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
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
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
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
Dedication
Dedicated to my family and teachers.
v
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
TABLE OF CONTENTS
Page
LIST OF TABLES……………………………………………………………………..…xi
LIST OF FIGURES……………………………………………………………………..xiii
CHAPTER
I.
INTRODUCTION ....................................................................................................... 1
1.1
Battery Chemistry ............................................................................................... 1
1.2
Battery Market .................................................................................................... 4
1.3
Cell Balancing in Battery Packs ......................................................................... 7
1.4
Goals of Research ............................................................................................. 11
1.4.1
Cell and Battery Protection....................................................................... 12
1.4.2
Charge Control.......................................................................................... 12
1.4.3
State of Charge (SOC) Determination ...................................................... 13
1.4.4
Cell Equalization....................................................................................... 14
1.4.5
Temperature Control................................................................................. 14
1.4.6
History (Log Book Function).................................................................... 14
1.5
II.
Thesis Outline ................................................................................................... 15
BACKGROUND AND RELATED WORK............................................................. 16
2.1
2.1.1
Battery Management System Strategies ........................................................... 16
Battery-Level Voltage Management......................................................... 17
vii
2.1.2
Modular Battery Management .................................................................. 18
2.1.3
Cell-Level Voltage Management.............................................................. 19
2.2
Cell Balancing Schemes ................................................................................... 19
2.2.1
Passive Cell Balancing Schemes .............................................................. 20
2.2.2
Active Cell Balancing Schemes................................................................ 24
2.3
Charging Techniques ........................................................................................ 33
2.3.1
Constant Current Charging (CC or I-charging) ........................................ 34
2.3.2
Constant Voltage Charging (CV or V-charging) ...................................... 34
2.3.3
Trickle Charging ....................................................................................... 35
2.3.4
Pulse Charging .......................................................................................... 35
2.3.5
IUI Charging ............................................................................................. 35
2.3.6
Other Charging Techniques ...................................................................... 36
2.4
SOC Determination........................................................................................... 36
2.4.1
Direct Measurement.................................................................................. 36
2.4.2
Voltage-based SOC Estimation ................................................................ 37
2.4.3
Current-Based SOC Estimation ................................................................ 38
2.4.4
Other State of Charge Measures ............................................................... 39
2.5
State of Charge (SOC) Observer....................................................................... 39
2.6
Conclusions....................................................................................................... 40
III. HARDWARE DESIGN FOR THE BATTERY MANAGEMENT SYSTEM ........ 42
3.1
Power Supply Considerations ........................................................................... 44
3.2
Proposed BMS Architecture ............................................................................. 45
3.3
Communication and Isolation ........................................................................... 47
viii
3.4
Calibration of Sensors....................................................................................... 49
3.4.1
Voltage Sensor .......................................................................................... 51
3.4.2
Temperature Sensor .................................................................................. 52
3.4.3
Current Sensor .......................................................................................... 55
3.5
Lithium-Ion Cell Charging Strategy ................................................................. 58
3.6
Cell Equalization............................................................................................... 59
3.6.1
Cell Equalization During Charging .......................................................... 61
3.6.2
Cell Equalization During Discharging...................................................... 63
3.6.3
Component Selection ................................................................................ 65
3.7
SD Card Interfacing for Data Logging ............................................................. 66
3.8
Other Hardware Issues...................................................................................... 68
3.9
PCB Design....................................................................................................... 72
3.10
Conclusions....................................................................................................... 75
IV. SOFTWARE IMLPEMENTATION FOR THE BATTERY
MANAGEMENT SYSTEM..................................................................................... 76
4.1
Lithium-Ion Battery Model............................................................................... 76
4.2
Fixed-Point Implementation Basics.................................................................. 82
4.3
Rules for Fixed-Point Arithmetic...................................................................... 84
4.4
PIC Fixed-Point Architecture ........................................................................... 87
4.5
Fixed-Point Implementation of Sensor Transfer Functions.............................. 88
4.5.1
Fixed-Point Implementation of Temperature Transfer Function.............. 88
4.5.2
Fixed-Point Implementation of Current Sensor Transfer Function .......... 90
4.6
Fixed-Point Implementation of Battery Model................................................. 92
ix
4.6.1
Fixed-Point Implementation of Stored Charge Differential Equation...... 92
4.6.2
Fixed-Point Implementation of Diffused Charge Differential Equation .. 95
4.6.3
Fixed-Point Implementation of Temperature Differential Equation ........ 97
4.6.4
Fixed-Point Implementation of Temperature Equation ............................ 99
4.6.5
Fixed-Point Implementation of Voltage Equation.................................. 101
4.7
SOC Estimation .............................................................................................. 107
4.8
Software Implementation-Algorithms and Flow Charts................................. 108
4.8.1
Algorithms and Flow Charts for Master PIC.......................................... 108
4.8.2
Algorithm and Flow Charts for Slave PIC.............................................. 113
4.9
Conclusions..................................................................................................... 115
V. RESULTS ................................................................................................................ 116
5.1
Cell Equalization During Charging Experiment............................................. 116
5.2
Cell Equalization During Discharging Experiment ........................................ 126
5.3
Cell Equalization for Five Charge-Discharge Cycle Experiment................... 134
5.3.1
5.4
Importance of an Observer...................................................................... 139
Conclusions..................................................................................................... 145
VI. CONCLUSIONS AND FUTURE WORK.............................................................. 147
REFERENCES………………………………………………………………………....152
x
LIST OF TABLES
Page
Table 1.1: Effect of voltage and charge imbalance........................................................... 10
Table 2.1: Cell balancing schemes.................................................................................... 20
Table 3.1: Voltages obtained from a sample temperature sensor for various
temperatures.................................................................................................... 54
Table 3.2: Voltages obtained from the current sensor for various currents...................... 57
Table 3.3: Pin description of SD Card adapter. ................................................................ 67
Table 3.4: Power consumed by the proposed BMS.......................................................... 70
Table 3.5: List of hardware components........................................................................... 71
Table 4.1: Constants in the cell model.............................................................................. 81
Table 4.2: Representation of constants in the temperature transfer function. .................. 88
Table 4.3: Representation of constants in the current transfer function. .......................... 91
Table 4.4: Representation of constants in the temperature differential equation. ............ 97
Table 4.5: Representation of constants in the temperature equation. ............................. 100
Table 4.6: Approximation of f(qs(t)) using curve fitting for different ranges of qs(t)..... 103
xi
Table 4.7: Representation of constants in f(qs(t)) for 20<qs≤30. .................................... 104
Table 4.8: Representation of constants in the voltage equation...................................... 105
Table 5.1: Starting voltages of cells for the charging experiment. ................................. 117
Table 5.2: Available energy in the battery pack of six lithium-ion cells for three different
charging strategies. ....................................................................................... 125
Table 5.3: Starting voltages of cells for the discharging experiment. ............................ 127
Table 5.4: Available energy in the battery pack of six lithium-ion cells for two different
discharging strategies.................................................................................... 133
Table 5.5: Voltage of cells at beginning of each charge and discharge cycle for the five
charge-discharge cycle experiment............................................................... 135
xii
LIST OF FIGURES
Page
Figure 1.1:
Battery working during discharge. ............................................................... 2
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]. ................................................................... 6
Figure 1.7:
Electrical symbols for cells and batteries. .................................................... 7
Figure 1.8:
Typical display of SOC [11]. ..................................................................... 13
Figure 2.1:
Battery management system....................................................................... 17
Figure 2.2:
Modular battery management from [12]. ................................................... 18
Figure 2.3:
Resistive equalization................................................................................. 21
Figure 2.4:
Equalization with switched resistors from [8]............................................ 22
Figure 2.5:
Simple control method for analog shunt equalization [13]. ....................... 23
Figure 2.6:
Analog shunt equalizer [8]. ........................................................................ 24
Figure 2.7:
Switched capacitor equalizer proposed by [8] [13] [14] [15] [16]............. 26
Figure 2.8:
Equalization results for switched capacitor system presented by
Pascual and Krein, from [16]. .................................................................... 27
Figure 2.9:
Switched reactor equalization [13]............................................................. 28
xiii
Figure2.10: Resonant equalization [8]............................................................................ 29
Figure 2.11: Battery string with individual cell equalizers, from [17]. .......................... 30
Figure 2.12: Battery ICE with fuzzy logic equalizer [17]. ............................................. 30
Figure 2.13: Equalization with individual DC-DC converters [18]................................ 31
Figure 2.14: DC-DC converter used in Figure 2.13........................................................ 31
Figure 2.15: Three implementations of magnetic core equalization [18] [19]. .............. 32
Figure 2.16: Equalization with non-dissipative current diverter [18]............................. 33
Figure 2.17: Typical discharge curve for lithium-ion cell. ............................................. 38
Figure 3.1:
Proposed BMS with individual cell monitoring......................................... 43
Figure 3.2:
Battery pack with six cells in series. .......................................................... 43
Figure 3.3:
Local power obtained from an individuall cell. ......................................... 44
Figure 3.4:
Main power supply using the voltage regulator. ........................................ 45
Figure 3.5:
Architecture of the proposed BMS............................................................. 46
Figure 3.6:
I2C communication with master and slave at same ground levels. ............ 48
Figure 3.7:
I2C communication with master and slave at different ground levels........ 48
Figure 3.8:
Local voltage regulator............................................................................... 50
Figure 3.9:
Plot of transfer function of the ADC as voltage varies from 0 to 2.5V...... 50
Figure 3.10: Interfacing voltage sensor to the PIC. ........................................................ 52
Figure 3.11: Interfacing temperature sensor to the PIC.................................................. 53
Figure 3.12: Temperature sensor calibration. ................................................................. 54
Figure 3.13: Interfacing current sensor to the PIC.......................................................... 55
Figure 3.14: Current sensor calibration. ......................................................................... 57
xiv
Figure 3.15: CV charge profile of the lithium-ion cell, from [23].................................. 58
Figure 3.16: Architecture of the proposed cell equalization........................................... 60
Figure 3.17: Cell equalizer for the ith cell. ...................................................................... 61
Figure 3.18: Working of the cell equalizer during charging:.......................................... 63
Figure 3.19: Working of the cell equalizer during discharge. ........................................ 64
Figure 3.20: Interfacing SD Card to Master PIC. ........................................................... 66
Figure 3.21: PCB Layout for the proposed BMS. .......................................................... 73
Figure 3.22: Unpopulated PCB for the proposed BMS. ................................................. 73
Figure 3.23: Top view of the proposed BMS. ................................................................ 74
Figure 3.24:
Bottom view of the proposed BMS........................................................... 75
Figure 4.1:
Charge-discharge cycle of a lithium-ion cell obtained from experiment... 79
Figure 4.2:
Temperature of the lithium-ion cell obtained from experiment. ................ 79
Figure 4.3:
Ten-minute charge-discharge cycle of a lithium-ion cell obtained from
experiment.................................................................................................. 80
Figure 4.4:
Comparison of actual cell voltage and the cell voltage obtained from the
model.......................................................................................................... 82
Figure 4.5:
Absolute error between the actual cell voltage and the cell voltage
obtained from the model. ........................................................................... 82
Figure 4.6:
The b-number representation of a fixed-point number. ............................. 83
Figure 4.7:
Data flow diagram for fixed-point multiplication. ..................................... 85
Figure 4.8:
Data flow diagram for fixed-point addition. .............................................. 86
Figure 4.9:
Data flow diagram for implementing temperature transfer function. ........ 89
Figure 4.10: Comparison of floating-point and 16-bit fixed-point implementation of
temperature transfer function..................................................................... 90
xv
Figure 4.11: Data flow diagram for implementing current transfer function. ................ 91
Figure 4.12: Comparison of floating-point and 16-bit fixed-point implementation of
current sensor transfer function. ................................................................ 92
Figure 4.13: Data flow diagram to obtain stored charge. ............................................... 93
Figure 4.14: Comparison of floating-point and 16-bit fixed-point implementation of
stored charge differential equation............................................................. 94
Figure 4.15: Data flow diagram to obtain diffused charge. ............................................ 95
Figure 4.16: Comparison of floating-point and 16-bit fixed-point implementation of
diffused charge differential equation. ......................................................... 96
Figure 4.17: Data flow diagram to obtain temperature................................................... 98
Figure 4.18: Comparison of floating-point and 16-bit fixed-point implementation of
temperature differential equation............................................................... 99
Figure 4.19: Data flow diagram to obtain Teq.............................................................. 100
Figure 4.20: Comparison of floating-point and 16-bit fixed-point implementation of
temperature equation................................................................................ 101
Figure 4.21: Plot of f(qs(t)) vs. qs(t) varies between 0 and 170A-min. ......................... 102
Figure 4.22: Comparison of approximated and actual implementation of f(qs(t))........ 104
Figure 4.23: Data flow diagram to implement f(qs(t)). ................................................. 105
Figure 4.24: Data flow diagram to obtain the voltage of the lithium-ion cell. ............. 106
Figure 4.25: Comparison of floating-point and 16-bit fixed-point implementation of
voltage equation. ...................................................................................... 107
Figure 4.26: Observer with feedback for SOC estimation............................................ 108
Figure 4.27: Flowchart for the Master PIC................................................................... 112
Figure 4.28: Flowchart for the Slave PIC. .................................................................... 114
Figure 5.1:
Parameters of cell #1 for the charging experiment................................... 119
xvi
Figure 5.2:
Parameters of cell #2 for the charging experiment................................... 119
Figure 5.3:
Parameters of cell #3 for the charging experiment................................... 120
Figure 5.4:
Parameters of cell #4 for the charging experiment................................... 120
Figure 5.5:
Parameters of cell #5 for the charging experiment................................... 121
Figure 5.6:
Parameters of cell #6 for the charging experiment................................... 121
Figure 5.7:
Voltages of six cells for the charging experiment.................................... 123
Figure 5.8:
Stored charge in the six cells for the charging experiment. ..................... 124
Figure 5.9:
Parameters for cell #1 for the discharging experiment............................. 128
Figure 5.10: Parameters for cell #2 for the discharging experiment............................. 129
Figure 5.11: Parameters for cell #3 for the discharging experiment............................. 129
Figure 5.12: Parameters for cell #4 for the discharging experiment............................. 130
Figure 5.13: Parameters for cell #5 for the discharging experiment............................. 130
Figure 5.14: Parameters for cell #6 for the discharging experiment............................. 131
Figure 5.15: Voltages of the six cells for the discharging experiment. ........................ 132
Figure 5.16: Stored charge in the six cells for the discharging experiment.................. 133
Figure 5.17: Voltages of the six cells during the five charge-discharge cycle
experiment................................................................................................ 136
Figure 5.18: Voltages of the six cells during the five charge-discharge cycle
experiment, superimposed on one plot. ................................................... 137
Figure 5.19: Stored charge of the six cells during the five charge-discharge cycle
experiment................................................................................................ 138
Figure 5.20: Stored charge of the six cells during the five charge-discharge cycle
experiment superimposed on one plot. .................................................... 139
Figure 5.21: Model voltages for the six cells during the five charge-discharge cycle
experiment................................................................................................ 140
xvii
Figure 5.22: Error in voltage for the six cells during the five charge-discharge cycle
experiment................................................................................................ 141
Figure 5.23: Correction in stored charge for the six cells during the five
charge-discharge cycle experiment.......................................................... 142
Figure 5.24: Corrected stored charge for the six cells during the five
charge-discharge cycle experiment.......................................................... 143
Figure 5.25: Predicted stored charge from columbic counting for the six cells
during the five charge-discharge cycle experiment. ................................ 144
Figure 5.26: Difference between the corrected and predicted stored charge for the six
cells during the five charge-discharge cycle experiment......................... 145
xviii
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
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
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 + Li x C 6 ↔ 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
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 $US 25 billion in the year
2012. A 2007 study [4] estimates that secondary batteries constitute 60% of the total
demand in US$; 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
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
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
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
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
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
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].
Cell#1
Cell#2
Voltage
Charge
Energy
Voltage
Charge
Energy
Total Energy
Table 1.1: Effect of voltage and charge imbalance.
Case 1
Case 2
Case 3
Charge-balanced
Charge-imbalanced Charge-imbalanced
Voltage-balanced
Voltage-imbalanced Voltage-balanced
4.2V
4.2V
4.2V
2.1Ah
1Ah
1Ah
31.75KJ
15.12KJ
15.12KJ
4.2V
2.1Ah
31.75KJ
63.5KJ
3.6V
0.5Ah
1.8KJ
16.92KJ
4.2V
0.8Ah
12.09KJ
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
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
•
Cell equalization
•
Temperature control
•
History (log book function)
The following sections describe various functional blocks implemented in a BMS
to achieve these objectives.
1.4.1 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.
1.4.2 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
2.3.
12
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
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.
1.4.5 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 0-60 0C). 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.
1.4.6 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
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
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
3. Cell-Level Voltage Management
2.1.1 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
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
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.
2.1.3 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 2.2.
2.2
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
(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.
Passive
Table 2.1: Cell balancing schemes.
Active
Resistive Equalization
Switched Capacitor Equalization
Analog Shunt Equalization
Switched Reactor Equalization
Resonant Equalization
Other Active Methods
2.2.1 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
2.2.1.1 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
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
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.
2.2.1.2 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
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].
2.2.2 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
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 2.2.2.1 to 2.2.2.3. 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 2.3.2.4.
2.2.2.1 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
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
Figure 2.8: Equalization results for switched capacitor system presented by Pascual
and Krein, from [16].
2.2.2.2 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
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].
2.2.2.3 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 Q1A and Q2A. The
MOSFETs Q1A and Q2A 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 Q1A is turned on,
which results in current flow from cell #1 through Q1A, to the inductor L1C. This results
in storage of charge in L1C; as a result, the voltage across cell #1 drops by a small
amount. Turning on the MOSFET Q2A and turning off the MOSFET Q1A results in a
28
current to flow from the inductor L1C to cell #2, thus charging cell #2 with the charge that
is stored in the inductor L1C. Like the switched capacitor method, this method can be
used during both charging and discharging.
Figure 2.10: Resonant equalization [8].
2.2.2.4 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
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
Figure 2.13: Equalization with individual DC-DC converters [18].
Another approach for charge equalization using an individual bidirectional DCDC 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 2.14. 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 2.13.
31
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 2.16. 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 L1 due to the flow of current I1 through it. This is
32
continued until the voltage of cell #1 falls to the reference voltage. When the MOSFET
Q1 is turned off, the energy stored in L1 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
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.
2.3.1 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.
2.3.2 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
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.
2.3.4 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.
2.3.5 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
carried out to achieve equal voltages among all cells for cell equalization in a string of
series-connected cells.
2.3.6 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.
2.4.1 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 Δq = iΔt . The controller that is being used to calculate the SOC keeps track of the
36
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.
2.4.2 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 2.17. 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
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.
2.4.3 Current-Based SOC Estimation
Like direct measurement, current-based SOC estimation uses the basic definition
t
of the charge q = ∫ i (t )dt to determine the SOC of a battery; charge is obtained by
0
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
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.
2.4.4 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
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
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
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 (I2C™) 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
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 S1 and S2.
Figure 3.2: Battery pack with six cells in series.
43
This chapter discusses in detail the power supply considerations, hardware
implementation of the proposed Battery Management System (BMS), I2C 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; VCCi is
used to denote the local supply voltage, while GNDi 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
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. Vccm is used to denote the positive supply voltage of the main power
supply, and GNDm 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 I2C bus. An additional Slave PIC (Slave PIC 0) is dedicated to
measuring the current through the battery string (both during charging and discharging)
45
using a current sensor; it transfers this current to the Master PIC through the serial I2C
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 S1 and S2 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
ground from the main power supply. Because all the PICs with their various powers and
grounds must communicate via a single I2C serial bus, isolation is required. An I2C
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 I2C 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 I2C 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 I2C is a
synchronous protocol. The clock and the data signals are generated by the I2C module of
a PIC with respect to that PIC’s ground. Therefore, for the signals on the I2C bus to be
valid, both the Master PIC and the slave PICs should have the same ground.
47
Figure 3.6: I2C 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 I2C isolator is used to adjust the signals
with respect to corresponding grounds. Figure 3.7 shows the connections for I2C
communication between two PICs with two different grounds.
Figure 3.7: I2C communication with master and slave at different ground levels.
The primary of the I2C 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 SDA1 and SCL1 are with respect
to the GND1. The I2C isolator transforms these signals to SDA2 and SCL2, respectively,
which are with respect to the GND2. Similarly, signals generated at SDA2 and SCL2 are
48
transformed to SDA1 and SCL1. Isolation allows valid communication between the Slave
PICs and the Master PIC.
Six I2C isolators (ADUM1250) are used in thesis work; one is needed for each
Slave PIC. The bidirectional I2C isolators are new to the market. Analog Devices is the
only company producing them. The I2C 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 nbit ADC module, the digital output is given by N =
V
* 2 n , where Vref is the reference
Vref
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.
49
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
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.
3.4.1 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 3.10. 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 Vcell = 2Vsensed , where Vsensed is the voltage at the ADC input and
Vcell 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
Vcell = 2Vsensed and
Vsensed =
N
Vref
2n
51
∴Vcell =
N
Vref where N is the digital output of the ADC.
2n−1
Figure 3.10: Interfacing voltage sensor to the PIC.
3.4.2 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, Vtemp, proportional to the temperature, which is
interfaced to the PIC’s ADC. The data sheet of the temperature sensor shows that the
52
transfer function of the temperature sensor is of the form Vtemp = aT + b and can measure
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 0.0072 and 0.6826, respectively. Therefore, the transfer function of the
temperature sensor is Vtemp = 0.0072T + 0.6826 and the temperature is given by
T = 138.888Vtemp − 94.80555 . Using the transfer function of the ADC module and the
53
transfer function of the temperature sensor, the actual temperature in ˚C can be
reconstructed in the PIC using
T=
138.888 NVref
− 94.80555
212
(3.1)
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
1.2
1
Sensor Voltage (V)
y = 0.0072x + 0.6826
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
Temeprature (˚C)
Figure 3.12: Temperature sensor calibration.
54
70
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 3.13. 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 I2C 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 (IIN+ and IOUT-) provide a path for the current being measured. The fifth
55
pin generates a voltage Vcurrent 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 IIN+ 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 form Vcurrent = 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 0.1247
and 2.4896, respectively. Therefore, the transfer function for a current sensor is
Vcurrent = 0.1247i + 2.4896 and the current is obtained as i = 8.0192Vcurrent − 19.9647 . The
ADC module generates a digital number proportional to the voltage Vcurrent. The actual
current in amperes can be reconstructed by combining the transfer functions of the ADC
module and the current sensor:
i=
8.0192 NVref
− 19.9647
212
where N is the digital output of the ADC.
56
(3.2)
Table 3.2: Voltages obtained from the current sensor for various currents.
Current vs. Sensor Voltage
2.8
2.7
Voltage (V)
2.6
y = 0.1247x + 2.4896
2.5
2.4
2.3
2.2
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
Current (A)
Figure 3.14: Current sensor calibration.
57
1.5
2
2.5
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 3.15. 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
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 3.16. MOSFETs QD and QC are controlled by the Master PIC, and are used to
control the discharging or charging of the overall battery. The Master PIC turns QD on
during the discharging process and QC 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
±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
3.6.1 Cell Equalization During Charging
Consider the ith (i=1 to 6) cell in the series pack with cell equalization shown in
Figure 3.17. The MOSFETs Q(2i) and Q(2i+1) are controlled by the Slave PIC i monitoring
the ith 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 ith 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
voltage reaches 4.2V (determined by the Slave PIC i monitoring the ith 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 Ri (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 VCCi and Vi to determine
the shunting current IB from the equation I B = (VCCi − Vi ) / Ri = 200 * (VCCi − Vi ) . Vi is
measured in the same way as VCCi. 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
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 QC. Now the battery pack is ready to supply energy to the load, and the
discharge process can be started by turning ON the MOSFET QD.
3.6.2 Cell Equalization During Discharging
The working principle of the cell equalizer during discharge is shown in the
Figure 3.19. 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
Once the cell voltage reaches 3.0V (determined by the Slave PIC i monitoring the
ith 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
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.
3.6.3 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 (RON) 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 0.0065Ω.
65
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
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.
Pin No.
1
Table 3.3: Pin description of SD Card adapter.
Name
Description
VCard
This is the Supply Voltage that the Controlling Processor
pins are running (3.3 - 5.5Vdc).
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.
6 -10
GND
Ground
67
The Master PIC receives voltage, current, temperature and battery model
parameters for each cell via an I2C 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 I2C or SPI communication. This
peripheral is used to communicate with the Slave PICs using I2C; 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 (I2C) 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
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 dsPIC30F4013
69
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 7.3728MHz 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)
dsPIC4013
45
8
360
ADUM1250
35
6
210
MOSFET
65
6
390
Schottky Diode
380
6
2280
Current Sensor
40
1
40
Temperature Sensor
18
6
108
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
Name
Table 3.5: List of hardware components.
Identification
Cost per unit
Qty
Microcontroller
dsPIC30F4013
$12.50
8
I2C Isolator
ADUM1250
$6.50
6
MOSFET
STP140NF55
$2.35
14
Schottky Diode
1N5820
$0.74
12
Crystal
7.3728MHz
$0.40
8
Capacitor
20µF
$0.05
16
Current Sensor
ACS706ELC-05C
$3.15
1
Temperature Sensor
LM61
$1.25
6
Voltage Regulator
7805SR
$2.00
1
Voltage Reference
LM 336
$0.96
6
Cell Holder
D-Cell Holder
$0.71
6
Resistor
1Ω 1%
$0.01
10
Resistor
13.7KΩ 0.1%
$0.01
35
Resistor
100Ω
$0.01
6
Resistor
220Ω
$0.01
12
Resistor
680Ω
$0.01
12
SD Card Adapter
ECS-ADP-01
$40.00
1
SD Card
SanDisk SD Card 1GB
$25.00
1
PCB
Customized
$160.00
1
Diode
Total Cost
$433.20
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
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, I2C 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 3.21.
72
Figure 3.21: PCB Layout for the proposed BMS.
Figure 3.22: Unpopulated PCB for the proposed BMS.
73
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 I2C isolators for the corresponding cells were
damaged. As the bi-directional I2C 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
Figure 3.24: Bottom view of the proposed BMS.
3.10
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
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.
Lithium-Ion Battery Model
4.1
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
t
by q = ∫ i(t )dt . Although coulomb counting gives an accurate accumulation of the charge
0
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
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 qs, the diffused charge qd and the temperature T. The
stored charge equation is
dq s (t )
= i(t ) − c1q s (t )
dt
.
(4.1)
where qs(t) is the stored charge in the cell and i(t) is the current flowing through the cell.
The diffused charge equation is
dq d (t )
= g1i (t ) − c2 q d (t )
dt
.
(4.2)
where qd(t)is the diffused charge in the cell.
The temperature equation is
dT (t )
= − c3 [T (t ) − Tamb (t )] + g 2i(t ) 2 .
dt
(4.3)
where T(t) is the temperature of the cell and Tamb(t) is the ambient temperature.
The terminal voltage is modeled in terms of the three state variables as:
v(t ) = (a + bT (t ) + cT 2 (t ))[k1 + k 2i (t ) + k3 qs (t ) + k 4 e − k31qs (t ) + k5e k41qs (t ) + k6 qd (t )] .
(4.4)
The constants c1 through c3 are the time constants and the constants g1 and g2 are
the gain constants. The constant c1 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
The constants c2 and g1 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 c2 is the time constant
obtained from the voltage waveform; once c2 is found, g1 is obtained by multiplying c2 by
the steady-state value of the voltage.
The constants c3 and g2 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 c3 is the time
constant obtained from the temperature waveform; once c3 is found, g2 is obtained by
multiplying c3 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 4.3.
78
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
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
dqs (t )
= i (t ) .
dt
(4.5)
dqd (t )
= i(t ) − 0.8qd (t ) .
dt
(4.6)
dT (t )
= − 0.5(T (t ) − 20) + 5i (t ) 2 .
dt
(4.7)
The diffused charge equation is
The temperature equation
80
The terminal voltage is modeled in terms of the three state variables as
v(t ) = (0.9514 + 0.003085T (t ) - 0.00002 T 2 (t ))
[3.6354 + 0.1500i(t ) + 0.0025q (t ) − 1.6300e
− 0.02 q s ( t )
s
]
+ 0.00007e 0.055qs (t ) + 0.0200q d (t ) .
(4.8)
Constant
c1
c2
Table 4.1: Constants in the cell model.
Value
Units
Constant Value
0
0.8
sec-1
-1
sec
-1
Units
k1
3.6354
V
k2
0.15
Ohms
c3
0.5
sec
k3
0.0025
VCoulomb-1
g1
1
-
k4
-1.63
V
g2
5
-
k5
0.00007
V
a
0.9514
-
k6
0.02
VCoulomb-1
b
0.00309
°C-1
k31
-0.02
Coulomb-1
c
0.00002
°C-2
k41
0.055
Coulomb-1
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
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
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 bnumber is generally selected on the basis of the number of bits required to represent the
83
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
. denotes the floor function. A floating-point equivalent can be
F(n,b)= ⎣ f * 2 b ⎦ , where ⎣⎦
reconstructed using f1 = F / 2 b . The floating-point reconstruction f1 is not exactly equal to
f because of the truncation error.
4.3
Rules for Fixed-Point Arithmetic
Multiplication of two fixed-point numbers F1 and F2 with b-numbers b1 and b2
respectively, results in a fixed-point number F3 whose b-number is given by b3=b1+b2. In
general, multiplication of x(n,b1) with y(n,b2) results in (xy) (2n,b1+b2). 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 2.125 in an 8-bit
fixed-point processor. The product should be 0.53125. The following steps obtain the
result in a fixed-point processor.
1. 0.25 can be represented in an 8-bit processor with 8 bits of fraction as
0.25* 28 =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.
2.125* 26 =136, so 2.125 is represented as 136(8, 6).
3. Fixed-point multiplication 64*136=8704(16, 14).
The result can be obtained back from 8704(16, 14) as 8704/ 214 =0.53125 which
84
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 2 k is same as shifting the number towards the left by
k bits and dividing a number by 2 k is same as shifting the number towards the right by k
bits.
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 2.125 in an 8-bit fixedpoint processor, which should yield 2.375. The following steps obtain the result in a
fixed-point processor.
1. 0.25 can be represented in an 8-bit processor with eight bits of fraction as
0.25* 28 =64 and so is represented as 64(8, 8).
85
2. For 2.125, two bits must be used for the integer part, leaving six bits for the
fraction. 2.125* 26 =136, so 2.125 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 16+136=152 (8, 6).
(a)
(b)
Figure 4.8: Data flow diagram for fixed-point addition: (a) in general and (b) example for
0.25+1.25.
The result can be obtained back from 152 as 152/ 26 =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
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)=0.4297 whereas the exact solution is 0.43. 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
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.
4.5.1 Fixed-Point Implementation of Temperature Transfer Function
The transfer function of the temperature sensor was given in Chapter 3 in
equation (3.1) as T =
138.888 NVref
N
− 94.80555 . For our setup, Vref = 2.5V and 12 can
12
2
2
be
N(16,12).
written
as
Therefore
the
temperature
is
given
by
T = 344.1664 N − 94.80555 ; for implementation 344.1664 and 94.80555 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
Vtemp(16,12)*44053(16,7) i.e. 44053Vtemp (40,19) is shifted left by ten bits so that the
result (40,9) can be subtracted from 48540(40,9). The constant 94.80555 is represented as
48540 (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
344.1664
44053 (16,7)
344.1641
94.80555
48540 (40,9)
88
94.8047
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 0.0011%. Another
possibility is to represent the constant 94.8055 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
Figure 4.10: Comparison of floating-point and 16-bit fixed-point implementation of
temperature transfer function.
4.5.2 Fixed-Point Implementation of Current Sensor Transfer Function
The transfer function of the current sensor was given in Chapter 3 in equation (3.2)
as i =
8.0192 NV ref
− 19.9647 . For our setup the current sensor is interfaced to the Master
212
PIC for which Vref = 5V and
N
can be written as N(16,12). Therefore the current is
212
given by i = 40.096 N − 19.9647 ; for implementation 40.096 and 19.9647 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 19.9647 is represented as 40888
(40,11) and is placed in the accumulator so that it can be added directly to the result in
90
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
40.096
41058 (16,10)
40.0957
19.9647
40888 (40,11)
19.9648
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 0.0032%.
Figure 4.11: Data flow diagram for implementing current transfer function.
91
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.
4.6.1 Fixed-Point Implementation of Stored Charge Differential Equation
The stored charge in a lithium-ion cell is obtained by solving the differential
equation
dqs
= i (t ) . The differential equation must first be converted to a difference
dt
92
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
qs (n + 1) = qs (n) + Ti (n + 1)
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 qs (n + 1) = qs (n) + i (n + 1) .
Figure 4.13: Data flow diagram to obtain stored charge.
The stored charge (qs) 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, qs is stored in the controller as a fixed-point
93
integer of the form qs(16,8). Figure 4.13 shows the data flow diagram used to solve for qs
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 0.017 A-min and the maximum percentage error is
0.011%.
94
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
equation
dqd (t )
= i (t ) − 0.8qd (t ) . The difference equation to solve for qd is obtained as
dt
qd (nT + T ) − qd (nT )
= i (nT ) − 0.8qd (nT )
(n + 1)T − (nT )
qd (n + 1) − qd (n)
= i ( n ) − 0 .8 q d ( n )
T
qd (n + 1) = i (n) + 0.2qd (n)
The diffused charge (qd) in a lithium-ion cell typically ranges from 0-2A-min in
magnitude. Thus, two bits of integer are required, and qd is stored in the controller as a
fixed-point integer of the form qd(16,14). The only constant (0.2) in the qd difference
equation is represented as 3277 (16,14). Figure 4.15 shows the data flow diagram to solve
for qd using fixed-point arithmetic. The result qd(40,28) is shifted left by fourteen bits to
get qd (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
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
4.6.3 Fixed-Point Implementation of Temperature Differential Equation
The temperature of a lithium-ion cell is obtained by solving the differential
equation
dT
= −0.5(T (t ) − 20) + 5i (t ) 2 . The difference equation that is implemented in
dt
the controller to solve for temperature (T) is obtained as
T (nT + T ) − T (nT )
= −0.5(T (nT ) − 20) + 5i (nT ) 2
(n + 1)T − nT
T (n + 1) − T (n)
= −0.5T (n) + 10 + 5i (n) 2
T
T (n + 1) = 5[0.1T (n) + 2 + i (n) 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
0.1
819 (16,13)
0.09997
2
8388608 (40,22)
2
5
5 (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
current of 1A. The maximum absolute error involved is 0.012°C and the maximum
percentage error is 0.034%.
Figure 4.17: Data flow diagram to obtain temperature.
98
Figure 4.18: Comparison of floating-point and 16-bit fixed-point implementation of
temperature differential equation.
4.6.4 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 by Teq = 0.9514 + 0.003085T (t ) − 0.00002T (t ) 2 . One way
of implementing a quadratic equation in the PIC is by using Horner’s method [26]. This
gives Teq = (0.003085 − 0.00002T (t ))T (t ) + 0.9514 , and this results in fewer multiplication
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 Teq in fixed-point processor.
99
Table 4.5: Representation of constants in the temperature equation.
Floating-point value Fixed-point format Fixed-point approximation
0.003085
103515 (40,25)
0.0030849
0.00002
1 (16,16)
0.0000152
0.9514
15587 (16,14)
0.95135
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 0.0092 and the maximum percentage
error is 0.85%.
Figure 4.19: Data flow diagram to obtain Teq.
100
Figure 4.20: Comparison of floating-point and 16-bit fixed-point implementation of
temperature equation.
4.6.5 Fixed-Point Implementation of Voltage Equation
Voltage of a lithium-ion cell (without considering the temperature) is given by
v (t ) = 3.6354 + 0.0025qs (t ) − 1.63e −0.02 q s ( t ) + 0.00007 e0.055 q s ( t ) + 0.15i (t ) + 0.02 qd (t )
The voltage equation can be re-written by grouping all the terms that are a function of
qs(t) together as v(t ) = f (qs (t )) + 0.15i (t ) + 0.02qd (t )
where f ( qs (t )) = 3.6354 + 0.0025qs (t ) − 1.63e −0.02 q s ( t ) + 0.00007 e0.055 q s (t ) .
Figure 4.21 shows the plot of f(qs(t)) vs. qs(t) as qs(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(qs(t)),
rather than computing its terms directly. To minimize the error between the original
function and the polynomial used for curve fitting, qs(t) is divided into twelve different
101
ranges and twelve different polynomials of different orders are used to fit the original
function f(qs(t)).
Figure 4.21: Plot of f(qs(t)) vs. qs(t) varies between 0 and 170A-min.
The polynomials are obtained by fitting a curve that approximates f(qs(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(qs(t)) for different ranges of qs(t). Figure 4.22 shows the error between
f(qs(t)) and the approximation of f(qs(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(qs(t)) for 20<qs(t)≤3. Table 4.7 shows the
representation of constants in the function in fixed-point format.
102
Table 4.6: Approximation of f(qs(t)) using curve fitting for different ranges of qs(t).
qs
f (qs (t ))
0 ≤ qs ≤ 10
0.00084506 qs (t )3 - 0.02555 qs (t ) 2 + 0.31432 qs (t ) + 2.0121
10 < qs ≤ 20
- 0.00174027 5qs (t ) 2 + 0.072629q s (t ) + 2.8943
20 < qs ≤ 30
- 0.00023513 2qs (t ) 2 + 0.016696 qs (t ) + 3.4167
30 < qs ≤ 60
0.00264692703470qs (t ) + 3.62902512919026
60 < qs ≤ 100
0.00285344461503qs (t ) + 3.61404629487104
100 < qs ≤ 120
0.00418322797984qs (t ) + 3.48145256808720
120 < qs ≤ 130
0.00625522123554qs (t ) + 3.23459880674008
130 < qs ≤ 140
0.00902486624390qs (t ) + 2.87344763015148
140 < qs ≤ 150
0.01380924410735qs (t ) + 2.20165131456564
150 < qs ≤ 155
0.01948713375649qs (t ) + 1.35325895703840
155 < qs ≤ 160
0.02486408266848qs (t ) + 0.51907089922698
160 < qs ≤ 165
0.03194300084832qs (t ) - 0.61455785839074
165 < qs ≤ 170
0.04126261377697qs (t ) - 2.15361295635059
103
Figure 4.22: Comparison of approximated and actual implementation of f(qs(t)).
The polynomial is evaluated using Horner’s Method. Therefore,
f (qs (t )) = (−0.00023513qs + 0.016696)qs + 3.41678 .
Table 4.7: Representation of constants in f(qs(t)) for 20<qs≤30.
Floating-point value Fixed-point format Fixed-point approximation
0.00023513
15 (16,16)
0.00022881
0.016696
1094 (16,16)
0.016693
3.41678
27990 (16,13)
3.416748
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
Figure 4.23: Data flow diagram to implement f(qs(t)).
Table 4.8: Representation of constants in the voltage equation.
Floating-point value Fixed-point format Fixed-point approximation
0.15
1229 (16,13)
0.15002
0.02
164 (16,13)
0.02002
105
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
Figure 4.25: Comparison of floating-point and 16-bit fixed-point implementation of
voltage equation.
4.7
SOC Estimation
t
The SOC of a cell is given by q = ∫ i(t )dt . Although coulomb counting gives an
0
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 4.26. 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
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.
4.8.1 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 QC of Figure 3.16 and
turning off the MOSFET QD. Discharging is initiated by turning on the MOSFET QD and
turning off the MOSFTE QC. 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
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 I2C 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 QC and turning off the
MOSFET QD. 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 3.
109
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 QC and turning on the
MOSFET QD. 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 1.
110
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 2.
111
Figure 4.27: Flowchart for the Master PIC.
112
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 I2C 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 I2C.
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
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 I2C bus.
Step 6: Go to step 2.
Figure 4.28: Flowchart for the Slave PIC.
114
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
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
The battery pack is charged by turning on the MOSFET Qc of Figure 3.16. 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 qs, diffused charge qd, 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 #
1
2
3
4
5
6
Starting Voltage (V)
3.30
3.25
3.82
3.59
3.36
3.13
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
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
Figure 5.1: Parameters of cell #1 for the charging experiment.
Figure 5.2: Parameters of cell #2 for the charging experiment.
119
Figure 5.3: Parameters of cell #3 for the charging experiment.
Figure 5.4: Parameters of cell #4 for the charging experiment.
120
Figure 5.5: Parameters of cell #5 for the charging experiment.
Figure 5.6: Parameters of cell #6 for the charging experiment.
121
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 g2 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
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
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 2792.27J. 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
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
3656.06J. 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 #
1
2
3
4
5
6
Voltage (V)
4.06
4.02
4.20
4.05
4.03
4.03
Charge (Amp-min)
105.37
100.19
145.84
132.73
109.49
91.85
Total Energy
Energy (J)
427.80
402.76
612.75
537.56
441.24
370.16
2792.27
(a) voltage imbalanced and charge imbalanced.
Cell #
1
2
3
4
5
6
Voltage (V)
4.20
4.20
4.20
4.20
4.20
4.20
Charge (Amp-min)
146.06
141.06
153.96
146.19
145.85
137.37
Total Energy
Energy (J)
613.45
592.45
646.63
614.00
612.57
576.95
3656.06
(b) voltage balanced and charge imbalanced.
Cell #
1
2
3
4
5
6
Voltage (V)
4.20
4.20
4.20
4.20
4.20
4.20
Charge (Amp-min)
155.41
154.73
154.18
153.96
154.25
153.78
Total Energy
(c) voltage and charge balanced.
125
Energy (J)
652.72
649.87
647.56
646.63
647.85
645.88
3890.50
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 3890.50J, 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
The battery pack is discharged by turning on the MOSFET QD 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 qs, the diffused charge qd,
and the temperature of the cell are presented.
Table 5.3: Starting voltages of cells for the discharging experiment.
Cell #
1
2
3
4
5
6
Starting Voltage (V)
4.20
4.16
3.72
3.80
4.10
3.64
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 (Q2i) 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 Q12 is
127
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 Q12. 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 Q12. 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 5.14. 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
Figure 5.10: Parameters for cell #2 for the discharging experiment.
Figure 5.11: Parameters for cell #3 for the discharging experiment.
129
Figure 5.12: Parameters for cell #4 for the discharging experiment.
Figure 5.13: Parameters for cell #5 for the discharging experiment.
130
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
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
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 #
1
2
3
4
5
6
Voltage (V)
3.48
3.43
3.09
3.07
3.37
3.00
Charge (Amp-min)
63.72
60.89
6.95
6.80
47.64
4.48
Total Energy
Energy (J)
221.75
208.85
21.48
20.88
160.55
13.44
646.94
(a) voltage and charge imbalanced.
Cell #
1
2
3
4
5
6
Voltage (V)
3.00
3.15
3.00
3.12
3.00
3.00
Charge (Amp-min)
8.04
5.18
5.03
7.94
5.60
4.40
Total Energy
Energy (J)
24.12
16.32
15.09
24.77
17.30
13.20
110.80
(b) voltages balanced and charge nearly balanced in four cells.
133
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 646.94J.
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
110.80J. 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
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 QC
and turning off the MOSFET QD of Figure 3.16. Discharging is initiated (charging is
terminated) by turning on the MOSFET QD and turning off the MOSFET QC.
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 #
1
2
3
4
5
6
Case
Charging
Discharging
Charging
Discharging
Charging
Discharging
Charging
Discharging
Charging
Discharging
Charging
Discharging
Cycle 1
3.30
4.20
3.27
4.13
3.83
3.63
3.57
3.77
3.38
4.12
3.09
3.72
Cycle 2
3.23
4.15
3.62
3.78
3.37
3.71
3.29
4.08
3.14
4.21
3.86
3.68
135
Cycle 3
3.80
3.78
3.33
4.12
3.25
4.20
3.62
3.66
3.32
3.73
3.16
4.13
Cycle 4
3.55
3.75
3.38
4.20
3.14
4.08
3.84
4.12
3.21
3.66
3.29
3.78
Cycle 5
3.10
4.10
3.80
3.66
3.62
4.14
3.22
3.77
3.28
3.83
3.38
4.20
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
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
Figure 5.19: Stored charge of the six cells during the five charge-discharge cycle
experiment.
138
Figure 5.20: Stored charge of the six cells during the five charge-discharge cycle
experiment superimposed on one plot.
5.3.1 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
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
Figure 5.22: Error in voltage for the six cells during the five charge-discharge cycle
experiment.
141
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
discharging. Also, the predicted stored charge in some of the cells goes beyond 200Ampmins; this is clearly inaccurate because the cell is rated for 126Amp-min.
Figure 5.24: Corrected stored charge for the six cells during the five chargedischarge cycle experiment.
Figure 5.26 shows the error in the stored charge, i.e., the difference between
Figure 5.24 and Figure 5.25. The error in the stored charge increases with time and again
falls to zero before the start of every charge and discharge cycle. This is because the
stored charge is physically reset at the beginning of the charge/discharge cycle. Without
the correction made possible by the observer, the error in the stored charge would
increase continuously with time. Comparing the stored charge obtained from columbic
counting (200 Amp-min) and the stored charge obtained after correction (155 Amp-min)
with the nominal rating of the cell (126 Amp-min), shows that the observer is effective in
143
correcting the predicted stored charge resulting in a more accurate stored charge. It also
eliminates the accumulation of error.
Figure 5.25: Predicted stored charge from columbic counting for the six cells during the
five charge-discharge cycle experiment.
144
Figure 5.26: Difference between the corrected and predicted stored charge for the six
cells during the five charge-discharge cycle experiment.
5.4
Conclusions
This chapter presents the results of implementing the proposed BMS for the
charging experiment, the discharging experiment, and the five charge-discharge cycle
experiment. The results of charging experiment show that the cells in the battery pack
equalize in terms of both voltage and stored charge. Using the proposed BMS during
charging results in an increase in the energy stored in the battery pack by 39.33%. The
results of discharging experiment show that the four strongest cells in the battery pack
equalize in terms of both voltage and nearly equal stored charge. By using the proposed
BMS during discharging an additional 82.87% of energy can be extracted from the
145
battery pack. The results of the five charge-discharge cycle experiment show that the
observer can work continuously to correct the predicted stored charge. Comparison of the
predicted and corrected stored charge shows that the observer is useful in adjusting the
predicted stored charge to take temperature and self-discharge into account.
146
CHAPTER VI
CONCLUSIONS AND FUTURE WORK
A battery management system (BMS) with individual cell equalizers and state of
charge (SOC) observers for a battery pack of six lithium-ion cells was developed in this
thesis work. A new cell equalization scheme was proposed that balances the cells in a
battery pack in terms of voltage and SOC during both charging and discharging.
The proposed architecture for the BMS monitors the performance of individual
cells using a dedicated local controller (Slave PIC) for each cell. This Slave PIC
controller measures the cell’s voltage, the current flowing through the cell based on the
battery pack current and the shunting current, and temperature and uses the measured
information to compute the parameters modeling the cell. Each Slave PIC communicates
with a master controller (Master PIC) through an I2C bus. The Slave PIC transmits all the
cell parameters and the results of the battery model to the Master PIC. These results
include the stored charge, the diffused charge, model temperature, and model voltage.
The battery model used for each cell includes differential equations to model state
variables tracking the cell’s stored charge, diffused charge, and temperature, and
equations to predict the cell’s voltage from the state variables. The model acts as an SOC
observer. The observer is only as good as the model. Each Slave PIC computes each of
147
the battery model equations for its corresponding cell based on the measured cell
parameters. The Slave PIC predicts the stored charge using the coulomb counting
method, and the observer corrects the predicted stored charge by comparing the actual
cell voltage with the model voltage. The battery model equations were converted to
fixed-point equations before implementation in the slave controllers.
The Master PIC processes the information received from each of the Slave PICs
and logs this information on a Secure Digital (SD) card through a Serial Peripheral
Interface (SPI) bus. The Master PIC sends control signals back to the individual Slave
PICs to control charging/discharging of the respective cells. The proposed hardware
allows the Slave PIC to shunt current around its cell during either charge or discharge. It
is this ability to shunt the cells that allows the strategy to achieve cell equalization during
both charging and discharging.
The proposed cell equalization scheme is a passive cell equalization scheme and
is distinguished from previously proposed equalization schemes in the following ways.
Previously proposed passive equalization schemes achieve cell equalization only during
charging; the proposed scheme achieves cell equalization during both charging and
discharging.
All the previously proposed schemes, both active and passive, achieve cell
equalization only in terms of voltage whereas the proposed scheme achieves equalization
in terms of both voltage and stored charge. Also, previously proposed schemes were not
practically tested on the bench; our strategy was complemented implemented and
experimentally verified. An attempt was made to reduce the power consumed by the
148
battery management system by choosing low power hardware components. The proposed
BMS consumes 3.39W of power and reduces the performance of the battery pack by
14%. The degradation in the performance is acceptable when compared to the advantages
the BMS offers. Balancing all the cells in the battery pack in terms of both voltage and
stored charge increases the available capacity of the battery pack. A PCB was designed to
test the proposed BMS on a battery pack of six series connected cells. The results
presented are a clear indication that the cell voltages and stored charge are balanced
during both charge and discharge. The results for the implementation of the proposed cell
equalization scheme show that an additional energy of 31% due to cell equalization in
terms of voltage and 39.33% of additional energy due to cell equalization in terms of
stored charge can be put into the battery pack during charging when compared to the
simpler strategies which end charging once the strongest cell in the battery pack reaches
maximum voltage. The proposed cell equalization scheme during discharge results in an
extraction of 82.87% of additional energy from the battery pack when compared to the
simpler strategies which stop discharging once the weak cell in the battery pack reaches
minimum voltage.
The proposed hardware for cell equalization switches each cell in the battery pack
out or in to charge and discharge using MOSFETs. With minor modifications in the
proposed BMS, any cell in the battery pack can be disconnected from the battery pack
without affecting the normal operation of the battery pack. In the case of a failure of a
cell, the cell can be disconnected from the battery pack. Therefore the battery continues
to operate normally even when individual cells in the battery pack fail assuming that the
149
application for which the pack is being used can work with reduced voltage, making our
proposed BMS a one that is accommodating to failures.
Modifications are required because for the existing system the Slave PIC
monitoring a cell loses its power when that cell fails. The Slave PIC requires power to
control the MOSFETs Q(2i+1) and Q(2i) to switch the failed cell out from the battery pack.
Power could be provided to the Slave PIC using an energy storage device like a capacitor
to remedy this shortcoming.
Though the proposed BMS was tested on a battery pack of six lithium-ion cells, it
can be generalized and used for a battery pack of any size and any cell chemistry. The
state of charge observer can be implemented by obtaining the battery model for specific
cells. The battery model equations have then to be implemented in a fixed-point
processor. Different cell chemistries have different maximum and minimum voltages.
These voltages have to be determined and the software has to be changed so that the cells
are charged and discharged to appropriate maximum and minimum voltages respectively.
The temperature model used in this thesis for lithium-ion cells does not clearly
predict the actual temperature. Adjusting the temperature model and correcting the
predicted stored charge on the basis of temperature is left for future work. Doing this
would further improve the accuracy of the corrected stored charge.
The stored charge in the cell depends on the aging of the cell. The stored charge
can also be corrected to take the aging of the cell into account by running the BMS for
several cycles (at least 100 cycles). In each cycle, the constants in the battery model can
be corrected based on the error voltage. Thus, the battery model would change over time
150
in a way that reflects the aging of the cell. This would help to improve the accuracy of the
corrected stored charge.
151
REFERENCES
[1]
C. Samuel Levy and Per Bro, “Battery Hazards and Accident Prevention,”
Plenum Press, NY, USA, 1994.
[2]
V.L. Teofilo, L.V. Merritt and R.P. Hollandsworth, “Advanced Lithium Ion
Battery Charger,” IEEE AES Systems Magazine, pp. 30-35, November 1997.
[3]
E. George Blomgren, “Current Status of Lithium Ion and Lithium Polymer
Secondary Batteries,” The Fifteenth Annual Battery Conference on Applications
and Advances, pp. 97-100, 2000.
[4]
Freedonia Group, Inc. www.freedoniagroup.com.
[5]
National Institute of Standards and Technology, Comparison of Battery
Technologies, http://www.atp.nist.gov/eao/wp05-01/append-4.htm.
[6]
BatteryUniversity.com,
“Is
Lithium-Ion
http://www.batteryuniversity.com/partone-5.htm.
[7]
N. H. Kutkut, “Prolong the life of series battery strings with individual battery
equalizers,” Electric & Hybrid Vehicle Technology International, pp. 116-121,
2000.
[8]
M.J. Isaacson, R.P. Hollandsworth, P.J. Giampaoli, F.A. Linkowsky, A. Salim,
and V.L. Teofilo, “Advanced Lithium Ion Battery Charger,” The Fifteenth Annual
IEEE Battery Conference on Applications and Advances, pp. 193-198, January
2000.
[9]
W.F. Bentley, “Cell Balancing Considerations for Lithium-Ion Battery Systems,”
Twelfth Annual IEEE Battery Conference on Applications and Advances, pp. 223226, January 1997.
152
the
Ideal
Battery?,”
[10]
R. Manfred Laidig and W. Job Wurst, “Technology Implementation of Stationary
Battery Failure Prediction,” Proceedings of the Ninth Annual IEEE Battery
Conference on Applications and Advances, pp. 168-172, January 1994.
[11]
Mpower Solutions Ltd., Copyright Woodlands Communication Ltd., Battery
Management System, http://www.mpoweruk.com/bms.htm.
[12]
Thomas Stuart, Fang Fang, Xiaopeng Wang, Cyrus Ashtiani, and Ahmad Pesaran,
“A Modular Battery Management System for HEVs,” National Renewable
Energy Laboratory, June 2002.
[13]
Dӧrffel. Dennis, “Energy Management of Hybrid Electric Vehicles:
Miphil/PhD project 9 months report,” Dissertation Report, University of South
Hampton
School
of
Eng.
Sciences,
December
2006.
<http://eprints.soton.ac.uk/822/01/9months_report.pdf>.
[14]
M. Amir Rahimi, “A Lithium-Ion Battery Charger for Charging up to Eight
Cells,” IEEE Conference on Vehicle Power and Propulsion, pp. 131-135,
September 2005.
[15]
M.F.M Elias, “Lithium-Ion Battery Charger for High Energy Application,” IEEE
National Power and Energy Conference, pp. 283-288, 2003.
[16]
Pascual, Cesar and T. Philip Krein. “Switched Capacitor System for Automatic
Series Batttery Equalization,” IEEE Applied Power Electronics Conference,
Twelfth Annual, Volume 2, pp. 848-854, February 1997.
[17]
Yuang-Shung Lee, and Ming-Wing Cheng, “Intelligent Control Battery
Equalization for Series Connected Lithium-Ion Battery Strings,” IEEE
Transactions on Industrial Electronics, Volume 52, pp. 1297-1307, October 2005.
[18]
N. H. Kutkut, and M. Deepak Divan, “Dynamic Equalization Techniques for
Series Battery Stacks,” IEEE Telecommunications Energy Conference, pp. 514521, October 1996.
[19]
N. H. Kutkut, and H. L. N. Wiegman, Deepak M. Divan, D.W. Novotny, “Charge
Equalization for an Electric Vehicle Battery System,” IEEE Transactions on
Aerospace and Electronic Systems, pp. 235-246, January 1998.
153
[20]
L. Plett Gregory, “Extended Kalman Filtering for Battery Management Systems of
LiPBbased HEV Battery Packs, Part 2: Modeling and Identification,” Journal of
Power Sources, vol.134, no. 2, pp. 262-276, August 2004.
[21]
D.Brendt, “Maintenance-Free Batteries Based on Aqueous Electrolyte,”
A Handbook of Battery Technology, Baldock, Hertfordshire, England: Research
Studies Press, Third Edition.
[22]
A. Affanni, A. Bellini, C. Concari, G. Franceschini, E. Lorenzani, and C. Tassoni,
“EV battery state of charge: Neural Network Based Estimation,” IEEE Electric
Machines and Drivers Conference, Volume 2, pp. 684-688, June 2003.
[23]
Chester
Simpson,
National
Semiconductor
http://www.national.com/appinfo/power/files/f7.pdf.
[24]
Tom Hartley and G. Anthony Jannette, “A First Principles Model for Nickel
Hydrogen Batteries,” American Institute of Aeronautics and Astronautics’ 3rd
International Energy Conversion Engineering Conference, August 2005, San
Francisco, CA.
[25]
Datasheet for dspic30f4013, Microchip, http://www1.microchip.com/downloads/
en/devicedoc/70138.pdf.
[26]
I. Navot, “A Simple Proof of Horners Method,” IEEE Transactions on Automatic
Control, Volume 8, no.1, pp. 76-77, January 1963.
154
Battery
Charging,