The Application of Genetic Algorithms to Parameter Estimation in Lead-Acid Battery Equivalent ...

137 Pages·2010·0.86 MB·English

by  Shen Guo

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The Application of Genetic Algorithms to
Parameter Estimation in Lead-Acid Battery
Equivalent Circuit Models

Thesis submitted in accordance with the requirements of
the University of Birmingham for the degree of
Master of Philosophy

in

School of Electronic Electrical & Computer Engineering

by

Shen Guo

May 2010
University of Birmingham Research Archive

e-theses repository

This unpublished thesis/dissertation is copyright of the author and/or third
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to my parents

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Acknowledgements
First and foremost, I would like to express my sincere appreciation to my
supervisors, Dr. Stuart Hillmansen and Dr. Jihong Wang, for their support,
guidance, inspiration and patience during my MPhil study. I have greatly
benefited from their knowledge and experience.
I am also grateful to Dr. Jianlin Wei and Dr. Nan Jia for their support and advices
during my research and to Dr. Leonid Shpanin for his assistance in my laboratory
experiments. Many thanks to Mr. Bo Fan, Mr. Shaofeng Lu and Mr. Lei Chen for
their valuable ideas shared with me. I would also like to thank Mr. Hao Sun, Mr.
Xing Luo as well as all the other colleagues for their discussions and their kind
assistant during my study.
Finally, I would like to thank my family and all my friends. Without their
encouragement, support and understanding, this thesis would not have been
possible.

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Abstract
Batteries are becoming increasingly important to our life as they are applied in a
range of different areas. Therefore the reliability of battery is a critical issue in
these battery applications. It has been noticed that most batteries have limited
cycle durability, that is, the total capacity drops when a battery is charged and
discharged for a number of cycles. If a battery is too weak to offer sufficient
energy, it should be replaced at the right time. But current problem is that there is
no reliable method available to quantify the capacity loss and to estimate whether
the remaining capacity of battery. Complete discharge, which is the only way of
capacity estimation, has a negative effect to the battery plates therefore it cannot
be used too frequently.
This thesis summarises the research work in the development of the battery status
estimation algorithm. The work initially focused on the mathematical descriptions
of lead acid batteries, and a mathematical model based on this study was then
developed and implemented to describe the process of battery discharge. Genetic
Algorithms (GAs) were used as a tool to identify the parameters related to the
battery, including the internal resistances, state of charge, and capacity. The
relevant simulation results show that the model is able to adequately simulate the
battery discharge process.
The aforementioned models were extended to a further investigation of the
batteries state of health. It was noticed that there is a link between the status of
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battery health and the internal resistance. In this project, six batteries were
discharged and charged in several times in order to simulate the capacity loss that
occurs in normal operation. This capacity loss is related to the state of health, and
the parameter estimation was able to adequately distinguish between different
state of health.
These results indicate that the internal resistance increases when the state of health
of a lead-acid battery decreases. This progress is at first very slow when the
battery is new but the change becomes faster when the remaining capacity of
battery drops to about 75% of the initial. It is found in the thesis that the value of
internal resistance is increased by 25% approximately when the state of health is
brought down to about 50%, meaning that the battery cannot offer enough energy
as new and should be replaced for safety consideration.
The method described within this thesis performed adequately in the limited tests
performed during the experimental work. Further investigations are recommended
in order to refine the method which is potentially suitable for online
implementation in battery condition monitoring systems.
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Contents

Chapter 1 Background and Objectives of the Project.............................................1
1.1. Overview.................................................................................................1
1.2. Review of Energy Storage Systems........................................................2
1.2.1. Applications of the Energy Storage Systems.................................2
1.2.2. Review of the Existing Energy Storage Devices...........................4
1.2.3. Review of Batteries........................................................................7
1.2.4. The Management of Batteries.......................................................11
1.3. Project Objectives.................................................................................12
1.4. Outline of the thesis..............................................................................13
Chapter 2 Introduction of Lead-acid Batteries......................................................15
2.1. A General Overview of the Lead-acid Battery.....................................15
2.2. Configuration of Lead-acid Batteries....................................................18
2.2.1. Electrochemical Principles...........................................................18
2.2.2. Lead-Acid Battery Types and Technologies................................20
2.2.3. Battery Designs for Different Applications..................................22
2.3. Mathematical Descriptions of Lead-acid Batteries...............................23
2.3.1. Capacity........................................................................................23
2.3.2. Electromotive force......................................................................24
2.3.3. State of Charge and Depth of Charge...........................................26
2.3.4. Internal Resistance and State of Health.......................................27
2.3.5. Multi-Cell Lead-Acid Batteries ...................................................29
2.4. Summary...............................................................................................29
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Chapter 3 Equivalent Circuit Modelling of Lead-acid Batteries.........................31
3.1. Requirements for the Battery Model.....................................................31
3.2. Overview of Battery Model Techniques...............................................32
3.2.1. Electrochemical Model................................................................32
3.2.2. Physical Models...........................................................................33
3.2.3. Equivalent Circuit Model.............................................................34
3.2.4. Discussion of Different Battery Model Methods.........................35
3.3. Introduction of the Existing Equivalent Circuit Models.......................37
3.3.1. Simple Battery Model..................................................................37
3.3.2. Advanced Simple Battery Model.................................................39
3.3.3. Thevenin Battery Model..............................................................40
3.3.4. Dynamic Battery Model...............................................................42
3.3.5. Fourth Order Dynamic Model......................................................43
3.3.6. Improved Battery Model..............................................................44
3.4. Mathematical Model of the Lead-acid Batteries...................................44
3.4.1. Capacity........................................................................................45
3.4.2. Electric Networks.........................................................................48
3.4.3. State of Charge and Depth of Discharge......................................50
3.4.4. Electromotive Force of the Battery..............................................50
3.4.5. Internal Resistance of a Battery...................................................51
3.4.6. The Behaviour of Parasitic Branch..............................................52
3.4.7. Main Branch Capacitance............................................................53
3.4.8. Thermal Behaviour of a Battery...................................................55
3.5. Mathematical Model of the Lead-acid Batteries...................................56
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3.6. Summary and Discussion......................................................................57
Chapter 4 Experimental System Set up and Improved Battery Model Simulation
Implementation.....................................................................................................59
4.1. The Experimental System.....................................................................59
4.2. Improvements of the Battery Model.....................................................61
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4.2.1. The Change of in Different Charge Status...............................63
4.2.2. Analysis in Variations of the Internal Resistance.........................64
4.2.3. Improved Lead-Acid Battery Mathematical Model.....................66
4.3. Simulation Study...................................................................................68
4.4. Summary and Discussion......................................................................72
Chapter 5 Model Parameter Identification and Model Validation........................73
5.1. Need for the Optimization Algorithms..................................................73
5.2. Overview of the Optimization Algorithms............................................74
5.3. The Study of the Genetic Algorithms....................................................77
5.3.1. Working Principle of GAs............................................................77
5.3.2. Simulation Studies of Genetic Algorithms...................................81
5.4. Model Parameter Identification.............................................................87
5.4.1. Implementation of Genetic Algorithms and Experimental Data sets
................................................................................................................87
5.4.2. Parameters of Battery Model.......................................................90
5.4.3. Battery Model Validation.............................................................92
5.5. Summary and Discussions....................................................................95
Chapter 6 The Analysis of State of Health (SOH) in association with the Internal
Resistance..............................................................................................................97
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6.1. Methodology.........................................................................................97
6.2. The identification of C , R and R ...................................................100
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6.3. Summary and Discussions..................................................................108
Chapter 7 Conclusions and Future Research.......................................................110
7.1. Summary..............................................................................................110
7.2. Limitations...........................................................................................111
7.3. Future Research Works........................................................................112

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