A FAILURE ACCOMMODATING BATTERY MANAGEMENT SYSTEM WITH INDIVIDUAL CELL EQUALIZERS AND STATE OF CHARGE OBSERVERS. A Thesis.

Transcription

1 A FAILURE ACCOMMODATING BATTERY MANAGEMENT SYSTEM WITH INDIVIDUAL CELL EQUALIZERS AND STATE OF CHARGE OBSERVERS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Vamsi Krishna Annavajjula December, 2007

2 A FAILURE ACCOMMODATING BATTERY MANAGEMENT SYSTEM WITH INDIVIDUAL CELL EQUALIZERS AND STATE OF CHARGE OBSERVERS Vamsi Krishna Annavajjula Thesis Approved Accepted Advisor Dr. Joan Carletta Department Chair Dr. Jose A. De Abreu-Garcia Co-Advisor Dr. Tom T. Hartley Dean of the College Dr. George K. Haritos Committee Member Dr. James Grover Dean of the Graduate School Dr. George R. Newkome Date ii

3 ABSTRACT Lithium-ion batteries are the most commonly chosen power source for many portable applications. Advantages like high energy density, high nominal voltage, less maintenance, and low self discharge rate are the driving force behind this choice. Although they have many advantages, lithium-ion batteries have not been used in various applications because of the difficulty of using them well and keeping the individual cells balanced in a series-connected battery pack. This provides our motivation to develop a Battery Management System (BMS) with individual cell equalizers and state of charge (SOC) observers. The main purpose of a BMS is to monitor the cells in a battery pack to ensure proper operation and balance the voltage and charge in the cells in a battery pack in order to maximize the available energy. A BMS was developed for a lithium-ion battery pack with six cells connected in series. The BMS monitors individual cell parameters like voltage, temperature, and current to ensure proper operating conditions and logs this information in an external memory for further processing. Battery model equations are derived, which serve as an SOC observer, to predict and correct the charge stored in the cell. A novel dissipative equalization scheme was proposed to achieve cell equalization among the seriesconnected cells in terms of both voltage and charge. In contrast to the already published equalization schemes, the proposed scheme achieves equalization among cells in the iii

4 battery pack in terms of both voltage and stored charge during charging and discharge. Also the proposed battery management system was implemented in hardware to demonstrate its operation. In the event that a cell in the series-connected battery pack fails, the proposed BMS with minor modifications can isolate the failed cell from the battery pack without disturbing the rest of the operation of the pack; this makes the proposed system failure accommodating. Experiments conducted using the implemented BMS show that a charging strategy that includes cell equalization in terms of voltage allows 31% more energy to be stored in the pack than does a simpler strategy that stops charging once the strongest cell in the battery pack reaches the maximum allowable cell voltage. A charging strategy that includes cell equalization in terms of both voltage and stored charge allows 39.33% more energy. The proposed cell equalization scheme during discharge results in an extraction of 82.87% more energy from the battery pack than does a simpler strategy that stops discharging once the weakest cell in the battery pack reaches the minimum allowable voltage. iv

5 Dedication Dedicated to my family and teachers. v

6 ACKNOWLEDGEMENTS I would like to thank the committee members Dr. Joan Carletta, Dr. Tom T. Hartley and Dr. James Grover for their guidance and support throughout my Master s program. I am grateful to Dr. Carletta and Dr. Hartley for giving me an opportunity to work on such a prestigious project. I would like to specially thank Dr. Carletta for helping me throughout this thesis work and shaping my research work, thoughts and ideas into a good manuscript. I am much obliged for the assistance provided by the ECE department for supporting me as a TA for the Circuits I and II Labs, and Programming for Engineers. In this context, I would like to thank Prof. Kult, and Dr. Sastry for making my teaching experience enjoyable and memorable. Thanks to Erik Ronaldo, and Greg Lewis for providing me with all the necessary infrastructure needed to complete my research work. I appreciate Gay Boden for her help right from the day I stepped into the graduate school. I owe my heartfelt regards to my Mom, Dad and Brother who have constantly been my force of inspiration, determination and encouragement. vi

7 TABLE OF CONTENTS Page LIST OF TABLES.. xi LIST OF FIGURES..xiii CHAPTER I. INTRODUCTION Battery Chemistry Battery Market Cell Balancing in Battery Packs Goals of Research Cell and Battery Protection Charge Control State of Charge (SOC) Determination Cell Equalization Temperature Control History (Log Book Function) Thesis Outline II. BACKGROUND AND RELATED WORK Battery Management System Strategies Battery-Level Voltage Management vii

8 2.1.2 Modular Battery Management Cell-Level Voltage Management Cell Balancing Schemes Passive Cell Balancing Schemes Active Cell Balancing Schemes Charging Techniques Constant Current Charging (CC or I-charging) Constant Voltage Charging (CV or V-charging) Trickle Charging Pulse Charging IUI Charging Other Charging Techniques SOC Determination Direct Measurement Voltage-based SOC Estimation Current-Based SOC Estimation Other State of Charge Measures State of Charge (SOC) Observer Conclusions III. HARDWARE DESIGN FOR THE BATTERY MANAGEMENT SYSTEM Power Supply Considerations Proposed BMS Architecture Communication and Isolation viii

9 3.4 Calibration of Sensors Voltage Sensor Temperature Sensor Current Sensor Lithium-Ion Cell Charging Strategy Cell Equalization Cell Equalization During Charging Cell Equalization During Discharging Component Selection SD Card Interfacing for Data Logging Other Hardware Issues PCB Design Conclusions IV. SOFTWARE IMLPEMENTATION FOR THE BATTERY MANAGEMENT SYSTEM Lithium-Ion Battery Model Fixed-Point Implementation Basics Rules for Fixed-Point Arithmetic PIC Fixed-Point Architecture Fixed-Point Implementation of Sensor Transfer Functions Fixed-Point Implementation of Temperature Transfer Function Fixed-Point Implementation of Current Sensor Transfer Function Fixed-Point Implementation of Battery Model ix

10 4.6.1 Fixed-Point Implementation of Stored Charge Differential Equation Fixed-Point Implementation of Diffused Charge Differential Equation Fixed-Point Implementation of Temperature Differential Equation Fixed-Point Implementation of Temperature Equation Fixed-Point Implementation of Voltage Equation SOC Estimation Software Implementation-Algorithms and Flow Charts Algorithms and Flow Charts for Master PIC Algorithm and Flow Charts for Slave PIC Conclusions V. RESULTS Cell Equalization During Charging Experiment Cell Equalization During Discharging Experiment Cell Equalization for Five Charge-Discharge Cycle Experiment Importance of an Observer Conclusions VI. CONCLUSIONS AND FUTURE WORK REFERENCES x

11 LIST OF TABLES Page Table 1.1: Effect of voltage and charge imbalance Table 2.1: Cell balancing schemes Table 3.1: Voltages obtained from a sample temperature sensor for various temperatures Table 3.2: Voltages obtained from the current sensor for various currents Table 3.3: Pin description of SD Card adapter Table 3.4: Power consumed by the proposed BMS Table 3.5: List of hardware components Table 4.1: Constants in the cell model Table 4.2: Representation of constants in the temperature transfer function Table 4.3: Representation of constants in the current transfer function Table 4.4: Representation of constants in the temperature differential equation Table 4.5: Representation of constants in the temperature equation Table 4.6: Approximation of f(q s (t)) using curve fitting for different ranges of q s (t) xi

12 Table 4.7: Representation of constants in f(q s (t)) for 20<q s Table 4.8: Representation of constants in the voltage equation Table 5.1: Starting voltages of cells for the charging experiment Table 5.2: Available energy in the battery pack of six lithium-ion cells for three different charging strategies Table 5.3: Starting voltages of cells for the discharging experiment Table 5.4: Available energy in the battery pack of six lithium-ion cells for two different discharging strategies Table 5.5: Voltage of cells at beginning of each charge and discharge cycle for the five charge-discharge cycle experiment xii

13 LIST OF FIGURES Page Figure 1.1: Battery working during discharge Figure 1.2: Reactions during the discharging of the lithium-ion battery... 3 Figure 1.3: Reactions during the charging of the lithium-ion battery... 4 Figure 1.4: Comparison of energy densities of various secondary batteries, from [5]... 5 Figure 1.5: Demand for secondary batteries, from [4]... 6 Figure 1.6: Battery world market, from [4] Figure 1.7: Electrical symbols for cells and batteries... 7 Figure 1.8: Typical display of SOC [11] Figure 2.1: Battery management system Figure 2.2: Modular battery management from [12] Figure 2.3: Resistive equalization Figure 2.4: Equalization with switched resistors from [8] Figure 2.5: Simple control method for analog shunt equalization [13] Figure 2.6: Analog shunt equalizer [8] Figure 2.7: Switched capacitor equalizer proposed by [8] [13] [14] [15] [16] Figure 2.8: Equalization results for switched capacitor system presented by Pascual and Krein, from [16] Figure 2.9: Switched reactor equalization [13] xiii

14 Figure2.10: Resonant equalization [8] Figure 2.11: Battery string with individual cell equalizers, from [17] Figure 2.12: Battery ICE with fuzzy logic equalizer [17] Figure 2.13: Equalization with individual DC-DC converters [18] Figure 2.14: DC-DC converter used in Figure Figure 2.15: Three implementations of magnetic core equalization [18] [19] Figure 2.16: Equalization with non-dissipative current diverter [18] Figure 2.17: Typical discharge curve for lithium-ion cell Figure 3.1: Proposed BMS with individual cell monitoring Figure 3.2: Battery pack with six cells in series Figure 3.3: Local power obtained from an individuall cell Figure 3.4: Main power supply using the voltage regulator Figure 3.5: Architecture of the proposed BMS Figure 3.6: I 2 C communication with master and slave at same ground levels Figure 3.7: I 2 C communication with master and slave at different ground levels Figure 3.8: Local voltage regulator Figure 3.9: Plot of transfer function of the ADC as voltage varies from 0 to 2.5V Figure 3.10: Interfacing voltage sensor to the PIC Figure 3.11: Interfacing temperature sensor to the PIC Figure 3.12: Temperature sensor calibration Figure 3.13: Interfacing current sensor to the PIC Figure 3.14: Current sensor calibration xiv

15 Figure 3.15: CV charge profile of the lithium-ion cell, from [23] Figure 3.16: Architecture of the proposed cell equalization Figure 3.17: Cell equalizer for the i th cell Figure 3.18: Working of the cell equalizer during charging: Figure 3.19: Working of the cell equalizer during discharge Figure 3.20: Interfacing SD Card to Master PIC Figure 3.21: PCB Layout for the proposed BMS Figure 3.22: Unpopulated PCB for the proposed BMS Figure 3.23: Top view of the proposed BMS Figure 3.24: Bottom view of the proposed BMS Figure 4.1: Charge-discharge cycle of a lithium-ion cell obtained from experiment Figure 4.2: Temperature of the lithium-ion cell obtained from experiment Figure 4.3: Figure 4.4: Figure 4.5: Ten-minute charge-discharge cycle of a lithium-ion cell obtained from experiment Comparison of actual cell voltage and the cell voltage obtained from the model Absolute error between the actual cell voltage and the cell voltage obtained from the model Figure 4.6: The b-number representation of a fixed-point number Figure 4.7: Data flow diagram for fixed-point multiplication Figure 4.8: Data flow diagram for fixed-point addition Figure 4.9: Data flow diagram for implementing temperature transfer function Figure 4.10: Comparison of floating-point and 16-bit fixed-point implementation of temperature transfer function xv

16 Figure 4.11: Data flow diagram for implementing current transfer function Figure 4.12: Comparison of floating-point and 16-bit fixed-point implementation of current sensor transfer function Figure 4.13: Data flow diagram to obtain stored charge Figure 4.14: Comparison of floating-point and 16-bit fixed-point implementation of stored charge differential equation Figure 4.15: Data flow diagram to obtain diffused charge Figure 4.16: Comparison of floating-point and 16-bit fixed-point implementation of diffused charge differential equation Figure 4.17: Data flow diagram to obtain temperature Figure 4.18: Comparison of floating-point and 16-bit fixed-point implementation of temperature differential equation Figure 4.19: Data flow diagram to obtain Teq Figure 4.20: Comparison of floating-point and 16-bit fixed-point implementation of temperature equation Figure 4.21: Plot of f(q s (t)) vs. q s (t) varies between 0 and 170A-min Figure 4.22: Comparison of approximated and actual implementation of f(q s (t)) Figure 4.23: Data flow diagram to implement f(q s (t)) Figure 4.24: Data flow diagram to obtain the voltage of the lithium-ion cell Figure 4.25: Comparison of floating-point and 16-bit fixed-point implementation of voltage equation Figure 4.26: Observer with feedback for SOC estimation Figure 4.27: Flowchart for the Master PIC Figure 4.28: Flowchart for the Slave PIC Figure 5.1: Parameters of cell #1 for the charging experiment xvi

17 Figure 5.2: Parameters of cell #2 for the charging experiment Figure 5.3: Parameters of cell #3 for the charging experiment Figure 5.4: Parameters of cell #4 for the charging experiment Figure 5.5: Parameters of cell #5 for the charging experiment Figure 5.6: Parameters of cell #6 for the charging experiment Figure 5.7: Voltages of six cells for the charging experiment Figure 5.8: Stored charge in the six cells for the charging experiment Figure 5.9: Parameters for cell #1 for the discharging experiment Figure 5.10: Parameters for cell #2 for the discharging experiment Figure 5.11: Parameters for cell #3 for the discharging experiment Figure 5.12: Parameters for cell #4 for the discharging experiment Figure 5.13: Parameters for cell #5 for the discharging experiment Figure 5.14: Parameters for cell #6 for the discharging experiment Figure 5.15: Voltages of the six cells for the discharging experiment Figure 5.16: Stored charge in the six cells for the discharging experiment Figure 5.17: Voltages of the six cells during the five charge-discharge cycle experiment Figure 5.18: Voltages of the six cells during the five charge-discharge cycle experiment, superimposed on one plot Figure 5.19: Stored charge of the six cells during the five charge-discharge cycle experiment Figure 5.20: Stored charge of the six cells during the five charge-discharge cycle experiment superimposed on one plot Figure 5.21: Model voltages for the six cells during the five charge-discharge cycle experiment xvii

18 Figure 5.22: Error in voltage for the six cells during the five charge-discharge cycle experiment Figure 5.23: Correction in stored charge for the six cells during the five charge-discharge cycle experiment Figure 5.24: Corrected stored charge for the six cells during the five charge-discharge cycle experiment Figure 5.25: Predicted stored charge from columbic counting for the six cells during the five charge-discharge cycle experiment Figure 5.26: Difference between the corrected and predicted stored charge for the six cells during the five charge-discharge cycle experiment xviii

19 CHAPTER I INTRODUCTION A battery is an electro-chemical device that stores energy in chemical form and delivers electrical energy when required. Batteries act as portable sources of electrical power and are thus responsible for the existence of almost all portable devices running on electrical energy. Batteries are used in PCs, laptops, cell phones, MP3 players, digital cameras, camcorders, power tools, electric vehicles, and hybrid electric vehicles. Different types of batteries that are in popular use today include lithium-manganese dioxide batteries, zinc-silver oxide batteries, alkaline-zinc manganese dioxide batteries, lead acid batteries, nickel cadmium (Ni-Cd) batteries, nickel metal hydride (Ni-MH) batteries, lithium-ion (Li-Ion) batteries and lithium-polymer batteries. 1.1 Battery Chemistry Often the terms battery and cell are used interchangeably. Strictly speaking, a battery is an interconnected array of cells, i.e., a cell is a basic building block of the battery. A cell consists of two electrodes, the positive electrode and the negative electrode, connected through an electrolyte [1]. The positive electrode is in a high energy state due to the electrochemical reactions. The battery discharge process is shown in 1

20 Figure 1.1. During the discharge process the electrons flow from the negative electrode to the load, where they give up most of their energy and travel back to the positive electrode. Since there cannot exist a net negative charge on the positive electrode (blocking further acceptance of electrons), this charge must be neutralized by the positive ions released at the negative electrode. For battery chemistries like lithium-ion in which positive ions are the charge carriers in the electrolyte, the positive ions move towards the positive electrode through the electrolyte, completing the electrical circuit. The discharge process continues until all the energized material is converted to its less-energized state. Figure 1.1: Battery working during discharge. Batteries in which the chemical energy can be converted to electrical energy, but not vice versa, are called primary batteries. Secondary batteries are batteries in which chemical energy can be converted to electrical energy (discharging) and vice versa (charging). Secondary batteries are also called rechargeable batteries. In primary batteries the donors and acceptors are known as anodes and cathodes, respectively, 2

21 whereas in secondary batteries they are known as positive electrodes and negative electrodes, respectively. A lithium-ion cell has a lithiated transition metal intercalation oxide for the positive electrode and lithiated carbon for the negative electrode [2]. The electrolyte may be a liquid organic solution or a solid polymer. When lithium carbon and lithiated metal oxide combine to form carbon and lithium metal oxide, electrical energy is released. The overall chemical reaction for a lithium-ion battery [3] is Li ( 1 x ) MO2 + LixC6 6C + LiMO2 where the transition metal, M, is cobalt in most cases and x is a fraction less than one. Figure 1.2: Reactions during the discharging of the lithium-ion battery. Figure 1.2 shows the reactions that take place in a lithium-ion battery during discharge. The negative electrode releases lithium ions and electrons. The electrons flow through the load towards the positive electrode, resulting in a current in the load. Notice that the electrolyte in a lithium-ion battery has floating lithium ions. 3

22 The reactions on each electrode of a lithium-ion battery during charging are shown in Figure 1.3. The electrons released by the external DC supply combine with the lithium ions at the negative electrode to form lithium metal oxide. The electrons released at positive electrode go back to the external DC supply, thus closing the circuit for current flow. Figure 1.3: Reactions during the charging of the lithium-ion battery. 1.2 Battery Market A rapid growth in energy-hungry electronic devices, such as digital cameras, cell phones, laptops and MP3 players, has resulted in a proportional growth in battery consumption. The Freedonia Group Inc. [4] predicts a US demand for primary and secondary batteries of $US 14 billion in the year 2007 and $US 25 billion in the year A 2007 study [4] estimates that secondary batteries constitute 60% of the total demand in US$; their rechargeable characteristic is suitable for most electronic devices. Different types of secondary or rechargeable batteries have been commercialized over the past fifteen years; some of these include lead acid batteries, nickel cadmium (Ni-Cd) batteries, nickel metal hydride (Ni-MH) batteries, lithium-ion (Li-Ion) batteries, and 4

23 lithium-polymer batteries. Energy density, expressed in watt-hours per liter (wh/l) or watt-hours per kilogram (wh/kg), plays a key role in choosing a battery for a particular application. High values of energy density are obvious requirements in any application for which volume and weight of the overall system are a concern. Figure 1.4 compares the energy densities of various secondary batteries. Lithium-ion batteries have a high energy density compared to other secondary batteries. A lithium-ion cell has a nominal voltage of 3.6V and therefore most electronic devices can be run with a single cell; in comparison, a nickel-based battery would require three 1.2V cells in series. Lithium-ion cells require less maintenance than other cell chemistries, and also the self discharge of lithium-ion cells is less than half of nickel cadmium cells [6]. In addition, lithium-ion cells do not have any memory effects, and no scheduled cycling is required to prolong the life cycle. Figure 1.4: Comparison of energy densities of various secondary batteries, from [5]. 5

24 Figure 1.5 and 1.6 shows the demand for various secondary batteries. Lead acid batteries are the most commonly used secondary batteries. Of non-lead acid batteries, lithium-ion cells are the most common. The market demand for lithium-ion batteries, with their higher energy density, is expected to overtake the demand for lead acid batteries, provided that the cost of lithium-ion batteries can be reduced and their lifetime can be prolonged. Figure 1.5: Demand for secondary batteries, from [4]. Figure 1.6: Battery world market, from [4]. 6

25 1.3 Cell Balancing in Battery Packs A battery pack consists of a number of cells. The number of cells connected in series depends on the required voltage rating. Such strings of series-connected cells can be connected in parallel when higher current ratings are required. The number of strings connected in parallel depends on the required current rating. Figure 1.7 shows electrical symbols for cells and batteries. One of the main problems associated with a string of series-connected cells is the imbalance of the state of charge (SOC) of cells among the series-connected cells. An imbalance in the SOC among the series-connected cells not only reduces the overall capacity of the battery, but also reduces the average battery life. The degree of imbalance tends to increase as the number of battery charge-discharge cycles experienced by the string increases. Cell imbalances reduce the battery life and performance drastically. The battery life is reduced by as much as 80% because of these imbalances [7]. (a) (b) (c) (d) Figure 1.7: Electrical symbols for cells and batteries: (a) a cell, (b) a string of series connected cells, (c) a battery with parallel-connected strings, and (d) symbol for a battery pack. 7

26 Despite the advantages of lithium-ion batteries, they also have certain drawbacks. One drawback of lithium-ion batteries relates to their maximum charge and discharge currents. For batteries, C is used to signify a charge or discharge rate equal to the rated capacity of the battery over one hour. For example, a battery with a capacity of 2Ah can deliver 2A to a load for one hour; as it does so it is said to have a discharge rate of 1C. If it were to deliver 1A for two hours, the discharge rate would be 0.5C. Lithium-ion batteries are limited in that the maximum charge or discharge rates must be no more than 1C or 2C. Aging is another issue for lithium-ion cells, and results in reduced battery life. Generally, manufacturers recommend that a lithium-ion cell be kept at least 40% charged to minimize aging. Another drawback of lithium-ion batteries is that each cell has to be prevented from being charged beyond a maximum voltage and from being discharged below a minimum voltage to avoid irreversible damage to the cell. Over-charge of the positive electrode can result in solvent oxidation and in an exothermic decomposition of the active material [8]. Over-discharge of the positive electrode can result in changes in the chemical structure of the active material. Over-charge/over-discharge of a cell results in irreversible damage to the cell, possibly accompanied by cell ignition. Typical upper limits and lower limits on the voltages of a lithium-ion cell are 4.2V and 3.0V, respectively. The limits on voltage for a cell can complicate charging and discharging strategies. In the simplest strategy for charging a series-connected string, charging is discontinued when the first (strongest) cell reaches the maximum voltage. This is 8

27 necessary unless the system has some way to shunt individual cells; otherwise, continuing charging in order to bring the voltage of weaker cells up would bring the strong cells over-voltage. Similarly, for the simplest discharging strategy, discharging is discontinued when the first (weakest) cell reaches the minimum voltage. This is necessary unless the system has some way to shunt individual cells; otherwise, continuing discharging in order to bring the voltage of stronger cells down to minimum voltage would bring the weak cells below the minimum voltage. The result of these simplest strategies is that the battery is not used to its full potential; the resulting charge and voltage imbalance among the cells means that less total energy is stored. An example is used to illustrate the effects of charge and voltage imbalance. Consider a battery pack with two cells connected in series. Table 1.1 shows the energy stored in the battery for three different cases. In the first case, the cells are balanced such that they have equal voltage and equal charge, in which case the total available energy is 63.5KJ. This is an ideal case in which all the cells are completely matched with respect to the voltage and charge, and therefore this is the maximum energy that can be stored in this battery pack. The second case corresponds to a situation in which charging is discontinued as soon as the first cell reaches its maximum voltage of 4.2V. In this case, cell #2 never gets to finish charging; the result is that the cells are both voltageimbalanced and charge-imbalanced. In this case the total available capacity is 16.92KJ, which is only 26.6% of the maximum energy that can be stored in the battery. The third case corresponds to a situation in which both the cells are charged to 4.2V but with different state of charge. The state of charge of the cells is not equal even though their 9

28 voltage is the same because the non-linear SOC vs. voltage characteristics can vary from cell-to-cell due to small cell-to-cell differences in chemistry. The imbalance in the state of charge among the series-connected cells increases with the number of charge/discharge cycles unless state of charge is corrected periodically. When only cell voltages are equalized, the battery stores only 42.86% of the maximum energy that it can store. Table 1.1 shows how important it is to balance both the cell voltages and SOC to maximize the available energy of the battery. Because the energy stored in a cell is given by E = qv, balancing for charge and voltage is same as balancing the energy in individual cells in a battery pack of series-connected cells. Cell imbalances not only reduce the available capacity of the battery but also affect the life of the cell. Other reasons for imbalances include uneven temperature distribution, production difference between the cells and different aging characteristics for each cell [9][10]. Table 1.1: Effect of voltage and charge imbalance. Case 1 Charge-balanced Voltage-balanced Case 2 Charge-imbalanced Voltage-imbalanced Case 3 Charge-imbalanced Voltage-balanced Cell#1 Voltage 4.2V 4.2V 4.2V Charge 2.1Ah 1Ah 1Ah Energy 31.75KJ 15.12KJ 15.12KJ Cell#2 Voltage 4.2V 3.6V 4.2V Charge 2.1Ah 0.5Ah 0.8Ah Energy 31.75KJ 1.8KJ 12.09KJ Total Energy 63.5KJ 16.92KJ 27.21KJ Another issue that is to be considered is the temperature of the cell. A low cell temperature reduces chemical activity, which increases the cell s internal resistance. The increased internal resistance reduces the cell s terminal voltage and thus the available 10

29 capacity. At high temperatures, gassing in the cell increases, which reduces the electrolyte and thus shortens the cell s life. An imbalance in the temperature among the cells changes the self discharge rates, causing imbalances in the state of charge of cells, which in turn reduces the available capacity. Thus, it is important to monitor temperature of the individual cells to ensure that temperatures remain in an appropriate range during operation of the battery. 1.4 Goals of Research Although the lithium-ion cells have many advantages, lithium-ion batteries have not been used in various applications because of the difficulty of using them well and keeping the individual cells balanced. This provides our motivation to develop a Battery Management System (BMS) with individual cell equalizers and state of charge observers. The purpose of a BMS is to ensure proper working and long life of a battery pack. An observer is used to keep track of the SOC of the cell. A BMS with individual cell monitoring improves the reliability of the system. A BMS was developed for a lithiumion battery pack with six cells connected in series. The BMS developed can be used for any other secondary batteries or for battery packs of different sizes with some minor changes. The goal of the research is to develop a Battery Management System (BMS) [11] that can achieve following objectives Cell and battery protection Charge control State of charge (SOC) determination 11

30 Cell equalization Temperature control History (log book function) The following sections describe various functional blocks implemented in a BMS to achieve these objectives Cell and Battery Protection Protecting the cell from operating outside its safe range is a fundamental function of all battery management systems. This eliminates not only the inconvenience but also the cost of replacing the battery. The manufacturers of lithium-ion cells have set maximum and minimum voltage limits of 4.2V and 2.5V (or 3.0V), respectively, to prevent over-charge and over-discharge. The BMS should be able to protect individual lithium-ion cells from over-charge/over-discharge conditions and also ensure that individual cell and battery currents and temperatures are in operating ranges Charge Control Charge control is an essential feature of a BMS. More batteries are damaged due to inappropriate charging than due to all other reasons combined [11]. As discussed earlier, the voltage across a lithium-ion cell should be within the maximum/minimum limits during charging and discharging. Charge control is described in detail in Section

31 1.4.3 State of Charge (SOC) Determination The state of charge of a battery is useful in determining the available capacity of the battery. It is expressed as the percentage of the rated capacity of the battery. State of charge tells the user how much more energy the battery can deliver to the application before it needs recharging. Figure 1.8 shows a typical display of SOC of a battery for a typical application. A BMS should determine the SOC of individual cells in a battery pack to check for uniform distribution of SOC among the cells. Usually the SOC is expressed as a percentage of the rated capacity, rather than of the capacity to which the battery was last charged. The rated capacity of the cell is not the same as the capacity of the battery to which it was last charged because of aging and environmental effects that prevent the battery from charging to its rated capacity as time passes. However, if the SOC is used only for cell equalization purposes, it can be expressed either way, as all the cells in a string generally experience the same environment. Different methods of determining the SOC are discussed in detail in Section 2.4. Figure 1.8: Typical display of SOC [11]. 13

32 1.4.4 Cell Equalization The problems associated with a battery pack with series-connected cells were detailed in Section 1.3. To improve the life of the battery pack and also maximize the available capacity of the battery, it is necessary to equalize the voltage and SOC of the cells in a battery pack. Cell equalization is one of the most important functions of a battery management system Temperature Control It is important to track the temperature for two reasons. The manufacturer specifies a limit on the operating temperature range of the cell (typically C). The SOC of a cell depends on the temperature. Temperature affects the self discharge rate, or the rate at which the cell loses its energy when not in use. Thus, imbalances in temperatures among the series-connected cells can result in imbalances in SOC. The battery management system should take temperature into account in determining SOC and should ensure that cells operate in a safe temperature range History (Log Book Function) Another possible function of a battery management system is log book keeping. The battery management system may store battery data in external memory for later analysis. This data may include voltages, currents, temperatures, states of charge and number of charge-discharge cycles. Analysis of the data can help in determining the state of health (SOH) of the battery. State of health is the working condition of the battery and measures the battery s ability to perform the required function when compared to a new 14

33 battery. The stored information also helps in determining whether the battery has experienced any unwanted operating conditions. 1.5 Thesis Outline The research work done is presented as a thesis in the following six chapters. This chapter gave an introductory material required to understand the objectives of a battery management system, and described the need to have cell equalization for a battery pack of series-connected cells. Chapter II provides the background on various battery management system strategies, cell equalization architectures and charging techniques. This chapter also presents related work previously published on battery management. Chapter III discusses in detail the hardware implementation of the proposed battery management system and cell equalization scheme, hardware components used, and PCB design to implement the proposed battery management system. Calibration of various sensors and the effect of the hardware on the performance of the battery pack are also discussed in this chapter. The battery model for the lithium-ion cells is presented in Chapter IV. This chapter deals with the implementation of the battery model and sensor transfer functions in a fixed-point processor. The chapter also presents software implementation details of the battery management system. The results of implementing the battery model and sensor transfers function in a fixed-point processor are presented in Chapter V. Chapter V also provides the voltage, current and temperature profile of the lithium-ion cells during charging and discharging with and without the observer. Chapter VI draws conclusions and makes recommendations for future work in this area. 15

34 CHAPTER II BACKGROUND AND RELATED WORK This chapter gives a detailed description of battery management system strategies, charge control architectures, charging techniques, charging phases and state of charge observers for battery management systems. The advantages and disadvantages of various techniques are discussed. This chapter also discusses the existing work on battery management systems, and the differences and advantages of the battery management system implemented in this thesis compared to others. 2.1 Battery Management System Strategies The main objective of a battery management system is to monitor the cells in the battery pack, and to control charging/discharging of individual cells. The BMS uses a microcontroller as a central control module for this purpose. The central module may monitor only system-level parameters of the battery pack, may divide the pack into group of cells and monitor parameters of each group, or may monitor individual cells. There are three basic methodologies or battery management system strategies used [8]; presented in increasing order of complexity, they are: 1. Battery-Level Voltage Management 2. Modular Battery Management 16

35 3. Cell-Level Voltage Management Battery-Level Voltage Management In battery-level voltage management, the battery-level voltage is used to control the charging and discharging process. Because only the voltage of the entire battery is monitored, this is the simplest and cheapest strategy. Individual cell voltages are neither measured nor controlled in this strategy. Figure 2.1 shows a typical implementation of battery-level voltage monitoring. Figure 2.1: Battery management system. The controller monitors the battery voltage and uses this information to control the charging/discharging of the battery. If the average cell voltage, computed based on the battery voltage, is greater than a maximum predetermined voltage, the charging process is discontinued. The discharging process is discontinued when the average cell voltage reaches the minimum predetermined voltage. The voltages of individual cells may be higher than the maximum during the charging process or less than the minimum during the discharging process, depending on cell-to-cell variations. Cell-to-cell variations must be small to implement this method successfully. 17

36 2.1.2 Modular Battery Management Figure 2.2: Modular battery management from [12]. In a modular battery management system, the series-connected cells are divided into groups of cells, and each group is monitored and controlled by its own local control module [12]. A local control module obtains voltage, current, and temperature information for each cell under its control, and transmits the information to a central control module. The central control module processes the information for the entire battery, and sends command signals to the equalizing units present in the local modules to equalize the cells monitored by the corresponding local module. Therefore, in this strategy, groups of cells are monitored and controlled to reduce the voltage and SOC imbalances among the cells. Figure 2.2 shows a typical implementation of modular battery management, used in [12]. The data transfer block senses the voltage, current and 18

37 temperature information of individual cells in a group and transfers this information to the local module, one cell at a time in the group, through the multiplexer. The local module transfers data about the cells in its group to the central module through a serial bus. The central module processes this information and sends command signals to the equalizer, which controls cell equalization for the entire battery Cell-Level Voltage Management In cell-level voltage management, individual cell voltages are measured and used to control the charging and discharging process. Charging is terminated when the first cell reaches the maximum voltage, and discharging is terminated when the first cell reaches the minimum voltage. This strategy ensures that all individual cell voltages are within the recommended range. However, the cell voltages are not equalized and the SOC is not actively managed. More sophisticated variations of cell-level voltage management systems like dissipative cell-level voltage management and non-dissipative cell-level management systems measure individual cell parameters to control the charging/discharging of individual cells to achieve cell equalization in terms of voltage, state of charge, or both. These methods are discussed in detail in Section Cell Balancing Schemes One of the main objectives of a more sophisticated BMS is to balance individual cell voltages and SOC in a series-connected battery pack. The cell balancing scheme refers to the hardware architecture adopted to achieve voltage/state of charge balancing. Voltage and SOC imbalances in series-connected cells can be eliminated by using some kind of cell balancing scheme. The cell balancing scheme monitors either the SOC 19

38 (in more critical applications) or the voltage (in less critical applications) of each cell, or both. Switching circuits then control the application of charge to individual cells during charging so that all the cells have equal SOC (or voltage). Some cell balancing schemes also monitor during discharge so that the capacity of the cell is not limited by the cell of lowest capacity in the series-string. Various cell balancing schemes for balancing lithiumion batteries [8] are summarized in Table 2.1. They can be classified into two types: passive and active balancing. These are explained in the following sections. Table 2.1: Cell balancing schemes. Passive Active Resistive Equalization Switched Capacitor Equalization Analog Shunt Equalization Switched Reactor Equalization Resonant Equalization Other Active Methods Passive Cell Balancing Schemes In passive or dissipative balancing scheme, individual cell voltages are measured and controlled. The charging process continues even after strong cells reach their maximum voltage until all the cells in the battery pack are completely charged. Passive cell balancing schemes can balance voltage, charge, or both; balancing both is the same as balancing the energy. Cells are balanced by passing the current through a dissipative element (resistor) around a strong cell so that it loses voltage, charge or both until it balances with other cells in the series-string. This ensures equal voltage, charge or both in all the cells in a series-string. However, in passive balancing schemes proposed so far, discharging stops when the first cell reaches minimum voltage; this limits the capacity of the battery, and cell balancing cannot be achieved during the discharging process. 20

39 Resistive Equalization Figure 2.3: Resistive equalization. The resistive equalization technique employs a resistor connected in parallel with each series-connected cell, as shown in Figure 2.3. This method is the simplest equalization method, and requires no external control, because the resistor is always connected in parallel to the cell. The resistance connected in parallel with each cell is large compared to the internal resistance of the cell. A strong cell with higher voltage results in a higher current through the resistor R, thereby dissipating more power. This results in the voltage drop of the strong cell accompanied by decrease in the current through the resistor. The differences in the individual cell voltages become smaller with 21

40 time. The main disadvantage of this method is that the resistor dissipates energy continuously during both charge and discharge cycles. Figure 2.4: Equalization with switched resistors [8]. An alternative is to dissipate the energy only when the cell has additional energy, i.e., to connect the dissipative element in parallel to the cell only when the cell has reached its maximum rated voltage. Figure 2.4 shows a resistive equalization scheme patented by Lockheed Martin [8]. The cells are connected in series, and each cell voltage is monitored. Each cell has a switch (realized using a MOSFET or a BJT) and resistance connected in parallel to the cell. Initially, during charging, all the switches are open. A microcontroller monitors cell voltages, and controls the switches based on the individual cell voltages. When a particular cell reaches its maximum rated voltage, the 22

41 corresponding switch is closed and diverts the charging current through the resistor. Thus, energy is drawn from the high energy cell and is dissipated in a resistor. Once all the cells reach the maximum rated voltage, the charging current to the string is reduced to zero Analog Shunt Equalization Figure 2.5: Simple control method for analog shunt equalization [13]. In analog shunt equalization, the dissipative element is connected in parallel to the cell using analog circuitry. Hence no microcontroller is required. One possible implementation is shown in Figure 2.5. The transistor turns on when the cell reaches the reference voltage, i.e., the breakdown voltage of the zener diode; at that point, the cell is shunted by the transistor and the charging current is shunted across the cell. Figure 2.6 shows an alternative analog shunt equalization circuit patented by Sony [8]. The cells are connected and are charged in series. The voltage of each cell is monitored by a comparator. When the cell reaches the reference voltage (i.e., the maximum rated voltage), the comparator turns the Darlington pair on, thereby connecting 23

42 the resistor R in parallel to the cell. The current is proportionally shunted through the resistor, and the cell is charged at a constant voltage thereafter. This process continues until all the cells are charged completely. This approach balances the voltage of even highly unmatched cells, but it requires relatively complex circuitry. Figure 2.6: Analog shunt equalizer [8] Active Cell Balancing Schemes In active or non-dissipative balancing, individual cell voltages are measured and the voltages or states of charge are managed by passing the current through nondissipative elements (capacitors and inductors) around the cell. This method continuously 24

43 transfers energy from high energy cells to low energy cells. Therefore, this strategy can be used to obtain cell balancing under both charging and discharging conditions. Active balancing schemes can be further divided into two types: local and global balancing schemes. Local balancing schemes are based on transferring energy between neighboring cells and thus the balancing is achieved relative to the neighboring cell voltages. Local balancing schemes are described in Sections to On the other hand, global balancing schemes balance the cells based on a reference voltage; therefore, all the cells are balanced relative to the same reference voltage. Global balancing schemes are described in Section Switched Capacitor Equalization Switched capacitor methods for equalizing series-connected cells were proposed in [8] [13] [14] [15] [16]. The working principle of the switched capacitor method or the flying capacitors method is shown in Figure 2.7. This method is a local balancing scheme where the voltage is balanced relative to the neighboring cells. A battery pack with n cells uses n-1 capacitors for equalization. The switches can be realized using either relays or pairs of transistors. Assuming cell #1 to have higher voltage than cell #2, capacitor C1 is connected in parallel to cell #1 using switches SW1 and SW2. During this period the capacitor C1 gets charged to the voltage same as that of cell #1 and the voltage of cell #1 drops by small amount. In the next cycle the capacitor C1 is connected across cell #2 and now cell #2 gets charged with the charge stored in capacitor C1. Therefore, the additional charge that was previously in cell #1 is transferred to cell #2; note that in a passive technique, this energy would have instead been dissipated in a resistor and lost. This 25

44 method is bidirectional, and thus if cell #2 has higher voltage than cell #1, then C1 stores the charge from cell #2 and transfers it to cell #1 in the next cycle. Similarly the charge can be transferred from cell #2 to cell #3, from cell #3 to cell #4, and so on. The voltages of all the cells tend to equalize after several such cycles. Figure 2.7: Switched capacitor equalizer proposed by [8] [13] [14] [15] [16]. The main disadvantage with this method is that the voltages of cells are equalized with their neighbors, rather than with a reference voltage. As a result there is an inherent delay in the transfer of charge across a long series-connected chain of cells. Figure 2.8 shows the cell voltages during charging in a battery pack of six series-connected cells; each cell is nominally 14V (11.5V to 14V). The time delay inherent in transferring energy from neighbor to neighbor can be seen in the Figure 2.8. This delay can be long enough for some of the cells to cross the maximum voltage, potentially causing damage to the cells. 26

45 Figure 2.8: Equalization results for switched capacitor system presented by Pascual and Krein, from [16] Switched Reactor Equalization The working principle of a switched reactor equalization technique [13] is illustrated in Figure 2.9. This method is based on transferring energy from a cell of higher energy to its neighboring lower energy cell. This is a bi-directional method and can be used in both charging and discharging. A daisy chain connection ensures equal energy among all cells. In phase-1 (assuming cell #1 to have higher voltage), the transistor Q1 (controlled by a PWM signal) is turned on, which results in current flow from cell #1 through Q1 to the reactor, as shown in Figure 2.9. This results in storage of charge in the reactor; as a result the voltage across cell #1 drops by a small amount. In phase-2, the transistor Q1 is turned off, which results in current flow from the reactor to cell #2 and D2, thus transferring the charge stored in the reactor to cell #2. Therefore, charge is moved from cell #1 to cell #2. The charging process is terminated once all the cells reach 27

46 the same voltage. The main drawback of this approach is its complexity; also, the voltages are compared only with the neighboring cells and not with a reference voltage. Figure 2.9: Switched reactor equalization [13] Resonant Equalization A resonant equalization circuit is shown in Figure 2.10 [8] (Lockheed Martin patent pending). The balancing circuit has a resonant circuit formed by L2 and C1 transfer the energy between cells and also to drive the MOSFETs Q1 A and Q2 A. The MOSFETs Q1 A and Q2 A are controlled (turned on and off) when the voltage across the resonant circuit is at the peak, i.e., when the current through the resonant circuit is zero. Assuming cell #1 to be at higher voltage than cell #2, the MOSFET Q1 A is turned on, which results in current flow from cell #1 through Q1 A, to the inductor L1 C. This results in storage of charge in L1 C ; as a result, the voltage across cell #1 drops by a small amount. Turning on the MOSFET Q2 A and turning off the MOSFET Q1 A results in a 28

47 current to flow from the inductor L1 C to cell #2, thus charging cell #2 with the charge that is stored in the inductor L1 C. Like the switched capacitor method, this method can be used during both charging and discharging. Figure 2.10: Resonant equalization [8] Other Active Methods Another method of active cell balancing uses individual DC-DC converters to transfer energy from one cell to another cell. One such approach was proposed in [17]. Like switched capacitor equalization, this approach also has n-1 individual cell equalizers (ICE) for n cells connected in series, as shown in Figure 2.11, and a capacitor is connected between each cell for energy transfer. This approach differs from switched capacitor equalization in that this method has inductors and diodes as shown in Figure 29

48 2.12. The purpose of inductors and diodes is to minimize current ripple. The direction of the energy transfer depends on the cell voltage difference and on how the power MOSFET switches are controlled. The MOSFETs are controlled by a Fuzzy Logic Equalization Controller. By the authors admission, the equalization speed and efficiency of this equalization scheme are too low for practical equalization applications. Figure 2.11: Battery string with individual cell equalizers, from [17]. Figure 2.12: Battery ICE with fuzzy logic equalizer [17]. 30

49 Figure 2.13: Equalization with individual DC-DC converters [18]. Another approach for charge equalization using an individual bidirectional DC- DC converter for each cell was proposed in [18]. The overall scheme is shown in Figure 2.13, and the DC-DC converter is shown in Figure During charging, energy from a strong cell is transferred to the main bus via a DC-DC converter, until its voltage drops to the reference voltage. During discharging, energy can be transferred from the battery pack to the weak cells; thus, all the cells are maintained at the same level and utilization of the battery pack is improved. Figure 2.14: DC-DC converter used in Figure

50 Another method of active cell balancing, proposed in [18] [19], uses a transformer with multiple secondary windings for energy transfer. The primary of the transformer is connected to the battery bus as shown in Figure 2.15, and the secondary windings are connected to the individual cells. This approach ensures transfer of energy from the battery bus to the weak cells in the stack. As shown in Figure 2.15(C), once a weak cell is detected, the switch associated with that cell is closed; as a result, energy is stored in the magnetizing coil and this energy is transferred to the weak cell upon opening the switch. Figure 2.15: Three implementations of magnetic core equalization [18] [19]. A non-dissipative current diverter for cell balancing was proposed in [18] as shown in Figure Each diverter consists of a MOSFET Q, inductor L and freewheeling diode D. During normal operation all the diverters are disabled and the charge current flows through the series-connected cells. Once a particular cell (say cell #1) reaches the reference voltage, the corresponding MOSFET Q1 is turned on. This results in storage of energy in the inductor L 1 due to the flow of current I 1 through it. This is 32

51 continued until the voltage of cell #1 falls to the reference voltage. When the MOSFET Q1 is turned off, the energy stored in L 1 is transferred to cell #2 through the freewheeling diode D1. Figure 2.16: Equalization with non-dissipative current diverter [18]. 2.3 Charging Techniques The batteries considered in this thesis are secondary batteries, i.e., the electrical energy lost during discharge can be replaced by recharging the battery. Recharging the battery is done in several phases. The phases are characterized based on the amount of energy the battery accepts during charging [13]. In the initial charging phase or bulk charging phase, the battery is charged with the maximum current specified by the manufacturer of the battery. Most of the energy lost in discharge is replaced in this stage, and the state of charge is brought up to within a few percentage points of the maximum capacity of the battery. The last few percentage 33

52 points of state of charge are returned to the battery in the absorption-charging phase. The charging current in this phase is very small in order not to damage the battery. Once the battery is fully charged, the float charge phase maintains the battery in its fully charged condition by compensating for energy lost over time due to self discharge. An equalization phase can be used for battery packs of series-connected cells in order to fully and equally charge the cells in series-strings. The charge to a cell can be restored by applying either a constant voltage or a constant current, or by using a variety of combinations of voltage and current. Common charging techniques [14] [20] are described next Constant Current Charging (CC or I-charging) For a constant current charging scheme, employed in the bulk charging phase, the charger voltage is varied continuously to maintain a constant charging current. The charging voltage is switched off when the battery voltage reaches its upper limit Constant Voltage Charging (CV or V-charging) In constant voltage charging, a constant DC voltage greater than the battery upper limit voltage is applied to the battery. The DC voltage is obtained from the AC mains using a rectifier, filter and regulator. A variation on this method known as the float charging method connects a DC voltage slightly lower than the battery upper limit voltage permanently across the battery. A slight drop in the battery voltage results in its charging through the DC voltage. Constant voltage charging is usually employed in the absorption-charging phase. 34

53 2.3.3 Trickle Charging Trickle charging is done for batteries in storage to compensate for self discharge. This is required to maintain the battery at its fully charged state. A low rate of continuous charge is applied. Trickle charging is used in the float charge phase Pulse Charging In pulse charging, the charging current is supplied in the form of pulses. The charging rate can be controlled by adjusting the pulse width. A short duration is allowed between the pulses for the chemical reactions within the battery to stabilize. In this way, the chemical reaction is in phase with the rate of input of electrical energy. Unwanted chemical reactions at the electrode surface, such as gas formation, can be avoided with this method. Pulse charging can be used for charging the cell in any of the phases by changing the width of the pulse in accordance to the phase in which its being used IUI Charging This is a very recently developed charging technique [20] in which the battery is charged initially with constant current, during what is termed I phase; this is the bulk charging phase. When the battery reaches the predetermined voltage at which gassing may start, the I phase ends, and the battery is charged instead with a higher constant voltage (U phase). The U phase continues until the battery voltage reaches a new higher preset voltage. Then, the charger is again switched back to constant current mode (I phase) until the battery reaches the next higher preset voltage. This phase is usually 35

54 carried out to achieve equal voltages among all cells for cell equalization in a string of series-connected cells Other Charging Techniques Other charging techniques include (i) taper charging, in which an unregulated voltage source is used for charging, (ii) burp charging, which is similar to pulse charging but includes some discharge pulses and (iii) random charging, in which the energy is supplied randomly in an uncontrolled way. 2.4 SOC Determination Because it is not possible to measure the SOC of a battery directly, a physical parameter that varies with the SOC is measured to determine the SOC of a battery. Based on the physical parameter that is measured, SOC determination methods are classified into the following types [11]: 1. Direct Measurement 2. Voltage-Based SOC Estimation 3. Current-Based SOC Estimation 4. Other State of Charge Measures Each of these methods is now described in more detail Direct Measurement The direct measurement method for SOC assumes that the current through the cell is constant. The state of charge is calculated solely in terms of the elapsed time, based on Δ q = iδt. The controller that is being used to calculate the SOC keeps track of the 36

55 charging and discharging process and accumulates time either positively or negatively to determine the SOC. This method has two problems associated with it. First, this method requires that the current through the battery be constant. The current through a battery is in fact not constant; it increases/decreases as the battery charges/discharges, in a nonlinear fashion. Therefore, a more accurate measure would require that actual current be measured and accumulated over time. Second, this method requires that the battery be discharged in order to determine how much charge it contained initially Voltage-based SOC Estimation This method is applicable to cell chemistries whose voltages are directly proportional to the available state of charge, as is the case with lead acid batteries. If this relation is known a priori, the SOC can be obtained by measuring the open circuit voltage. In practice, the SOC varies widely with temperature, discharge rate and aging of the battery; all these factors must be considered for an accurate determination of SOC. Voltage-based SOC estimation cannot be used at all for lithium-ion cells, since they have only a very small voltage change over most of the charge/discharge cycle. A sudden fall in the voltage can be used to determine that a lithium-ion cell is near the end of its discharge cycle. The voltage characteristics of a lithium-ion cell are shown in Figure The voltage of the lithium-ion cell falls sharply from 3.0V. However, using this drop to decide when to stop discharging is dangerous because discharging a lithium-ion battery below 3.0V negatively impacts the life of the battery dramatically. 37

56 Therefore, a better method is required to determine the state of charge of a lithium-ion battery. Figure 2.17: Typical discharge curve for lithium-ion cell Current-Based SOC Estimation Like direct measurement, current-based SOC estimation uses the basic definition of the charge q = t 0 i( t) dt to determine the SOC of a battery; charge is obtained by integrating the current. This method accumulates the current drawn in and out of the battery over time to determine the capacity of the battery. Therefore, this method is also known as Coulomb counting. The current flowing in and out of the battery is obtained by measuring the voltage drop across a known low ohmic, high precision, series resistor. Coulomb counting takes into account only the current flowing in and out of the battery to the external circuit; this method assumes that the charge is a function of only current. However, SOC of a battery also depends on temperature, self-discharge rate, charge acceptance and aging of the battery. Coulomb counting causes errors to accumulate unless the calculations are calibrated or reset periodically. Although coulomb counting is 38

57 accurate enough for many applications, temperature, self discharge rate, charge acceptance and aging should be taken into account if a more accurate determination of SOC is needed Other State of Charge Measures The SOC of lead acid batteries can be determined by the specific gravity method. As the battery discharges, the active electrolyte (sulfuric acid) is consumed and the concentration of sulfuric acid is decreased. This in turn changes the specific gravity of the solution. Because there is a direct relationship between specific gravity and the SOC of the battery, specific gravity can be used to determine the SOC. 2.5 State of Charge (SOC) Observer Section 2.4 discusses the various methods available to measure the SOC. However, all these methods estimate the SOC based on the measurement of a physical quantity (current or voltage) and do not take into account the effect of factors like temperature, self-discharge rate, charge acceptance and aging of the battery. Thus, none of these methods are error-free. One way to improve accuracy is to have an observer to track the SOC. A mathematical model for the battery is implemented in the processor monitoring the battery; this model takes into account the various parameters affecting the SOC of a battery. The mathematical model is obtained by performing experiments on the battery under controlled conditions that account for changes in temperature, selfdischarge rate, charge acceptance and aging of the battery. The battery model is then used to correct (track) the SOC obtained from the measurements. Several different techniques 39

58 such as Fuzzy Logic, Kalman Filtering, Neural Networks and recursive, self-learning methods [17] [21] [22] have been employed to improve the accuracy of SOC estimation. Our approach to modeling and implementation of a lithium-ion battery model is discussed in detail in Chapter IV. 2.6 Conclusions The purpose of a BMS is to charge and discharge the battery, balance the cells, determine the SOC and maintain proper operating conditions for the battery in terms of voltage, current and temperature. A BMS may also log data. The main parts of the BMS perform battery monitoring and cell balancing. This chapter explains various architectures for BMS, different cell balancing schemes (both dissipative and nondissipative), charging techniques, and SOC determination techniques and it provides overview of previously published research. Previously published research concentrates either on equalization techniques or on the battery monitoring system, but not on both. Also the ideas previously presented have not been implemented practically. A complete battery management system is implemented in this thesis, with individual cell equalizers and individual state of charge observers to track the SOC. A new cell equalization technique is presented that is essentially a dissipative method, although it incorporates some advantages of both dissipative methods and non-dissipative methods. This technique has simple circuitry and simple control, and can be used during both charge and discharge. In addition, energy lost through dissipation is lower than for other dissipation methods. Cell balancing is carried out not based solely on the reference voltage but also with respect to the SOC. Another 40

59 advantage of the proposed cell balancing scheme is the capability for accommodating failures; in the event that an individual cell fails, the proposed BMS with minor modifications can isolate the cell from the battery pack without disturbing the normal operation of the battery. 41

60 CHAPTER III HARDWARE DESIGN FOR THE BATTERY MANAGEMENT SYSTEM A high-level block diagram of the proposed battery management system (BMS) is shown in Figure 3.1. In the proposed BMS, each cell is monitored and managed by its own individual local controller, implemented on a microcontroller and referred to here as a Slave PIC. This controller senses cell voltage, temperature and current, and uses the sensed data to compute parameters modeling the cell. The parameters of the individual cell models are transmitted by their respective Slave PICs to a single Master controller (Master PIC) through a serial Inter Integrated Circuit (I 2 C ) bus. The Master PIC processes the information received from each Slave PIC, and sends control signals used for cell equalization back to the Slave PICs. The Slave PICs use these control signals to charge/discharge individual cells. The Master PIC also logs all received data in an external memory through an SPI bus for later analysis. 42

61 Figure 3.1: Proposed BMS with individual cell monitoring. The proposed BMS is implemented for a battery pack with six cells connected in series as shown in Figure 3.2. The battery is either charged or discharged depending on the positions of switches S 1 and S 2. Figure 3.2: Battery pack with six cells in series. 43

62 This chapter discusses in detail the power supply considerations, hardware implementation of the proposed Battery Management System (BMS), I 2 C communication with isolation, calibration of voltage, current and temperature sensors, charging strategy for lithium-ion cells, proposed cell equalization technique and SD card interface for data logging. It also details the reasons for choosing various hardware components for the implementation of the proposed battery management system and evaluates the effect of the battery management system on the performance of the battery pack. 3.1 Power Supply Considerations Power is supplied to various hardware components in the BMS in one of two ways. Some components receive power directly from the individual lithium-ion cell with which they are associated. Figure 3.3 shows the local power supplied by cell i; V CCi is used to denote the local supply voltage, while GND i is used to denote the local ground. Because the cell voltage can fluctuate from 3.0V to 4.2V, local power can be used only for components that can operate throughout this range. Figure 3.3: Local power obtained from an individual cell. Other hardware components are powered via a 5V, 500mA voltage regulator that receives its input supply from the battery pack as shown in Figure 3.4. The input to the 44

63 voltage regulator is unregulated and ranges from 18.0V-25.2V (since it comes from eight cells connected in series, each in the range of 3.0V-4.2V) and the output is a regulated 5V constant voltage. V ccm is used to denote the positive supply voltage of the main power supply, and GND m denotes the ground of the main power supply, which is also ground of the series-connected stack. Datel s 7805SR voltage regulator is used for this purpose. The input voltage range of 7805SR is 7.5V to 36V, and it generates an output voltage of 5V with a maximum current of 0.5A. The proposed battery management system draws a maximum of 0.1A from the voltage regulator. Figure 3.4: Main power supply using the voltage regulator. 3.2 Proposed BMS Architecture The architecture of the proposed BMS is shown in the Figure 3.5. Each cell (1 through 6) is monitored by an individual controller called the Slave PIC (1 through 6). Each Slave PIC measures the voltage, current and temperature of its respective cell using appropriate sensors, and uses the sensed information to compute the parameters modeling the cell. Each Slave PIC transmits the results of its computation to the Master PIC through the serial I 2 C bus. An additional Slave PIC (Slave PIC 0) is dedicated to measuring the current through the battery string (both during charging and discharging) 45

64 using a current sensor; it transfers this current to the Master PIC through the serial I 2 C bus. The Master PIC processes the information it receives and sends control signals for cell equalization (discussed in section 3.8) back to Slave PICs 1 through 6, where these signals are used to control the charging and discharging of individual cells. The Master PIC also controls the charging and discharging process of the overall battery pack by controlling the switches S 1 and S 2 respectively of Figure 3.2 which are realized using MOSFETs. Figure 3.5: Architecture of the proposed BMS. The sensors and Slave PIC associated with an individual cell receive local power and ground directly from that cell. The current sensor and Slave PIC 0 receive power and 46

65 ground from the main power supply. Because all the PICs with their various powers and grounds must communicate via a single I 2 C serial bus, isolation is required. An I 2 C isolator, labeled i-coupler in Figure 3.5, is used for each PIC. This is explained further in Section 3.3. The Master PIC is also responsible for saving the information received from each cell in an external memory for data logging. This requires a non-volatile memory with large storage space that can be easily used and connected to a remote desktop for processing the stored information. As the I 2 C bus of the Master PIC is used for Slave communication, the non-volatile memory is interfaced to the PIC through an alternate bus. A Secured Digital (SD) card is used for this purpose. The SD card is interfaced to the Master PIC through a serial peripheral interface (SPI) bus. 3.3 Communication and Isolation The I 2 C is a serial protocol that needs only two lines to communicate between two or more devices as shown in Figure 3.6. The two lines are the clock line (SCL) and the data line (SDA). SCL is a unidirectional line driven by the master device. SDA is a bidirectional line with data going between the master and the slave. All the data is transmitted between the master and slave based on the clock signals and therefore I 2 C is a synchronous protocol. The clock and the data signals are generated by the I 2 C module of a PIC with respect to that PIC s ground. Therefore, for the signals on the I 2 C bus to be valid, both the Master PIC and the slave PICs should have the same ground. 47

66 Figure 3.6: I 2 C communication with master and slave at same ground levels. In the case of the proposed BMS, each Slave PIC (1 through 6) is powered by a separate cell in the battery stack, and so each PIC has a different ground. The Master PIC, powered by the main supply, uses yet another ground. For the slave PICs to transmit valid signals to the Master PIC and vice versa, an I 2 C isolator is used to adjust the signals with respect to corresponding grounds. Figure 3.7 shows the connections for I 2 C communication between two PICs with two different grounds. Figure 3.7: I 2 C communication with master and slave at different ground levels. The primary of the I 2 C isolator is powered from the same supply as that of the Master PIC and the secondary is powered from the same supply as that of the corresponding Slave PIC. The signals generated on the SDA 1 and SCL 1 are with respect to the GND 1. The I 2 C isolator transforms these signals to SDA 2 and SCL 2, respectively, which are with respect to the GND 2. Similarly, signals generated at SDA 2 and SCL 2 are 48

67 transformed to SDA 1 and SCL 1. Isolation allows valid communication between the Slave PICs and the Master PIC. Six I 2 C isolators (ADUM1250) are used in thesis work; one is needed for each Slave PIC. The bidirectional I 2 C isolators are new to the market. Analog Devices is the only company producing them. The I 2 C isolator requires 3.0V in the primary side and 5.0V in the secondary side. It draws currents of 3mA and 5mA from the primary and secondary sides, respectively. 3.4 Calibration of Sensors Analog-to-digital converters are used by the Slave PICs to capture data from sensors. An analog-to-digital converter (ADC) module converts the analog voltage V applied at its input to a digital number N with respect to the reference voltage. For an n- V n bit ADC module, the digital output is given by N = * 2, where V ref is the reference V voltage for the ADC module. For consistent conversion, therefore, the ADC module of the PIC requires a constant reference voltage. By default the reference voltage to the ADC module is the supply voltage to the PIC. Because slave PICs (1 through 6) are powered directly from the cells that they monitor, the supply voltage and thus the default reference voltage are not constant, so that the default cannot be used. Instead, a 2.5V zener diode operating at the breakdown region is used to provide a constant reference voltage to the ADC, as shown in Figure 3.8. The LM336 produced by National Semiconductor is used for this purpose. ref 49

68 Figure 3.8: Local voltage regulator. On each Slave PIC, an ADC module is used to capture voltage, temperature, and current data. The PICs chosen have n=12-bit ADC s. Figure 3.9 plots the digital output N of the ADC as a function of the input voltage as that voltage varies from 0 to 2.5V. The ADC module can be used to measure any physical parameter, provided there exists a sensor that generates a voltage proportional to the physical quantity. Code in the PIC is used to convert the digital output N back into engineering units for the physical quantity. Figure 3.9: Plot of transfer function of the ADC as voltage varies from 0 to 2.5V. 50

69 Each Slave PICs 1 through 6 measure the voltage and temperature of their corresponding cells, and Slave PIC 0 measures the current through the series stack. Appropriate sensors are needed to sense the voltage, current and temperature and convert them to proportional voltages that can be measured using the ADC module of the appropriate PIC. The following sections explain how the transfer function for each sensor was determined, so that the captured ADC data can be mapped back to the original physical parameter being measured Voltage Sensor During operation, the voltage of the lithium-ion cell varies from 3.0V to 4.2V. Because the reference voltage to the ADC module of the Slave PIC is 2.5V, the ADC module can measure only voltages between 0V and 2.5V. The voltage range of [3.0V, 4.2V] for the lithium-ion cell is brought down to [1.5V-2.1V] for input to the ADC using a voltage divider circuit, as shown in the Figure Two highly matched, 0.1% precision 13.7KΩ resistors are used to get a voltage division ratio of 1:2. The transfer function for this setup is V = 2V, where V sensed is the voltage at the ADC input and cell sensed V cell is the voltage of the cell. Thus, the cell voltage can be reconstructed in volts on the PIC by simply combining the transfer function for the voltage sensor and the ADC module as follows V cell = 2V sensed and V sensed N = 2 V n ref 51

70 N Vcell = V n 1 ref where N is the digital output of the ADC. 2 Figure 3.10: Interfacing voltage sensor to the PIC Temperature Sensor Six temperature sensors are used to monitor the temperature of the six individual lithium-ion cells. The operating range of a lithium-ion cell is 0 C-60 C. Therefore, the temperature sensor chosen must sense the temperature in this range. Also because the sensor is powered directly from the cell, the sensor supply voltage should lie in the range 3.0V to 4.2V. An LM61 temperature sensor produced by National Semiconductor is used for this purpose. The power supply voltage range of LM61 is 2.7V to 10V and the sensor operates in the range -30 C to 100 C. It draws a current of 5mA from the supply voltage. A temperature sensor senses the temperature and generates a voltage proportional to the temperature. Figure 3.11 shows the interfacing of the temperature sensor to a Slave PIC. The temperature sensor is a three terminal device with two pins for the power supply. The third pin generates a voltage, V temp, proportional to the temperature, which is interfaced to the PIC s ADC. The data sheet of the temperature sensor shows that the 52

71 transfer function of the temperature sensor is of the form V = at + b and can measure temp temperatures ranging -30 C to 100 C. Here b is an offset introduced so that the sensor can be used for both negative and positive temperatures; it is the voltage measured at 0 C. Figure 3.11: Interfacing temperature sensor to the PIC. The manufacturers of the lithium-ion cell specify an operating range of 0 C-60 C. The constant a and b in the transfer function of the temperature sensor are obtained by varying the temperature in this range and measuring the voltage obtained at the sensor output. Table 3.1 shows the voltages obtained experimentally from a sample temperature sensor. Voltages from the temperature sensor are obtained by varying the temperature from 15 C to 60 C. Figure 3.12 shows the plot of the obtained voltages versus the temperature. The constants a and b are obtained by using a linear curve fit; they are determined to have values and , respectively. Therefore, the transfer function of the temperature sensor is V = T and the temperature is given by temp + T = Vtemp Using the transfer function of the ADC module and the 53

72 transfer function of the temperature sensor, the actual temperature in C can be reconstructed in the PIC using NVref T = (3.1) 12 2 where N is the digital output of the ADC. Table 3.1: Voltages obtained from a sample temperature sensor for various temperatures. Temperature vs. Sensor Voltage Sensor Voltage (V) y = x Temeprature ( C) Figure 3.12: Temperature sensor calibration. 54

73 3.4.3 Current Sensor One current sensor is used to measure the current flowing in and out of the battery pack during charging and discharging, respectively. Therefore, the current sensor should be able to sense the current in the range -2.1A to 2.1A; which is the maximum current rating of the cell. As the current sensor obtains power directly from the main voltage regulator, it should be able to work at 5V. ACS706ELC-05C produced by Allegro Microsystems INC. has been used for this purpose. The power supply range is 4.5V to 5.5V, and the sensor works for currents in the range -15A to 15A. It draws a current of 8mA from the supply voltage. Slave PIC 0 is dedicated to measure the current in the battery pack; it transmits the value to the Master PIC as shown in Figure The Master PIC is then responsible to send the current value to each of the Slave PICs (1 through 6). Because the Master PIC is also running from the main power supply, there is no need for an I 2 C isolator between Slave PIC 0 and the Master PIC. Figure 3.13: Interfacing current sensor to the PIC. The current sensor used is a five terminal device. Two pins are for power and ground. Two pins (I IN+ and I OUT- ) provide a path for the current being measured. The fifth 55

74 pin generates a voltage V current proportional to the current. Current entering the battery pack (charging) is considered positive and the current leaving the battery pack (discharging) is considered negative. Therefore, the current sensor is connected in such a way that the charging current enters the pin I IN+ of the current sensor. The current sensor can be used to measure both positive and negative currents. The transfer function for the current sensor is of the formv = ai + b, where b is the offset voltage obtained for zero current. The constants a and b can be determined by varying the current through the current sensor and measuring the voltage at the output. Table 3.2 shows the voltages obtained experimentally from the current sensor for various currents. Voltages are obtained from the current sensor by varying the current flowing through the sensor from -2A to +2A. Figure 3.14 plots the sensor output voltage as a function of current. A linear curve fitting is used to obtain the constants a and b as and , respectively. Therefore, the transfer function for a current sensor is V = i and the current is obtained as i = Vcurrent The current + ADC module generates a digital number proportional to the voltage V current. The actual current in amperes can be reconstructed by combining the transfer functions of the ADC module and the current sensor: NVref i = (3.2) 12 2 where N is the digital output of the ADC. current 56

75 Table 3.2: Voltages obtained from the current sensor for various currents. Current vs. Sensor Voltage Voltage (V) y = x Current (A) Figure 3.14: Current sensor calibration. 57

76 3.5 Lithium-Ion Cell Charging Strategy Charging a lithium-ion cell is carried out in two phases. Charging follows the current-voltage (CV) profile for a lithium-ion cell. An example profile from [23] is shown in Figure During the first phase, the cell is charged using constant current during which the charging current through the cell is maximum (1C as specified by the manufacturer) and the cell voltage rises from 2.5V (or more often 3.0V; the minimum voltage is specified by the manufacturer) to 4.2V. For this profile, 65% of the charge is returned to the cell during this phase, which takes 35% of the total charging time. Charging cannot be discontinued at this point as the cell has an SOC of only 65%. In the second phase, the cell is charged using constant voltage, i.e., the charge current through the cell is varied so as to maintain a constant cell voltage of 4.2V. This phase results in an exponential decay of the current as the charge rises. The remaining 35% of the charge is returned to the cell in this phase, which takes 75 minutes or 65% of the total charging time. The total charging time is 2 hours for this profile. Figure 3.15: CV charge profile of the lithium-ion cell, from [23]. 58

77 3.6 Cell Equalization One of the main objectives of the BMS is cell balancing or cell equalization. The proposed cell equalization is a passive method that is based on shunting the current proportionally around a cell once that cell has reached its maximum/minimum voltage. This is a very simple method that is unlike other passive methods in that it can also be used in the discharging process. The energy dissipated during cell equalization is minimized by shunting the cells only when they reach the maximum voltage and also by using components with minimum power loss. Another advantage of this method is its potential for accommodating failures; in the event of the failure of an individual cell, that cell can be disconnected from the battery pack without disturbing the operation of the battery. This eliminates the cost of replacing the whole battery when a single cell fails assuming the particular application using the battery pack can operate with the reduced voltage level. The architecture of the proposed cell equalization scheme is shown in Figure MOSFETs Q D and Q C are controlled by the Master PIC, and are used to control the discharging or charging of the overall battery. The Master PIC turns Q D on during the discharging process and Q C on during charging process. Control of individual cells is accomplished using MOSFET and Schottky diode pairs. Two pairs are used for each cell, connected in anti-parallel, i.e., the pairs are connected in parallel but with opposite conducting directions (opposite polarity). These pairs achieve cell equalization during charging and discharging. The first pair is connected in series with the cell, and the second pair is connected in parallel to the series combination of the cell and the first pair to provide a shunting path around the cell. A precisely known small resistance of 1Ω 59

78 ±1% is connected in the shunting path. The voltage drop across this resistor is measured to determine the current in the shunting path. Figure 3.16: Architecture of the proposed cell equalization. 60

79 3.6.1 Cell Equalization During Charging Consider the i th (i=1 to 6) cell in the series pack with cell equalization shown in Figure The MOSFETs Q (2i) and Q (2i+1) are controlled by the Slave PIC i monitoring the i th cell. The MOSFET Q (2i+1) is associated with charging and the MOSFET Q (2i) s associated with discharging. Figure 3.17: Cell equalizer for the i th cell. Figure 3.18 explains the working principle of the cell equalizer during the charging process. During phase-1 of the charging process, which charges the cell with a constant current, the maximum allowable charge current is allowed to pass through the cell. This is accomplished by using Slave PIC i to set gate-to-source voltage of MOSFET Q (2i+1) to zero, thereby turning the MOSFET off completely and removing the shunting path. The flow of charge current in this case is shown in the Figure 3.18(a). Once the cell 61

80 voltage reaches 4.2V (determined by the Slave PIC i monitoring the i th cell), the cell is switched to phase-2 (constant voltage charging). During phase-2, the cell voltage is maintained at 4.2V. This is accomplished by supplying the current necessary to maintain the voltage; all other current is shunted across the cell. Implementation requires that the controller know the current flowing through the cell. A known resistance R i (0.1%, 0.005Ω) is connected in the shunting path for this purpose. By determining the voltage drop across this resistance the shunting current can be calculated. The controller measures the voltages V CCi and V i to determine the shunting current I B from the equation I = V V ) / R = 200*( V V ). V i is B ( CCi i i CCi i measured in the same way as V CCi. The effective current flowing through the cells is the difference between the battery pack current measured using the current sensor and the shunting current. The MOSFET Q (2i+1) is turned on in such a way that the current flowing through the cell maintains the cell voltage at 4.2V. This is achieved by adjusting the gate-to-source voltage of the MOSFET Q (2i+1) continuously to keep the voltage at 4.2V; when the cell voltage is above 4.2V, the gate-to-source voltage is raised to raise the shunting current, and when the cell voltage is below 4.2V, the gate-to-source voltage is lowered to lower the shunting current. The remaining current is forced to flow through the diode D (2i) (across the cell) as shown in Figure 3.18(b). Once the cell s SOC reaches 100% at 4.2V, all of the charging current is shunted around the cell as shown in the Figure 3.18(c). This is accomplished by completely turning on the MOSFET Q (2i+1) by setting its gate-to-source voltage to the maximum possible voltage, which is the cell voltage. This allows charging of the overall battery 62

81 pack to continue until all of the cells in the series-connected string are charged to 100% SOC at 4.2V. (a) (b) (c) Figure 3.18: Working of the cell equalizer during charging: (a) phase-1, (b) phase-2 and (c) at the end of charging. The charging process for the overall battery pack is terminated by turning OFF the MOSFET Q C. Now the battery pack is ready to supply energy to the load, and the discharge process can be started by turning ON the MOSFET Q D Cell Equalization During Discharging The working principle of the cell equalizer during discharge is shown in the Figure When the cell voltage lies between 3.0V-4.2V (as monitored by Slave PIC i), the cell continues to deliver current to the load; during this period, MOSFET Q (2i) is turned on completely by setting its gate-to-source voltage equal to the maximum possible voltage, which is the cell voltage. The flow of discharge current during this period (phase-1) is shown in Figure 3.19(a). 63

82 Once the cell voltage reaches 3.0V (determined by the Slave PIC i monitoring the i th cell), the cell is switched to phase-2 of discharge (constant voltage charging). During phase-2, the cell voltage is maintained at 3.0V. This is accomplished by limiting the current through the cell such that the cell voltage is maintained at 3.0V; all other current is shunted across the cell. This is achieved by adjusting the gate-to-source voltage of the MOSFET Q (2i) continuously to keep the voltage at 3.0V; when the cell voltage is above 3.0V, the gate-to-source voltage is raised to raise the current through the cell, and when the cell voltage is below 3.0V, the gate-to-source voltage is lowered to lower the current through the cell. The remaining current is forced to flow through the diode D (2i+1) (across the cell) as shown in Figure 3.19(b). (a) (b) (c) Figure 3.19: Working of the cell equalizer during discharge: (a) phase-1, (b) phase-2 and (c) at the end of discharge. Once the cell s SOC reaches almost 0% at 3.0V, all of the discharge current is shunted around the cell as shown in the Figure 3.19(c). This is accomplished by 64

83 completely turning off the MOSFET Q (2i) by setting its gate-to-source voltage to zero. This allows discharge of the overall battery pack to continue until all of the cells in the series-connected string are discharged to 0% SOC at 3.0V Component Selection The rated capacity of a lithium-ion cell is 2.1Ah, which means that the cell can be charged at a maximum current of 2.1A. Therefore, the MOSFETs must carry a maximum of 2.1A. The power loss in a MOSFET depends on its drain-to-source resistance and the current flowing through it. Therefore the MOSFET should have a very low drain-tosource resistance (R ON ) when on in order to minimize the power loss in the MOSFET. Because the MOSFET in the shunting path is connected across the cell, the drain-tosource voltage rating of the MOSFET should be at least 4.2V, the maximum voltage of a cell. The MOSFET needs a power dissipation rating of at least 9W so that it can handle 2.1A at 4.2V. The MOSFET is controlled by the slave microcontroller, which is powered directly from the cell; this implies that the slave microcontroller will produce a logic-1 output that may be as low as 3.0V, the minimum voltage of cell. Therefore, the MOSFET used must have a threshold voltage of less than 3.0V. MOSFETs produced by different manufacturers have been compared in terms of the drain-to-source resistance to find one with lower power loss. The n-channel STP140NF55 MOSFET produced by STMicroelectronics has been selected. The STP140NF55 MOSFET is rated for a maximum current of 80A, a maximum drain-to-source voltage of 55V, and a maximum power dissipation of 300W. The MOSFET turns on completely at 3.0V and has a drain to source resistance as low as Ω. 65

84 Schottky diodes are connected in parallel to their corresponding MOSFETs. Therefore, the voltage, current and power ratings required for the Schottky diodes are the same as those of the MOSFET. The power dissipated in a diode depends on the current flowing through it and the forward voltage drop across it. Schottky diodes were chosen over regular diodes because they have a smaller forward voltage drop which implies less power loss. Various Schottky diodes have been compared in terms of their forward voltage drop. The Schottky diode 1N5820 produced by ON Semiconductor was selected for this work. It has a maximum current rating of 3A, a maximum reverse breakdown voltage rating of 40V, and a maximum power dissipation of 25W and a forward voltage drop of 0.38V. 3.7 SD Card Interfacing for Data Logging Figure 3.20: Interfacing SD Card to Master PIC. Data logging is another important objective of the BMS. Data logging is required not only to determine the state of health of the battery but also to determine if the battery 66

85 has been subjected to any abnormal operating conditions. Battery information such as voltage, temperature, current, and number of charge/discharge cycles are stored in a nonvolatile memory for further evaluation. In this thesis, an SD Card is used for storing battery information. Figure 3.20 shows the interfacing of an SD Card to the Master PIC. The SD Card is connected to the Master PIC through an SD Card adapter. Table 3.3 gives the pin description of the SD Card adapter. Table 3.3: Pin description of SD Card adapter. Pin No. Name Description 1 VCard This is the Supply Voltage that the Controlling Processor pins are running ( Vdc). 2 SDO This is the SD card data output. It should be connected to the SPI data input of the Master PIC. 3 SCK This is the SD Clock input. 4 CS This is the SD Card Select input. 5 SDI This is the SD card data input. It should be connected to the SPI data output of the Master PIC. 7 Card Detect This output is high when there is no card in the socket and is low when a card is inserted. 8 Write Protect This output is high when the SD card is write protected. The software is responsible for preventing writes to the card when it is write protected. 9 Vcpu By default, this is a 3.3 volt on-board supply that is used to power the Serial Flash Cards GND Ground 67

86 The Master PIC receives voltage, current, temperature and battery model parameters for each cell via an I 2 C bus. The Master PIC communicates these parameters to SD Card via an SPI bus. The Master PIC has only one serial communication peripheral that can be configured at any given time for either I 2 C or SPI communication. This peripheral is used to communicate with the Slave PICs using I 2 C; as a result it was necessary to implement a software based SPI protocol (SPI bit banging) to interface the Master PIC with the SD Card. The software for implementing the software SPI protocol and for storing the information from the Master PIC to the SD Card is discussed in detail in Chapter IV. 3.8 Other Hardware Issues This section explains in detail the rationale for selection of other hardware components, including the microcontrollers. It also describes the total cost and the power consumed by the proposed battery management system. Microcontroller Requirements: Eight microcontrollers were needed for implementation: one slave to monitor and control each of the six lithium-ion cells in the string, one additional slave for measuring the current through the string and one for the master controller. Each slave microcontroller communicates with the master through a serial bus; this communication requires an Inter Integrated Circuit (I 2 C) module. The master microcontroller needs a Serial Peripheral Interface (SPI) bus in order to log data on the SD Card. The slave microcontroller should also have an analog-to-digital converter (ADC) module to measure the voltage, current, temperature information. An AD 68

87 converter with at least twelve bits is preferred to measure the data with good accuracy. As the slave microcontroller is powered directly from the cell, whose voltage varies from 3.0V-4.2V, the microcontroller should be able to run in this voltage range. Preference is given to microcontroller that draws less current/power, since that power must be supplied by the cell. The system specifications call for voltage, current, temperature, stored charge and diffused charge to be calculated with a precision of 1%. The state variables for stored charge, diffused charge and temperature are discussed in Section 4.2. In the system specification, stored charge is the variable that has the largest magnitude; its value may be as high as 170A-min. Eight bits are needed to implement the integer part of this value. Diffused charge is the variable with smallest magnitude of 2.1 A-min. In order to calculate the diffused charge with a precision of 1% or to the nearest 0.021, six bits are needed to implement the fractional part. Eight bits of integer and six bits of fraction gives a total minimum required size of fourteen bits; therefore, a sixteen bit microcontroller was chosen. The microcontroller must be capable of computing the battery model in real time; i.e. calculation of all the equations in the cell model must be computed at least as quickly as the time between the samples. Computation of the battery model involves additions and multiplications and thus it is important to choose a microcontroller that supports single-cycle multiplication. Also the microcontroller should be available in a dual in-line (DIP) package, so that it can be easily placed on the prototype board and PCB for testing purposes. Various microcontrollers developed by Microchip Technology, Atmel, Motorola and TI were compared for these requirements. A dspic30f

88 developed by Microchip Technology meets all the requirements, and was selected for this thesis. PIC is the registered trademark of Microchip Technology. Crystal and Capacitors: Each of the eight microcontrollers receives a clock signal from its own MHz crystal; these crystals each also require an auxiliary capacitor of 20µF. Cell Holders: Lithium-ion cells are approximately the same size as D cells. Six D-cell holders were used to hold the lithium-ion cells. Table 3.4: Power consumed by the proposed BMS. Name Power in mw Qty Total (mw) dspic ADUM MOSFET Schottky Diode Current Sensor Temperature Sensor Total power in mw 3388 Table 3.4 shows the power consumed by the hardware used for implementing the battery management system. The power calculation is carried out assuming that the battery is charging/discharging a load current of 1A at a nominal voltage of 21.60V. For these conditions the total power generated by the battery is 21.60W and the power consumed by the BMS is 3.39W. The majority of the power is consumed by the diodes; that is why it was important to choose a diode with as small a forward voltage drop as possible. 70

89 Table 3.5: List of hardware components. Name Identification Cost per unit Qty Microcontroller dspic30f4013 $ I 2 C Isolator ADUM1250 $ MOSFET STP140NF55 $ Schottky Diode 1N5820 $ Crystal MHz $ Capacitor 20µF $ Current Sensor ACS706ELC-05C $ Temperature Sensor LM61 $ Voltage Regulator 7805SR $ Voltage Reference Diode LM 336 $ Cell Holder D-Cell Holder $ Resistor 1Ω 1% $ Resistor 13.7KΩ 0.1% $ Resistor 100Ω $ Resistor 220Ω $ Resistor 680Ω $ SD Card Adapter ECS-ADP-01 $ SD Card SanDisk SD Card 1GB $ PCB Customized $ Total Cost $ The battery pack would deliver a current of 1A at 21.60V for two hours if the battery management system (BMS) were ideal, i.e., if the BMS consumed no power. Because the battery model consumes a power of 3.39W, the BMS can deliver a current of 1A at 21.60V for only 1 hour 44 minutes. Therefore, the presence of the BMS brings 71

90 down the performance of the battery pack by 14%. All possible methods result in a performance drop; the advantages of the BMS overweigh this drop. Chapter V presents the advantages offered by the proposed battery management system. In the absence of the load (the load is the application for which the battery pack is sourcing power), the only power consumed by the BMS is due to the presence of the microcontrollers, I 2 C isolators, current sensors, and temperature sensors. This amounts to 718mW. Therefore, the battery pack can source the BMS for 60 hours in the absence of any load. Table 3.5 shows the list of various hardware components with part numbers used for the battery management system. It also gives the cost of all the individual components and thus the total cost involved in developing the proposed battery management system. 3.9 PCB Design The printed circuit board (PCB) to implement the proposed battery management system for eight lithium-ion cells is developed using ExpressPCB. The hardware for implementing the proposed battery management system is achieved by combining the schematics for each Slave PIC 1 through 6, Master PIC, and the SD Card interface presented in Chapter IV. Figure 3.22 shows the unpopulated PCB developed by the ExpressPCB for the PCB schematics of Figure

91 Figure 3.21: PCB Layout for the proposed BMS. Figure 3.22: Unpopulated PCB for the proposed BMS. 73

92 Figure 3.23 and Figure 3.24 shows the top and bottom view of the populated PCB to implement the proposed BMS. Various parts of the PCB are labeled in these figures. The PCB was designed for a battery pack of eight series- connected cells. Two cells were not used during testing. This is because the I 2 C isolators for the corresponding cells were damaged. As the bi-directional I 2 C isolators are new to the market, they were not readily available and could not be easily replaced. Therefore, the proposed battery management system was tested for a battery pack of six series-connected cells. Figures 3.23 and 3.24 show the unused cells and corresponding PICs. Figure 3.23: Top view of the proposed BMS. 74

93 Figure 3.24: Bottom view of the proposed BMS Conclusions This chapter presents the architecture of the proposed battery management system and the proposed cell equalization technique, with detailed descriptions of their operations. Sensors used for measuring the voltage, current, and temperature are calibrated and their transfer functions are obtained. The charging strategy for the lithiumion cells and achievement of the same through the proposed cell equalization technique is discussed. This chapter also presents the hardware details for storing all the required battery information on the SD Card. Various hardware components used in the hardware implementation of the proposed battery management system with part numbers and cost is provided. The effect of the battery management system on the performance of the battery pack is analyzed. 75

94 CHAPTER IV SOFTWARE IMLPEMENTATION FOR THE BATTERY MANAGEMENT SYSTEM This chapter derives the battery model for lithium-ion cells and presents the implementation of the battery model and the sensor transfer functions in the Slave PICs. Implementation of the state of charge observer with feedback for correcting the state of charge is also discussed. Algorithms and flowcharts for the software implemented in Slave PICs and Master PIC are presented. 4.1 Lithium-Ion Battery Model Because there is no sensor that measures the SOC of a cell, the SOC has to be measured indirectly by measuring other physical parameters, as discussed in Chapter 2. In this thesis work, current-based SOC determination is used; coulombs going in or out of the cell are counted to determine the SOC of a cell. The SOC of a cell is given by q = t 0 i( t) dt. Although coulomb counting gives an accurate accumulation of the charge put into and removed from a cell, the SOC must be adjusted to compensate for temperature, discharge rate and aging of the battery. Therefore, a mathematical model (used as a state of charge observer) is developed that measures the SOC by correcting the SOC obtained from coulomb counting. The correction factor takes into account the 76

95 effects of self-discharge, temperature, charge acceptance and aging of the battery on SOC of the battery. This section derives the mathematical model for lithium-ion cells used in this thesis. The battery model for lithium-ion cells is obtained from [24], and was proposed by Hartley and Janette. The battery model for the lithium-ion cells is a function of three state variables: the stored charge q s, the diffused charge q d and the temperature T. The stored charge equation is dqs ( t) = i( t) c1q s ( t). (4.1) dt where q s (t) is the stored charge in the cell and i(t) is the current flowing through the cell. The diffused charge equation is where q d (t)is the diffused charge in the cell. dqd ( t) = g1i( t) c2qd ( t). (4.2) dt The temperature equation is dt( t) 2 = c3 [ T( t) Tamb( t)] + g2i( t) dt. (4.3) where T(t) is the temperature of the cell and T amb (t) is the ambient temperature. The terminal voltage is modeled in terms of the three state variables as: 2 k qs ( t) k41qs ( t) v( t) = ( a + bt( t) + ct ( t))[ k1 + k2i( t) + k3qs ( t) + k4e + k5e + k6q 31 t d ( )]. (4.4) The constants c 1 through c 3 are the time constants and the constants g 1 and g 2 are the gain constants. The constant c 1 in the stored charge equation (4.1) corresponds to self discharge; since self discharge is almost negligible for lithium-ion cells, this constant is set to zero. 77

96 The constants c 2 and g 1 in the diffused charge equation (4.2) are obtained by conducting a ten minute charge-discharge cycle on the lithium-ion cell. Results of the experiment are shown in Figure 4.1; the voltage of the lithium-ion cell was monitored while first charging the cells for ten minutes, and then discharging it for ten minutes. Three such charge-discharge cycles were conducted. The constant c 2 is the time constant obtained from the voltage waveform; once c 2 is found, g 1 is obtained by multiplying c 2 by the steady-state value of the voltage. The constants c 3 and g 2 in the temperature differential equation (4.3) are obtained from the thermal characteristics of the cell. The thermal characteristics are obtained experimentally by charging the cell from 3.0V to 4.2V while monitoring the temperature of the cell; the temperature waveform is shown in Figure 4.2. The constant c 3 is the time constant obtained from the temperature waveform; once c 3 is found, g 2 is obtained by multiplying c 3 by the steady-state value of the temperature. The voltage equation (4.4) is a function that approximates the voltage characteristics of the lithium-ion cell. Constants in the voltage equation are chosen so as to minimize the square of the error between an actual voltage profile and the approximated. The actual voltage profile of a lithium-ion cell was obtained experimentally by first charging and then discharging the cell; the current profile used and the voltage profile obtained are shown in Figure

97 Figure 4.1: Charge-discharge cycle of a lithium-ion cell obtained from experiment. Figure 4.2: Temperature of the lithium-ion cell obtained from experiment. 79

98 Figure 4.3: Ten-minute charge-discharge cycle of a lithium-ion cell obtained from experiment. Table 4.1 shows the values of all constants needed to complete the mathematical model. When the experimentally fitted coefficients are used, the lithium-ion battery model equations become as follows. The stored charge equation is dq s ( t) = i( t). (4.5) dt The diffused charge equation is dqd ( t) dt = i( t) 0.8q ( t). (4.6) d The temperature equation dt( t) 2 = 0.5( T( t) 20) + 5i( t). (4.7) dt 80

99 The terminal voltage is modeled in terms of the three state variables as 2 v( t) = ( T ( t) T ( t)) 0.02qs ( t) 0.055qs ( t) [ i( t) q ( t) e e q ( t) ]. s d Table 4.1: Constants in the cell model. Constant Value Units Constant Value Units c 1 0 sec -1 k V c sec -1 k Ohms c sec -1 k VCoulomb -1 g k V g k V a k VCoulomb -1 b C -1 k Coulomb -1 c C -2 k Coulomb -1 (4.8) Figure 4.4 compares the actual cell voltage and the cell voltage obtained from the model for a 100 minute charge-discharge cycle and Figure 4.5 shows the absolute error of the model. The model is close to the actual voltage except at the start and end of the charge and discharge cycle. Therefore, when the above battery model is used as a state of charge observer to correct the stored charge in the cell, we expect the correction to occur at the start and end of the charge/discharge cycle. 81

100 Figure 4.4: Comparison of actual cell voltage and the cell voltage obtained from the model. Figure 4.5: Absolute error between the actual cell voltage and the cell voltage obtained from the model. 4.2 Fixed-Point Implementation Basics The processors used today can be classified into two types, based on how numbers are represented internally: fixed-point processors and floating-point processors. In fixed-point processors, all the numbers are represented as integers, and fixed-point arithmetic instructions operate on the fixed-point data. On the other hand, floating-point 82

101 processors perform floating-point operations on floating-point numbers. Fixed-point processors consume less power, are available at lower cost and are faster in processing than floating-point processors. A fixed-point processor is used in this thesis to minimize the cost and the power consumed by the controllers; power is especially important because the battery management system (BMS) is powered from the battery stack and the presence of the BMS should not significantly affect the battery s operation. Because a fixed-point processor represents numbers as integers and uses integer arithmetic, the mathematical equations for the battery model, which were developed in floating-point format, have to be converted to fixed-point format for implementation on the processor. This section describes the rules for fixed-point arithmetic and the procedure for converting floating-point computations to fixed-point computations. Figure 4.6: The b-number representation of a fixed-point number. Let F be the fixed-point representation of the floating-point number f in an n-bit fixed point processor. Then, F is represented as F(n,b) where b is called the b-number of F. The b-number indicates the location of the binary point in an n-bit number; b is the number of bits in the fraction part of the number. This is illustrated in Figure 4.6. The b- number is generally selected on the basis of the number of bits required to represent the 83

102 integer part of the floating-point number, i.e., if a bits are required to represent the integer part of a floating-point number, the b number is given by (n-a). This ensures that the fixed-point representation of the number comes with as many fraction bits as possible. The fixed-point number F is obtained from the floating-point number f from the equation b F(n,b)= f * 2, where. denotes the floor function. A floating-point equivalent can be reconstructed using f 2 b 1 = F /. The floating-point reconstruction f 1 is not exactly equal to f because of the truncation error. 4.3 Rules for Fixed-Point Arithmetic Multiplication of two fixed-point numbers F 1 and F 2 with b-numbers b 1 and b 2 respectively, results in a fixed-point number F 3 whose b-number is given by b 3 =b 1 +b 2. In general, multiplication of x(n,b 1 ) with y(n,b 2 ) results in (xy) (2n,b 1 +b 2 ). The data flow diagram for this case is shown in Figure 4.7(a). Consider the multiplication of two floating-point numbers 0.25 and in an 8-bit fixed-point processor. The product should be The following steps obtain the result in a fixed-point processor can be represented in an 8-bit processor with 8 bits of fraction as 0.25* 2 8 =64 and so is represented as 64(8, 8). 2. For 2.125, two bits must be used for the integer part, leaving 6 bits for fraction * 2 6 =136, so is represented as 136(8, 6). 3. Fixed-point multiplication 64*136=8704(16, 14). 14 The result can be obtained back from 8704(16, 14) as 8704/ 2 = which 84

103 matches with the original floating-point arithmetic. Figure 4.7(b) shows the data flow diagram representation of this multiplication. (a) (b) Figure 4.7: Data flow diagram for fixed-point multiplication: (a) in general, and (b) example for 0.25*1.25. Note: Multiplying a number by k bits and dividing a number by bits. k 2 is same as shifting the number towards the left by k 2 is same as shifting the number towards the right by k Before two fixed-point numbers are added/subtracted on a fixed-point processor, they must be adjusted so that they have a common b-number. The resulting fixed-point sum will have the same b-number. In general, addition of x(n,b) with y(n,b) will result in (x+y) (n,b). The data flow diagram for this case is shown in Figure 4.8(a). Consider the addition of two floating-point numbers 0.25 and in an 8-bit fixedpoint processor, which should yield The following steps obtain the result in a fixed-point processor can be represented in an 8-bit processor with eight bits of fraction as 0.25* 2 8 =64 and so is represented as 64(8, 8). 85

104 2. For 2.125, two bits must be used for the integer part, leaving six bits for the fraction * 2 6 =136, so is represented as 136(8, 6). 3. Addition of two numbers is possible only when they have same b-numbers. Therefore, one of the numbers has to be shifted so that the two operands have the same b-number. In this case 64 is shifted right by two bits to get 16(8,6). Note that this implies the loss of two bits of precision at the least significant end. 4. Fixed-point addition =152 (8, 6). (a) (b) Figure 4.8: Data flow diagram for fixed-point addition: (a) in general and (b) example for The result can be obtained back from 152 as 152/ 2 =2.375 which matches with the original floating-point arithmetic. Figure 4.8(b) shows the data flow diagram representation of the addition example. The examples provided for fixed-point addition and multiplication perform arithmetic on operands that are powers of two with a small number of bits and therefore 86

105 the fixed-point results match the ideal results exactly. In practice, not all numbers can be exactly represented as sums of powers of two using a fixed number of bits. For example, consider the addition of numbers 0.2=51(8,8) and 0.23=59(8,8). The fixed-point result is 110(8,8)= whereas the exact solution is The error in the result is due to quantization; here for example, 0.2 has been approximated as closely as possible using eight bits, as 51(8,8). The following sections show the implementation of battery model in 16-bit fixed-point processors and the error involved in the fixed-point implementation due to quantization and truncation compared to a presumed ideal floating-point implementation. 4.4 PIC Fixed-Point Architecture The dspic30f4013 has sixteen 16-bit working registers and two 40-bit accumulators [24]. The PIC performs all integer arithmetic operations, such as addition, subtraction, and shifting operations, on the working registers. The integer arithmetic and logic unit (ALU) performs arithmetic operations on two operands stored in the working registers and stores the result in any working register. The DSP engine of the dspic30f4013 consists of a high speed 17-bit 17-bit multiplier. It performs multiplication on two operands stored in the working registers and stores the result in one of the 40-bit accumulators. The DSP engine also has the capability to perform operations like addition, subtraction and negation on the accumulators. Multiplication of 16-bit integers results in a 32-bit result which is sign extended and stored in a 40-bit accumulator. The lower 16-bits of the 40-bit accumulator can be moved to a working register. 87

106 4.5 Fixed-Point Implementation of Sensor Transfer Functions This section provides the implementation of transfer function of temperature sensor and current sensor in a fixed-point processor Fixed-Point Implementation of Temperature Transfer Function The transfer function of the temperature sensor was given in Chapter 3 in NVref N equation (3.1) as T = For our setup, V 12 ref = 2.5V and can be written as N(16,12). Therefore the temperature is given by T = N ; for implementation and must be converted to fixed-point. Table 4.2 shows the representation of constants in the temperature transfer function in fixed-point format. The result obtained from V temp (16,12)*44053(16,7) i.e V temp (40,19) is shifted left by ten bits so that the result (40,9) can be subtracted from 48540(40,9). The constant is represented as (40,9) and is placed in the accumulator so that it can be added directly to the result in the previous stage. Figure 4.9 shows the implementation of temperature transfer function in fixed-point format. The truncation operator moves the data from the 40-bit accumulator to a 16-bit register. Table 4.2: Representation of constants in the temperature transfer function. Floating-point value Fixed-point format Fixed-point approximation (16,7) (40,9)

107 Figure 4.9: Data flow diagram for implementing temperature transfer function. Figure 4.10 compares the implementation of the temperature sensor transfer function in 16-bit fixed-point processor with a floating-point implementation obtained from MATLAB simulation. The maximum absolute error over the entire range of operating temperatures is 2.2m C and maximum percentage error is %. Another possibility is to represent the constant in the form (40,19), so that it can be added directly to the result of the multiplication; however, this choice was shown to result in more error in simulation. 89

108 Figure 4.10: Comparison of floating-point and 16-bit fixed-point implementation of temperature transfer function Fixed-Point Implementation of Current Sensor Transfer Function The transfer function of the current sensor was given in Chapter 3 in equation (3.2) NVref asi = For our setup the current sensor is interfaced to the Master 12 2 N PIC for which V ref = 5V and 2 12 can be written as N(16,12). Therefore the current is given byi = N ; for implementation and must be converted to fixed-point. Table 4.3 shows the representation of constants in the current transfer function in fixed-point format. The constant is represented as (40,11) and is placed in the accumulator so that it can be added directly to the result in 90

109 the previous stage. Figure 4.11 shows the implementation of current transfer function in fixed-point format. Table 4.3: Representation of constants in the current transfer function. Floating-point value Fixed-point format Fixed-point approximation (16,10) (40,11) Figure 4.12 compares a 16-bit fixed-point implementation of the current sensor transfer function with a floating-point implementation obtained from MATLAB simulation. The maximum absolute error over the full range of operating values is 0.64mA and the maximum percentage error is %. Figure 4.11: Data flow diagram for implementing current transfer function. 91

110 Figure 4.12: Comparison of floating-point and 16-bit fixed-point implementation of current sensor transfer function. 4.6 Fixed-Point Implementation of Battery Model This section presents the fixed-point implementation of the battery model, which includes the stored charge the differential equation, the diffused charge differential equation, the temperature differential equation, the temperature equation and the voltage equation Fixed-Point Implementation of Stored Charge Differential Equation The stored charge in a lithium-ion cell is obtained by solving the differential equation dq s i(t) dt =. The differential equation must first be converted to a difference 92

111 equation, as it is to be solved using a digital processor. The difference equation is obtained using Euler s approximation as qs ( nt + T ) qs( nt ) = i( nt + T ) ( n + 1) T nt qs ( n + 1) qs( n) = i( n + 1) T q ( n + 1) = q ( n) + Ti( n + 1) s where T is the sampling period. In this thesis, the battery model is computed every one minute, i.e., the sampling period T=1min, so that the equation computed within the PIC is simply q ( n + 1) = q ( n) + i( n + 1) s s. s Figure 4.13: Data flow diagram to obtain stored charge. The stored charge (q s ) in a lithium-ion cell typically lies in the range 0-170A-min and therefore eight bits are needed to represent the integer part. The other eight bits can be used to represent the fractional part. Thus, q s is stored in the controller as a fixed-point 93

112 integer of the form q s (16,8). Figure 4.13 shows the data flow diagram used to solve for q s using fixed- point arithmetic. Figure 4.14: Comparison of floating-point and 16-bit fixed-point implementation of stored charge differential equation. Figure 4.14 compares a 16-bit fixed-point implementation of the stored charge equation of the battery model with a floating-point implementation obtained from MATLAB simulation. The simulations are carried out for a charge/discharge current of 1A. The maximum absolute error is A-min and the maximum percentage error is 0.011%. 94

113 4.6.2 Fixed-Point Implementation of Diffused Charge Differential Equation The diffused charge in a lithium-ion cell is obtained by solving the differential dqd ( t) equation = i( t) 0.8qd ( t). The difference equation to solve for q d is obtained as dt qd ( nt + T ) qd ( nt ) = i( nt ) 0.8qd ( n + 1) T ( nt ) qd ( n + 1) qd ( n) = i( n) 0.8qd ( n) T q ( n + 1) = i( n) 0.2q ( n) d + d ( nt ) The diffused charge (q d ) in a lithium-ion cell typically ranges from 0-2A-min in magnitude. Thus, two bits of integer are required, and q d is stored in the controller as a fixed-point integer of the form q d (16,14). The only constant (0.2) in the q d difference equation is represented as 3277 (16,14). Figure 4.15 shows the data flow diagram to solve for q d using fixed-point arithmetic. The result q d (40,28) is shifted left by fourteen bits to get q d (40,14) so that it can be transferred to the working register from the accumulator. Figure 4.15: Data flow diagram to obtain diffused charge. 95

114 Figure 4.16 compares a 16-bit fixed-point implementation of the diffused charge equation of the battery model with a floating-point processor obtained from MATLAB simulation. The simulations are carried out for a charge/discharge current of 1A. The maximum absolute error involved is 0.32mA-min and the maximum percentage error is 0.015%. Figure 4.16: Comparison of floating-point and 16-bit fixed-point implementation of diffused charge differential equation. 96

115 4.6.3 Fixed-Point Implementation of Temperature Differential Equation equation The temperature of a lithium-ion cell is obtained by solving the differential dt dt 2 = 0.5( T ( t) 20) + 5i( t). The difference equation that is implemented in the controller to solve for temperature (T) is obtained as T ( nt + T ) T ( nt ) = 0.5( T ( nt ) 20) + 5i( nt ) ( n + 1) T nt T ( n + 1) T ( n) = 0.5T ( n) i( n) T 2 T ( n + 1) = 5[0.1T ( n) i( n) ] 2 2 The temperature of a lithium-ion cell lies between 0 C-100 C, and therefore requires seven integer bits. Therefore, the temperature is stored in the controller in the fixed-point format as T (16,9). Table 4.4 shows the representation of constants in the temperature differential equation in fixed-point format. Figure 4.17 shows the data flow diagram to solve for the temperature in fixed-point arithmetic. Table 4.4: Representation of constants in the temperature differential equation. Floating-point value Fixed-point format Fixed-point approximation (16,13) (40,22) (16,0) 5 Figure 4.18 compares a 16-bit fixed-point implementation of the temperature differential equation of the battery model with a floating-point implementation obtained from MATLAB simulation. The simulations are carried out for a charge/discharge 97

116 current of 1A. The maximum absolute error involved is C and the maximum percentage error is 0.034%. Figure 4.17: Data flow diagram to obtain temperature. 98

117 Figure 4.18: Comparison of floating-point and 16-bit fixed-point implementation of temperature differential equation Fixed-Point Implementation of Temperature Equation The voltage of a lithium-ion cell is affected by the temperature of the cell. Therefore the voltage is multiplied by a factor that depends on the temperature of the cell. The multiplying factor is given byt 2 eq T ( t) T ( t) =. One way of implementing a quadratic equation in the PIC is by using Horner s method [26]. This givest = ( T ( t)) T ( t) , and this results in fewer multiplication eq + and addition operations (two multiplications and two additions) than does a direct computation of the quadratic equation (four multiplications and two additions). Table 4.5 shows the representation of constants in the temperature equation in a fixed-point format. Figure 4.19 shows the data flow diagram to implement T eq in fixed-point processor. 99

118 Table 4.5: Representation of constants in the temperature equation. Floating-point value Fixed-point format Fixed-point approximation (40,25) (16,16) (16,14) Figure 4.20 compares a 16-bit fixed-point implementation of the temperature equation of the battery model with a floating-point processor obtained from MATLAB simulation. The simulations are carried out for a charge/discharge current of 1A. The maximum absolute error for the entire range of temperatures is and the maximum percentage error is 0.85%. Figure 4.19: Data flow diagram to obtain T eq. 100

119 Figure 4.20: Comparison of floating-point and 16-bit fixed-point implementation of temperature equation Fixed-Point Implementation of Voltage Equation Voltage of a lithium-ion cell (without considering the temperature) is given by v( t) = q ( t) 1.63e s 0.02q s ( t ) 0.055qs ( t) e i( t) q The voltage equation can be re-written by grouping all the terms that are a function of q s (t) together as v( t) = f ( q ( t)) i( t) 0.02q ( t) s + d d ( t) where 0.02qs ( t) f ( qs( t)) = qs( t) 1.63e e 0.055qs ( t ). Figure 4.21 shows the plot of f(q s (t)) vs. q s (t) as q s (t) varies from 0 to 170A-min. The evaluation of exponential functions is computationally complex; the calculation of our model is simplified in the controller by using polynomials to fit the function f(q s (t)), rather than computing its terms directly. To minimize the error between the original function and the polynomial used for curve fitting, q s (t) is divided into twelve different 101

120 ranges and twelve different polynomials of different orders are used to fit the original function f(q s (t)). Figure 4.21: Plot of f(q s (t)) vs. q s (t) varies between 0 and 170A-min. The polynomials are obtained by fitting a curve that approximates f(q s (t)) using the polyfit command in MATLAB. The order of polynomials is chosen such that there is a tradeoff between the error and the order. Table 4.6 shows the polynomials used for curve fitting for f(q s (t)) for different ranges of q s (t). Figure 4.22 shows the error between f(q s (t)) and the approximation of f(q s (t)) using polynomials. Each of the polynomials in Table 4.15 is implemented in fixed-point mathematics on the PIC processor. Not all details are shown here. As an example, Figure 4.23 shows the data flow diagram for implementing f(q s (t)) for 20<q s (t) 3. Table 4.7 shows the representation of constants in the function in fixed-point format. 102

121 Table 4.6: Approximation of f(q s (t)) using curve fitting for different ranges of q s (t). q ( q ( t)) s q s q ( t) q ( t) q ( t) s f s 2 10 < q s q ( t) q ( t) < q s q ( t) q ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) < q s q s ( t) s s s s s s 103

122 Figure 4.22: Comparison of approximated and actual implementation of f(q s (t)). The polynomial is evaluated using Horner s Method. Therefore, f ( q ( t)) ( q ) q s = s s Table 4.7: Representation of constants in f(q s (t)) for 20<q s 30. Floating-point value Fixed-point format Fixed-point approximation (16,16) (16,16) (16,13) Figure 4.24 shows the implementation of the lithium-ion cell voltage when the temperature term is not used. Table 4.8 shows the representation of constants in the voltage equation in a fixed-point processor. 104

123 Figure 4.23: Data flow diagram to implement f(q s (t)). Table 4.8: Representation of constants in the voltage equation. Floating-point value Fixed-point format Fixed-point approximation (16,13) (16,13)

124 Figure 4.24: Data flow diagram to obtain the voltage of the lithium-ion cell. Figure 4.25 compares a 16-bit fixed point implementation of the stored charge equation of the battery model with a floating-point implementation obtained from MATLAB simulation. The simulations are carried out for a charge/discharge current of 1A. The maximum error is 1.0V; this error occurs at the start and end of charge/discharge cycle. The SOC observer tracks this error to correct the state of charge. Thus, we expect the correction in the SOC to occur at the start and end of the charge/discharge cycle. 106

125 Figure 4.25: Comparison of floating-point and 16-bit fixed-point implementation of voltage equation. 4.7 SOC Estimation The SOC of a cell is given by q = t 0 i( t) dt. Although coulomb counting gives an accurate accumulation of the charge put into and removed from a cell, the SOC must be adjusted to compensate for temperature, discharge rate and aging of the battery. The battery model equations are used to adjust the SOC of the cell. The strategy for correcting the predicted SOC is shown in Figure The observer, i.e. the set of cell model equations, is implemented in the PIC to determine the SOC of the cell. The model voltage is compared with the actual voltage and the error voltage, e(v), is fed back to the observer. The PIC corrects the estimated SOC based on the error voltage. In this thesis, 107

126 the SOC is corrected by +1% if the error voltage is greater than +0.2V and by -1% if the error voltage is less than -0.2V. The SOC can also be corrected on the basis of the error in the temperature, e(t), which is the difference between the model temperature and the actual temperature. Correction of SOC based on e(t) is not done in this work. Figure 4.26: Observer with feedback for SOC estimation. 4.8 Software Implementation-Algorithms and Flow Charts This section presents the algorithm and flow chart implemented in the Master and Slave PICs Algorithms and Flow Charts for Master PIC The Master PIC controls the charging/discharging of the battery pack. Charging is initiated (discharging is terminated) by turning on the MOSFET Q C of Figure 3.16 and turning off the MOSFET Q D. Discharging is initiated by turning on the MOSFET Q D and turning off the MOSFTE Q C. The Master PIC also decides when to terminate the charging/discharging process for individual cells, and sends the corresponding control signals to the individual cells. 108

127 Figure 4.27 shows the flowchart for software implementation in the Master PIC. The steps used for initializing the Master PIC are as follows. o Initialize the I/O ports. Initialize the I 2 C module as a master. o Initialize the timer to generate an interrupt every 10ms. The software assumes that the battery is first being charged. Charging is continued until all of the cells in the battery pack have reached 4.2V. The steps used for charging are as follows. Step 1: Start the charging process by turning on the MOSFET Q C and turning off the MOSFET Q D. A variable, status, is zero when charging and one when discharging. A variable count keeps track of number of cells that are charged completely; it is initialized to 0. A variable slavecount keeps track of the slave with which the master is currently communicating; it is initialized to 1. Step 2: When the next timer interrupt is generated, generate a general call interrupt and transmit status to all the Slave PICs; wait for 1ms. Step 3: Receive the voltage, current, temperature, and results of the battery model from the slave with which the master is currently communicating. Log the received information on the SD Card. Increment the slavecount by 1 to setup communication with the next slave. Step 4: If the voltage of the cell being monitored by the current slave is greater than 4.2V, increment the count of cells that are charged completely by 1. Step 5: If slavecount<6, i.e., if the master is not done communicating with all the slaves, go to step

128 Step 6: If count<6, i.e., if all the cells are not charged completely, go to step 2. When charging is complete the discharging routine is started. The discharging process is continued until four cells in the battery pack reach 3.0V. The decision to end the discharging process when four cells have reached a voltage of 3.0V was chosen arbitrarily assuming that the load requires a minimum of 9V. Continuing the discharging process even after the fourth cell reaches 3.0V results in the battery pack voltage to go below 9V. This is because three cells have already been switched out from the battery pack from discharging. The steps for discharging the battery pack are as follows. Step 1: Start the discharging process by turning off the MOSFET Q C and turning on the MOSFET Q D. A variable, status, is zero when charging and one when discharging. A variable count keeps track of number of cells that are charged completely; it is initialized to 6. A variable slavecount keeps track of the slave with which the master is currently communicating; it is initialized to 1. Step 2: When the next timer interrupt is generated, generate a general call interrupt and transmit status to all the Slave PICs; wait for 1ms. Step 3: Receive the voltage, current, temperature, and results of the battery model from the slave with which the master is currently communicating. Log the received information on the SD Card. Increment the slavecount by 1 to setup communication with the next slave. Step 4: If the voltage of the cell being monitored by the current slave is less than 3.0V, decrement the count of cells that are discharged completely by

129 Step 5: If slavecount<6, i.e., if the master is not done communicating with all the slaves, go to step 3. Step 6: If count<3, i.e., if all the cells are not discharged completely, go to step

130 Figure 4.27: Flowchart for the Master PIC. 112

131 4.8.2 Algorithm and Flow Charts for Slave PIC The purpose of Slave PIC (1 through 6) is to monitor an individual cell s voltage, temperature, and shunting current, use this information to compute the battery model and transmit the results to the Master PIC and to control the charging/discharging of individual cells based on the control signals received by the Master PIC. The Slave PIC receives the battery pack current from the Master PIC and computes the current through the cell which is the difference between the battery pack current and the shunting current. The Slave PIC i charges cell i by turning off the MOSFET Q (2i+1) of Figure 3.17 and shunts charging by turning on the MOSFET Q (2i+1). The Slave PIC i discharges cell i by turning on the MOSFET Q (2i) and shunts discharging by turning off the MOSFET Q (2i). The Slave PIC receives a status variable from the Master PIC that tells the Slave PIC whether the battery pack is charging (status=0) or discharging (status=1). Figure 4.28 shows the flowchart for software implementation in the Slave PIC. The steps used in the Slave PIC are as follows. Step 1: Initialize the I/O ports connected to the MOSFETs being controlled by the Slave PIC as outputs, the ADC module to perform analog to digital conversion from the channels to which the sensors are connected, and the I 2 C module as a slave by initializing the corresponding registers. Step 2: Wait for a general call interrupt generated by the master. The receive status and battery pack current via I 2 C. Step 3: Get the voltage, current and temperature data of the cell from the ADC module. Step 4: If status=0 (battery pack is charging) and if the voltage is greater than 4.2V 113

132 shunt the cell from charging by turning on MOSFET Q (2i+1). If status=1 (battery pack is discharging) and if the voltage is less than 3.0V, shunt the cell from discharging by turning the MOSFET Q (2i). Step 5: Transmit the voltage, current through the cell, temperature and the results of the battery model to the master through the I 2 C bus. Step 6: Go to step 2. Figure 4.28: Flowchart for the Slave PIC. 114

133 4.9 Conclusions This chapter derives the battery model for a lithium-ion cell. Implementation of the battery model and the sensor transfer functions obtained in Chapter III in a 16-bit fixed-point processor and are compared with implementations in a floating-point processor. The method for correcting the SOC predicted by coulomb counting using an SOC observer is presented. The algorithms and flowcharts implemented in the Master PIC and Slave PICs are also presented. 115

134 CHAPTER V RESULTS The proposed battery management system (BMS) with individual cell equalization was tested for a battery pack of six cells connected in series for a 0.5C or 1A charge/discharge. This chapter presents the results for cell equalization for the battery pack of six cells for one charge cycle, one discharge cycle, and five consecutive chargedischarge cycles. 5.1 Cell Equalization During Charging Experiment A charging experiment was conducted on the battery pack of six lithium-ion cells connected in series in order to test the proposed cell equalization scheme during charging. The battery pack was charged at a constant current of 1A until all the cells in the battery pack were charged to a voltage of 4.2V. Charging was discontinued once all the cells in the battery pack had reached a voltage of 4.2V. Charging all the cells in a battery pack once completely constitutes one charge cycle. The purpose of this experiment was to test for cell equalization, in terms of voltage and stored charge, among all six cells in the battery pack. 116

135 The battery pack is charged by turning on the MOSFET Q c of Figure The six cells are intentionally started at different initial voltages (i.e. not equalized) so that the effect of equalization becomes evident. Table 5.1 shows the initial voltages for each of the six cells. Figures 5.1 through 5.6 show the results of the charging experiment for the six cells, one cell per figure for cell #1 through cell #6. The three graphs on the left hand side of each figure show the actual voltage, the model voltage, and the error in the model voltage for the cells. The error in the model voltage always stays negative during charging, i.e., the model voltage is greater than the actual voltage. On the right hand side of each figure, the stored charge q s, diffused charge q d, and the temperature of the cell are presented. The temperature graph shows the actual temperature, model temperature and the error in the temperature. In this thesis, the SOC is corrected only on the basis of error voltage. It is also possible to correct the SOC based on the error in the temperature, but this is not done in this work. Table 5.1: Starting voltages of cells for the charging experiment. Cell # Starting Voltage (V) An individual cell is charged with 100% charge current as long as the cell voltage is between 3.0V and 4.2V. Once the cell voltage reaches 4.2V, the shunting MOSFET Q (2i+1) of Figure 3.17 is turned on, thus shunting all of the charge current around the cell. 117

136 When the cell voltage falls below 4.2V, the shunting MOSFET is turned off, thus applying the charging current. The shunting MOSFET will switch on and off repeatedly, but with decrementing frequency, as the cell voltage settles to 4.2V. If the cell voltage is below 4.2V the shunting MOSFET is off and if the cell voltage is above 4.2V the shunting MOSFET is turned on. For example, consider the charging of cell #6, which starts charging from an initial voltage of 3.13V. The voltage rises instantaneously when the charge current is applied from 3.13V to 3.28V; this is due to the cell s internal resistance. The cell voltage reaches 4.2V at about 90 minutes, after which the current is shunted across the cell. As soon as the shunting MOSFET is turned off, the voltage of the cell drops to 4.05V, again because of its internal resistance. This causes the shunting MOSFET to be turned off again, reapplying the charge current and bringing the voltage of the cell back up above 4.2V. The frequency of switching decreases as the voltage comes closer and eventually settles at 4.2V. The stored charge rises linearly until the switching starts and then settles at a charge of 155A-min once the switching starts. 118

137 Figure 5.1: Parameters of cell #1 for the charging experiment. Figure 5.2: Parameters of cell #2 for the charging experiment. 119

138 Figure 5.3: Parameters of cell #3 for the charging experiment. Figure 5.4: Parameters of cell #4 for the charging experiment. 120

139 Figure 5.5: Parameters of cell #5 for the charging experiment. Figure 5.6: Parameters of cell #6 for the charging experiment. 121

140 An observer attached to each cell continuously monitors the error in voltage, which is the difference between the actual (measured) voltage and the model voltage. The observer corrects the model s state variable for the stored charge of the cell based on the error in voltage. The value of the stored charge is raised by 1% if the error in the voltage is greater than 0.2V. The value of the stored charge is decreased by -1% if the error in the voltage is less than -0.2V. The plots for the cell s temperature show that the model temperature is off from the actual temperature of the cell. This error can be corrected by adjusting the gain g 2 in the temperature equation (4.3). Adjusting the temperature model and correcting the SOC based on the error in the temperature are left for future work. Figure 5.7 replots the cell voltages of the six cells during the charging experiment on a single graph. Although the cells start from different initial voltages, all the cell voltages reach 4.2V by the end of charge cycle. Even after the strong cells reach 4.2V, the charge cycle continues so that the weak cells in the battery pack can also charge to 4.2V. Therefore, charging continues until the weakest cell in the battery reaches 4.2V; this is how cell equalization in terms of cell voltages is achieved during charging. This is in contrast with simpler strategies that stop charging when the strongest cell reaches 4.2V. 122

141 Figure 5.7: Voltages of six cells for the charging experiment. Figure 5.8 shows the stored charge in the six cells during the charging experiment. Even though the cells start from different initial stored charges, the stored charge in all the cells reaches 155 Amp-min at the end of charge cycle; cell equalization is achieved in terms of stored charge during charging. This is in contrast to the other strategies previously published that achieve equalization only in terms of voltage but not in terms of stored charge. 123

142 Figure 5.8: Stored charge in the six cells for the charging experiment. An analysis was done to determine the benefit our charging strategy provides. Three different charging strategies were evaluated, using data collected from the charging experiment. In the first strategy, it is assumed that charging is discontinued once the strongest cell in the battery pack reaches 4.2V. Table 5.2(a) shows the voltage, stored charge and the stored energy of each cell at the instant t =48 minutes when the strongest cell reaches 4.2V. The vertical dotted lines in Figure 5.7 and Figure 5.8 indicate the instants at which the data has been collected. The total available energy in the battery pack at the end of charging in this case is J. This strategy is chosen as a base strategy with which to compare more sophisticated strategies. In the second strategy, it is assumed that charging is discontinued once all six cells in the battery pack reach 4.2V but before stored charge has been equalized. Table 5.2(b) shows the voltage, stored charge 124

143 and the energy stored in each cell and thus the total energy at the end of the charge cycle for this strategy; this is read from the experiment data at the instant t = 183 minutes, i.e., when all the six cells in the battery pack reach 4.2V and the frequency of switching is reasonably small (two minutes). The available energy in the battery pack in this case is J. Therefore, cell equalization in terms of voltage results in an increase of stored energy in the battery pack by 31% when compared to the first strategy. Table 5.2: Available energy in the battery pack of six lithium-ion cells for three different charging strategies. Cell # Voltage (V) Charge (Amp-min) Energy (J) Total Energy (a) voltage imbalanced and charge imbalanced. Cell # Voltage (V) Charge (Amp-min) Energy (J) Total Energy (b) voltage balanced and charge imbalanced. Cell # Voltage (V) Charge (Amp-min) Energy (J) Total Energy (c) voltage and charge balanced. 125

144 In the third strategy, charging is discontinued once all six cells in the battery pack reach 4.2V and have nearly equal stored charge. Table 5.2(c) shows the case for which the cells are equalized in terms of both voltage and stored charge. In this case the available energy in the battery pack at the end of charging is J, resulting in an increase of 39.33% in the available energy in the battery pack when compared to the first strategy. Even though the voltages are same in Table 5.2(b) and Table 5.2(c) the charges are different because of cell transients. All the energy calculations in Table 5.2 assume that the cells have 100% charge acceptance. 5.2 Cell Equalization During Discharging Experiment A discharging experiment was conducted on the battery pack of six lithium-ion cells connected in series in order to test the proposed cell equalization scheme during discharging. The battery pack was discharged across a resistive load at a constant current of 1A until four cells in the battery pack are discharged to a voltage of 3.0V. Discharging is complete once four cells in the battery pack reach a voltage of 3.0V. Discharging the battery completely once constitutes one discharge cycle. The purpose of this experiment was to test for cell equalization, in terms of voltage and stored charge, among all the six cells in the battery pack during discharge. The decision to end the discharging process once the fourth cell reaches a voltage of 3.0V was chosen arbitrarily assuming that the load requires a minimum of 9V. Continuing the discharging process even after the fourth cell has reached 3.0V results in the battery pack voltage to go below 9V. This is because three cells have already been switched out from the battery pack from discharging. 126

145 The battery pack is discharged by turning on the MOSFET Q D of Figure 3.16 with a discharge current of 1A. Each of the six cells is discharged starting from intentionally different initial voltages so that the effect of equalization at the end of discharge cycle becomes evident. Table 5.3 shows the initial voltages for each of the six cells. Figure 5.9 through 5.14 shows the results for cell equalization for cell #1 through cell #6 during discharging. For each cell, the actual voltage, the model voltage, the error in the voltage based on which the SOC correction is done, the stored charge q s, the diffused charge q d, and the temperature of the cell are presented. Table 5.3: Starting voltages of cells for the discharging experiment. Cell # Starting Voltage (V) The cells are discharged with 100% discharge current initially, and for as long as the cell voltage is in the range 4.2V-3.0V. Once a cell voltage reaches 3.0V, the corresponding MOSFET (Q (2i) of Figure 3.17) is turned off, thus shunting 100% of the discharge current. When the cell voltage rises above 3.0V the MOSFET (Q 2i ) is again turned off, thus discharging the cell further. Thus the cell voltage is allowed to settle at a voltage of 3.0V by switching the discharging current in and out of the cell based on the cell voltage. If the cell voltage is above 3.0V the MOSFET Q (2i) is on and if the cell voltage is below 3.0V the MOSFET Q (2i) is turned off. For example, consider cell #6, which starts discharging from an initial voltage of 3.72V. The voltage drops instantaneously from 3.72V to 3.57V when the MOSFET Q 12 is 127

146 turned on because of the cell s internal resistance. The cell voltage reaches 3.0V at about 90 minutes, at which point the current is shunted across the cell by turning off the MOSFET Q 12. In response, the voltage of the cell rises to 3.15V, again because of the cell s internal resistance. The discharge current is again applied to the cell by turning on the MOSFET Q 12. This in turn results in another voltage drop. The shunt MOSFET switches on and off, with the cell slowly losing charge. Over time, the cell voltage becomes more settled near 3.0V and the frequency of switching decreases; this can be seen after t=100 minutes in Figure The stored charge falls linearly until the switching starts and then settles at a charge of 3A-min. Figure 5.9: Parameters for cell #1 for the discharging experiment. 128

147 Figure 5.10: Parameters for cell #2 for the discharging experiment. Figure 5.11: Parameters for cell #3 for the discharging experiment. 129

148 Figure 5.12: Parameters for cell #4 for the discharging experiment. Figure 5.13: Parameters for cell #5 for the discharging experiment. 130

149 Figure 5.14: Parameters for cell #6 for the discharging experiment. Figure 5.15 replots the voltages of the six cells for the discharging experiment on a single graph. Even though the cells start from different initial voltages, four of the cells reach 3.0V at the end of discharge cycle. The advantage of this discharge strategy is that the strong cells in the battery pack can continue to discharge even after the weakest cell reaches 3.0V. Discharging is continued until the fourth strongest cell in the battery reaches 3.0V. Therefore four cells in the battery pack are equalized in terms of voltage. This is in contrast to simpler strategies that stop discharging as soon as the weakest cell reaches 3.0V. Continuing the discharge process further achieves equalization in terms of voltage in all the six cells, but is not often practical; typically the application to which the 131

150 battery pack is supplying power has a minimum voltage requirement, presumed to be 9.0V here. Figure 5.15: Voltages of the six cells for the discharging experiment. 132

151 Figure 5.16: Stored charge in the six cells for the discharging experiment. Table 5.4: Available energy in the battery pack of six lithium-ion cells for two different discharging strategies. Cell # Voltage (V) Charge (Amp-min) Energy (J) Total Energy (a) voltage and charge imbalanced. Cell # Voltage (V) Charge (Amp-min) Energy (J) Total Energy (b) voltages balanced and charge nearly balanced in four cells. 133

152 Figure 5.16 shows the stored charge in the six cells during the discharging experiment. Even though the cells start from different initial stored charge, the stored charge in four of the cells is nearly equalized at the end of the discharging experiment. It is possible to continue discharging so that all the cells are equalized; again, this is typically restricted by the minimum voltage requirement of the application. An analysis was done to determine how much benefit our discharging strategy provides. Two different discharging strategies were evaluated, using the data collected from the discharging experiment. In the first strategy, it is assumed that discharging is discontinued once the weakest cell in the battery pack reaches 3.0V. Table 5.4(a) shows the voltage, stored charge and the energy stored in each cell at the instant when the weak cell reaches 3.0V. The vertical dotted lines in Figure 5.15 and Figure 5.16 indicate the instants at which the data has been collected. The available energy in this case is J. In the second strategy, discharging is discontinued once four cells in the battery pack reach a voltage of 3.0V. Table 5.4(b) shows energy stored in the battery pack for this strategy. In this case the available energy in the battery pack at the end of discharging is J. Therefore, by using cell equalization during discharge, an additional energy of 82.87% can be extracted from the battery pack when compared to the first strategy. All the energy calculations in Table 5.4 assume that all the energy in cells can be extracted. 5.3 Cell Equalization for Five Charge-Discharge Cycle Experiment Charging a battery pack completely at a constant current of 1A once constitutes a 1A charge cycle. Discharging a battery pack at a constant current of 1A once constitutes a 1A discharge cycle. Charging a battery at 1A and discharging the battery at 1A 134

153 consecutively constitutes a 1A charge-discharge cycle. In this experiment the battery pack is charged and discharged consecutively at 1A for five such cycles. The five chargedischarge cycle experiment is conducted to test the working of the observer in continuously correcting the predicted stored charge. The experiment also helps in marking the importance of the observer by comparing the predicted and corrected stored charge. Charging is initiated (discharging is terminated) by turning on the MOSFET Q C and turning off the MOSFET Q D of Figure Discharging is initiated (charging is terminated) by turning on the MOSFET Q D and turning off the MOSFET Q C. This section shows the results of cell equalization for five consecutive 1A chargedischarge cycles. Each of the six cells in the battery pack is charged/discharged starting from intentionally different initial voltages. Table 5.5 shows the starting voltages of the cells in each of the five cycles. Initial voltages of cells during charging are obtained by charging each cell separately until its cell voltage reaches the desired voltage. Similarly, the starting voltages of cells during discharge are obtained by discharging each cell separately across a resistor until its cell voltage reaches the desired voltage. Table 5.5: Voltage of cells at beginning of each charge and discharge cycle for the five charge-discharge cycle experiment. Cell # Case Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 1 Charging Discharging Charging Discharging Charging Discharging Charging Discharging Charging Discharging Charging Discharging

154 Figure 5.17: Voltages of the six cells during the five charging-discharging cycle experiment. Figure 5.17 shows the voltage of each cell (cell #1 through 6) for five chargedischarge cycles separately and Figure 5.18 shows the voltages of all the six cells for the five charge-discharge cycles experiment superimposed on one plot. The vertical dotted lines represent end of each charge/discharge cycle with a delay of ten minutes; this is required to set the cells to the initial voltages shown in Table 5.5. It is evident from these figures that the cell voltages equalize at 4.2V during charging and four cells equalize at 3.0V during discharging even though the cells start from different starting voltages. The strategy is effective in equalizing the cells in terms of voltage during both charging and discharging. 136

155 Figure 5.18: Voltages of the six cells during the five charge-discharge cycle experiment, superimposed on one plot. Figure 5.19 shows the stored charge of each cell for five charge-discharge cycles separately and Figure 5.20 shows the stored charge of all the six cells for five chargedischarge cycles superimposed on one plot. It is evident from these figures that the stored charge in all the cells equalize at 155Amp-min during charging, and that the charge in four cells equalize at nearly 3 Amp-min during discharging. Therefore, the strategy is effective in achieving cell equalization in terms of stored charge during both charging and discharging. 137

156 Figure 5.19: Stored charge of the six cells during the five charge-discharge cycle experiment. 138

157 Figure 5.20: Stored charge of the six cells during the five charge-discharge cycle experiment superimposed on one plot Importance of an Observer The purpose of an observer is to correct the predicted stored charge in a cell obtained from the columbic counting method. Columbic counting method involves accumulating the current over time, which results in accumulation of error over time. Also, the columbic counting method accumulates only the current put in and out of the cell but is not an exact measure of stored charge; the stored charge is affected also by self-discharge, temperature, charge acceptance and aging effects by comparing the predicted and corrected stored charge. The importance of observer in overcoming the above disadvantages can be demonstrated. The observer raises the value of the predicted 139

158 stored charge in a cell by 1% if the error in the voltage is greater than 0.2V, and lowers the value by -1% if the error in the voltage is less than -0.2V. Figure 5.21 shows the voltages of the six cells obtained from the model. The vertical dotted lines represent end of each charge/discharge cycle. Figure 5.22 shows the error in voltage. The horizontal dotted line shows the threshold voltage. Figure 5.23 shows the correction in the stored charge, which is fed back to the observer. The figures show evidence of correction in the predicted stored charge when the error voltage exceeds 0.2V in magnitude. As mentioned in Chapter IV, the model voltage differs from the actual voltage at the start and end of the charging/discharging cycles; these are the points at which we expect to see the most correction in the stored charge. This is evident from Figure 5.22 and Figure 5.23; correction occurs mostly at the end and start of each charge/discharge cycle. Figure 5.21: Model voltages for the six cells during the five charge-discharge cycle experiment. 140

159 Figure 5.22: Error in voltage for the six cells during the five charge-discharge cycle experiment. 141

160 Figure 5.23: Correction in stored charge for the six cells during the five charge-discharge cycle experiment. Figure 5.24 shows the stored charge in six cells for five charge-discharge cycles corrected by the observer and Figure 5.25 shows the stored charge in six cells for five charge-discharge cycles predicted from columbic counting without any correction, i.e., in the absence of the observer feedback. With correction, the corrected stored charge in each of the six cells stabilizes to 155Amp-min during charging, and in four cells to 3Amp-min during discharging, thus achieving equalization in terms of stored charge. Without correction, the predicted stored charge is different for different cells, and the cells do not stabilize at a constant stored charge value during both charging and 142