dynamic modeling, monitoring and control of energy storage system

Faculty of Technology and Science
Department of Physics and Electrical Engineering
Quree Bajracharya
DYNAMIC MODELING, MONITORING AND
CONTROL OF ENERGY STORAGE SYSTEM
Degree Project of 30 credit points
Master’s Program in Electrical Engineering
Date:
Supervisor:
Examiner:
Karlstad University, 651
i 88 Karlstad
Phone: 054-7001000, Fax: 054-7001460
Information@kau.se www.kau.se
13-02-27
Dr. Magnus Mossberg
Karlstad University
Dr. Jorge Solis
Acknowledgements
I would like to express my sincere gratitude to Karlstad University, department of Electrical Engineering
for including ELAD 11 in the final year course and for proving an opportunity to undertake the thesis. A
project is not possible without a lot of helping hands and support. First of all, I would like to thanks
Glava Energy Centre for providing an opportunity to conduct my thesis and with all the equipments and
facilities during the project. I would like to thanks Dr. Magnus Mossberg for his supervision, continuous
guidance and invaluable suggestions. I would also like to thanks Mr. Daniel Palsson (Macbat) for giving
me his valuable suggestion in the initial phase of the thesis and introducing me to Glava Energy centre,
Mr. Bjorn Andersson (Macbat) for his suggestion in charging of the battery and sharing his experience.
It’s a great pleasure to acknowledge Mr. Magnus Nilsson for arranging the facilities and treating me as
one of the member of the company. I am very happy that this project has given me an opportunity to
enroll in the company and I am proud to confess that I have gained a lot of knowledge regarding
batteries and renewable technology.
Last but not least I would like to thank our examiner Jorge Solis.
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Abstract
Today there is a great interest on the small scale renewable electricity generation due to the changing
economics and the demand for highly sustainable electricity generation. However, renewable energy
sources are unreliable and fluctuating which causes variation of power flow. In this situation, there can
be server problems such as frequency oscillations, violation of the power line capability jeopardizing the
security of the power system. Batteries can be an emerging technology which acts as the fast acting
spinning reserve that can balance between the load and generation. Conversely, it very difficult to
accurately predict battery performance and the total cost of the investment of storage system by
integrating batteries to the renewable system as batteries in this situation have to bear a wide range of
the operational conditions . Henceforth, modeling of the battery is extremely important. This master
thesis gives the dynamic modeling of the batteries which can replicate the relevant behavior of the
battery.
The proposed methodology is the model based approach where the parameters are determined to
develop a suitable model. In this thesis, the battery is modeled as an R-C circuit comprising of elements
each of which represents certain battery characteristics. An appropriate model is selected based on the
comparative study of the characteristics of experimental output of the battery using model
identification. Parameters of the battery are computed in the MATLAB Simulink parameter estimation
toolbox using least square estimation .The initial parameter values for the simulink are found with the
help of the lab test. Validation results from the two experimental data shows that the model can
accurately estimate the battery characteristics with an error of 0.3%.The aforementioned battery model
is later used to make an appropriate charge controller.
The methods used in the thesis performed quite well within the limited tests performed during the
experimental works. To use the model online in the future, further investigation is recommended in
order to refine the model.
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Table of Contents
CHAPTER 1 .................................................................................................................................................... 1
Introduction .................................................................................................................................................. 1
1. 1. Background ....................................................................................................................................... 1
1.1.1. Energy storage system an enabling technology ......................................................................... 2
1.1.2. Overview of existing energy storage system .............................................................................. 3
1.1.3. Comparisons of Different Storage Techniques ........................................................................... 4
1.1.4. Types of batteries ....................................................................................................................... 5
1.2. Problems and Solutions ..................................................................................................................... 6
1.3. Objective of the thesis ....................................................................................................................... 8
1.4. Limitations ......................................................................................................................................... 8
1.5. Organization of the report ................................................................................................................. 9
CHAPTER 2 .................................................................................................................................................. 10
Lead Acid Battery ........................................................................................................................................ 10
2.1. General Overview of Lead Acid Battery ........................................................................................... 10
2.1.1. Background ............................................................................................................................... 10
2.1.2. Structure and Operation ........................................................................................................... 10
2.1.3. Types of Lead acid Battery ........................................................................................................ 11
2.2. Terminology used in batteries ......................................................................................................... 12
2.2.1. Battery Capacity ........................................................................................................................ 12
2.2.2. Cut off Voltage .......................................................................................................................... 12
2.2.3. Rate of Charge/Discharge ......................................................................................................... 12
2.2.4. Open Circuit Voltage ................................................................................................................. 13
2.2.5. Electromotive force................................................................................................................... 13
2.2.6. Depth of Discharge (DOD) ......................................................................................................... 13
2.2.7. State of charge (SOC) ................................................................................................................ 13
2.2.8. Internal Resistance .................................................................................................................... 13
2.2.9. Self Discharge Rate ................................................................................................................... 13
2.2.10. State of Health ........................................................................................................................ 14
2.2.11. Battery Lifetime ...................................................................................................................... 14
2.2.12. Battery Efficiency .................................................................................................................... 15
2.2.13. Thermal Runaway ................................................................................................................... 15
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CHAPTER 3 .................................................................................................................................................. 16
Types of Lead Acid Battery models ............................................................................................................. 16
3.1 Simple Battery Model ....................................................................................................................... 16
3.2. Modified Simple Battery Model....................................................................................................... 17
3.3. Advanced simple battery model ...................................................................................................... 18
3.3. Thevenin Battery Model .................................................................................................................. 19
3.4. Dynamic Battery Model ................................................................................................................... 19
3.5. Modified Thevenin Equivalent battery model ................................................................................. 20
3.6. Copetti Model: ................................................................................................................................. 21
3.7. Randle’s Battery Model ................................................................................................................... 22
3.8. Third Order Model ........................................................................................................................... 23
CHAPTER 4 .................................................................................................................................................. 25
Charging/discharging methods and technique ........................................................................................... 25
4.1. Various Charging Methods and Techniques used for lead acid batteries ....................................... 25
4.1. Wa charging ................................................................................................................................ 25
4.1.1. WOWa Charging ........................................................................................................................ 26
4.1.2. IUIa Charging ............................................................................................................................. 26
4.1.3. Pulsed charging ......................................................................................................................... 27
4.1.4. Quick Charging ......................................................................................................................... 27
4.2. Discharging....................................................................................................................................... 28
4.3. Choice of appropriate charging method .......................................................................................... 28
CHAPTER 5 .................................................................................................................................................. 29
Experiment and Model Selection................................................................................................................ 29
5.1. Experimental Setup:......................................................................................................................... 29
5.2. Model Selection ............................................................................................................................... 33
5.2.1. Simple Battery model................................................................................................................ 34
5.2.2. Modified Simple Battery Model ................................................................................................ 34
5.2.2. Advanced simple battery model ............................................................................................... 35
5.2.4. Thevenin Battery Model ........................................................................................................... 36
5.2.5. Copetti Model ........................................................................................................................... 36
5.2.7. Randle’s Battery Model............................................................................................................. 38
5.2.8. Third Order Model .................................................................................................................... 38
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5.3. Discussion of the Results ................................................................................................................. 39
5.4. Conclusion ........................................................................................................................................ 40
CHAPTER 6 .................................................................................................................................................. 41
Final Model of the Lead acid battery .......................................................................................................... 41
6.1.1. Capacity Model ............................................................................................................................. 42
6.1.2. Voltage Model............................................................................................................................... 43
6.1.3. Thermal Model.............................................................................................................................. 44
6.2. Summary of the final Model ............................................................................................................ 45
CHAPTER 7 .................................................................................................................................................. 46
Parameter Estimation of the Model ........................................................................................................... 46
7.1. Parameter Estimation for the Project .............................................................................................. 46
7.2. Implementation of the parameter estimation ................................................................................ 47
7.2.1.Parameter estimation using Lab Test ........................................................................................ 47
Parameters referring to Battery Capacity ........................................................................................... 48
Parameters referring to the voltage parameters................................................................................ 48
Parameters referring to the battery thermal model .......................................................................... 49
7.2.2. Model Parameter Identification using Simulink Parameter estimation ................................... 49
7.2.3. Validation of the model ............................................................................................................ 53
7.4. Discussions ....................................................................................................................................... 55
7.5. Summary .......................................................................................................................................... 55
CHAPTER 8 .................................................................................................................................................. 56
Charge Controller Implemented in the Project .......................................................................................... 56
8.1. IUIa Charging .................................................................................................................................... 56
8.1.1. Bulk charging ............................................................................................................................. 56
8.1.2. Absorption Charging ................................................................................................................. 56
8.1.3. Float charging ............................................................................................................................ 56
8.2. Charging Algorithm .......................................................................................................................... 57
8.3. Final System Block Diagram ............................................................................................................. 58
8.4. Results after implementing the charge controller ........................................................................... 59
Chapter 9..................................................................................................................................................... 60
Conclusions and Future Research ............................................................................................................... 60
9.1. Summary .......................................................................................................................................... 60
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List of Figures
Fig: 1 Energy Storage Diagram [6]................................................................................................................. 2
Fig: 2 Existing Problems and solution for the problems ............................................................................... 7
Fig: 3 Lead Acid battery and its components .............................................................................................. 10
Fig: 4 Equivalent circuit model of simple model ......................................................................................... 16
Fig: 5 Equivalent circuit of modified simple battery ................................................................................... 17
Fig: 6 Equivalent circuit of advanced simple battery .................................................................................. 18
Fig: 7 Equivalent circuit of Thevenin model [24] ........................................................................................ 19
Fig: 8 Equivalent model of modified Thevenin battery [24] ....................................................................... 20
Fig: 9 Equivalent circuit of Copetti model [26] ........................................................................................... 21
Fig: 10 Equivalent circuit of Randle’s model [27]........................................................................................ 22
Fig: 11 Equivalent circuit of third model [28] ............................................................................................. 23
Fig: 12 Voltage and current characteristics for Wa charging ...................................................................... 26
Fig: 13 Voltage and current characteristics for WOWa Charging. .............................................................. 26
Fig: 14 Voltage and Current characteristics for IUIa Charging. ................................................................... 27
Fig: 15 Current Characteristics for Pulsed charging .................................................................................... 27
Fig: 16 Voltage and Current Characteristics for quick charging. ................................................................. 28
Fig: 17 Experimental Setup layouts............................................................................................................. 29
Fig: 18 Experimental setup ......................................................................................................................... 30
Fig: 19 charging curve from the Experiment............................................................................................... 31
Fig: 20 Discharge curve for discharge current 18A ..................................................................................... 32
Fig: 21 Discharge curve for discharge current 10A ..................................................................................... 32
Fig: 22 Discharge curve for discharge current 15A ..................................................................................... 33
Fig: 23 Discharge curve from the experiment ............................................................................................ 34
Fig: 24 Simulink output for modified simple battery .................................................................................. 34
Fig: 25 Simulink output for linear variation for advanced simple model ................................................... 35
Fig: 26 Simulink output for Non linear variation for the advanced simple battery .................................... 36
Fig: 27 Charging output from simulink for copetti model .......................................................................... 37
Fig: 28 discharging output for the Copetti model from Simulink ............................................................... 37
Fig: 29 Simulation Output for the Randle’s model ..................................................................................... 38
Fig: 30 Simulation result for the third order model .................................................................................... 39
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Fig: 31 Final Structure model for the thesis ................................................................................................ 41
Fig: 32 Dynamic model of the battery ........................................................................................................ 42
Fig : 33 Final Equivalent Circuit model for the system [28] ........................................................................ 45
Fig: 34 typical voltage and current profile for a constant current discharge [21] ...................................... 48
Fig: 35 Model based parameter Identification Algorithm .......................................................................... 50
Fig: 36 The cost function for simulating the model in Simulink parameter estimation. ............................ 51
Fig: 37 the trajectories of the estimated parameters after the simulation ................................................ 52
Fig: 38 Final estimated parameter values from the Simulink parameter estimation. ................................ 52
Fig: 39 Plot of the measured and simulated result (Validation Data 1)...................................................... 53
Fig: 40 Plot of the residual result (Validation Data 1) ................................................................................. 53
Fig: 41 Plot of the measured and simulated result (Validation Data 2)...................................................... 54
Fig: 42 Plot of Error voltage (Validation Data 2) ......................................................................................... 54
Fig: 43 Ideal three steps or IUIa Charging Method ..................................................................................... 56
Fig: 44 Algorithm for battery charging ........................................................................................................ 57
Fig: 45 Final System Block Diagram implementing the battery model ....................................................... 58
Fig: 46 Output of the implementation of the algorithm in Simulink .......................................................... 59
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CHAPTER 1
Introduction
1. 1. Background
Each year modern society uses approximately 500 exajoules (EJ) of the total primary energy which has
been increasing at roughly 2% per year for the past two hundred years. Modern society has been shaped
by the use of the fossil fuels as over 80% of the energy used by the mankind comes from fossil fuels [1].
The population of the world is skyrocketing and the stored amount of the fossil fuel is diminishing. Fossil
fuel has been very convenient way to power the energy demand but it also brings serve consequences.
Two major problems that arise from the use of the fossil fuel are that the resources are limited and
there is the serve impact on the environment.
Carbon dioxide is created while burning fossil fuel which in turn contributes to global warming. It is
projected that by the year 2020, world energy consumption will increase by 50 percent, or an additional
207 quadrillion BTUs. If the same scenario of the fossil fuel consumption remains then the fossil fuel
reserves will be finished in 104 years [2].In addition to influence to the environment, derogating fossil
fuels reserves and fluctuations of the global energy market, have increased the needs to explore
renewable feedstock and to look for novel sustainable production systems.
Renewable energy sources include wind power, solar power (thermal, photovoltaic and concentrated),
hydroelectric power, tidal power, geothermal energy and biomass. The global capacity of wind power
has increased from 50 GW to 240 GW from 2005 to 2011 whereas solar power has increased from 5 GW
to 60 GW [3]. In 2011, excluding the large hydropower plants, the installed worldwide capacity based on
wind sources was estimated at 41.7 GW [4]. They are mainly installed in Europe, North America and
Asia-Oceania. Taking the upcoming problems into consideration, the European Union (EU) by means of
the SET Plan, will further support the energy production from renewable source. By 2020, the SET Plan
have target to increase the energy production from the renewable energy sources to 20%. Also other
countries, such as the USA and Canada, are going to increase the generation from renewable in the next
decades [5].
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1.1.1. Energy storage system an enabling technology
From the above statistics we can see that the overall structure of the electric power system is changing.
The increasing demand for the alternative energy it is moving from fossil fuel to renewable energy that
are more environmentally friendly and sustainable. In addition to that electric power systems should be
more reliable and should meet the demand of the increasing energy. There is a great challenge when
integrating renewable energy, as wind energy and photovoltaic do not behave like conventional power
plants. Some major challenges with the use of renewable energy are:
 Weather dependent
 Non dispatchable
 Uncertainty of the time of generation
 Power quality and reliability issues
 Unable to produce electricity demand-driven
 Economic factors including tax and energy credits
This is where energy storage systems become an enabling technology. They provide the means to the
non dispatchable resources into dispatchable energy sources. According to the technology selected they
can provide spinning reserves, load leveling and shifting, load forecasting, frequency control, VAR
support voltage regulation, relief of overloaded transmission line, and more effective and efficient use
of the capital resources [6].The principle energy storage applications and types of the energy storage
system can be seen in fig. 1.
Fig: 1 Energy Storage Diagram [6]
2
1.1.2. Overview of existing energy storage system
Depending on the variety of the applications a number of the energy storage system had been
developed. Some of them are described below:
Super capacitor or ultracapacitor
In this kind of the storage system the energy is stored in an electric field between a pair of the
conductors. The storing process is highly reversible and allows the ultracapacitor to charged and
discharged hundreds of times. Further, it is also temperature resistant with an operating range between
-40 to +65 degree and is also shock and vibration resistant [7].With these attributes the ultracapacitor
can be highly effective energy storage device. However, it has a low electric density and often used for
short term energy storage. Current challenges are the low energy density and high cost of the system
[8].
Pumped Hydroelectricity (PHS)
For more than 70 years pumped hydro storage has been used. The principle of the operation of pumped
hydro is same as that of hydroelectric power plant. When there is no electric demand the surplus power
water is pumped from a lower reservoir to a higher level reservoir. The stored water is released during
the times of high electrical demand .The major drawback to this design is the amount of land required to
create the reservoir and the elevation needed between them. Pumped hydro storage plants are costly
and take long time to plan and build [9].
Compressed air energy storage (CAES)
During the off peak electricity produced is used to compress air into an underground reservoir or surface
vessel/piping system. When there is demand for electricity the air is released so that it could be heated
through combustion with any one of a variety of fuels which later on run through expansion turbines to
drive an electric generator. About 85% of the efficiency can be achieved but the main problem with this
type of system is the reservoir has to be air tight and very large [6].
Flywheels
In this kind of the energy storage system the energy is stored in the form of the kinetic energy .The
energy is stored in rotor which is spinning in very high velocity and the amount of energy stored in the
rotor is proportional to the square of its angular momentum. When the demand of the energy is high
the flywheel switches operational modes to produce the power needed .Flywheels are mainly used and
efficient for short duration storage cycles due to their fast response speed. These energy storage devices
are mainly used in applications that require high numbers of deep discharge cycles [10].
3
Superconducting Magnetic energy storage (SMES)
In this kind of the energy storage system super conducting magnets are cooled to produce an essentially
loss-less coil. These magnets stored as DC energy and when the demand is high this energy is to be
released from the system the process is reversed. The efficiencies of these SMES systems have been
reported to be in the range of 95 to 98%. In addition, it takes very small time to supply the power to the
system [11].
Hydrogen Fuel Cell
The main working principle of hydrogen fuel cell is a very high energy density converts the chemical
energy in a source fuel into an electrical current. It mainly consists of three stages: electrolyzing stage,
hydrogen storage stage and the fuel cell stage. Hydrogen ion is created by the electrolyze water which is
produced during the off peak. When there is need for the electricity hydrogen is combine with oxygen to
make water and this reaction is converted to electrical energy. Hydrogen storage is relatively immature
technology with efficiency between 50 to 60% with high cost of fuel cells [6].
Chemical storage or Batteries
Chemical storage is the most popular method of energy storage. The charge and discharge phase in the
batteries helps to use batteries for double function i.e. storage and release of electricity. The main
working principle of the battery is it converts chemical energy into electrical energy when the
electrolytes flow through the electrochemical cell. They are often used in portable systems, but also in
permanent applications such as emergency network back-up, renewable-energy storage in isolated
areas, etc [6].
1.1.3. Comparisons of Different Storage Techniques
The storage system is selected on the basis of the necessity of system used. Some of the criteria
included for the project are reliability, efficiency, cost technical maturity, life span and environmental
impact. Efficiency and life expectancy plays a vital role while choosing any storage technology, as they
affect the overall storage costs. Low efficiency increases the effective energy costs since only a fraction
of the stored energy can be used in addition a short lifespan also increases long-term costs as the
storage unit needs to be replaced more often. Further investment cost also affects the selection of the
storage system. Comparison of different storage system is particularly important for the transmission
industry, portable applications, and isolated sites.
SMES has the highest efficiency but it is relatively new technology with high cost. While hydrogen
storage and super capacitor seems promising but their immaturity makes them unsuitable for the
4
system where support is not readily available. CAES and PHS have very large installation cost so they are
not preferred for the small project. In addition to that CAES needs a wide amount of location to preserve
it underground. Although flywheel is efficient and low cost system, their self discharge rate is high and
supply energy density is low. Henceforth for small systems (a few kWh) and larger systems (a few
100kWh in isolated areas relying on intermittent renewable energy, the battery remains the best
compromise between performance and cost.
1.1.4. Types of batteries
From the previous discussion we come to know that batteries are the most efficient storage system for a
small system. There are various kind of batteries applied on the large range. The most popular batteries
are discussed here and among them highly efficient battery is chosen.
Lead Acid Batteries
Lead acid batteries are the oldest rechargeable battery, invented by Planté in 1859. Battery cell has lead
(Pb) and lead oxide (PbO2) as electrodes and sulfuric acid (H2SO4) as electrolyte.These batterries are
widely used as engine starting or backup power systems.Mostly popular for its low price but short
lifetime (500-1000 cycles) makes energy management applications limited. In addition to its deep
discharge quality it also have low self discharge rate. Largest installations of 40 MWh/10 MW can be
seen in Chino, California, and 8.5 MWh in Berlin. lead is toxic but is 98% recycled [12] .
Lithium Ion (Li Ion) batteries
The cathode is made of lithiated metal oxide (e.g. LiCoO2, LiNiO2, LiMn2O4, LiFePO4) and anode of
graphited carbon.Electrolyte of lithium ion batteries is made of lithium salts like LiPF6 dissolved in
organic carbonates. When battery is charged, lithium atoms in the cathode become ions and migrate
through the electrolyte to the carbon anode where they combine with external electrons and are
deposited between carbon layers as lithium atoms. High efficiency, energy density and long lifetime are
the quatilities seen in Li ion batteries. However, litium ion battery have low economic efficiencies and
stability of the chemicals should be considered because of the chemical activeness of lithium[13].
Sodium Sulphur (NaS) batteries
NaS battery consists of molten sulphur at the positive electrolyte and molten sodium at the negative
electrode which are separated by a solid beta alumina ceramic electrolyte.NaS have efficiency of about
80-90% and lifetime of 2500 cycles at 100% discharge. In order to keep the sodium and sulphur molten
in the battery, and to obtain adequate conductivity in the electrolyte, they are housed in a
thermally‐insulated enclosure that must keep it above 270°C, usually at 320°C to 340°C. One of the
5
greatest characteristics of NaS batteries is its ability to provide power in a single, continuous discharge .
NaS batteries have also been used for deferringtransmission upgrades. The major disadvantage of NaS
batteries is retaining the device at elevated temperatures above 270°C. It is not only energy consuming,
but it also brings with it problems such as thermal management and safety regulations [14].
Nickel Cadmium (NiCd) Batteries
Most common nickel battery is nickel- cadmium (NiCd) which has nickel as cathode and cadmium as
anode with an alkaline like potassium hydroxide (KOH) as electrolyte.Because cadmium is toxic, metal
hydrides are now replacing cadmium as anode. Metal is usually a compound of rare earth metals and Ni,
Co, Mn and/or aluminium. NiMH have lower energy density than Li-ion batteries. Nickel batteries have a
low internal resistance and can tolerate high discharge currents at deep discharge levels. Most
application are portable like in power tools or in automobiles and other vehicles.A problem preventing
the large scale application of this kind of battery is that nickel cadmium batteries suffer from faster self
discharge rate and cadmium is toxic as well as expensive [15].
Zinc Bromine (ZnBr) Batteries
Anode is pure metal like zinc or aluminium whereas cathode is made of porous carbon structure or a
metal mesh covered with catalysts and uses the incoming air as the oxidant. The electrolytes used in this
kind of battery are good ion conductors like KOH liquid or saturated in solid polymer membrane.ZnBr
are compact and potentially inexpensive but chargeable batteries are difficult to make.Efficiency is
below 50% and lifetime 100-300 cycles which makes it less popular[14].
Battery selection criteria are basically performance and energy density versus life cycle cost and
environment concerns. While NiCd batteries are well understood, but their relatively low density make
them less popular. Similarly, due to energy management NaS and low efficiency of ZnBr makes them less
popular in the battery market. However, Li ion and lead acid battery seems to be the idle choice. For
storage system having small systems (a few kWh) and larger systems (a few 100kWh in isolated areas
relying on intermittent renewable energy size is not the main concern so lead acid batteries are most
economical choices with their recyclable capability which can double their life span.
1.2. Problems and Solutions
Today there is an increasing demand of new technology for standalone energy system in remote areas.
Availability issues and environmental issues have shifted the interest of the people towards integration
of renewable energy towards these systems. In contrast to this due to the intermittency and
unpredictability nature of the renewable energy sources the integration of renewable energy system to
the power system becomes more challenging. These challenges can be minimized by using batteries as
6
the storage system. Battery storage has proven to be necessary in the autonomous power supply where
there is continuous power demand. So, in small scale off grid system battery performance is considered
as the key for the overall system performance and the battery also contribute a significant investment
cost.
Batteries that are integrated to the renewable system have to bear a wide range of operational
conditions such as varying rates of charge and discharge, frequency and depth of discharges,
temperature fluctuations etc [16]. These variables make it very difficult to accurately predict battery
performance in renewable systems and also the total cost of the storage system. Therefore, premature
failure and possibilities of extended life span of batteries are major concerns within the renewable
industry. The major sources of battery premature failure are due to the high discharge rate, over
charging, temperature etc. Taking these parameters into consideration, a proper charge and discharge
controller is required for reliability and safe operation of the battery. Consequently, modeling of battery
becomes very necessary in order to enhance the performance of the battery by integrating a controller
and to determine the cost of the storage system.
Fig: 2 Existing Problems and solution for the problems
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1.3. Objective of the thesis
The main objective of the thesis is to come up with the dynamic model which can replicate the battery
energy storage system. The dynamic model will replicate the relevant behavior of the battery such as
state of charge, depth of discharge, terminal voltage and cell temperature as that in the real battery.
These outputs from the model are then used to design a charge controller in order to prolong the life
time of the battery.
The proposed methodology is the model based approach where the parameters are determined to
develop a suitable model. The main steps taken during the project are; a various models are studied first
from the literature in order to be familiar with battery and the selection of the model is done according
to the requirement of the battery model. Then the unknown parameter of the dynamic model is found
using the methodology of the experimental test. These values were used as the initial parameter to find
the optimum value of the parameter from the MATLAB Simulink parameter estimation toolbox. Later,
the model is used to design appropriate charge controller.
The intension of the battery modeling is to integrate it with the PV simulation platform in the small scale
off grid system specially developed for remote areas. A complete system simulation is necessary to
predict the performance and the cost of the system.
1.4. Limitations
The key limitation of the thesis is the proposed model can determine the state of charge of the battery
but cannot determine the state of the health of the battery. Because for determining state of health
different types of battery are necessary and various experimental tests needed to be conducted. A
battery needs at least six months to become weak even continuously charged and discharged. Due to
the time limitations and lack of resources the battery state of health was not studied in the project. A
charge controller is designed to prolong the battery life but discharge controller is not discussed.
8
1.5. Organization of the report
The thesis is organized into nine chapters. First chapter gives the general background of the project and
objective of the thesis. The over view of remaining chapters are described as below:
Chapter 2 gives an overview of the lead acid batteries such as its structure and types of lead acid
batteries. In order to be familiar with the battery terms and concept various terminology used in the
batteries are briefly described in the second part of the chapter.
Chapter 3 gives the theoretical introduction of different existing lead acid battery model. The model is
introduced systematically from a simple model to the complex model. The detailed analysis of the
selected model is presented in chapter 6.
Chapter 4 starts with the description of importance of the charging methodology. The methods and
techniques used for charging lead acid batteries are described in this chapter. A comparison is done
between the different charging techniques to come up with the appropriate charging technique for our
system.
Chapter 5 is the experiment and model selection. The experimental setup used in the project is briefly
described and the output from the experiment is presented. The simulated output of the existing
theoretical models is presented. At the end section a comparison is made between the model outputs
and the experimental output. Based on the comparisons an appropriate model is selected for the
project.
Chapter 6 deals with the final model of the lead acid battery. A detailed analysis of the model is
presented.
Chapter 7 presents the model parameter identification. The chapter provides a detailed analysis of the
estimation method used. The chapter is divided into two parts. Firstly, the parameters are analyzed
according to the lab test. In the second part principle of Simulink parameter estimation is introduced
The parameter is estimated using the Matlab Simulink toolbox using the experimental value of the
parameter as the initial value. The validation of the model is also presented.
Chapter 8 develops an algorithm for the design of the charge controller used in the project. The
algorithm is implemented in the Simulink and the output is discussed.
Chapter 9 gives the future work and improvements that can be implemented are projected.
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CHAPTER 2
Lead Acid Battery
2.1. General Overview of Lead Acid Battery
2.1.1. Background
Lead acid was the first rechargeable battery for commercial use. It was invented by the French physician
Gaston Planté in 1859. His model consisted of two lead sheets separated by rubber strips and rolled into
a spiral. These batteries were first used to power the lights in train carriages while the train stopped at a
station. In 1881, Camille Alphonse Faure invented an improved version that consisted of a lead grid
lattice forming a plate into which a lead oxide paste was pressed. This design was easier to massproduce. During the mid 1970’s, researches developed a maintenance-free lead acid battery that could
operate in any position. The liquid electrolyte was transformed into moistened separators and the
enclosure was sealed. Safety valves were added to allow venting of gas during charge and discharge
[12].
2.1.2. Structure and Operation
Lead acid batteries are constructed with the positive electrode (anode) made from lead dioxide and the
negative electrode (cathode) is made from pure lead. Both electrodes are immersed into the electrolyte
which is sulphuric acid for lead acid batteries. These structures make the battery energy storage device,
as they can convert electrical energy into chemical energy and vice versa [17].
Fig: 3 Lead Acid battery and its components
10
Discharging
During discharging the negative plate acts as the anode and the positive plate act as the cathode. When
a load is connected between two electrodes the excess electrons move from anode to cathode as a
current and electricity is generated.
At Anode
At Cathode
Charging
During charging an external power supply is connected to the electrodes. The lead sulphate is changed
back to lead and lead dioxide as the electrons are forced to flow backward against the electro potential.
Sulphuric acid is restored back to the liquid electrolyte.
At Anode
At Cathode
2.1.3. Types of Lead acid Battery
Flooded battery
Flooded batteries have a conventional liquid electrolyte and have removable caps so that the electrolyte
can be diluted . These batteries are used for large capacity backup power, computer centres, offgrid
system etc.Flooded lead acid batteries are less sensitive to the charging and should be kept upright[17].
Gelled elctrolyte
The electrolyte in the battery as the name suggested is gelled so will not leak. However, these
electrolyte cannot be diluted so that overcharging must be avoided. These batteries only last for 1 to 2
years but they are environmentally friendly and easy to work technically [17].
Valve Regulated Lead Avid Battery (VRLA)
The electrolyte in VRLA batteries are sealed in the container.The plates ,size and weight of these kind of
batteries are differnet from other kind of batteries as they are totally dependent on the container
type.they can be mobilized and mounted in any position.there is very low gassing due to the internal gas
recombination and used in vehicles [17].
11
Absorbed Glass Mat (AGM) Batteries
The electrolyte in these kind of batteries is held between the plates absorbed into the mat in such a
way that the electrolyte is immobilized.Unlike gelled batteries they can withstand overcharging but the
electrolyte is not leaked as in gelled batteries. However these batteries are much more expensive [17].
2.2. Terminology used in batteries
2.2.1. Battery Capacity
Battery capacity is the measure of a battery’s ability to store or deliver electrical energy and is
commonly expressed in units of ampere-hours. Ampere-Hour is calculated by integrating the discharge
current in amperes over a specific time period. The transfer of one-ampere over one-hour is equal to an
ampere hour or is equal to 3600 coulombs of charge. Let’s say if a battery delivers 5-amps for 20-hours
it is said to have delivered 100 ampere-hours. The quantity of active material, the number, design and
physical dimensions of the plates, and the electrolyte specific gravity etc determines the capacity of the
battery. Generally, capacity is specified at a specific discharge rate or over a certain time period [18].
According to Peukert’s law:
Where
capacity on one ampere discharge rate
Discharge current
Peukert’s constant
Time of discharge
Battery capacity is always referred as “Cn” which means to complete discharge the battery in n hours.
The capacity under ten hour discharge rate “C10” is always taken as the nominal capacity.
2.2.2. Cut off Voltage
It is the lowest voltage which a battery system is allowed to reach in operation. It is provided by the
manufacturing datasheet at a defined discharge rate.
2.2.3. Rate of Charge/Discharge
It is the ratio of the nominal battery capacity to the charge or discharge time period in hours. For
example, a 5-amp discharge for a nominal 100 ampere-hour battery would be considered a C/20
discharge rate.
12
2.2.4. Open Circuit Voltage
When the battery is in rest or steady state the output is called open circuit voltage. The open circuit
voltage depends on the battery design, specific gravity and temperature, the open circuit voltage of a
fully charged lead-acid battery is typically about 2.1-volts.
2.2.5. Electromotive force
Energy is transferred to the electron by the batteries so that they flow around a circuit. Total amount of
energy per coulomb of charge supplied by the battery is referred as electromotive force. It is calculated
by the difference between the electric potential of the two electrodes of each cell. This electromotive
force is numerically equal to the battery open circuit voltage.
2.2.6. Depth of Discharge (DOD)
The depth of discharge (DOD) of a battery is defined as the percentage of capacity that has been
withdrawn from a battery compared to the total fully charged capacity.
2.2.7. State of charge (SOC)
The state of charge (SOC) is defined as the percentage of the energy stored in a fully charged battery.
State of charge increases when the battery is charged and decreases as the battery is discharged.
2.2.8. Internal Resistance
The path of the electron while flowing through the battery will have internal resistance. This internal
resistance depends on the cells design, construction, age and condition. Therefore, on discharge this
internal resistance causes the voltage measured across the cells terminal to be less than the EMF
voltage. Thus when the current flows the resistance is given by
Various factors cause the increase in internal resistance of the battery such as sulphation, temperature,
complete or deep discharge leading to excessive use of the active material. Sulphation is a process of
formation of the stable crystalline form of the lead sulphate which cannot be converted to lead, lead
oxide and sulphuric acid and cannot conduct electricity [19].High temperature operation increase the
aging rate of the battery therefore increasing the internal resistance.
2.2.9. Self Discharge Rate
Even if the battery is not charged or discharged in open-circuit mode a battery undergoes a reduction in
state of charge, due to internal mechanisms and losses within the battery. Self discharge rate depends
13
on the active materials and grid alloying elements used in the design so different batteries have
different self discharge rate.
2.2.10. State of Health
State of health is a defined to show how weak the battery is and represents the percentage of remaining
capacity to the initial capacity when the battery is brand new.
2.2.11. Battery Lifetime
Battery lifetime will be affected in different ways depending on the conditions they are treated and in a
number of design factors. The stress factor of the battery is a function of the design, selection of the
materials and manufacturing processes. Generally, the battery life span is quoted by the number of
cycles that it is expected to perform. Some of the major damaged factors are discussed below:
Positive Grid Corrosion
The available capacity and internal resistance of the battery is affected by the corrosion of the positive
grid. As the grid corrodes some of the active mass has reduced connection to the terminal as a result the
capacity is decreased. The internal resistance increases as the corrosion increases because of the
reduced connectivity of the corroded material and decrease in the cross section of the positive grid. The
corrosion of the positive grid takes place with the increase in the voltage, acid concentration and
temperature. Generally, as the temperature increases by 10oC the rate of an electrochemical reaction
doubles, battery life decreases by a factor of two for every 10oC increase in average operating
temperature [17].
Irreversible sulphation
Sulphate crystals are formed while the battery is discharged and these crystals are dissolved during
charging. However, if the battery is not operated properly the sulphate crystals grow in size and
resulting in irreversible sulphation. This leads the loss in capacity of the batter and low battery lifetime
as the large sulphate crystals will not take part in chemical reaction and also will leave part of active
material insulated from the terminal [19].
Shedding
The process of detachment of the active material from the electrode due to overcharging and sulphation
reducing the battery capacity is called shedding. While sulphation creates the difference in volume of
the sulphate crystals and lead oxide on the positive electrode leading to shedding, gassing bubbles
created during overcharging detach the active material from electrode [19].
14
Softening of the electrodes
It is the change in the mechanical structure of the electrodes and active material due to overcharging
and undercharging. Softening of the electrodes decreases the capacity of the battery as the porosity and
surface area of the electrolyte is decreased as the chemical reaction is concentrated to less space [19].
2.2.12. Battery Efficiency
Due to the internal resistance and the fact that the charging voltage is greater than the discharge
voltage the energy returned by the battery upon discharge will be less than the energy used for
recharging. Typically a lead acid battery will be 80 to 90% efficient when considering ampere hours [17].
2.2.13. Thermal Runaway
Thermal runaway is the extreme example of battery getting heated, at which point the battery is almost
certain to be damaged beyond repair. If the battery is not operated properly like operating in high
temperature, high voltage beyond gassing voltage which results in extreme
gas evolution ,high
increased water loss ,excessive shedding of positive active material and increased positive grid
corrosion. At thermal runaway, the heat generated internally in the battery is more than that can be
dissipated to the surrounding so this can also damage the surrounding equipment. Henceforth, it is
extremely important that the battery’s temperature is not high a while charging at high voltage [17].
15
CHAPTER 3
Types of Lead Acid Battery models
Modeling of the lead acid batteries can be done in numerous ways depending on the system
requirement and accuracy [20]. These include Electrochemical Models, Computational Fluid Dynamics
Models, Finite Element Models and Electrical Equivalent model. These models need experimentation to
ascertain the characteristics and plot response curves for the battery, measuring voltage and currents
during charge and discharging process. Electrochemical Models, Computational Fluid Dynamics Models,
Finite Element Models are effective in gaining technical knowledge on the battery, but not very helpful
in actual simulation and system behavior analysis purposes. But Electrical equivalent circuit Model
represents the various parameters and characteristics of the battery by the electrical equation and is
useful in simulation and system behavior analysis purpose.
Modeling of the lead acid battery is a new topic for me. The study of the various models is done from a
very simple battery model to a complex battery model. The study is done in order to gain in depth
knowledge of the electrical behavior of the battery. Hence, various electrical battery models are
described below:
3.1 Simple Battery Model
Fig: 4 Equivalent circuit model of simple model
16
If battery was linear then it acts as an electric bipole. A simple ideal model consists of E0 as the
electromotive force of the battery and a constant equivalent resistor ESR connected in series as an
internal resistance.V0 is the terminal voltage of the battery [21]. V0 can be obtained by measuring the
open circuit voltage and ESR can be obtained from both open circuit measurement and with load
connected when the battery is fully charged.
3.2. Modified Simple Battery Model
Fig: 5 Equivalent circuit of modified simple battery
It is the modified form of the simple battery model. The fixed resistance from the simple battery model
is changed into a variable resistance which is dependent on state of charge. Here the resistance ESR is
varying accordance with the battery state of charge [22].
Where, E0 is the open circuit voltage, R0 is the internal resistance R with the battery fully charged, C10 is
the nominal battery capacity given by the manufacture, K is the capacity coefficient and S is the state of
charge varying from 0 to 1.
17
3.3. Advanced simple battery model
Fig: 6 Equivalent circuit of advanced simple battery
Similar to the modified battery model more advanced simple battery model is presented in [23].
In this model the constant resistance is no longer constant but varies with the depth of discharge. The
variation upon depth of discharge is either linear or non linear.
is the output voltage,
is the open circuit voltage,
is the battery current and
is the
resistance
and
vary with the depth of discharge(Q), where
and
The variation upon depth of discharge is either linear or non linear which is given below:.
For linear variation:
Voc and Ri vary linearly with depth of discharge (Q).
Here, a0, a1, b0, and b1 are the coefficient and the values are found experimentally in [23].The internal
resistance of the battery was given by
18
For Nonlinear variation:
The
and
vary non-linearly with the depth of discharge (Q).
Here, a0, a1, a2, a3, a4, a5, b0, b1, b3, b4 and b5 are the coefficient and the values are found experimentally
in [23].
3.3. Thevenin Battery Model
Fig: 7 Equivalent circuit of Thevenin model [24]
Thevenin battery model is one of the most commonly used battery model. The model consists of ideal
no-load battery voltage Voc, internal resistance (R), Capacitance (Co) and over voltage resistance (R0).
Capacitance between electrolyte and electrodes is given by (C0) whereas R0 represents the battery
overvoltage due to the contact resistance of plate to electrolyte [24].
3.4. Dynamic Battery Model
This model is the modified Thevenin battery model. Similar to modified simple battery model it takes
account the non linear characteristics of the open circuit voltage and the internal resistance [25].
19
The internal resistance is given by
Where,
.
is the terminal battery voltage,
is the open circuit voltage and
is the battery terminal
resistor.
3.5. Modified Thevenin Equivalent battery model
Fig: 8 Equivalent model of modified Thevenin battery [24]
Thevenin Battery Model was modified to improve accuracy so the modified Thevenin equivalent battery
model is introduced. This model uses a capacitor (C), to represent the polarization capacitance and a
shunt resistor Rb to represent its self-discharge. Rid and Ric are the resistors connected to the two
parallel branches of the circuit and each diode facing the opposite direction respectively. This type of
construction is to enable different resistances to be used to model the charging and discharging
behavior of the internal resistance of the battery.
20
3.6. Copetti Model:
Fig: 9 Equivalent circuit of Copetti model [26]
The model is a generic battery model with constant parameters that is valid for any size of the battery.
This model is simple, because the experimental identification of empirical parameters is not required.
The model is described by the following equation:
If
If
With
21
Here, ibat is the battery current, ubat is the battery voltage, n is the number of the cells, Vg = 2.35V is the
gassing voltage, Vcp is the polarization voltage, Vcb is the electromotive force, R is the internal resistance,
Cp is the polarization capacitor,C10 is the nominal capacity and I10 is the charge current corresponding to
C10.
3.7. Randle’s Battery Model
Fig: 10 Equivalent circuit of Randle’s model [27]
The fig 15 represents the Randles model circuit where Ri is the resistance of the battery’s terminals and
inter-cell connections. Similarly, Rt and Cs describe transient effects due to shifting ion concentrations
and plate current densities. While Rd represents the self-discharging resistance, Cb is considered the
main charge store, and the voltage across it is the suitable indicator of SOC, whilst SOH can be inferred
by any decrease in the value of Cb [27].
A large time constants is involved with typical combinations of Cb and Rd, the accurate estimation of the
exact values of these large components might hindrance the transient parameter variation. Thus, a
22
structured subspace estimation model is used in which the time constant associated with the product
CbRd is assumed to be large, hence neglected. Likewise, Rd is assumed to be sufficiently large so that a
negligible current is drawn by the discharge resistance. The modified Randles model is then given by
[25]:
Where Cs, Rt ,Cb and Ri are the parameters to be estimated.
3.8. Third Order Model
Fig: 11 Equivalent circuit of third model [28]
The model is described by equivalent electric network as shown in figure 10. The dynamic equation of
the model represents the charge storage process in the battery and the electrolyte heating which is
given as follows [28]:
where
23
“extracted charge,” i.e., the charge that has been actually extracted from the battery starting from
a battery completely full,
battery thermal capacitance,
thermal resistance and
heating
power generated inside the battery by conversion from electrical or chemical energy.
Where
Where,
,
,
,
,
,
and
are the constant for the particular battery. The
detailed analysis and the explanation of the model are presented in chapter 6.
24
CHAPTER 4
Charging/discharging methods and technique
The charging of lead acid battery is done with direct current. The charging and discharging of the battery
plays a vital role on the battery lifetime. During discharge the chemical reaction is such that the active
components of the battery plate i.e. lead and lead dioxide in the negative plate and positive plate
respectively converts into free electrons, water and lead sulphate. The tricky part is during recharge,
these sulphates are eliminated by recombining water into acid; however this should be carried on
without losing hydrogen and oxygen gases which makes up water. The major reason of the losses of the
gases is if the charging is done beyond the gassing voltage (2.54 V) and charging at higher temperature.
Battery charging technique also should consider the complete conversion of the active components.
Battery can accept very high current energy but the chemical process in the battery is very slow.
Pumping electrical energy faster than the chemicals can react to it can cause local overcharge,
overheating, and unwanted chemical reaction near to the electrodes thus damaging the cell.
Henceforth, a rest period is desirable so that the chemical process can propagate throughout the
battery. As an analogy battery charging is like pouring a beer into the glass. If the beer is pour very
quickly then a lot of froth can be seen and a very little beer at the bottom but if the beer is poured very
slowly the beer settle till the forth disperses and then topping up results in completely filled glass [30].
4.1. Various Charging Methods and Techniques used for lead acid batteries
Usually the charging time of the sealed lead acid battery is 12-16 hours, up to 36-48 hours for the
stationary batteries .But the charging time can be reduced to 10 hours or less with higher and multistage
charging methods, the topping charge may not be complete [30]. Therefore, the charging techniques
and methodology of lead acid vary with demand and charging time. Some of the charging techniques are
discussed below:
4.1. Wa charging
This is the simplest kind of the charging method. The charger is built according to the type of the
battery. If there is large amount of the charging time (10 hours) available then this kind of the charging
technique is used. The battery is initially charged with the high current defined by the manufacture and
then exponentially decreased as the voltage rises until the battery is fully charged. The charger is then
deactivated. The efficiency is around 70 to 75% and the temperature increases up to +70C.With this kind
of charging method the battery lifetime is approximately 5 to 6 years [29].
25
Fig: 12 Voltage and current characteristics for Wa charging
4.1.1. WOWa Charging
In this type of the charging method the battery is initially charged at the constant current (nominal
current) until the gassing voltage is reached then the current is decreased exponentially as in the Wa
characteristics. The charge efficiency is about 85% and the temperature increases up to +70C. The
charging time is usually 6-7 hours. The battery lifetime is usually 5 years from this kind of the charging
methods [29].
Fig: 13 Voltage and current characteristics for WOWa Charging.
4.1.2. IUIa Charging
In this kind of charging methods initially the battery is charged at a constant current until the cell voltage
is reached to pre-set value. This type of charging is called the bulk phase. The second part is as the
voltage reaches to the pre-set value the voltage is made constant and the current decreases
exponentially until it reaches another pre-set value this is called the absorption. In this phase the
saturation is provided to the battery. Finally the charger switches to the constant current mode until the
voltage reached up to another pre-set value which is called the float charge. During this phase the losses
due to self discharge is compensated. Finally the charger is switched off. This kind of the charger is
26
highly efficient with efficiency about 95% and the battery is charged 5 to 6 hours. The temperature rises
upto 150C and the life expectancy is about 3 to 4 years [29].
Fig: 14 Voltage and Current characteristics for IUIa Charging.
4.1.3. Pulsed charging
The battery is charged by the pulse current. The battery is initially charged by a constant current and
then there is no current. After a small rest period the battery is again charged. These rest periods allows
the chemical actions in the battery to stabilize by equalizing the reaction throughout the bulk of the
electrode. It also helps in reducing the gas formation, crystal growth and passivation. It takes long time
to charge the battery however the battery lifetime can be increased from this kind of charger [30].
Fig: 15 Current Characteristics for Pulsed charging
4.1.4. Quick Charging
The battery is charged with constant current above the current limit from the manufacture data sheet
taking temperature into consideration. The battery is stopped charging before the gassing voltage is
reached. With this kind of the charger the battery is charged only 80% but the battery can be charged
27
within an hour. The battery life time is about 2 to 2.5 years. It is mostly applicable where there is no
time to charge the battery [30].
Fig: 16 Voltage and Current Characteristics for quick charging.
4.2. Discharging
The battery should be discharged at the rated nominal current and the discharged rate is maintained
constant. When the state of charge of the battery reaches 20 % then the discharging should be stopped.
If the battery is over discharged then the sulphuric acid electrolyte can be depleted of the sulphate ion
and becomes essentially water. The deficiency of the sulphate ion will cause cell impedance to rise and
the resistance there will be hindrance in current flow.
4.3. Choice of appropriate charging method
The charging method depends on the demand and the available of charging time. For our project the
charging is done by the renewable sources and generally for PV module the battery can be charged
during the day and discharged during the night. Our main concern is the efficiency of the battery and the
battery lifetime. Using Wa requires large amount of time while WOWa is least efficient compared to
IUIa. Pulse charging requires large amount of time and quick charging is not possible as the huge current
cannot be produced by small PV module. Henceforth, the choice for appropriate charging method will
be IUIa with its advantages of high efficiency, charging time and life expectancy.
28
CHAPTER 5
Experiment and Model Selection
Experimental test based on 12V lead acid battery having a nominal capacity of 100 Ah was carried out.
Some of the characteristics of the battery can be found in the tests. The data’s from the test will be used
to select the appropriate model and the parameters for the model. Basically charging and discharging of
the battery at different temperature was done.
5.1. Experimental Setup:
In the experiment, SMP charger 120 V/10A was used to charge the battery, a multimeter to log the data
and Torkel 820 Battery load Unit was used as a discharger whose specification are provided in the
appendix. Two temperature sensors were employed in the experiment and a heater was used to vary
the temperature. The state of charge of the battery was measured with the help of specific gravity
hydrometer. The equivalent circuit of the test designed for the experiment is shown in figure:
Fig: 17 Experimental Setup layouts
29
Fig: 18 Experimental setup
30
Charging:
During charging the Torkel load unit was disconnected and the SMP charger was connected to the
battery. The battery was charged from the charger at a constant voltage of 14 V at normal room
temperature and the current was maintained constant so that the charging voltage was constant. Once
the charging voltage remain constant the battery starts charging the charging current steadily decreases.
When the battery is empty the battery takes sufficiently large current however when the charge inside
the battery increases, the charging current starts decreasing. The initial 90% of the charge was charged
quickly but the remaining 10% took sufficiently large time to charge.
Fig: 19 charging curve from the Experiment
Discharging:
During discharging SMP charger was disconnected and Torkel load unit was connected. A constant load
was applied on the battery and the performance of the battery was recorded. Four test were done for
the discharging
i.
Discharge at 18A at 250C
ii.
Discharge at 18A at 350C
iii.
Discharge at 10A at 250C
iv.
Discharge at 15A at 250C
When the load was applied the battery terminal voltage drops significantly at the beginning. When the
battery was approaching its minimum voltage the terminal voltage starts decreasing rapidly. The
31
temperature in the battery cell was also recorded and it shows that for normal temperature (25 0C) the
cell temperature was also same however for the same load the discharge time decreases with the
increasing in the temperature.
Fig: 20 Discharge curve for discharge current 18A
Fig: 21 Discharge curve for discharge current 10A
32
Fig: 22 Discharge curve for discharge current 15A
5.2. Model Selection
Modeling and simulation are important for electrical system capacity determination and optimum
component selection. The battery model is an important part of electrical system simulation so the
battery model needs to have high fidelity to achieve meaningful simulation results. So, a model based
approach is used in the project to estimate the status of the battery. Hence a suitable mathematical
model was to be introduced that can characterize the battery.
First of all, from the experiment various discharge tests were performed in the battery and the data’s
were recorded to examine the characteristic of the battery. Then, these data’s recorded were used to
find the approximate model of the system. Secondly, from the literature various models were
researched and analyzed. Then the models were simulated with the parameters given in the research
papers. Then a comparative study was done between the graph obtained from the experimental data
and from the models. Finally, an appropriate model was chosen based on the comparative study. Our
final model must give the approximate output as the experimental data which is shown in fig 23 and the
key output such as terminal voltage, cell temperature and state of charge of the battery.
33
Fig: 23 Discharge curve from the experiment
5.2.1. Simple Battery model
The simple battery model is an ideal battery model where the resistance is considered constant. The
model fails to account the varying characteristics of the internal resistance of the battery with the state
of charge, sulphate formation and electrolyte concentration. This type of model can be used only where
the state of charge of battery is little important and battery plays very less role and energy drawn out
the battery is assumed to be unlimited.
5.2.2. Modified Simple Battery Model
The output from the simulation of the battery with capacity is given as
Fig: 24 Simulink output for modified simple battery
34
The output from this model fails to give the similar behavior as we required and also this model fails to
describe the transient behavior of the battery. This kind of model can be used for the application where
state of charge irrelevant to calculation such as sizing a system where the system has a fairly constant
charge.
5.2.2. Advanced simple battery model
For linear variation:
Here, a0, a1, b0, and b1 are the coefficient and the values are found experimentally in [23].The internal
resistance of the battery was given by
The simulation result is shown below
Fig: 25 Simulink output for linear variation for advanced simple model
For Nonlinear variation:
The
and
vary non-linearly with the depth of discharge (Q).
35
Here, a0, a1, a2, a3, a4, a5, b0, b1, b3, b4 and b5 are the coefficient and the values are found experimentally
in [23].The experimental procedure mentioned in [23] consisted of a motorcycle battery and it was
made to discharge under a constant current of 2A. The terminal voltage of the battery was monitored
and the open circuit voltage was measured at regular time intervals. Thus, simulating the battery model
with the nonlinear relation with the values given in [23] gave us the following graph.
Fig: 26 Simulink output for Non linear variation for the advanced simple battery
The advanced modified battery model also cannot give the output as we desired. The output of the
battery did not match with the output we found experimentally so the model was discarded.
5.2.4. Thevenin Battery Model
In Thevenin battery model all the elements are assumed to be constant. Therefore this model is limited
due to its dynamic accuracy as this model does not take account into the state of charge. This model can
be used which do not consider the dynamic state of charge. Hence, it is not suitable for our project.
5.2.5. Copetti Model
As described in section 3.6 the Copetti model was simulated in the Matlab Simulink with the provided
equation and the model was tested with the constant discharged battery current of 18A.And found the
output as shown in fig 27
36
Fig: 27 Charging output from simulink for copetti model
Fig: 28 discharging output for the Copetti model from Simulink
The charging curve was similar to the charging curve found experimentally however the discharge curve
was not similar to our experimental output. The discharge curve should have been decreasing and when
the minimum voltage approaches it should have been increasing but the output from the model is
constant and then it starts decreasing linearly. So the model was also discarded as it could not fulfill our
requirement.
37
5.2.7. Randle’s Battery Model
The above equation can be represented in state space matrix form as
The simulation output for the Randles model is given as
Fig: 29 Simulation Output for the Randle’s model
The output from this model is very similar to the output we got from the experimental observation.
Initially the output voltage decreases rapidly and then starts decreasing rapidly, when the battery
reaches the minimum voltage there is a sharp decrease and then the terminal voltage increase at the
end and then the output voltage stops. However, in this model the temperature is considered to be
constant during the whole process. So, the model is not appropriate for the system.
5.2.8. Third Order Model
Using the parameter given in [21] the model was simulated and the output was generated which is given
in fig 29.
38
Fig: 30 Simulation result for the third order model
The experimental curve fig 23 and the model output fig 30 are very similar. On comparison of these two
figures the characteristic of the curves are very similar and suits more approximately than the previous
model discussed above.
5.3. Discussion of the Results
The main purpose of the theoretical simulation of the model is to find the model that best suits the
experimental observation of our battery. Henceforth, we compare the simulation results with our
experimental results to find the model which can describe our system.
In accordingly, let us discuss each of the results obtained. Considering the model output from the
modified simple battery model from fig 23, we see that the terminal voltage decreases exponentially.
However, our experimental observation shows that the voltage decreases rapidly but at the end it again
increases so this model cannot be used.
When considering the advanced simple battery model for the linear case from fig 25 we see that the
terminal voltage decreases linearly till the end. However from our actual experiment result from fig 23,
here there is linear decrease for majority of discharge but for the last few percentage of discharge the
decrease is non linear. Hence this model is discarded. Similarly, for non linear case of the same model in
fig 26 the terminal voltage decreases nonlinearly throughout the experiment. In contrast to this in our
39
experiment non linearity is felt only at the end of the discharge. Hence the model cannot be used for our
system.
From Copetti model from fig 28 we see that the terminal voltage is constant and then starts decreasing
linearly. But from fig 23 the output should have been decreasing and when the minimum voltage
approaches it should have been increasing. Hence, the model is discarded.
When we consider the result from the Randle’s battery model in fig 29, the result is very similar to our
experimental observation. The battery decreases linearly and at certain point there is a sharp decrease
in battery and then the terminal voltage increases at the end. The model can be used as our model as
this gives the similar output as we needed. However the model fails to describe the state of charge of
the battery and cell temperature. The model assumes the cell temperature to be constant throughout
the process. But this is not the case hence the model is discarded.
When comparing fig 30 of the third order model with the experimental output in fig 23, the output is
very similar and the model also describe about the state of charge, cell temperature and value of the
resistance. Hence this model is the appropriate model to describe our system.
5.4. Conclusion
Simulation were performed for the model given in [22],[23],[26],[27] and [28]. On comparison with the
experimental data we found that model in [27] and [28] is very similar to the experimental data.
However, model [27] considers the battery temperature constant but our model should give the
variation of the output with respect to the temperature. In regard of this Randles model is not suitable
for our project. Hence the final battery model for the project is chosen as the third order model.
40
CHAPTER 6
Final Model of the Lead acid battery
From chapter 4 we found that the third order model is the appropriate model for our system. In section
3.8 a brief introduction of the model is given. However, a detailed analysis of the model is given in this
chapter. A slight modification is done in the model. The final model is divided into three sub models
Capacity model, Voltage model and Thermal model. The following structure model gives the detailed
analysis of the model.
Fig: 31 Final Structure model for the thesis
41
Fig: 32 Dynamic model of the battery
The model can be divided into three sub models:
6.1.1. Capacity Model
The input for the model is charge/discharge current. The rated capacity, Used capacity and Actual
capacity is calculated with the help of this input current and under different state of charge. The
modeling of battery requires various circuit elements. The dependence of the capacity in the electrolyte
temperature during fixed discharge current is given by:
is the electrolyte freezing temperature and
is the rated capacity at the rated discharge current in
00C.
The capacity based on the discharge can be calculated as below [28]:
Where Kc is a constant,
is the no load capacity, θ is the electrolyte temperature, I* is the nominal
battery current and I is the discharge current. With the help of these capacities the state of charge and
depth of discharge is calculated.
The charge extracted from the battery was a simple integration of the current flowing into and out of
the battery. The initial value of the extracted charge is necessary for the simulation purpose [28].
42
Qe is the extracted charge, Qeint is the initial extracted charge, Im is the main branch current τ is an
integration variable and t is the simulation time.
State of charge (SOC)
State of charge measure the fraction of charge remaining in the battery
Depth of charge (DOC)
Depth of charge measure the fraction of the usable charge remaining in the battery
6.1.2. Voltage Model
The state of charge and depth of discharge from the capacity model is used to find the resistance (R0, R1,
R2) and electromotive force (Em) of the battery.
Electromotive force(Em)
When fully charged the electromotive force (emf) was assumed to be constant. The emf varied with
temperature and state of charge (SOC) and is given by the equation [28]:
Where,
Em is the open-circuit voltage (EMF) in volts, Emo is the open-circuit voltage at full charge in volts, Ke is
a constant, θ is electrolyte temperature in 0C, and SOC is battery state of charge.
Resistance (R1)
This resistance depends on the depth of discharge increases exponentially during discharge is given by:
Where R1 is the resistance, R10 is a constant, and DOC is the depth of discharge.
Resistance (R2)
The resistance increased exponentially as the battery state of charge increased. The resistance primarily
affected the battery during charging. The resistance became relatively insignificant for discharge
currents
43
Where R2 is a main branch resistance in Ohms, R20 is a constant in Ohms, A21 is a constant, A22 is a
constant, Em is the open-circuit voltage (EMF) in volts, SOC is the battery state of charge, Im is the main
branch current in Amps, I* is the nominal battery current in Amps.
Terminal resistance (RO)
The resistance was assumed constant at all temperatures, and varied with the state of charge and is
given by
Where Ro is a resistance in Ohms, Roo is the value of RO at SOC=1 in Ohms, Ao is a constant, SOC was the
battery state of charge
Terminal Voltage (V0)
The terminal voltage is given by
Where Vpn is the voltage at the parasitic branch and is given by
Where Em is the EMF voltage and R1 is the resistance.
6.1.3. Thermal Model
The thermal model estimates the change in electrolyte due to internal resistive losses and due to
ambient temperature [28].
Where Ps is the power loss of R0 and R2,
is the thermal resistance,
θa is the ambient temperature.
44
is the thermal capacitance and
6.2. Summary of the final Model
Fig : 33 Final Equivalent Circuit model for the system [28]
This model is constituted by:

The electrical equivalent of the model consist of main branch (two RC block) and a parasitic
branch

Capacity model gives state of charge and depth of charge, Voltage model gives the resistances
as a function of state of charge and depth of charge, Thermal model gives the internal
temperature
The dynamic equations of the model are therefore
45
CHAPTER 7
Parameter Estimation of the Model
Estimation theory one of the branches of statistics and signal processing where parameters are
estimated based on measured data. These parameters describe the whole physical setting such that the
parameters affect the distribution of the measured data. Using the measured data the estimator
estimates the unknown parameter. Thus, estimation is a process where the measured data is the input
and output is the estimate of parameter. However, an optimal estimator is always desirable [31].
Estimation process consists of following steps:
1. Firstly, a model is found from the probability distribution of the measured data .The model shows
how the measured data depends on parameter to be estimated.
2. A theoretical precision is found by the model.
3. An estimator is developed. A comparison is done between optimal performances in step 2.
4. Finally, simulation is run using the estimation to test the performance.
Parameter estimation is a discipline that provides tools for the efficient use of data for aiding in
mathematically modeling of phenomena and the estimation of constants appearing in these models
[32].
7.1. Parameter Estimation for the Project
In our project let
is the input vector (charging current or the discharging
current) and
is the output vector (terminal voltage) observed. Let us consider
be the vector of the parameters that need to be determined (thirteen
parameters that needed to be determined). Then,
Our main objective is to find the value of parameter vector (
when both the input vector (X) and
output vector (Y) is known.
In order to estimate
let
be the vector of the estimated parameters for the
same input (X) and for the estimated output ( ). Then,
46
Let є is the error between the observed output and estimated output.
Then,
i.e.
The values of T is updated in such a way that the error (є) tends to zero and hence the estimated output
converges to observed output. Hence the mean square error is given by
Hence, є
Implies
0.
and T
θ.
Thus, our estimated parameters converge to the actual parameters.
7.2. Implementation of the parameter estimation
The parameter estimation used in this project can be divided into two parts. Firstly the parameter is
estimated with the lab test using the instruction given in [28] and then using Simulink parameter
estimation. The Simulink parameter estimation needs an initial value of the parameters. But the
parameter that defines the final model is very large and the initial values cannot be guessed. Therefore,
the parameter estimation of the battery was firstly done with the lab test as instructed in [26] and these
data were used as the initial values for the parameter estimation using the Simulink parameter
estimation.
7.2.1.Parameter estimation using Lab Test
The equation mentioned in the mathematical model contains constant that must be determined
experimentally. These constants or parameters can be divided in three categories:

The capacitance parameters

The voltage parameters

The thermal parameters
47
Parameters referring to Battery Capacity
To find the parameters four test were performed using different currents and temperature. The data’s
are given in table 1.
Table: 1 Parameters referring to battery capacity
Discharge Current
18 A
18 A
10 A
15 A
Temperature
(degree Celsius)
25
35
25
25
Capacity(Ah)
68.1
75
100
76.6
Battery freezing temperature is -40 degree Celsius. These four couples
are used in the system of four equations to find the constants
Using
,
and
, є and δ.
the value of the temperature coefficient α was found. Є and α are
related as
. So the value of є is found. Similarly,
. Hence
was found by the relation
and δ were found by the relation
Table: 2 Final parameter value from the experiment
Parameters
Values
72.37 Ah
1.2
0.75
2
0.011
Parameters referring to the voltage parameters
Fig: 34 typical voltage and current profile for a constant current discharge [21]
48
0.47
To identify
and
one needs two equations, these equations were obtained while measuring the
voltage at the beginning and end of the discharge test, V0 and V1 .The corresponding state of charge at
the beginning and end was measured. Similarly, R1 was identified by making the difference of (V4V3).From the lab test following values were obtained.
Table: 3 Voltage found at the end and beginning of the experiment
Discharge Currents
18 A
12.95
15 A
12.95
10 A
12.95
12.30
12.6
12.7
Table: 4 Parameters found experimentally
Parameters
Values
0.0047
2
11.14
11.3
11.57
12.32
12.03
12.04
0.049
Parameters referring to the battery thermal model
The two parameters are identified from manufactured data sheets:
Table: 5 Parameters found in the manufacture data sheet
Thermal Capacitance
Thermal Reactance
12
1.8
7.2.2. Model Parameter Identification using Simulink Parameter estimation
The parameters found experimentally are not the optimum parameter and all of the parameters cannot
be found experimentally. Therefore optimum parameter identification becomes an integral part of the
project. The parameter estimation in the project was done using Simulink parameter estimation
method.
The Simulink parameter estimation method is an optimization process that adjusts the parameter by
comparing the data generated by Simulink model with the measured experimental data. The parameter
estimation method estimates the parameter to minimize the user selected cost function that typically
calculates a least square error between the empirical and model data signals .The set of the parameters
to achieve the least value of the objective function is considered to be the fittest set.
49
Fig: 35 Model based parameter Identification Algorithm
The cost function in the project is the difference between the output voltage from the experimental
data and the simulated output. The parameter is identified in such a way that the cost function is
minimized and the simulated output is fitted to the experimental output.
Where,
= weights of the difference in the simulated and experimental results
= experimental voltage data
= simulated voltage data
50
The cost function represents the sum of error values at each time interval. Fig 36 shows the cost
function of the simulated voltage data and the experimental data after the Simulink parameter
estimation. Fig 37 shows the adjustment of the parameter in order to minimize the cost function. The
simulation is stopped when the local minimum is obtained and the parameter values converge.
Fig: 36 The cost function for simulating the model in Simulink parameter estimation.
51
Fig: 37 the trajectories of the estimated parameters after the simulation
As the parameter value improve, the simulation curve gets closer to the experimental curve. Once the
simulation is completed the estimated parameter value was inspected.
.
Fig: 38 Final estimated parameter values from the Simulink parameter estimation.
52
7.2.3. Validation of the model
In order to validate the model two sets of experimental test have been adopted to compare with the
simulation results. The validation results using two experimental tests are shown in fig 36 and 38.
Fig: 39 Plot of the measured and simulated result (Validation Data 1)
Fig: 40 Plot of the residual result (Validation Data 1)
From the simulation result fig 39 and 40, the discharge begins at the voltage 12.62 and the simulation
result shows a little variation at the first 300s. While the experimental terminal voltage decreases
linearly the simulated result is constant for 50s. Then both simulated result and experimental result
decreases linearly. It can be seen that the experimental terminal voltage and simulated terminal voltage
shows a reasonable agreements for 1750s. The error voltage is 0.01%.
53
Fig: 41 Plot of the measured and simulated result (Validation Data 2)
Fig: 42 Plot of Error voltage (Validation Data 2)
From fig 41 and 42, the discharge starts at 13.2 V and the experimental terminal voltage decreases
linearly from 12.6V but the simulated voltage is not uniform at the beginning of the discharge. However,
the voltage starts decreasing linearly after 200s. The error between simulated and experimental voltage
54
is increasing after 1000s.However at the end of the discharge the outputs shows a reasonable
agreement. The error is 0.3 %.
7.4. Discussions
Two sets of experimental data’s were used in order to validate the mathematical model of the battery.
The first validation data shows a reasonable agreement with the simulation result with an error of 0.01%
at the beginning of the data. This is due to the ‘coup de fouet’, a phenomenon associated with the
voltage drop at the beginning of the discharge [33]. In addition to this ‘coup de fouet’ can be also seen in
the second validation data. There was however an error of 0.3% between simulated and experimental
voltage. This is due to the fact that the initial thermal parameters were taken directly from the
manufactured data sheet instead from the experiment. Also, the experiment was carried out
immediately after being charged so the lead acid battery was not stable enough. Hence the deviation
can be observed between simulated and experimental voltage.
7.5. Summary
Estimation theory and parameter estimation is discussed and
two methods to estimate parameters
are described in this chapter. Parameter estimation of the final model is done by two methods. Firstly
the parameters are estimated by the Lab test and then the values obtained are used as the initial value
for the Simulink Parameter Estimation. The algorithm of Simulink Parameter Estimation is discussed and
implemented to find the values of the parameters. The parameters identified are validated by the two
sets of other experimental test results. The average result found is 0.2%. The two results show the same
transient but with different time scale.
The final values of the parameters found are:
Parameter referring to Capacity Model
Parameter referring to Voltage Model
Parameter referring to Thermal Model
55
CHAPTER 8
Charge Controller Implemented in the Project
In chapter 4 we discussed the various charging and discharging methods and techniques. We also
discuss the application of various charging techniques. From the discussion we came to the conclusion
that IUIa method is the appropriate charging method for our system. In this chapter a detailed overview
of the method is discussed and the algorithm for the method is discussed and the implemented in the
Simulink is discussed.
8.1. IUIa Charging
This charging method is also known as the three step charging method [30]. The three steps taken are
8.1.1. Bulk charging
In this step the battery is charged with the constant rated current and the output voltage is increased. In
this step the battery refills all the energy drawn during the discharge process. However this is done
without losing water. In this step the battery replenished up to 80 to 90 percent. The output voltage
increases until the desired voltage then the charging process is changed to next step.
8.1.2. Absorption Charging
In this process the current is decreased and the output voltage is constant. In this step the water loss is
minimized. This process balance 10 to 20 percent of charge.
8.1.3. Float charging
When the current decreases to 3% of the rated current the float charging occurs. In this step a constant
voltage is applied to prevent the self discharge of the battery.
Fig: 43 Ideal three steps or IUIa Charging Method
56
8.2. Charging Algorithm
Start
Check the state
of charge of
battery
Charge the battery
with constant rated
current
<60%
Yes
No
Decrease the current
No
< 3% of rated
current
Yes
Charge the battery
with constant current
Check the state
of charge of
battery
No
>80%
Yes
Stop
Fig: 44 Algorithm for battery charging
57
The algorithm developed to charge the battery is shown in the fig 44. At the starting the state of charge
is determined and the steps that need to be implemented are determined. The battery is charged
initially with the rated current. When the battery’s state of charge is more than 60 percent then the
charging current is decreased until the current decreases to 3 % of the rated current. Then the battery is
charged with constant current until the state of charge of the battery is more than 80 percent. Finally
the charging process is stop when the battery reaches more than 80 percent.
8.3. Final System Block Diagram
Fig: 45 Final System Block Diagram implementing the battery model
Fig 45 shows the final block diagram of the system after implementing the charge controller and the
battery model. The system is an open loop charge controller. Here the system input is the discharge/
charge input current (U) and the system output is terminal voltage (V).The output (Y) is the state of
charge of the battery that triggers the set point and the input is then given to the charge controller
according to the set point.
58
8.4. Results after implementing the charge controller
Fig: 46 Output of the implementation of the algorithm in Simulink
The algorithm was implemented in the Matlab Simulink using the output from the final model. Fig 46
shows the output obtained from the implementation of the algorithm. When a constant rated current
was applied the terminal voltage increases until the output voltage is 14.8V or 2.46V per cell. This shows
the bulk charging phase of the charge controller. The current is decreased and the output of the battery
remains constant showing the absorption state and when the current is 3% of the rated current the
battery is charged with constant current. The battery is in float state and in the fig 46 a slight change
can be seen and then the charging was stopped when the battery was fully charged.
In nutshell, the charge controller was successfully implemented in the simulink using the battery model .
59
Chapter 9
Conclusions and Future Research
This chapter gives the summary of the achievement of the project work in battery modeling and charge
controller design. The possible direction of the future work is also described in this chapter.
9.1. Summary
Lead acid batteries are used as the storage system in renewable energy due to the intermittency nature
of the renewable energy system. The capacity loss is observed in these batteries due to the repeated
charge and discharge cycle. As a result it is very essential to know the performance of the battery, their
time of replacement and a significant investment cost needed for the system installation.
In this thesis, the capacity status of the battery is studied in relation to the internal resistance of the
battery. Based on the experimental testing of the battery, various models were studied first and a
suitable model was chosen for estimating battery parameter. An equivalent final model of lead acid
battery has been developed and implemented under Matlab/Simulink software. The model consists of
important concept of battery that reflects the dynamic response of terminal voltage. The model was
then validated with two of the experimental data. From the validation result it is found that the model
can accurately estimate the battery characteristics with an error of 0.3%.
A charging methods and technology were studied and an appropriate charge controller was
implemented for the storage system based on the model designed in Matlab Simulink. Henceforth, the
design of the battery storage system was successfully done.
9.2. Future Research Work
Taking the limitation of the project from section 1.4 into consideration in the future using the model the
state of health of the battery can be tested by deep cycle discharge of the battery for their whole
lifetime. The state of health can be determined by the internal resistance. Hence, an improvement in the
model to find the internal resistance at various discharge rates so that the model can be used for the
online application can be done in the future. A discharge controller can be designed using the model for
the storage system can be designed. The model can be integrated with the PV module so that a
complete storage system can be designed. These kinds of system consist of PV array, battery, the
converters and the controllers. Hence a digitally controlled stand alone photovoltaic power supply can
be designed using the model presented in the thesis.
60
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63
Appendix A
Fig: A1 Simulink diagram for the modified simple battery model
Fig: A2 Simulink diagram for the advanced linear battery model
64
Fig: A3 Simulink diagram for non linear battery variation for advanced simple battery model
Fig: A4 Simulink diagram for Copetti model for discharge
65
Fig: A5 Simulation of Copetti model for Charge
Fig: A6 Simulation of the Randle’s model
66
Appendix B
Final Model
Fig: B1 Simulink diagram for Final Battery Model
67
Capacity Model
Fig: B1 Simulink diagram for Actual Capacity
Fig: B2 Simulink diagram for Used Capacity
68
Fig: B3 Simulink diagram for Rated Capacity
Fig: B5 Simulink diagram for DOC
Fig: B6 Simulink diagram for SOC
69
Voltage Model
Fig: B7 Simulink diagram for R1
Fig: B8 Simulink diagram for EMF
70
Fig: B9 Simulink diagram for R0
Fig: B9 Simulink diagram for Ip
Fig: B9 Simulink diagram for Terminal voltage
71
Thermal Model
Fig: B10 Simulink Diagram for Power
Fig: B11 Simulink Diagram for Cell temperature
72
Charge Controller
Fig: B12 Simulink Diagram for Charge Controller
73
Appendix C
From manufacturer data sheet
74
Discharger for the experiment
75
Charger for the experiment
76
Battery characteristics from the manufacturer data sheet
77
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