THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING

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1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING DYNAMIC SYSTEMS MODELING OF LITHIUM-ION BATTERY SYSTEMS IN MATLAB INCLUSIVE OF TEMPERATURE DEPENDENCY JOSHUA SAVITZ SPRING 2017 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Mechanical Engineering with honors in Mechanical Engineering Reviewed and approved* by the following: Jay Martin Associate Professor of Mechanical Engineering Thesis Supervisor Hosam Fathy Professor of Mechanical Engineering Thesis Supervisor Sean Brennan Professor of Mechanical Engineering Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 i ABSTRACT In order to design a battery system to be used in an electric vehicle, dynamic battery system models must be created to understand the complex performance of the system when loaded with varying discharge profiles and in various temperature environments. In this way, prototyping of the battery systems is partially replaced by simulations that predict the performance instead of battery testing. In this thesis, performance models were created based on system geometry, ambient temperature, and current profile to track the runtime, voltage output, and cell temperature accurately of individual cells and of the system as a whole. A single cell, 6 cells in series, and a parallel set of 6 cell in series in each branch geometries are analyzed at 0 C, 23 C, and 35 C with a constant, pulsed, and constant with pulsed current profiles. An equivalent circuit model with 1 RC pair inclusive of temperature dependency is hence utilized for the single cell model and then will be implemented into battery system configurations. The focus is put on ambient temperature rather than discharge rate, so the model parameters are set as functions of state of charge and ambient temperature and found through a parameter estimation conducted within MATLAB Simulink. This simple equivalent circuit model captures the dynamic processes happening within the cell(s) but not to the extent it could with a 2 RC pair model. Experimental tests were conducted to derive the model parameters and validate the models. The accuracy achieved in the prediction of voltage output within the single cell model is around 50mV, which was the initially determined tolerance for max error. The multi-cell battery system models and thermal models had large amounts of error.

3 ii TABLE OF CONTENTS ACRONYMS AND ABBREVIATIONS... iv LIST OF FIGURES... v LIST OF TABLES... vii ACKNOWLEDGEMENTS... viii Chapter 1 Introduction... 1 Chapter 2 Background to Battery Systems... 4 Introduction... 4 Battery Chemistries... 5 Battery Performance Metrics and Properties... 7 Choosing the Panasonic 18650B Li-Ion Cell... 9 Battery System Modeling Single Cell Modeling Multi-Cell Modeling Summary Chapter 3 The Single Cell Electrothermal Battery Model Introduction The Equivalent Circuit Model The Thermal Model Identification of Model Parameters Capacity and SOC RC Pair Internal Resistance Open Circuit Voltage ECM Implementation in MATLAB Parameter Estimation Summary Chapter 4 Battery Systems Modeling Introduction Development of Single Cell Model into a Multi-Cell System Expanding Upon the Thermal Model Implementation in MATLAB... 37

4 iii Summary Chapter 5 Experimentation Introduction Experimental Setup Measurement Battery Setup Safety Precautions Charging Discharging Types of Tests Test Schedule Summary Chapter 6 Analysis and Validation of the Performance Models Introduction Single Cell Tests Constant Discharge Pulsed Discharge Validating Simulated Voltage Output Effects of Discharge Rate Single Cell Thermal Validation Multi-Cell Tests Series Configuration Tests Parallel Configuration Tests Thermal Modeling Results of Multi-Cell Configurations Summary Chapter 7 Conclusions and Future Work Conclusions Future Work Appendix A Specification Sheet for the Panasonic 18650B Battery Cell Appendix B Estimated Parameters BIBLIOGRAPHY Academic Vita... 78

5 iv ACRONYMS AND ABBREVIATIONS ECM: Equivalent Circuit Model SOC: State of Charge SOD: State of Discharge OCV: Open Circuit Voltage EIS: Electrochemical Impedance Spectroscopy RMSE: Root Mean Square Error NiCd: Nickel-cadmium NiMH: Nickel-metal-hydride LTO: Lithium Titanate LFP: Lithium Iron Phosphate LMO: Lithium Manganese Oxide NMC: Lithium Nickel Manganese Cobalt Oxide LCO: Lithium Cobalt Oxide NCA: Lithium Nickel Cobalt Aluminum Oxide

6 v LIST OF FIGURES Figure 2.1: Internal Cell Structure of an Cell [1]... 5 Figure 2.2: Typical specific energy of lead, nickel, and lithium based batteries [1] Figure 2.3: Panasonic 18650B Cell Figure 2.4: (a) Thevenin, (b) Impedance, and (c) Runtime Based Models [21] Figure 3.1: Equivalent Circuit Model for a SIngle Cell Figure 3.2: Voltage Response for a Constant Current Pulse [32] Figure 3.3: MATLAB Simulink Single Cell Model Figure 3.4: ECM Modeled in MATLAB Simulink Figure 3.5: Single Cell Thermal Model Figure 3.6: Scope of the Parameter Estimation Figure 3.7: Root Mean Squared Error Minimization During the Parameter Estimation Process Figure 4.1: Different Cell Configurations for Modeling Battery Systems [28] Figure 4.2: Interpretation of Cell-to-Cell and Cell to the Environment Interactions Between Cells Within A 10 Cell Battery Pack [37] Figure 4.3: MATLAB Simulink Full Model for 6 Cells in Series Figure 4.4: MATLAB Simulink Block Representation of 6 Cells in Series Figure 4.5: MATLAB Simulink Full Model of Parallel System of 6 Cells in Series in Each Branch Figure 4.6: MATLAB Simulink Block Representation of two, 6 Cells in Series Blocks in Parallel Figure 5.1: Single Cell Test Stand with Inserted Cell and Attached Thermocouple Figure 5.2: 6 Cells in Series Test Stand with Inserted Cells and Attached Thermocouples43 Figure 6.1: 3A Constant Discharge Experiments at Different Temperatures Figure 6.2: Pulse Discharge Experiments at Different Temperatures... 54

7 vi Figure 6.3: Validation Profile Test and Simulation for a Single Cell Figure 6.4: Validation Profile Test and Simulation Error for a Single Cell Figure 6.5: Effect of Two Discharge Rates at Two Temperatures Figure 6.6: Example of High Error Within the Thermal Model for the 0C and 3A Pulse Test Figure 6.7: Experimental Test Showing Individual Cell Variations within a Multi-Cell System Figure 6.8: Experimental and Simulated Voltage Output Results for Two Temperatures 63 Figure 6.9: Validation Profile Test and Simulation Error for a Six Cells in Series... 64

8 vii LIST OF TABLES Table 2.1: Characteristics of commonly used rechargeable batteries [1]... 8 Table 6.1: Panasonic 18650B Cell Capacity from Constant Discharge Experimental Data52 Table 6.2: Panasonic 18650B Cell Capacity from Pulsed Discharge Experimental Data 54

9 viii ACKNOWLEDGEMENTS First of all, I would like to thank the Applied Research Laboratory (ARL) at Penn State in involving me in a research environment from freshman year. Through the opportunities I have had with different divisions working on various projects, I will graduate college as a much more knowledgeable student of engineering and have the ability to apply research with understanding to any project I may work on in the future. Within ARL, I have to thank Dr. Rich Martukanitz for introducing me into ARL and supporting me up through the point of my academic career at which I began my thesis topic with a new supervisor. Additionally, within ARL I wish to recognize all ARL employees who assisted me within the laboratories to conduct the testing of my thesis. The individual I would like to thank the most is my main thesis supervisor Dr. Jay Martin of ARL. By initially meeting him as my professor of an engineering design methodology class, I was able to form a connection and became interested in design optimization. Though he challenged me within my thesis work, I know that it was the best for my academic and personal development. Dr. Martin was there when I was struggling through problems but also gave me the space to learn and overcome challenges myself. I must also thank Dr. Hosam Fathy for agreeing to be my co-supervisor with great knowledge in the field of battery systems. Though his involvement was not vast, he was able to provide feedback and lead me on a path towards success and quality work. Dr. Sean Brennan is also to thank for his role as my honors adviser and thesis reader. He has been a valuable support system through my undergraduate studies in helping me through the processes of planning classes and pursuing many educational opportunities such as study abroad.

10 ix Last but by far not least, I thank my family and friends that have been an invaluable asset within my life and throughout the thesis process. To my father, I thank you for being the source of motivation and achievement within all I strive to complete and for the help you supply when a tough decision needs to be made. You have shaped me into a son of drive, ambition, and responsibility. To my mother, I owe my personality of calmness, optimism, and patience that at all times and within times of trouble, truly help me find a path for success without causing myself to be down. It s these values that have shaped me into a helper of others. Finally, to my friends, it goes without saying that you have been the direct support, encouragement, and enjoyment to have had such an incredible and successful academic career.

11 1 Chapter 1 Introduction Batteries are a common component to a variety of applications ranging from toys to powering computers and control systems. Stated simply, they store the energy needed to conduct some task such as moving a part or heating an object up, essentially being the source of energy transfer. As technology has rapidly progressed in recent decades, batteries have become one of the most used energy storage methods and are being utilized within demanding applications such as electric vehicles. Designing battery systems for these applications is a complicated task due to the complexity of their dynamic performance and with each type and brand of battery performing differently. In many vehicle applications, there has been a push for electric vehicles to protect the environment and improve powertrain efficiency. This is possible due to the advancement of battery technology to be able to store energy and provide high power. There are many different types of battery cells that can be used, each with different properties such as chemistry, voltage, capacity, energy and power densities, current limits, and properties that influence the performance of the battery itself. In the context of a battery system with multiple cells, other factors such as the internal layout of cells, size, and shape of the battery system play a role in its performance. Additionally, the conditions and the application in which the battery system is implemented affects its performance such as the ambient temperature and current requirements. Finding the right combination of battery cells with subsystems that need electric power can be difficult due to all the interdependencies.

12 2 In order to design these systems, dynamic, time-based performance models are needed to simulate the results of potential battery systems before being constructed. The goal of this thesis is to create dynamic system models of Panasonic 18650B Li-ion battery systems to predict performance. There has been a lot of previous research on performance models that describe what happens to the internal distribution of charge, potential, and temperature inside a battery as it is charged and discharged for various applications. These models are specific to the type of battery and application conditions because each type and brand of battery perform differently [1]. There are models for battery systems inclusive of temperature effects that can predict battery performance within 5mV by studying the specific chemical reactions happening at the internal interfaces [2]. Researchers have created these proprietary models for their specific battery and analyzed its performance based on the application. The precision desired in this thesis is 50 mv. The reason this value was chosen is because the performance models being developed in this initial stage are for a general understanding, which is commensurate with 50 mv accuracy for the cells being tested, before being further developed for high accuracy thereafter. Although modeling the chemical processes is important for high accuracy models, a desired precision of 50 mv is achievable by simplifying the chemical analysis within the model to only include ohmic heating and entropic effects due to temperature. Hence, the models developed for this thesis involve a simplification of the chemical analysis and focus on the system geometry of the battery cells, the discharge curve, the temperature effects, the heat transfer between these cells, and the safety precautions utilized in the system. The intended use of these models is to predict performance and prevent load cells from causing catastrophe for Panasonic 18650B battery systems.

13 3 These models provide an understanding of the effects of temperature and current profile on different geometry systems, so that a battery system may be designed for the long-runtime and high-performance application while guaranteeing safety. Specifically, input variables of ambient temperature, discharge profile, and battery system geometry on voltage, state of charge, and internal battery temperature over time. Due to the simplification of the chemical analysis, only an Equivalent Circuit Model (ECM) is necessary for the analysis as opposed to a single particle model or porous 2D model. The ECM will be made using MATLAB Simulink and Simscape. MATLAB has a publicly available ECM to use, but it models temperature effects only by varying the ECM parameters. The models created in this thesis further develops this public model to include temperature effects within the governing equations, by allowing different system configurations, and by including more accurate heat transfer effects while varying the discharge rate. The work presented in this thesis utilizes the single cell model developed in [3] but extends it to include more advanced temperature effects. This model is then aggregated into battery system models. The remainder of this thesis is organized as follows. In Chapter 3, a single cell equivalent circuit model is derived, implemented into MATLAB, and the calculation of its parameters are identified. In Chapter 4, battery system models are derived from the single cell model. In Chapter 5, the battery experimentation is explained. In Chapter 6, the experimental data is analyzed for the model parameters, and the performance models are validated. Finally, in Chapter 7, the thesis is summarized, and future work is explained.

14 4 Chapter 2 Background to Battery Systems Introduction Batteries have been at the forefront of technological innovation since the 1800s. Most notably throughout years of battery chemistry development, the lead-acid cell was introduced in 1859, nickel-cadmium in 1899, and lithium ion in Today, further research is being conducted on battery chemistries to ultimately find a super battery in which can store high amounts of energy but can also supply high levels of current. A battery cell can come in various shapes such as a pouch or cylinder. The same concept of internal battery structure applies to the two forms, so only the cylindrical form will be shown. Figure 2.1 shows the internal cell structure of a cylindrical cell and labels the components. The battery operates via a cathode, anode, and a separator between the two of some electrolyte acting as a conductor. During discharge, the lithium ions flow from the anode to the cathode through the separator. The opposite process occurs for charging.

15 5 Figure 2.1: Internal Cell Structure of an Cell [1] Battery Chemistries Battery cells come in many different chemistries, which determine their capabilities. There are two types of batteries: primary and secondary. Primary types of batteries include Zinccarbon, alkaline, and some lithium-metal forms. These batteries hold a high amount of initial energy, even more so than secondary (rechargeable) batteries, and provide varying low levels of power until there is no more charge. These batteries are meant for applications that do not require high power and in which the battery need not be recharged. Secondary batteries, also known as rechargeable batteries, are the other battery type. These cells are able to provide higher levels of power and hence can be used in much more *All figures and tables in this thesis are either open source, approved or in the process of being approved by their original author, or have been created by the author of this thesis.

16 6 demanding applications. The capacity is much lower for these types than a primary cell. In this category are many chemistries including lead-acid, nickel based, and lithium-ion based. 1. Lead-Acid: This chemistry is the first to produce a rechargeable battery system. Some major advantages are that these batteries are forgiving in demanding applications and are less expensive. There are several disadvantages including its low energy capacity, selfdischarge, limited cycle ability, and weight. 2. Nickel: Nickel based batteries come in two main chemistries: nickel-cadmium and nickel-metal-hydride. These batteries have been very popular over the last several decades due to their high-energy density, long service life, high discharging current capability, and ability to operate under extreme temperatures. These also allow for rapid recharging. 3. Lithium-Ion: Lithium-Ion based batteries come in many different chemistries and are currently a large topic of research as other lithium chemistries are being developed. These batteries have become the replacement of many applications previously served by lead and nickel batteries due to their ability to store more energy and provide equivalent power. These cells also require less maintenance but are the most unsafe to use, requiring an additional protection circuit and a battery management system to carefully monitor and operate the cells. These batteries are currently among the most expensive up front, but are usually able to serve long enough to reduce its cost per cycle lower than other chemistries.

17 Battery Performance Metrics and Properties 7 There are many different performance metrics to be considered before selecting the battery chemistry used in the system being designed. These performance metrics include: Runtime: The duration of time in which the battery operates before fully discharged. Current output limits: The minimum and maximum discharge rate the battery can provide. Service life: The number of cycles the battery can undergo before losing a significant amount of its capacity and open circuit voltage. Safety and Reliability: The danger associated with varying levels of thermal stability based on the cell chemistry and maintenance required to maintain a battery. Each type of battery has positive and negative implications on these performance metrics, which mostly can be analyzed from the battery s properties. It is also important to note that the temperature in which the battery operates strongly influences each performance metric and battery property. Table 2.1 provides critical data of the different characteristics of these secondary batteries. Certain properties in the table tell us a lot about how the battery will perform: a higher specific energy, higher voltage range before cutoff, and shorter sitting time with self-discharge before use increase runtime; the load current or C-rate range at which the battery operates and hence its current output limitations are important for performance requirements; service life is dependent on the number of cycles the battery can undergo; safety and reliability depend on the maintenance required and the thermal stability of the chemistry, which only for lithium ion is low enough to require an additional protection circuit.

18 Table 2.1: Characteristics of commonly used rechargeable batteries [1] 8 A few of the properties in the table do not necessarily relate to the performance of the battery itself but of the restrictions to the battery system s design. These would include the size, weight, and cost of each battery. Unlisted in Table 2.1 is the weight of each battery which is highest for lead acid and lowest for lithium ion. Battery size is dependent on the application the battery is used. It can be of cylindrical, prismatic, or pouch shape and of various dimensions.

19 9 These properties heavily affect the application in which the battery should be utilized. In general, lead-acid batteries are used in applications that don t have a limitation on weight but require power at a low cost with a low number of cycles. Nickel-cadmium and nickel-metalhydride batteries are used for applications with long service life and high discharge rates. Lithium ion is replacing lead acid and nickel type batteries in most applications due to its ability to hold more energy while having just as long of a service life, ability to discharge fast to provide high power, and low self-discharge. More safety precautions do have to be in place for lithium ion batteries due to their thermal instability. Choosing the Panasonic 18650B Li-Ion Cell In considering an application that requires high energy and power capabilities, one type of battery may be eliminated from being considered for the system being developed. Primary type of batteries will not work for this system because a rechargeable system is necessary and a highly dynamic performance is required. Of the secondary batteries with a focus on high energy and performance applications, lithium ion is the battery of choice. Although it is the most expensive, this type of battery holds the most amount of energy important for longer runtime performance while being able to produce high discharge rates. These batteries have a long service life as well. The biggest problem with the battery is its ability to fail due to its thermal instability. Therefore, a protection circuit is necessary, and a battery management system must be used in order to prevent battery system failure. Due to the high performance of lithium ion batteries, different lithium chemistries have been developed and pose their own property differences. These include lithium-polymer, LTO,

20 LFP, LMO, NMC, LCO, and NCA. Properties can be seen in the previous Table 2.1 for the 10 LCO (cobalt), LMO (manganese), and LFP (phosphate) chemistries. The differences in specific energy between each chemistry can be seen in Figure 2.2. Figure 2.2: Typical specific energy of lead, nickel, and lithium based batteries [1]. In evaluating the optimal lithium battery chemistry for a long-runtime and highperformance system, there is one main tradeoff. The problem with most batteries is that they are optimal for energy or power, which means there is not a battery that is the best for both runtime and performance. Although the NCA chemistry has the highest specific energy, it does not have the highest specific power which means it is not meant to discharge as fast as other lithium chemistries. For the battery system being designed, energy has been designated as more important than power. For this reason, the NCA chemistry was chosen and specifically the Panasonic 18650B.

21 There are a few different brands for the NCA chemistry including Panasonic and LG. 11 The Panasonic 18650B cell is being utilized within Tesla cars which inspired its choice for the battery system being developed here. Under consideration also was the fact that Sony brand battery cells of NMC chemistry had higher tolerances in manufacturing and hence each individual cell performed much more similarly. This is important because cell to cell differences within a battery system will be minimized resulting in a battery pack with a higher efficiency of energy usage. Despite this advantage, the higher energy density of the Panasonic 18650B cell was desired. Via a battery management system, the variation of cell performance can be controlled to enhance the system s performance, but these systems are not addressed in this thesis. Figure 2.3 displays the Panasonic 18650B cell. The specification sheet of the Panasonic 18650B cell can be found in Appendix A. Figure 2.3: Panasonic 18650B Cell This battery is less safe and more expensive than other lithium chemistries, but recent development of battery management systems, methods for removing the heat generated during operation, and internal design of the cell connections have allowed for safe use of NCA battery

22 12 systems. Although the cost is higher for this chemistry, the benefits of higher energy capacity while maintaining moderate power is ideal due to the tradeoff between energy and power capabilities. Battery System Modeling Single Cell Modeling The main tradeoff that must be considered in developing a model is the accuracy and fidelity desired. Hence, a higher accuracy model desired requires an analysis with higher computational effort, cost, and mathematical relations. There are several different types of models that have been developed for these varying complexities. These include electrochemical models, mathematical models, equivalent circuit models (ECMs), and empirical models. As previously stated, there have been large amounts of research conducted on modeling a single lithium ion battery cell. Each of these studies vary in complexity depending on the depth involved in the chemical process studied, the inclusion of temperature effects, and the simplifications made throughout the study. It is important to note that a single cell model in most cases is used as the starting point for a battery system model, meaning the single cell model is multiplied or utilized for each cell within a system model. The strategy implemented in this thesis is to start with a single cell model. Electrochemical models are one class of models that have been developed. They are the most complex and accurate models because they solve the intricacies of the chemical reactions occurring at the cathode and anode within a battery cell, essentially characterizing the fundamentals of power generation. They utilize principles from chemistry and physics such as

23 13 chemical/electrochemical kinetics and transport phenomena to predict battery performance [4]. The most widely used electrochemical models ranging from least to most complex are the Single Particle Model, Ohmic Porous Electrode Model, and Porous-2D Model [5]. The porous 2D model, developed by Fuller et al. [6], is the highest quality model as it solves the 2-dimensional problem for diffusion dynamics and charge transfer kinetics through time-variant spatial partial differential equations [7]. These high accuracy and high fidelity models are ideal for investigating new cell design. However, this specific 2D model as well as the other electrochemical models are very complex and time consuming and therefore are likely unnecessary for the battery system level design required for this work. Other models involving higher complexity analysis include mathematical models and some simplified reduced-order electrochemical models. Mathematical models [8], [9], and [10] can predict some behavior like battery runtime, efficiency, and capacity but do not supply other vital information such as the voltage response to a current profile over time. They also are more inaccurate than other models. Some reduced order models include Chebyshev polynomial methods [11], Galerkin s method [12], residue grouping methods [13], and proper orthogonal decomposition methods [14]. These models slightly reduce the computational cost and time, but they are still more complex than need be for the results that can be attained with a simpler model. The simplest models are empirical models [15]. They apply a curve fitting function to experimental data for a specific set of operating conditions. This results in very fast computation but poor results when used to predict behavior for other operating conditions. This is the negative of using estimation within a model as extrapolation can be very error prone. Prediction on the other hand, in the case of electrochemical and mathematical models, utilizes physicsbased models resulting in higher accuracy at the cost of complexity.

24 14 Most recent literature identifies that the best balance for both accuracy and fidelity comes with ECMs. These models substitute the electrochemical elements with electrical elements (voltage sources, resistors, and capacitors) that produce an equivalent process. The equivalent circuit mocks the electrochemical reactions in a lumped sense. For example, a parallel resistor and capacitor represents the charge transfer across a boundary while the ion diffusion process is represented by waves propagating on a transmission line [16]. ECMs are easy to simulate, can be used alongside application circuits, and only involve ordinary differential equations. However, these models have varying complexities due to the factors included and the fact that each circuit element becomes a parameter based on SOC and temperature when temperature dependence is included. The discharge rate is also a factor in the calculation of these circuit elements. This facilitates the need for parameter estimation from a set of data under specific conditions in order to find the value of each equivalent circuit element. This poses difficulties as many parameter estimation methods can be utilized. Overall, ECMs fall under three general categories: Thevenin [17], impedance [18], [19], and runtime-based models [20]. It is important to note that a Thevenin ECM is the basis of impedance and runtime-based models. These ECMS can be distinguished by the circuit representations in Figure 2.4.

25 15 Figure 2.4: (a) Thevenin, (b) Impedance, and (c) Runtime Based Models [21] Impedance based models use a method called electrochemical impedance spectroscopy (EIS). An equivalent impedance circuit network is found through a fitting process of the impedance spectra [18], [19]. This method is useful because different elements of the battery and hence ECM show varying behaviors based on the range of frequencies. The wide frequency range of the dynamic response is caused by the chemical and physical effects within the electrochemical processes such as mass transport, the electrochemical double layer, and other electrical effects [22]. Impedance models are specific to a fixed SOC and temperature. Additionally, they are only accurate for smaller magnitude currents and a smaller frequency range. Thevenin based models are the most basic form of analysis, but different variations of the model provide for increasing accuracy to a sufficient level. These models include a voltage source, resistor, and, if so, a number of parallel resistor and capacitor pairs in series. The most

26 basic Thevenin model is a resistor in series with a voltage source. This model is simple to 16 parameterize and put into simulations, but it is unable to capture the phenomenon of charge transfer and the dynamic response that occurs in the battery [23]. To capture this, a resistor and capacitor pair in parallel is added in series with the resistor and voltage source. With the RC pair added to the model, the transient response of the battery when pulsed is modeled with sufficient accuracy. Adding a number of RC pairs in series improves the accuracy of the model at the cost of higher order and computational complexity for the parameter estimation as seen in the previous reference. It was found that the accuracy improvement with more than three RC pairs is negligible in most circumstances. There are many variations and improvements upon given Thevenin models within literature. One of these is the inclusion of temperature as a variable in the analysis, forming a new type of model called electrothermal models. These vary in complexity as well but are implemented into the ECMs by a governing equation of the thermal effects. The extent to which the thermal modeling is accurate depends on the simplifications made within the governing thermal equation. The battery cell temperature is almost always assumed to be constant and uniform throughout the cell. Knowing the cell temperature is important for preventing the cell from reaching the melting temperature of Lithium at 186 C, which can cause the cell to have thermal runaway and catastrophic failure [24]. Cell temperature changes as a result of electrochemical reactions, phase changes, mixing effects, and joule heating [25]. A general governing thermal equation is found to include all these factors but parts can be eliminated based on the simplifications involved. This equation is then implemented into the Thevenin ECM to find the dependence of temperature on the voltage response. The model in [26] uses a thermal model inclusive of entropy change to solely find the cell and battery pack temperatures for a

27 17 given constant discharge but does not relate this to the battery performance. Often the entropy change, phase change, and mixing effects are excluded from the ECMs thermal component in literature without forfeiting much accuracy [27], [28]. Another variation of the Thevenin model is a runtime based model, which includes an extra circuit component that models self-discharge and capacity fading [20]. Many researchers interested in runtime as well as voltage profiling have built off the Thevenin ECM by creating runtime-based models. These runtime-based models are used for constant discharge profiles and thus can become inaccurate for varying load currents. Recent publications further develop the runtime based model into a comprehensive model inclusive of two Thevenin RC pairs to capture the transient response and AC current effects from impedance spectroscopy [21], [29]. The work in [30] adds temperature effects to a very similar comprehensive model but still sees errors up to 5%. The literature suggests that the complexity of these comprehensive Thevenin, impedance, and runtime models appears unnecessary for a negligible amount of voltage error difference. This thesis does not require modeling of runtime performance as the system being designed will not involve self-discharge and capacity fading as factors. There were other papers reviewed which combine variations of the Thevenin model with temperature dependence, circuit modeling additions, and advanced analysis techniques. For example, the model in [3] utilizes MATLAB s parameter estimation tool with a standard 1 RC pair ECM for a single cell, but the model does not expand on to battery systems and include temperature effects. The model in [27] provides an in-depth model for the Sony cell by additionally collecting battery temperature data as a function of the C-rate and state of discharge (SOD) to expand upon the thermal dependence. This model seeks to predict cell temperature as a function of C-rate and SOD, and also it can correlate the current drawn to the voltage response,

28 18 to the temperature, and to the C-rate. This model though fails to parameterize the ECM elements based on both SOD and temperature and only deals with constant discharge. The model in [31] uses a comprehensive model that includes temperature dependence, voltage hysteresis, selfdischarge, and diffusion limitation with an acausal approach instead of the traditional inputoutput simulation structure. By having the mathematical equations defined at model compilation, the model can adapt to varying battery system configurations. This approach is quite beneficial for analyzing different geometry battery systems but is quite complex relative to the goals of this thesis. The model in [28] further develops the parameter estimation to using 2D linear splines and proposes a new SOC calculation method that better addresses SOC below 30% and above 85%. The paper s main focus is on modeling different configurations of battery systems, which will be discussed in the multi-cell modeling section and relates to this thesis closely. The model in [32] follows a similar characterization of the single cell model employed in this thesis, but it predicts SOC and discharge rate as opposed to SOC and temperature. The single cell model employed in this thesis combines different aspects of the literature reviewed. For example, the model in this thesis closely follows the one RC pair ECM, standard coulomb counting SOC calculation, and parameter estimation model in [3], it utilizes a slightly more advanced thermal model like the one in [27], and it follows similar qualification testing to that in [32]. Although the single cell model does not propose any new advancement, it combines various works and will be uniquely developed within battery system modeling.

29 Multi-Cell Modeling 19 As seen within the single cell modeling literature review, there are an overwhelming number of published works concerning single cell battery models. This is not the case with battery pack models. It is much harder to find battery pack modeling literature, and the examples available usually create models of the simple connection of individual cells in series. This may be due to the proprietary nature of much deep-level research into battery system design and different system geometries involving serial and parallel connections. Modeling a battery pack of cells in series is a relatively simple process in which single cell ECMs only have to be summed together to retrieve the overall voltage of the pack [33]. The challenge arises when battery packs with parallel strings of cells are modeled. The problem here lies in calculating the current split that occurs between each parallel branch when the battery is under operation, whether managed or unmanaged. This is due to each cell being slightly different and hence drawing different currents in each parallel branch. This unique challenge is also part of the reason parallel string battery packs have not been widely researched. There are three approaches to modeling battery systems as seen in literature. The first approach is to use a single cell model for a battery pack by just implementing all battery specifications into the cell model such as the total capacity of the battery pack [26]. A parameter estimation can then be run to get the cell ECM parameters representing the full battery pack. In this way, a model will be made for the specific battery pack with little relevance to other system geometries. The biggest problems with this approach are the fact that individual cells are not monitored within the pack for their discrepancies from one another, and that the thermal distribution is unknown within the pack. This approach may simplify the computation but does not provide sufficiently useful information for a battery management model for this thesis.

30 20 The second battery system modeling approach involves taking the single cell model and replicating it a number of times into serial and parallel configurations [34]. This approach requires less effort to create as the pack model is only a combination of single cell models. Because of the extensive single cell modeling, this is the most popular approach for battery system modeling. The problems with this approach are that it ignores cell variations and thermal unbalancing by using the same single cell model, and that it involves higher computational effort due to each cell having its own model and governing equations. The third approach utilizes the first approach and builds a battery pack model with these single-cell modeled battery packs [35]. This method naturally includes the characteristics of battery cells and thermal influences as a result of cell averaging and its cumulative effects. Although this approach simplifies the computational effort when compared to the second approach, it is primarily useful for very large battery systems and not small ones. This thesis employs battery models for battery systems of 12 cells or fewer, and therefore does not require the model simplification of combining single cells into groups. The method chosen in this thesis is therefore selected to be a form of the second approach creating battery pack models from the single cell model used in this thesis. The combinations of cells are unique to the future battery system design work being conducted. Summary In this chapter, a background was given on battery operation, battery chemistries, and battery performance metrics, and important battery system design requirements were applied to the characteristics of these chemistries to find the optimal battery chemistry and cell for the long-

31 runtime and high performing systems being developed as a result of this thesis. Additionally, 21 battery system modeling of both single cell and multi-cell systems were introduced as relating to current literature and the models developed in this thesis.

32 22 Chapter 3 The Single Cell Electrothermal Battery Model Introduction This chapter introduces the single cell battery model that will eventually be used to model the performance of Panasonic 18650B battery systems and demonstrates how the model parameters are both derived and modeled in Simulink. This model is the foundation block of a battery system as it represents how a single cell operates. A common approach to modeling battery systems is to use a black box and evaluate the system as a whole. Modeling in this manner does not capture the depth of the internal dynamics required and restricts the use of the model to only that geometry. Individual cells must therefore be modeled first before implementing into different geometry systems. As discussed in the literature review section on single cell modeling, there are varying complexities of models that can be used. These range from the most complicated electrochemical models to the simplest empirical models. An equivalent circuit model was chosen because it is a lower order model in which provides a sufficient degree of accuracy. The Equivalent Circuit Model The equivalent circuit model that has been chosen is a one RC pair Thevenin model. This first order system was chosen as opposed to that of a 2 nd order, two RC pair Thevenin

33 23 model to simplify the computational effort required in solving the system s governing equations and determining the model s parameters. Although the accuracy will be worse, its level of accuracy nearly fulfills the range of 50mV error desired. The electrical components that are comprised within this model are a voltage source, a parallel RC network, and a resistor all connected in series. The voltage source represents the open circuit voltage, the RC pair captures the dynamic voltage response, and the resistor represents the internal cell resistance. Figure 3.1 shows the equivalent circuit model employed. Figure 3.1: Equivalent Circuit Model for a SIngle Cell There are a few governing equations to the model. To begin, the voltage V(t) across the battery is given by: V(t) = V OCV (t) R 0 I(t) v c1 (t) where VOCV(t) is the ideal voltage source which models the open circuit voltage (OCV), R0 is the resistor in series, I(t) is the input current, and vc1(t) is the voltage across the RC pair. The voltage across the RC pair vc1(t) is satisfied by the following first order differential equation.

34 dv c1 dt = 1 RC v c1(t) + 1 C I(t) 24 The Thermal Model A thermal component is necessary for the model for two reasons. First, cell performance is dependent on the temperature of the cell. Secondly, it is important to track the cell s temperature to prevent thermal runaway and cell failure. For these reasons, a thermal governing equation is implemented into the model assuming, as most literature does, that the internal cell temperature is uniform throughout the entire cell, is taken as an average, and satisfies the lumped capacitance method. A battery s temperature is a function of the loading conditions and cell layout for heat transfer effects. A simple equation for a battery experiencing temperature change, as governed by a thermal energy balance, is as follows: mc p dt(t) dt = I(t) (V(t) V OCV T ref dv OCV dt ) h ca(t(t) T amb ) where the differential OCV term represents the reversible heat generation due to entropy change, the last term the convection heat transfer of the surroundings, and the I(t)(V-VOCV) term the irreversible joule heating. For simplification, entropic effects are not considered in this thesis, so that term is eliminated. The I(t)(V-VOCV) can be expanded to: I(t) 2 R R 2 [V(t) V OCV I(t)R 1 ] 2 This resistive heating term is easily implemented into the models and is written as PR. Overall, two terms contribute to the heat power generated for a single cell thermal model: the resistive heating and temperature exchange due to convection. Therefore, the equation can be simplified in the end to:

35 mc p dt(t) dt = P R h c A(T(t) T amb ) 25 where m is the cell s mass, cp the specific heat capacity, hc the convection coefficient, A the surface area of the cell, and Tamb the ambient temperature. The value for the specific heat capacity cp is found by using a bespoke calorimeter and has been found to be around 880 J/(kg*K) for cells [36]. The convection coefficient will range depending on whether cooling is applied to the cell during operation. In the experiments, no fan was used and hence the heat transfer coefficient for natural/free convection is found to be around 10 W/(m 2 *K) for air. Identification of Model Parameters There are many parameters to the model. A few of them are discussed here due to their simple calculation, while the remaining ones will be discussed later on via a more complicated means of calculation involving parameter estimation in MATLAB. These remaining parameters are internal to the ECM and are difficult to predict without an optimization process. Capacity and SOC A battery s capacity is a very important parameter as it determines the amount of charge that can be supplied to a load. The higher the capacity, the more energy that is stored within the cell. It depends on both the discharge rate and the ambient temperature. For a constant discharge rate, also known as a C-rate, the capacity of the cell can easily be found. The capacity Cn is defined as the number of amp-hours (A hr) that the fully charged battery can discharge at a C-

36 rate of 1C at room temperature. A 1C C-rate means the battery would be discharged at an 26 amperage that would fully discharge the cell in one hour, whereas a 2C C-rate would be run at an amperage that fully discharges the cell in 30 minutes and 1 C C-rate in 2 hours. This implies that 2 the SOC of the cell is at 100% before being discharged. Applying this definition, SOC is calculated by the most mainstream and simple technique of Coulomb counting (current integration) as: SOC(t) = SOC ini I(t)dt C n The capacity of the cell is given on the specification sheet of the cell. Two problems with the reported value are that it is only measured at 25 C, and it is often higher than the true value. The ambient temperature highly influences the capacity of the battery. For these reasons, part of the testing conducted was designed to find out what the capacity of the cell truly is for the desired ambient temperatures and discharge rates. In this thesis, emphasis is put on temperature effects. These capacity values are found via constant discharge tests at different temperatures and evaluating the area under the current amplitude versus time curves. C n (I, T) = I(t)dt Because the discharge rate, I(t), is constant, the integration can be simplified to just multiplying the current magnitude by the time duration of the test from fully charged to fully discharged.

37 RC Pair 27 The parallel RC pair provides the model with the time constant of the delayed voltage response of the battery cell in operation. This is necessary due to the dynamic nature of the cell creating a transient response. Figure 3.2 shows the voltage response to a current pulse and is marked with the time constant regions. If a second RC pair was used within the model, one would represent the drop and the other the raise as opposed to one time constant representing both in the model of this thesis. To find the values of R and C, a parameter estimation needs to be conducted on experimental data, which will be discussed in the next subsection. Figure 3.2: Voltage Response for a Constant Current Pulse [32] Internal Resistance The resistor R0 in the ECM represents the internal resistance of the cell. This parameter exists due to the instantaneous voltage drop and raise that can be seen in Figure 3.2 at the

38 28 beginning and end of the discharge. This figure is marked with these regions. To calculate R0, a variation of ohm s law can be applied to each of the temperatures and SOC levels tested by: R 0 (SOC, T) = V 2 V 1 I where V2-V1 is the voltage drop before the transient curve and I is the constant current of the pulse. Open Circuit Voltage The open circuit voltage is the unloaded voltage of the battery at different states of charge. It therefore is a function of SOC but is also dependent on temperature. Although literature has shown that OCV only slightly varies with temperature, in this thesis temperature has been chosen to be a factor in its calculation. The OCV can be found by varying the levels of SOC and letting the battery rest for a period of time with no current. The voltage the cell reaches at this rest state is its OCV. In Figure 3.2 the OCV has been shown after the pulse for a given SOC and temperature. It is important to note that for mid-range SOC values, the OCV and SOC relationship is linear but at low and high SOC values the OCV changes drastically. The work in [28] states that the range is between 30% and 85% for this linear region, so for higher accuracy their model implements a double exponential function to model OCV. The model used here compares experimental data and the parameter estimation to obtain the OCV versus SOC curve for each temperature to implement into the models.

39 ECM Implementation in MATLAB 29 The proposed ECM is modeled using MATLAB Simulink and Simscape. As previously stated, MATLAB has a publicly available ECM to use for a single cell lithium ion battery developed in [3]. This model has been edited to reflect the battery cell used for this thesis, the current profiles, various external conditions, and the thermal model. The model is based on the governing equations presented earlier. Figure 3.3 shows the full single cell model of a general lithium ion battery. One can see the cell is in the center, which within is the ECM as seen in Figure 3.4. On the left side of the full model is the modeling for the effect of the ambient temperature on the cell via convection. On the right is the signal builder which inputs the current profile into the simulation. Figure 3.3: MATLAB Simulink Single Cell Model The ECM is modeled in Simulink as shown in Figure 3.4. All of the ECM circuit-based parameters, VOCV, C1, R0, and R1, involve a 2-dimensional lookup table as their values depend on both SOC and temperature. The manner in which these values are retrieved is discussed in the

40 next subsection. Because the lookup tables do not have every combination of SOC and 30 temperature, the model interpolates between values for simulations with different conditions. Figure 3.4: ECM Modeled in MATLAB Simulink The thermal model for the cell is displayed in various ways in each of Figures 3.3, 3.4, and 3.5. Figure 3.3 contains the convective heating. Figure 3.4 shows the power sum of the resistive heating. Figure 3.5 is the underlying thermal model represented by the pink (shaded) block in Figure 3.4 of the ECM. This thermal model represents the mc p dt(t) dt part of the governing thermal equation.

41 31 Figure 3.5: Single Cell Thermal Model Parameter Estimation The remaining elements within the model, VOCV, C1, R0, and R1, are internal parameters to the model that are difficult to directly observe or measure. Therefore, an iterative technique is used in this thesis to quantify these model parameters that minimize the error between prediction of the model and observation from experimentation. There are several different methods for parameter estimation including electrochemical impedance spectroscopy, ohm s law, and curve fitting in MATLAB. This thesis utilized Simulink Design Optimization within MATLAB/Simulink and Simscape blocks, and this approach is also used in [3]. Although all of the equivalent circuit parameters are functions of SOC, temperature, and discharge rate, this thesis focuses on the dependence of temperature and SOC upon the values of these parameters. Therefore, the 2-dimensional lookup tables for these values are matrices of SOC for each row and temperature for each column.

42 The pulse discharge curve was used for the parameter estimation for each temperature 32 individually, producing a one-dimensional lookup table. These tables were then put together to form four two-dimensional tables, one for each parameter. The SOC parameter was chosen to be taken at eleven breakpoints spaced equally by 10%. This was decided so that more points would capture the lower and higher SOC differences due to its non-linearity in those regions as opposed to greater intermediate levels where parameter variation is expected to be small. Eleven was also chosen as it reduces the time in which the estimation takes to complete without being limiting or excessive. An iterative technique was used within Simulink Design Optimization to estimate the parameters at the different SOC and temperature conditions. A pulsed discharge test was run at different temperatures experimentally, and then Simulink Design Optimization was used to update the parameter values to match the simulated data to the experimental data. The iterations continued until the simulated voltage and experimental voltage had a RMSE (root mean squared error) voltage difference of less than 0.75V. In Figure 3.6, the scope of the parameter estimation is seen. The blue curve represents the simulated voltage whereas the yellow, the experimental. As each iteration went on, the blue simulation curve adjusted over time to the yellow curve in order to minimize the RMSE. The middle plot is the current profile, and the bottommost plot is the SOC profile as the cell is discharged over time. In Figure 3.7, the RMSE is plotted for each iteration. Model accuracy improved as the number of iterations was increased, and it steadied at a value of V for this specific set of data.

43 33 Figure 3.6: Scope of the Parameter Estimation Figure 3.7: Root Mean Squared Error Minimization During the Parameter Estimation Process

44 Summary 34 In this chapter, a single cell battery model was introduced before implementation within full-scale battery systems. This model utilized a 1 st order Thevenin ECM, hence it had one RC pair to capture the transient voltage response. Governing equations were presented and simplified before implementing into MATLAB Simulink and Simscape software to create the performance models. The calculations for all model parameters were also shown and specifically of the parameter estimation from a least RMSE methodology. The parameter estimation estimated values based on SOC and the temperature environment the battery system may be implemented. Therefore, the models developed are more accurate for varying ambient temperature as opposed to varying discharge rate. The results of this parameter estimation and of the performance models are discussed in Chapter 6.

45 32 Chapter 4 Battery Systems Modeling Introduction The previous chapter introduced and derived the fundamental building block of battery systems, the single cell model. Using the single cell battery model, multi-cell battery systems are built for various cell configurations and modeled in MATLAB Simulink. The configurations modeled within this thesis include both series and parallel connections but do not include series connection of multiple parallel strings. Figure 4.1 demonstrates the differences between these configurations. Figure 4.1: Different Cell Configurations for Modeling Battery Systems [28]

46 There will be two battery system configurations modeled in this thesis. The first is a 33 string of 6 cells in series, and the second is a parallel string of 6 cells in series in each branch. The series configuration is easy to model, but the parallel system poses its own challenges. Although these systems are still quite small only including 6 or 12 cells, this approach enables models to be expanded to pertain to much larger battery packs. Building the cell connections is the easier part to creating the battery system models. A much more intensive process is to accurately model the thermal contributions from cell-to-cell, from the environment to the cells, and from other added cooling effects to the cells. Hence, the thermal model to the battery systems developed will also be derived and discussed. Development of Single Cell Model into a Multi-Cell System The approach taken to model the battery systems in this thesis is to add the single cell equivalent circuit model for each cell in the proposed battery system and connect them in the correct manner, whether in series or parallel. The single cell ECM is inclusive of the electrical and thermal governing equations, capacity values, and parameter estimated values derived and found previously. Now that multiple cells are added within one model, the simulation requires solving an ordinary differential equation for each cell, creating a set to solve simultaneously. For both systems modeled, several system parameters must be recalculated to support the new system s properties. By taking this approach, it is assumed that each cell is exactly the same and has the same parameter values. It is known that this is not really the case, and it is possible that cell discrepancies are the main source of problems for battery management systems to fix. This a problem for models of any configuration but has a greater effect on parallel systems.

47 34 The modeling of the 6 cells in series system was quite simple: the single cell model was added 6 times into the system model. There was no change in the governing equations or derivation of the model, but some model parameters had to be updated to reflect the system rather than a single cell. The total voltage of the system in this approach is assumed the sum of all individual cell voltages. The capacity of the overall system is assumed to be equal to that of one cell. The effect of cell discrepancies on series connections is easy to understand; the max voltage is dependent on the sum of all cell voltages, and the runtime performance will depend on the cell with the lowest capacity as that cell will limit the total amount of charge the system can provide. The modeling of a parallel string of 6 cells in series in each branch is more complicated due to cell discrepancies. The same single cell models were placed and connected in the correct configuration as in the series model. Due to cell discrepancies, however, for parallel configuration systems the current splits between the branches according to the circuit properties of the branch, and therefore the current through each branch is different, draining the SOC of each branch at different rates. For this thesis, it is assumed that these branches draw the exact same current because each cell is modeled with the same parameters. This is practical to assume if a battery management system controls the battery system to supply the exact same current in each branch. The voltage of the system is assumed then to be the sum of the voltages of one of the branches in parallel. The capacity of the system is assumed to be equal to the sum of the lowest capacity cell of each branch, hence it is about twice as much as the 6 cells in series system.

48 Expanding Upon the Thermal Model 35 The importance of knowing the cell temperature of each cell within a battery system is of crucial importance to ensure thermal runaway and to ensure that cell failure does not occur. A single cell only interacts internally and with the environment. Once a battery system is created, there are many more heat transfer and thermal processes involved in each cell s temperature calculation and of the battery system as a whole. An interpretation of the environment and cellto-cell influences can be seen in Figure 4.2, where each of the 10 cells is imagined to be on the outer edge of the sphere. Each cell interacts with each of the other 9 cells as represented by the internal lines and is dependent on how the cells are assembled within an enclosure. The outer lines represent the interaction of each cell with the environment. Moreover, if additional cooling is used within the system via water, air, or some other compound, there is an additional heat transfer via convection component that must be added to the model. Figure 4.2: Interpretation of Cell-to-Cell and Cell to the Environment Interactions Between Cells Within A 10 Cell Battery Pack [37]

49 36 There is quite a large amount of literature surrounding the thermal management of battery systems. Most of this literature is highly dependent on the topology and geometric configuration of the battery system. Many large systems will see a high variation in temperature between the cells at the center of the battery pack as opposed to those near the edges of the enclosure. These battery systems require a more complex thermal analysis. The battery systems modeled in this thesis are not large enough to necessitate such an analysis as all maximum of 12 cells in the parallel system are exposed to the environment when tested rather than compacted together without some seeing the environment. For this reason, only the addition of cell-to-cell thermal effects were necessary to add into that of the multi-cell models since convection with the environment was previously modeled for single cells. Within literature, there are thermal models with varying complexities. The model in [31] does not include the cell-to-cell effects but only that of convection to the environment and cooling medium. If cooling effects were to be considered, a forced convection correlation could have been used to calculate the heat transfer coefficient from the Reynolds number, Nusselt number, and Prandtl number as in [38]. This mentioned paper also addresses the change in the heat transfer coefficient of each row of cells within a pack due to the increase in temperature of the cooling medium. Because the cell used in this this thesis is cylindrical, the cell stack thermal model produced in [39] seems inapplicable to this thesis despite completely describing the conduction and convection effects within a cell stack. The same thermal model explained earlier for a single cell is used but with the addition of convection effects between each cell within a series connection. This is necessary to model the heat transferred to the next cell in series. For a typical parallel connection of cells, the branches would be in close proximity and have a thermal effect on each other. The testing conducted in

50 37 this thesis had each parallel branch separated by a far distance and therefore no thermal effects were modeled between each branch. The heat transfer by convection between cells in series was modeled by: Q n n+1 = h conv A(T n T n+1 ) where hconv is the convection coefficient between cells, A the surface area of the cell that is transferring the heat, and Tn+1 the cell after Tn in series. The heat transfer by convection the cells and the environment is the same as the single cell model and is given by the following equation. The distinction lies in the fact the heat is transferred to the ambient environment rather than the next cell in series. Q cell amb = h conv_end A(T cell T amb ) Implementation in MATLAB The proposed ECM is modeled using MATLAB Simulink and Simscape. As previously stated, the work in [3] had developed a publicly available ECM to use for a single cell lithium ion battery in MATLAB. In addition to this, they created a model for 80 cells in series. The battery system models developed here have utilized this model available and edited it to reflect the battery systems, current profiles, various external conditions, and thermal model used in this thesis. The model is based on the governing equations presented earlier. Figure 4.3 shows the model of the 6 cells in series. One can see that a custom block has been made for the 6 cells in series and lies in the center of the model. The current input is on the left of the model, and in the center above the cell block is the modeling of the ambient temperature on the cells via convection.

51 38 Figure 4.3: MATLAB Simulink Full Model for 6 Cells in Series Figure 4.4 shows the underlying connection of each cell in series in the battery of 6 cells block. The heat transfer via convection is shown between each cell as well as the vector concatenate to keep track and organize all data within the model. Each Lithium cell block in this figure represents the single cell ECM displayed in Figure 3.4 inclusive of all components explained previously in Chapter 3 on single cell modeling. Figure 4.4: MATLAB Simulink Block Representation of 6 Cells in Series

52 39 The difference between modeling the series system and parallel system is that a 12 cell block is created in the full model as shown in Figure 4.5, and within is two of the 6 cells in series blocks connected in parallel as shown in Figure 4.6. These 6 cell in series blocks have the same exact internal structure as explained just previously for the 6 cells in series system and shown in Figure 4.4. Figure 4.5: MATLAB Simulink Full Model of Parallel System of 6 Cells in Series in Each Branch

53 40 Figure 4.6: MATLAB Simulink Block Representation of two, 6 Cells in Series Blocks in Parallel Summary In this chapter, the single cell battery model was extended to include multiple cells by adding the single cell model for each cell in the system configuration. Two different configurations were modeled in MATLAB Simulink and Simscape, that of a series system and that of a parallel system, but the editing of the models for different geometry systems was an easy task. Simplifications were made to assume each cell was exactly the same resulting in no need to incorporate unequal current splits into the model of the parallel system. The thermal model was updated to include cell-to-cell interactions involving heat transfer. The results of the performance model in comparison to the experimental test data will be discussed in Chapter 6.

54 41 Chapter 5 Experimentation Introduction There are several experiments necessary to qualify and validate the performance models of the Panasonic NCR18650B Li Ion battery cell and systems. Experimentation of battery cells and systems was necessary for parameter extraction and validation of the models. This chapter presents how the modeled battery cell and systems were tested and the reasons for each test conducted. The next chapter analyzes the results of the tests and simulations. Experimental Setup Measurement Cell stack voltage as well as individual cell voltages were monitored using a National Instruments NI USB-6363 DAQ device. Individual cell skin temperature was monitored using a National Instruments NI cdaq up compact DAQ chassis and a NI 9213 single compact DAQ module. These three devices made up the full DAQ system. A series shunt resistor was utilized to measure load current, also using the DAQ system. The DAQ system sampling rate was 10Hz to minimize the overall size of collected data. Also, all tests were cut off once the cells reached 2.6V to not damage the cells.

55 Battery Setup 42 The Panasonic 18650B cell configurations for each test consisted of either 1 cell, 6 cells connected in series, or a parallel set of 6 cells in series in each branch. The test stands created included interconnections between cells as well as top and bottom cell terminals. This allowed cell stack voltage as well as individual cell voltages to be monitored during tests. Three single cell and two 6 cells in series test stands were made. For the parallel system, the two 6 cell stands were connected in parallel. Furthermore, the outside surface of each cell was monitored for skin temperature via thermocouples. Figure 5.1 shows the single cell test stand, and Figure 5.2 shows the 6-cell test stand. Figure 5.1: Single Cell Test Stand with Inserted Cell and Attached Thermocouple

56 43 Figure 5.2: 6 Cells in Series Test Stand with Inserted Cells and Attached Thermocouples The cells were put within a controlled temperature environment to test the difference in performance during different temperature conditions for each test. Three different temperature environments were tested: 0 C, 23 C, and 35 C. These specific temperatures were chosen for several reasons. The lowest temperature relates closest the cold environment in which the battery system being designed will be utilized. Room temperature allows for validation between rated values of the battery parameters from Panasonic in relation to experimentally collected values. The highest temperature allows for the model to predict cell performance over a greater range of temperatures. These conditions were achieved by using a Chart Industries, now a part of Qualmark Corporation, REAL -30 environmental chamber. The chamber utilizes a heater and nitrogen to set and maintain a certain temperature within the chamber. This chamber was never more than 2 C from the set temperature during testing. The test stand and cells were set within

57 44 the chamber while the wiring was fed through a vacuum tight hole of the chamber to the DAQ measurement system. The room temperature tests at 23 C were conducted in open air as opposed to using the environmental chamber. Safety Precautions There are several risks associated with the testing of lithium ion batteries. When subjected to high currents and temperatures, these batteries can undergo thermal runaway and fail, which can be in the form of an explosion. Therefore, several safety precautions were taken to prevent and provide safety if cell failure had occurred during testing. The cells themselves had their own protection circuit built in, but this does not guarantee safety under some conditions. The simplest precaution taken was the use of a fuse within the cell circuit setup. If the current spiked, the entire circuit would be cut off which would have prevented cell failure. A benefit to having used the environmental chamber is the fact that it has a vent to the outside. This would have been beneficial in the case of an emergency as the fume effects would be lesser inside the lab. Nothing was set on top or near the environmental chamber besides the DAQ and computer, so that miscellaneous items would not get in the way or help accelerate the negative effects of a potential thermal runaway. The nitrogen tank and heater used to maintain the chamber s temperature were secured and placed away from potential threats of being damaged, punctured, etc. There was also an O2 sensor in the laboratory, which is of standard use for tests involving nitrogen. During the duration of each test, one of the personnel was monitoring the test at all times to ensure prompt response if something unexpected occurred. If an unexpected

58 situation had arisen, the test would have been immediately stopped, the situation would have 45 been assessed, and resolutions would have been made to move on ensuring safety. The personnel conducting the tests wore safety glasses and had access to thermal resistant gloves and the right type of fire extinguisher in the case of an emergency. A foam extinguisher, CO2, ABC dry chemical, powdered graphite, copper powder or soda (sodium carbonate) would stop a fire of a lithium ion battery system. An ABC dry chemical extinguisher was accessible during the tests. Charging Charging was performed for a single cell and the 6-cell system as a whole. 6-cell charging was performed using a Hitec X4 AC Plus COTs charger connected to the custom cell holder circuit card assembly of the 6-cell test stand, using both the power terminal block connector as well as the cell-to-cell interface terminal block connector. Single cell charging was performed manually using a bench top power supply with programmable current limit or within the 6-cell charging test stand. In both the single cell and 6 cell series configurations, the cell voltages and temperatures were monitored using the DAQ systems during the charge process. Discharging A BK Precision 8610 electronic load drove the discharge of the battery cell and systems. This programmable load could operate in constant current, constant voltage, constant power, or constant resistance modes. The constant current mode was the only used in the tests of this

59 46 thesis, but future work could use constant power mode. This electronic load runs up to 500V and 240A, hence it is within the operational range of the tests in this thesis. Types of Tests There were three types of tests conducted in this thesis each important for either the creation or validation of the performance models. The first was a constant discharge test, second a pulsed discharge test, and the third a custom profile involving constant discharge with pulses. 1. Constant Discharge Test This test discharges a cell or battery system at a constant current. This test is used to evaluate the overall capacity of the battery cell or system at different conditions. The two main variables affecting the result of this overall capacity are the ambient temperature and discharge rate. This thesis focused on temperature effects but also briefly looked at two different constant discharge rates, primarily 3A but also 1.25A. Although the capacity of the battery cell is listed on the specifications sheet, testing for the capacities of different load conditions was necessary because the manufacturer s listed value is at room temperature and often exceeds the true value. The true capacity of the cell is important as it is the source of how SOC is calculated using coulomb counting. This test can be done on a single cell, but in desiring more accurate values, a multicell system was tested to get an averaged value for capacity. 2. Pulse Discharge Test This test applies a pulsed current profile to a single cell to measure the transient response of the cell to pulses at varying levels of SOC. This is necessary in order to calculate the

60 equivalent circuit model parameters (VOCV, R0, R1, and C1). The current profile was 47 designed so that the SOC drops 10% around 0% and 100% SOC and 15% in the middle SOC region during each pulse, hence eight pulses were discharged at a 1C C-rate of the capacity of the given temperature being tested with a between 21 and 24 minute period of rest in between the end of one pulse and start of the next. The first two and last two pulses were held for 6 minutes each while the 4 pulses in between were held for 9 minutes. The 1C C-rate was found from the capacity found from the constant discharge tests at the three different temperatures. During this rest time, the voltage steadied at its OCV, which is one of the model parameters needed for each temperature and SOC state. 3. Custom Current Profile Test This test applies a constant 1.25A current to the battery cell or system and superimposes pulses of 0.625A. Each pulse was held for 30 seconds and occurred three or four times throughout the test spaced out by 30 minutes. This test was used to validate the single cell and multi-cell system performance models developed in this thesis by providing a cell with a current profile that relates to the application in which the battery being designed will be utilized. The maximum error of these models will be examined in the next chapter. Additional factors to consider within these types of tests are the temperature dependency and battery system geometry. For each of these tests, it was necessary to test the cell and multicell systems at different temperatures to produce lookup tables of capacity versus temperature and SOC versus temperature for the ECM parameters. For system geometry, some single cell values such as the capacity were found using a multi-cell system to eliminate unnecessary and

61 repetitive testing. Due to the time limitation of testing, the cost of testing, and the number of 48 cells in possession, the parallel battery system was not tested at varying temperatures. Test Schedule There were 15 cells in possession, but only one test could be run at a time due to only having one electronic load. Also, charging took up to 4 hours, and the cells needed to be soaked within a certain temperature before being tested. The following schedule factored in these constraints to minimize the number of days of testing and of the resetting of temperature in the environmental chamber. It was ideally desired to have more than one of each test, but the time and cost limitation facilitated the minimization of the number of tests run. This schedule was followed and had no changes involved. Day 1: Constant 3A DC current load, 6 series cells, 0 C 0A DC current load with 3A current pulses superimposed, single cell, 0 C Constant 3A DC current load, 6 series cells, 23 C Constant 3A DC current load, 6 series cells, 35 C Day 2: 0A DC current load with 3A current pulses superimposed, single cell, 23 C 0A DC current load with 3A current pulses superimposed, single cell, 35 C Day 3: 1.25A DC current load with 0.625A pulses superimposed, single cell, 0 C 1.25A DC current load with 0.625A pulses superimposed, 6 series cells, 0 C

62 1.25A DC current load with 0.625A pulses superimposed, single cell, 23 C A DC current load with 0.625A pulses superimposed, 6 series cells, 23 C Day 4: Constant 3A DC current load, parallel set of 6 series cells, 23 C Day 5: 1.25A DC current load w/ 0.625A pulses superimposed, parallel set of 6 series cells, 23 C Summary In this chapter, all equipment involved in the experimentation of the battery cell and systems were discussed. The types of tests and schedule was included to demonstrate the need for the testing to find the model parameters of the ECM and minimize the amount of testing conducted. An additional component of the chapter discussed the safety precautions taken to prevent negative effects in the case of battery failure.

63 50 Chapter 6 Analysis and Validation of the Performance Models Introduction This chapter presents the results of the testing, draws out the specific values important to the performance models, and discusses the differences among certain testing conditions and systems. First, the single cell tests are discussed to find all ECM parameters. Immediate implementation of these parameters into the MATLAB code finished the performance models, and all simulations were then run to be compared with experimental data. Both the voltage response and the battery temperature were compared for the tests. Validation was then achieved for the single cell performance model using the custom current profile simulation and experimental data. The error was slightly higher than desired. Because the error was not far from the 50mV desired error for the single cell performance model, multi-cell systems were then attempted to be validated using the custom current profile. Additional analyses included the effect of discharge rate on voltage output, the variation of single cell performance within a multi-cell system, and the closeness of the thermal modeled to experimental results of battery cell temperature. Throughout all analyses, the ambient temperature had an effect, so it is discussed for each test. An initial look at the experimental results showed the rated battery capacity to be higher than that achieved in the testing conducted. This led to the SOC breakpoints tested within the pulse discharge test to be minimally skewed from the breakpoints desired. Additionally, due to

64 51 the not perfectly even charge throughout the 6-cell in series charging process, the multi-cell tests were limited by the least charged cell. This caused the multi-cell systems to be fully discharged sooner than they should have. For the cell temperature measurement, there was slight fluctuation of temperature within the environmental chamber, which affected the measured temperature of the cells. Although these negative implications took place, the data was still of high quality and successfully achieves its goal of extracting the parameter values and validating the performance models. Single Cell Tests Constant Discharge The first tests conducted were 3A constant discharge tests at three different temperatures for 6 cells in series. The reason a 6-cell setup was used is because each individual cell voltage and temperature is tracked, so that an average curve can be extracted to represent the cell performance the best while the full system performance can be verified using the same test in the multi-cell testing analysis. Due to the different ambient conditions, the total amount of charge that can be utilized within a cell will change. These capacity values are found by multiplying the constant current by the number of hours of runtime from fully charged until the average cell curve reached 2.6V, only.1v above its cutoff value. This represents the area under the current versus time curve for the full voltage spectrum. Due to the constant current, the calculation does not involve complex integration. The curves were extended to the 2.5V cutoff value to more accurately capture the capacity of the cell. Figure 6.1 shows the average cell voltage versus time curves for the 3A constant discharge rate at the three temperatures.

65 52 Figure 6.1: 3A Constant Discharge Experiments at Different Temperatures The capacity values found for each temperature are organized in Table 6.1 in order from lowest to highest temperature. It is clear that battery cell capacity is significantly lower for low temperatures. Table 6.1: Panasonic 18650B Cell Capacity from Constant Discharge Experimental Data 0 C 23 C 35 C Capacity (mah) These values were lower than those quoted in the specification sheet. The reasons the values found in this thesis are lower is due to both the method of charging and the cutoff voltage. The Hitec charger only charges the battery cells to a little under 4.1V as opposed to its max voltage of 4.2V. This tenth of a volt can have a big influence on the amount of charge stored in the cells, which is why the specification sheet had higher values. Additionally, due to the cutting

66 off of the voltage at 2.6V rather than 2.5V, some runtime was neglected to ensure battery 53 preservation. This error is minimal due to the rapid decreasing of voltage as the cell approaches 0% SOC. The data recorded does not accurately capture the 35 C ambient temperature due to its lower capacity value than that of room temperature, but different capacity values were found with the pulse discharge tests next, and it is likely that these pulse results better represent the cell s capacities. Pulsed Discharge The next set of tests conducted were pulse discharge tests of single cells at the three different temperatures. The pulsed current profiles were discussed in the previous chapter on experimentation. With each temperature pulse discharge curve and capacity value for that temperature found previously, all required data was implemented into Simulink Design Optimization to estimate the parameter values of the ECM for each temperature. These then were compiled together into a complete matrix for each parameter of SOC versus temperature. Figure 6.2 shows the plot of the pulse discharge test data voltage versus time for all temperature curves combined. For the last pulses of each curve, different pulse durations were required to facilitate the full discharge of the cell down to 2.6V. Therefore, the individual SOC levels of the OCV vary for each test. This does not highly affect the results as each curve was analyzed and estimated for its parameters individually in the estimation process.

67 54 Figure 6.2: Pulse Discharge Experiments at Different Temperatures The results of this test do not align as closely with that of the constant 3A discharge test for a few reasons. The capacity of the cell for the 0 C pulse discharge test is 332mAh higher than that of a constant discharge, and the 35 C pulse discharge test is 135mAh higher. The new capacity values are listed in Table 6.2 and are used within the parameter estimation as opposed to the previously listed values in Table 6.1. The fact that the 35 C capacity value is higher than that of the 23 C test helps confirm these values to be more accurate than those extracted from the constant discharge test. Table 6.2: Panasonic 18650B Cell Capacity from Pulsed Discharge Experimental Data 0 C 23 C 35 C Capacity (mah)

68 The MATLAB parameter estimation was run for each curve and capacity value, and 55 stopped when the root mean squared error changed by less than 0.001V. The number of iterations ranged from 9 to 16 and the RMSE ranged between 0.31V and 0.7V. Upon completion of the parameter estimation, the following matrices were obtained for each model parameter. The final parameter values were used for SOC breakpoints [ ] descending downwards and temperatures [ ] across, which can be seen the following matrices of the parameter values. Also, figures of these estimated parameters can be found in Appendix B V OCV = [ ] V R 0 = Ω [ ]

69 R 1 = [ ] Ω C 1 = [ ] F Two sets of these parameters could have been found by analyzing the instantaneous voltage drop to find R0 and the settling voltage after a pulse for VOCV for each curve and pulse specifically. This has been done for a few pulses, and the parameter estimation closely predicted these values. For example, VOCV for an SOC of 90% at 23 C is estimated to be V, whereas it is measured to be 4.017V. At this same breakpoint, R0 is estimated to be Ω and is measured to be 0.105Ω. Yet to be tried but as a future action, the VOCV and R0 values can be calculated by hand, and so only the remaining RC pair need be estimated. This may improve accuracy. In the experiments ran, sufficient time for the cells to fully settle to the correct OCV value was not permitted due to the time limitation of each test, but one update was made to these VOCV values to reduce their error. The work in [40] states that an error of around 5mV was due

70 57 to allowing only 20 to 30 minutes of rest time. This value has been added to each VOCV state to increase the model accuracy for all simulations. Validating Simulated Voltage Output With the completion of the parameter estimation, all model parameters were found to enable simulation of any single or multi-cell system. The validation current profile was run at two different temperatures specific to the application of the battery system being developed. The custom current profile is discussed in the experimentation chapter and was run at 0 C and 23 C. Figure 6.3 shows the measured versus simulated data for these two temperatures. Figure 6.3: Validation Profile Test and Simulation for a Single Cell

71 58 For both sets of curves, the model represents the experimental results until the SOC level is between 0% and 10%. When there is little charge left in a battery, the internal reactions are sped up and undergo a more complex process that is not as easy to predict. Future work could address modeling the state of charge at such low levels. The max error found for the 0 C curve is 74.4mV and 51.7mV for the 23 C curve within the SOC range of 10% to 100%. These are both near the 50mV max error tolerance range established for the models developed in this work, disregarding the max errors of nearly 0.5V seen at 0% SOC. The model could be improved to record errors of less than 50mV in the future. Figure 6.4 shows this voltage error over time for the two temperatures tested. Figure 6.4: Validation Profile Test and Simulation Error for a Single Cell

72 Effects of Discharge Rate 59 Although the current profile utilized for validation is specific to a future application, it also closely resembled a constant discharge curve at a different rate than the 3A rate tested earlier. Because cell capacity depends on both temperature and discharge rate, a general understanding can be drawn of how much more charge can be drawn for the smaller 1.25A current magnitude than that of the 3A rate. Initial consideration of the pulses determined that they did not significantly affect the capacity due to their 30 second duration, their frequency of only 3 or 4 times throughout the 2.5 hour test, and their small added magnitude of only 0.625V superimposed. Figure 6.5 shows the difference in the voltage response curves due to two discharge rates for the 0 C and 23 C temperatures. Figure 6.5: Effect of Two Discharge Rates at Two Temperatures

73 60 The capacity of the cell increased by 299mAh for a 0 C ambient temperature and 30mAh for a 23 C ambient temperature at a discharge rate of 1.25A instead of 3A A is a C-rate of about 2 5 C. Single Cell Thermal Validation Another part of the modeling conducted in this thesis was an attempt to correctly model the cell temperature as the cell was discharged. The ambient temperature, SOC, and current profile all contribute to the cell s temperature and are highly complex to model accurately. The thermal model was discussed earlier in Chapter 3. The thermal model was highly inaccurate, even after individual parameters such as the cell specific heat and the coefficient of heat transfer via convection were varied for both constant and pulsed current profiles. The main problem, as seen in Figure 6.6, occurred when a pulse is applied to the battery cell. The thermal model instantly assumed a large spike in temperature whereas it was measured to be a much slower process in reality. It is important to note that the cell s external surface temperature was taken, so the process of the heating up of the surface was much slower than the internal cell temperature. It is unknown therefore the extent of error within the thermal model with the experimental data taken in this thesis. A future piece of work could apply heat transfer analysis to model the surface temperature instead of the internal temperature to determine the accuracy of the thermal model.

74 61 Figure 6.6: Example of High Error Within the Thermal Model for the 0C and 3A Pulse Test Multi-Cell Tests Series Configuration Tests As explained in the single cell analysis, the first tests ran were a constant discharge of six cells in series at three different temperatures. The average voltage was then used for the single cell model, whereas the individual cell voltages are analyzed here. The first analysis that is done on this system geometry is the variation of properties of the individual cells within the system setup. Looking at Figure 6.7 allows one to see each individual cell has a different voltage over

75 62 the duration of the constant discharge test and hence a different capacity value. The cell with the lowest capacity was the limiting factor on the battery system s runtime. This figure is of the 3A constant discharge of six cells in series at 23 C but is representative of each temperature having variations between individual cells. Figure 6.7: Experimental Test Showing Individual Cell Variations within a Multi-Cell System Due to these cell variations, it becomes more difficult to create an accurate model if the exact properties of each individual cell are unknown. To examine the influence of this uncertainty, the model parameters R0, R1, and C1 were made to include a very slight variation using a randomize function. It is also important to note that the error within the single cell model was compounded by using the single cell model within the model of multi-cell systems. Initially, the 3A constant discharge test was simulated to be compared with the experimental results, but the validation current profile of 1.25A constant with small pulses up to

76 1.875A total showed the same amount of error. It is for this reason that only the simulated 63 validation profile results are discussed for this geometry to forgo repetitive results. This same validation current profile was tested on six cells in series at 0 C and 23 C. Each individual cell voltage was measured and then summed up to calculate the total system s voltage. Figure 6.8 shows the measured versus simulated data for these two temperatures for the system as a whole. Figure 6.8: Experimental and Simulated Voltage Output Results for Two Temperatures It is clear that there was larger error associated with the battery system model of six cells in series than that of the single cell model. The red and blue curves representing the 0 C ambient temperature condition have more error than the 23 C ambient temperature. The max error found for the 0 C curve is 1.06V and 0.434V for the 23 C curve within the SOC range of 10% to 100%. Again, the internal reactions are sped up and undergo a more complex process within the

77 last 10% of the SOC range and hence cause an exponential increase in model error within the 64 low SOC region. This can be seen in the voltage error plot for the two temperatures in Figure 6.9. The amount of error within the six cells in series model was deemed unacceptable for the goals of this model. There are ways in which this model could be edited to better reflect the battery system and could be a part of the future work conducted after this thesis. This is discussed in the conclusions chapter. Figure 6.9: Validation Profile Test and Simulation Error for a Six Cells in Series

78 Parallel Configuration Tests 65 Due to the high amount of error within the series geometry setup, the parallel system model was not simulated. The series model must produce satisfactory accuracy before the parallel system model could be run. The experimental data was collected and will be utilized in a future effort. Thermal Modeling Results of Multi-Cell Configurations The results of the thermal modeling for the six cells in series system geometry is not provided in this work. Just as in the case of the single cell thermal model, the single cell error was quite high, and the correlation between inner and surface cell temperature was not yet calculated. Each individual cell temperature was measured in the experimentation and simulated within the system configuration. The inner cells within the series setup were assumed to have both cells on either side contributing to its temperature in the simulation. For this reason, the model was seen to be highly inaccurate by overestimating the inner cells temperatures. The model could be further edited to better reflect each individual cell temperature in the future. Summary In this chapter, the experimental data taken was analyzed to complete the performance models. After implementation of the required parameters, the models were simulated and then compared with the experimental data. The model error for the single cell model was higher than expected and on the level or just above that of the max error desired for this thesis at 50mV. For

79 the multi-cell system model of six cells in series, the model error was well higher due to the 66 compounding effect of each individual cell s error. The multi-cell model was deemed unacceptable for use in additional simulations as these required accurate prediction. These results show that the development of geometric battery models require single cell models of improved accuracy before they can be utilized for real predictions.

80 67 Chapter 7 Conclusions and Future Work Conclusions An approach was taken in this thesis to create dynamic system performance models of the Panasonic 18650B battery cell within several different configurations and ambient temperatures. This approach utilized a simplified Thevenin 1 RC pair model, edited a public MATLAB Li-ion battery performance model for different system geometries and testing conditions, and added more extensive temperature effects to create an adequate single cell model that can be used for predicting results for a wide range of testing conditions. It was observed that the multi-cell models had too much error in their simulated results for beneficial use. This error came as a result of the compounding effect of the error within the single cell equivalent circuit model. This error was also compounded by not modeling cell variations. The thorough process taken within this project made sure each step accounted for primary variables affecting battery performance. The following order was followed to successfully create the performance models: understanding battery chemistries, proposing the single cell model, extending an ECM to a multi-cell system model, analyzing the thermal effects within a battery cell and system, designing experiments to capture cell dynamics and performance metrics, implementing the found and estimated parameters into the models, and evaluating the measured versus simulated data.

81 Specifically, single cell, 6 cells in series, and a parallel set of 6 cells in series in each 68 branch were modeled, simulated, and compared to experimental data at three different temperatures and for three different current profiles. This work focused on temperature effects upon varying loading conditions and slightly compared discharge rate upon constant discharge conditions. The output data compared was the voltage and temperature of the cell or system as a whole. The error associated with the voltage was only adequate for the single cell model, while the thermal model was highly inaccurate within all models. The models could be improved in future work. Future Work There are 5 main initiatives that are planned to be conducted following this thesis. The priority is given to correctly model voltage, next the cell temperature, and lastly a different loading condition. First and foremost, the below 10% SOC region of the single cell model needs to be modeled with higher accuracy to correctly predict the rapid decrease of the voltage output at low charge levels. This will be attempted to be done by adding more SOC breakpoints between 0% and 10% SOC. Additionally, a parameter estimation will be conducted on the single cell validation current profile to compare the parameters at each SOC level to understand how these values might change with discharge profile. This may lead to a better understanding of the parameter estimation and in implementing parameters that are more general to work with a wider array of current profiles. It is by this that the single cell model may have a reduced max error to well below 50mV.

82 69 The next initiative is to increase the model accuracy of voltage prediction for the 6 cells in series model. In the work shown in this thesis, it seemed as though the model was accurate but overpredicted the voltage by a relatively constant value. This might be fixed by using new parameter estimation values found only in the just previous initiative. If this does not work, an analysis could be conducted on the reason the model overshoots the real voltage; this error might lie in the implementation from the parameter estimation to model simulation. The last two initiatives are to correctly simulate the cell(s) temperatures whether as a single cell or within a multi-cell system. A heat transfer analysis could correlate inner cell temperature to the surface temperature, and ideally this would be consistent with the results of the models. Additional internal cell processes during discharge such as entropy change could be added to the model to better reflect temperature effects and improve upon model accuracy in predicting cell temperature. One other application in which the battery system for this thesis could be utilized is under a constant power condition. Therefore, a model with constant power as opposed to constant current could be created and simulated for validation.

83 70 Appendix A Specification Sheet for the Panasonic 18650B Battery Cell Figure A1: Specification Sheet for the Panasonic 18650B Battery Cell

84 Appendix B 71 Estimated Parameters Figure B1: Estimated Values for VOCV as a Function of SOC and Temperature Figure B2: Estimated Values for R0 as a Function of SOC and Temperature

85 72 Figure B3: Estimated Values for R1 as a Function of SOC and Temperature Figure B4: Estimated Values for C1 as a Function of SOC and Temperature