell Voltage (V) - 2.7UC cell capacitance(F) - 100UC bank capacitance(F) - 7212UC cells in series - 5UC cells in parallel - 334

The initial state of charge of the battery was kept at 0.8 keeping in mind the load cycle starts

with a charging cycle. The battery reaches a state of charge of 1 after the charging cycle. During


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Figure 3.3. Solar C-Rate

the discharge cycle the state of charge of the battery falls to 0.76. The depth of discharge(DOD)

of the battery in this case was found to be 24% which was lower than expected. This couldbe due to the model overestimating the battery capacity. This however, is a problem with

the implementation and not the model itself. The initial voltage for the battery was noted to

be 12.79V. At the end of the charging cycle the battery reaches a voltage of 13.7V. The end of

discharge voltage for the battery was 12.45V. No charge controlling component was employed and

hence for the given model it is possible for the battery to reach voltages not usually recommended

in practice.The battery current is same as the load current given that no ultracapacitor is present

to share the load. The RMS value of battery currents was found to be 6.94 A.

3.2.2 Battery response with ultracapacitor

For case 2 the ultracapacitor was added in parallel to complement the battery. A DC-DC

converter was not used in the configuration. The battery is sized to meet the average discharge

load (6A) for the duration of the discharge which came upto be 19.6 Ah. The ultracapacitor

is sized to deliver the peak discharge current (12A) for a period of 900 seconds. A 7212 F

ultracapacitor bank of 100F Maxwell cells is used for the simulation.

The parameters for this ultracapacitor bank are given in Table 2.3.The initial state of charge

of the battery was kept at 0.66. The battery reaches a state of charge of 1.03 after the charging


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Figure 3.4. Solar Load cycle:Battery Performance w/o ultracapacitor

cycle. During the discharge cycle the state of charge of the battery falls to 0.59 because of the

smaller capacity of the battery used. The depth of discharge(DOD) of the battery in this case is

44.6%.

It should be noted that, with the ultracapacitor sharing the load, the current profile of the

battery has been smoothened as shown in Figure 3.13. The maximum current delivered by the

battery was noted to be 8.9A. The RMS value of battery currents was reduced to 6.24A from

6.94A for the case w/o ultracapacitor. Hence a reduction of 10.1% was found in the RMS value

for the case with an ultracapacitor.

3.2.3 Ultracapacitor Response

The initial state of charge of ultracapacitor was kept at 0.7. The end of charge SOC for the ultra-

capacitor was 0.77 and the end of discharge SOC was 0.68. Hence the depth of discharge (DoD)


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Figure 3.5. Solar Load cycle: Battery Performance with Ultracapacitor

for the ultracapacitor was noted to be only 9%. During the discharge cycle the ultracapacitor

voltage drops rapidly as it gets discharged. Due to this the battery recharges the ultracapacitor

because of the difference in voltages. This frequent recharging of the ultracapacitor does not al-

low the full utilization of the ultracapacitor. This problem can be eliminated by using a DC-DC

converter that maintains the ultracapacitor voltage at a prescribed level. It was thus noted that

a simple parallel combination of the battery-ultracapacitor system does not fully utilize the ca-

pabilities of the ultracapacitor. A DC-DC converter and charge control mechanisms are essential

for optimum utilization of the ultracapacitor.


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Figure 3.7. Solar Load cycle: Battery-Ultracapacitor currents

current of 30A. From figure 3.9 it can be seen that the power requirement for the solar load cycle

is not high .Results were obtained for the 12V, 170 Ah battery w/o ultracapacitor subjected tothe wind load cycle . The battery voltage, current and state of charge were obtained for the wind

load cycle. The initial state of charge of the battery was given to be 0.85. The battery reaches

a state of charge of 1 after the charging cycle. During the discharge cycle the state of charge of

the battery falls to 0.84. It was noted that the depth of discharge(DOD) of the battery in this

case was 15%. Again the DoD value is lower than expected for the given battery size. The RMS

value of battery currents was found to be 12.21 A.

3.3.2 Battery response with ultracapacitor

For case 2, the battery is sized to meet the average discharge load (10.72A) for the duration

of the discharge which came upto be 83.4Ah . The ultracapacitor is sized to deliver the peak

discharge current (30A) for a period of 900 seconds. A 18030 F ultracapacitor bank of 100F

maxwell cells is used for the simulation. The initial state of charge of the battery was at 0.70.

The battery reaches a state of charge of 0.97 after the charging cycle. During the discharge cycle

the state of charge of the battery fell to 0.68. The depth of discharge (DOD) of the battery in

this case is 29%. The RMS value of battery currents was reduced to 10.35A from 12.21A for the

case without an ultracapacitor. A reduction of 15.2% was found in the battery RMS currents for


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Figure 3.8. Wind Load cycle

Table 3.4. Energy Storage System Specifications: WInd

System Parameters w/o Ultracapacitor with Ultracapacitor

Battery Pack Voltage(V) 12.5 12.5Battery Capacity (Ah) 170 83.4Discharge Period(h) 9 9UC cell Voltage (V) - 2.7UC cell capacitance(F) - 100UC bank capacitance(F) - 18030UC cells in series - 5UC cells in parallel - 835

the case with an ultracapacitor.

3.3.3 Ultracapacitor Response

The initial state of charge of ultracapacitor was given to be 0.88. The end of charge SOC for the

ultracapacitor was 0.95 and the end of discharge SOC was 0.86. Hence the depth of discharge

(DoD) for the ultracapacitor was noted to be 9%. Again by employing a DC-DC converter the

ultracapacitor utilization can be increased.


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Figure 3.9. Wind C-Rate

Table 3.5. Wind Load Cycle: Energy Storage System Performance

System Performance Battery Battery/UC Battery/UC/DC-DC converterBattery Size(Ah) 170 83.4 83.44Ultracapacitor size(F) - 18030 18030Battery DoD (%) 15 29 18Max Voltage(V) 14.1 13.4 12.8Min Voltage(V) 10.7 12.27 12.4Ultracapacitor DoD(%) - 9 40.5Battery RMS current(A) 12.21 10.35 4.772%Improvement - 15.2 60.9in Battery RMS current

3.4 Impact of DC-DC converter blockTo improve the utilization a voltage source block was modeled to simulate the effect of the DC-DC

converter. This voltage source block maintains the voltage of the ultracapacitor at a prescribed

level. The impact of the converter block has been checked for the solar load cycle and wind

load cycle. The converter block maintained the ultracapacitor voltage close to 12.5V. It was

observed that the utilization of the ultracapacitor improved with the addition of the converter

block. For the solar load cycle, the ultracapacitor DoD was found to be 40.5% improving from


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Figure 3.10. Wind Load cycle: Battery Performance w/o ultracapacitor

9% for the case without a converter block. A reduction of 50.5% was found in the battery RMS

current values when compared to the case without ultracapacitor. For the wind load cycle, the

ultracapacitor DoD was found to be 40.5% improving from 9% for the case without a converter

block. A reduction of 60.9% was found in the battery RMS current values when compared to the

case without ultracapacitor. To further ensure optimum utilization, charge control algorithms

can be implemented to control the SOC and DoC levels of both the battery and ultracapacitor.

3.5 Initial System costs

For both wind and solar the battery sizing is done for energy as the power requirements are not

very high. Hence the /Wh becomes an important metric when comparing prices of different

energy storage techonologies for solar and wind. The market price of a 2.7V 3000F ultracapacitor

was found to be 95. From this the /Wh value was calculated to be 31.275/Wh. Similarly the

price of a 12V, 55Ah battery was found to be 170 and /Wh was found to be 0.257/Wh. The


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Figure 3.11. Wind Load cycle: Battery Performance with ultracapacitor

Figure 3.12. Wind Load cycle: Ultracapacitor Performance


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Figure 3.13. Wind Load cycle: Battery-Ultracapacitor currents

total energy storage system cost for the solar load cycle was 128.7 for the battery system and

4959 for the battery-ultracapacitor system. Similarly for the wind load cycle, the cost of batterysystem was 547.3 and 120505.9 for the battery-ultracapacitor system. The details of the cost

comparison for the solar and wind load cycle are attached in Appendix A.

It can be seen from Table A.2 that the initial costs for battery-ultracapacitor system are much

higher than the battery system alone. In order to calculate the life cycle savings of the energy

storage system, the improvement in battery life-time must first be quantified with the addition

of the ultracapacitor. The battery replacement costs that have been offset with the addition of

ultracapacitors must then be quantified. The /throughput Ah must be calculated for both the

cases. If this value is lesser for battery-ultracapacitor system than the battery system, it can

lead to life cycle savings otherwise it is not justified to use an ultracapacitor.


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Figure 3.14. Solar Load cycle: Impact of DC-DC converter


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Figure 3.15. Solar Load cycle:Battery Current Histogram w/o ultracapacitor

Figure 3.16. Solar Load cycle:Battery Current Histogram with ultracapacitor


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Figure 3.17. Wind Load cycle: Battery Current Histogram w/o ultracapacitor

Figure 3.18. Wind Load cycle: Battery Current Histogram with ultracapacitor


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Chapter4

Conclusions

The purpose of this study was to quantify the improvement in the battery performance via

a reduction in battery C-rates with the addition of an ultracapacitor as an auxillary energy

storage device for solar and wind applications. In order to quantify the improvement in battery

performance, a battery-ultracapacitor model was developed, capable of accurately predicting the

system performance in solar and wind applications. Time averaged sample battery load cycles for

solar and wind applications were obtained from literature and the battery C-rates were quantified

to identify the limits of operation for the sample load cycles. The battery system that was sized

for energy for both the load cycles was subjected to a maximum C-rate of 0.3C for the solar load

cycle and 0.2C for the wind load cycle. An analysis via literature survey of failure modes of the

battery subjected to various discharge rates revealed that for the given the C-rates (


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rectly impact the reduction of battery RMS currents. It was observed that the depth of discharge

(DoD) of the ultracapacitor was 9% for a battery-ultracapacitor in simple parallel circuit. This

is due to the rapid drop in voltage of the ultracapacitor as it gets discharged. A simple DC-DC

converter was then modeled and added to the system to regulate the voltage. With the usage

of DC-DC converter the ultracapacitor’s depth of discharge (DoD) improved significantly to the

aforementioned values of 50.5% for solar and 60.9% for wind. It was hence noted that the DC-DC

converter is a key component in battery-ultracapacitor systems without which the capabilities of

ultracapacitor cannot be fully utilized and thus only a fraction of total possible improvement in

battery lifetime can be attained.

A simple cost comparison revealed that the cost of the battery-ultracapacitor system is much

higher than the battery system alone. Hence there is a need to conduct a life cycle savings

analysis of the battery-ultracapacitor system for both low and high power applications to justify

the inclusion of an ultracapacitor. It will be essential to use other sample load cycles with

small timesteps for solar and wind applications and quantify the reduction in battery RMS

currents using the model. Applications with highest % improvement in battery RMS currents

per installed capacity of ultracapacitor must be given the highest preference for a life cycle savings

analysis. Quantification of % reduction in battery RMS currents for several sample solar and

wind load cycles and the subsequent life cycle savings analysis should result in the identification

of applications where ultracapacitors are cost effective.


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AppendixA

Model Implementation In Matlab

A.1 Battery and Ultracapacitor Models

Shown in figures A.1 and A.2 are the battery and ultracapacitor models implemented in Matlab.


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F i g u r e A . 1 .

B a t t e r y M o d e l i n M a t l a b


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F i g u r e A . 2

. U l t r a c a p a c i t o r M o d e l i n M a t l a b


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