LEAD-ACID BATTERY AGING AND STATE OF HEALTH DIAGNOSIS
A Thesis
Presented in Partial Fulfillment of the Requirements for
the Degree Master of Science in the
Graduate School of The Ohio State University
By
Christopher Suozzo, B.S.E.E.
*****
The Ohio State University
2008
Dissertation Committee:
Approved by
Professor Giorgio Rizzoni, Advisor
Professor Yann Guezennec
Adviser
Graduate Program in Electrical Engineering
ii
ABSTRACT
The lead-acid battery has served as the standard electrical energy storage device
in vehicles for nearly 100 years. In this time, its role has expanded well beyond its
original duty of engine cranking to now include supplementing the alternator’s power
output during load transients to meet the needs of a growing vehicle electrical system. As
more safety-critical systems previously operated by cable or hydraulics become
electrified, it has become increasingly important to ascertain the battery’s ability to
provide power and energy. A fundamental understanding of the underlying chemical
processes governing battery performance degradation and eventual failure can give rise to
diagnostic techniques that may be used to determine the battery’s state of health. The
goal of this thesis is to propose new battery monitoring and state of health evaluation
algorithms that may be run onboard a vehicle for the purpose of establishing battery
electrical performance characteristics.
iii
Dedicated to Mom and Dad
iv
ACKNOWLEDGMENTS
I would first like to thank my advisor, Professor Giorgio Rizzoni, for giving me the
opportunity to participate in this project, and for being a consummate source of
invaluable feedback and guidance that has both catalyzed many of the ideas developed in
this thesis and transformed me into a better engineer. I’d also like to thank The Ohio
State University’s Center for Automotive Research (CAR) for its GATE fellowship
program that has allowed me to maintain a focus on academic growth and research
experience throughout my career as a graduate student. Many thanks also go to Nick
Picciano for his ideas and laboratory experience, and for his masterful administration of
the lead-acid battery aging experiments, without which this thesis would not have been
possible. Thanks to Dr. Simona Onori for her management, support and thoughts that
have helped guide the direction of this project. I would also like to extend my gratitude
to Dr. Mutasim Salman from General Motors for awarding funding for this project, and
for his sharp perception that has led to a more robust battery diagnostic and prognostic
strategy. Professor Emeritus Larry Anderson is thanked for sharing his keen insight on
the nature of electrochemical reactions in lead-acid batteries. Thanks to Don Butler for
his role in managing this project with GM, and providing a levity that has made the
experience all the more enjoyable. I would also like to thank Professor Yann Guezennec,
though I regret that our interactions were few, each was profoundly insightful. Weiwu
Li, Lorenzo Serrao, Annalisa Scacchioli, and all that worked on battery modeling and
prognosis at CAR before me are thanked for building the foundation from which this
v
thesis was constructed. Thanks to Ben Yurkovich, Jim Shively, John Neal and all those
who designed and built the battery test benches.
Finally, I would like to extend my heartfelt thanks to my entire family for all their
positive support over these seven long years of higher education. All of the academic
accomplishments and success I have enjoyed in this time would not have been possible
without them.
vi
VITA
February 21, 1983 …………………………….…
Born – Albany, New York
May, 2006 ………………………………………...
B.S. Electrical Engineering,
B.A. Physics,
Alfred University
January, 2007 to present……………………….…
Graduate Research Fellow,
The Ohio State University
Center for Automotive Research
FIELDS OF STUDY
Major Field: Electrical Engineering
vii
TABLE OF CONTENTS
Page
Abstract…………………………………………………...…...............................…..…...iii
Dedication………………………………………..……....…………………….………....iv
Acknowledgments………………………………..…..……………...................................v
Vita……………………………………………………………………………………....vii
List of Tables…………………………………….…..…………………………………...xi
List of Figures……………………………………..…..……..………………..…………xii
Chapters:
1 BACKGROUND..........................................................................................................1
1.1 Introduction .............................................................................................................................. 1
1.2 History ...................................................................................................................................... 1
1.3 Battery Terminology................................................................................................................ 6
1.4 General Battery Background................................................................................................... 8
1.5 Conclusion.............................................................................................................................. 22
2 BATTERY MODELING............................................................................................23
2.1 Introduction ............................................................................................................................ 23
2.2 Basic Electrical Model .......................................................................................................... 23
viii
2.3 Dynamic battery models........................................................................................................ 28
2.4 Conclusion.............................................................................................................................. 35
3 AGING MECHANISMS............................................................................................36
3.1 Introduction ............................................................................................................................ 36
3.2 Background ............................................................................................................................ 36
3.3 Hard Sulfation ........................................................................................................................ 38
3.4 Positive Grid Corrosion......................................................................................................... 43
3.5 Positive Active Mass Degradation........................................................................................ 47
3.6 VRLA Battery Aging Experiments Conducted at CAR...................................................... 50
4 BATTERY DIAGNOSTIC TECHNIQUES................................................................53
4.1 Introduction ............................................................................................................................ 53
4.2 Automotive Battery Performance Specifications ................................................................ 53
4.3 Cranking Resistance Tests .................................................................................................... 54
4.4 Capacity Tests ........................................................................................................................ 58
4.5 Analysis of Aging Data ......................................................................................................... 66
4.5.1 Energy Cycle Data ........................................................................................................................... 67
4.5.2 Power Cycle Data............................................................................................................................. 75
4.6 Dynamic Response Test ........................................................................................................ 89
4.7 Conclusion............................................................................................................................ 102
5 LEAD-ACID BATTERY STATE OF HEALTH ESTIMATION ALGORITHM......104
5.1 Introduction .......................................................................................................................... 104
5.2 Battery Mapping .................................................................................................................. 104
5.3 Diagnostic Tests................................................................................................................... 108
5.4 State of Health Calculations................................................................................................ 110
ix
5.5 Health Assessment............................................................................................................... 111
5.6 Conclusions and Future Work............................................................................................. 112
Bibliography……………………………………………………………………………113
Appendix………………………………………………………………………………..115
x
LIST OF TABLES
Table
Page
Table 4. 1: Estimated parameters for battery N1............................................................................................... 96
Table 4. 2: Estimated parameters for battery N2............................................................................................... 97
Table 4. 3: Parameters estimated for battery N4 at various SOC................................................................... 100
Table 5. 1: Battery rested open circuit voltage vs Amp-hours discharged .................................................... 105
xi
LIST OF FIGURES
Figure
Page
Figure 1. 1: Simplified Diagram of Vehicle Electrical System [1] .....................................................................2
Figure 1. 2: Onboard electrical generation requirements for (a) luxury car, (b) intermediate-size car [2] ......3
Figure 1. 3: Basic Battery Cell Configuration ......................................................................................................8
Figure 1. 4: Diagram of ion and electron flows in a discharging lead-acid cell.............................................. 11
Figure 1. 5: Diagram of Lead Acid Discharge Reactions at NAM [5] ............................................................ 11
Figure 1. 6: Schematic of basic structural elements of PAM [6] ..................................................................... 13
Figure 1. 7: Scanning electron micrograph (SEM) of formed PAM [12]........................................................ 13
Figure 1. 8: Top view of NAM utilization under (a) low discharge rate, (b) high discharge rate [7] ........... 15
Figure 1. 9: AGM separator SEM image [8] ..................................................................................................... 18
Figure 1. 10: Diagram of AGM Separator gas channels [1]............................................................................ 18
Figure 1. 11: Overpotential at negative and positive electrodes during constant current charging at high
SOC [9] ...................................................................................................................................................... 19
Figure 1. 12: Typical Automotive Lead-Acid Battery Architectures, (a) Prismatic [2], (b) Spirally wound
[10] ............................................................................................................................................................. 21
xii
Figure 2. 1: Basic Battery Electrical models [11] ............................................................................................. 24
Figure 2. 2: Open-circuit voltage settling: battery (a) current, and (b) voltage............................................... 25
Figure 2. 3: VOC (E0) vs SOC map for 20°C ................................................................................................... 26
Figure 2. 4: Measured vs Static Model Response: (a) load, (b) voltage .......................................................... 27
Figure 2. 5: General form of Randle battery model .......................................................................................... 29
Figure 2. 6: Measured vs First Order Randle Model Response........................................................................ 30
Figure 2. 7: Measured vs Second Order Randle Model Response................................................................... 31
Figure 2. 8: Randle First order battery electrical model ................................................................................... 32
Figure 3. 1: Diagram of VRLA components ..................................................................................................... 37
Figure 3. 2: Large Lead-sulfate crystals on NAM surface [15]........................................................................ 39
Figure 3. 3: Atomic Force Microscope (AFM) Image of lead-sulfate crystal formed (a) immediately after
discharge, and (b) after open-circuit stand [18]....................................................................................... 40
Figure 3. 4: Diagram of PbSO4 formation [18] ................................................................................................. 41
Figure 3. 5: Changes in maximum SOC for a battery with 18% sulfation ...................................................... 42
Figure 3. 6: Corrosion reaction during charging [16] ....................................................................................... 44
Figure 3. 7: Corrosion during open circuit conditions [16] .............................................................................. 45
Figure 3. 8: Corroded positive plate of a starter battery after 5 years of service [16] .................................... 46
xiii
Figure 3. 9: SEM images of PAM when: (a) new (α & β ), and (b) after failure ( β only) [12].................... 48
Figure 3. 10: Positive Grid with substantial loss of active mass (PbO2) after serving 6 months as a starter
battery in a city bus [16] ........................................................................................................................... 48
Figure 3. 11: Energy Cycle Load Profile ........................................................................................................... 51
Figure 3. 12: Power Cycle Load Profile ............................................................................................................ 52
Figure 4. 1: Voltage and Current during Engine Cranking............................................................................... 55
Figure 4. 2: Cranking Resistance of N1 and N2 vs Total Amp-hours ............................................................. 57
Figure 4. 3: Discharge curves of a 12V, 80Ah battery at various discharge rates [1] .................................... 60
Figure 4. 4: Voltage vs Capacity curves at 50A and 5A discharge rates [26]................................................. 61
Figure 4. 5: Initial Capacity Tests for Batteries N1 and N2 ............................................................................. 62
Figure 4. 6: Voltage vs Capacity of N1 for different cycles............................................................................. 63
Figure 4. 7: Voltage vs Capacity of N2 for different cycles............................................................................. 63
Figure 4. 8: Capacity of N1 and N2 vs Total Amp-hours................................................................................. 65
Figure 4. 9Figure 4.9: VRLA Cell Electrode Potentials during discharge and charge [23] ........................... 66
Figure 4. 10: Energy Cycles before and after Capacity Test 6......................................................................... 68
Figure 4. 11: Energy Cycles before and after Capacity Test 13....................................................................... 70
Figure 4. 12: Typical ranges of voltage regulation for alternators [1] ............................................................. 71
xiv
Figure 4. 13: Energy Cycle Voltage Response on Cycles after Capacity Tests.............................................. 72
Figure 4. 14: Analysis of Energy Cycle 84........................................................................................................ 74
Figure 4. 15: Remaining Discharge Capacity vs Voltage drop every 100sec ................................................. 74
Figure 4. 16: Discharge voltage and current of power cycle before capacity test 3 ....................................... 76
Figure 4. 17: Power output before capacity test 3 ............................................................................................. 77
Figure 4. 18: Discharge voltage and current of power cycle after capacity test 3 .......................................... 77
Figure 4. 19: Power output after capacity test 3 ................................................................................................ 78
Figure 4. 20: Discharge voltage and current of power cycle before capacity test 4 ....................................... 78
Figure 4. 21: Power output before capacity test 4 ............................................................................................. 79
Figure 4. 22: Discharge voltage and current of power cycle after capacity test 4 .......................................... 79
Figure 4. 23: Power output after capacity test 4 ................................................................................................ 80
Figure 4. 24: 5sec average differential resistance over pulse 1 ........................................................................ 81
Figure 4. 25: 300msec average differential resistance over pulse 1................................................................. 82
Figure 4. 26: Voltage during charging in cycles 33 and 37 .............................................................................. 83
Figure 4. 27: Discharge Voltage and Current of Power Cycle 151.................................................................. 84
Figure 4. 28: Power output of Power Cycle 151 ............................................................................................... 85
Figure 4. 29: Charging voltage of Power Cycle 151......................................................................................... 85
Figure 4. 30: Discharge Voltage and Current of Power Cycle 152.................................................................. 86
xv
Figure 4. 31: Power output of Power Cycle 152 ............................................................................................... 86
Figure 4. 32: Charging Voltage of Power Cycle 152........................................................................................ 87
Figure 4. 33: Discharge voltage and current for Power Cycle 158 .................................................................. 88
Figure 4. 34: Power output for Power Cycle 158.............................................................................................. 88
Figure 4. 35: Voltage ‘Heel’ in step response ................................................................................................... 91
Figure 4. 36: Current and Voltage Captured during Dynamic Response Test ................................................ 92
Figure 4. 37: Filtered Voltage and Current Data from Figure 4.36 ................................................................. 93
Figure 4. 38: Process of Parameter Estimation.................................................................................................. 94
Figure 4. 39: Comparison between measured and modeled voltage................................................................ 95
Figure 4. 40: Parameter R0 estimates for N1 and N2 vs Capacity................................................................... 97
Figure 4. 41: Parameter R1 estimates for N1 and N2 vs Capacity................................................................... 98
Figure 4. 42: Parameter C1 estimates for N1 and N2 vs Capacity................................................................... 98
Figure 4. 43: Parameter Tau estimates for N1 and N2 vs Capacity ................................................................. 99
Figure 4. 44: Parameter C1 estimates for N4 vs SOC..................................................................................... 101
Figure 4. 45: Parameter Tau estimates for N4 vs SOC ................................................................................... 101
Figure 5. 1: Battery rested open circuit voltage vs Amp-hours discharged................................................... 106
Figure 5. 2: Remaining amp-hours vs change in voltage over 100sec period............................................... 107
xvi
Figure 5. 3: Step response test .......................................................................................................................... 109
xvii
1 BACKGROUND
1.1 Introduction
This chapter presents a background on the evolving role of the lead-acid battery within
vehicle electrical systems, and identifies the need for advanced onboard battery
monitoring and diagnosis strategies. A detailed examination of battery composition and
electrochemistry is also provided to reveal the underlying mechanisms responsible for a
battery’s dynamic electrical characteristics.
An adequate knowledge of these
fundamental properties is important when developing battery models, and is essential to
understanding the impact of different aging processes and how they may be detected.
1.2 History
The vehicular application of lead-acid batteries can be traced all the way back to the
popularization of the automobile itself in the early 1900’s. The inclusion of a batterydriven electric starter motor that eliminated the need to hank-crank engines helped
catalyze the widespread adoption of automobiles throughout the world. The function of
automotive lead-acid batteries for the next 30 years would be restricted primarily to
engine starting, ignition and vehicle lighting. Belt-driven DC generators were then used
to recharge the battery and supply power to electric loads during engine operation. The
1
addition of more powerful loads in the 1960s led most auto manufacturers to adopt a 14V
vehicle electrical system and replace DC generators in favor of more powerful 3-phase
rectified alternators. Today, the battery acts as a buffer between the alternator and the
vehicle electrical system when the engine is on. Occasionally, when the electrical power
required by the system exceeds what the alternator is able to provide, the battery will
discharge to meet these short-term demands. However, the battery’s primary duties have
remained largely unchanged: provide power for engine cranking and electrical energy
while the engine is off. [1]
Figure 1. 1: Simplified Diagram of Vehicle Electrical System [1]
The past 50 years has seen the continued expansion of consumers within the vehicle
electrical system, forcing improvements in both alternator and battery technology.
2
Figure 1. 2: Onboard electrical generation requirements for (a) luxury car, (b)
intermediate-size car [2]
Systems once controlled exclusively by cable or hydraulics, like throttle and braking, are
rapidly being supplanted by electromechanical actuators in an effort to improve vehicle
responsiveness, efficiency and feel. The increased demand of electric power has often
forced the battery to assume a more active role as a supply during engine-on operation.
Furthermore, the shift in control of some safety-critical systems from the driver to the
vehicle management system is making the areas of battery and alternator monitoring a
high priority for vehicle designers.
For their part, lead-acid battery manufacturers have developed better materials and
manufacturing processes that have resulted in increased power output, capacity and
3
cycle-life. However, the most notable change in automotive batteries has occurred in just
the last 15 years, with the transition from flooded (vented) to valve-regulated (‘sealed’)
designs eliminating the need to periodically add water to the battery electrolyte, making
them essentially ‘maintenance free’. Despite all the incremental progress, the passive
nature of the traditional automotive battery has led the industry to focus more on cost
reductions than radical design changes. In the present climate of 100,000 mile vehicle
warranties and increased demand of onboard electrical power, significant challenges lie
ahead for battery manufacturers that will necessitate a more aggressive approach to
innovation.
The quest for improved vehicle fuel economy serves as another driver for a more
powerful and fully utilized automotive battery. Skyrocketing fuel prices and an increased
awareness about the impact of global warming have caused the United States Congress to
raise the corporate average fuel economy standard (CAFE) for passenger vehicles from
about 25 miles per gallon to 35 mpg by the year 2020. To avoid the stiff fines associated
with failing to meet this requirement, auto manufacturers are spending billions of dollars
searching for ways to improve vehicle fuel efficiency. One strategy employed on BMW
production vehicles, called ‘Intelligent Alternator Control’, essentially turns off the
alternator during engine operation, allowing the battery to act as the primary power
source for the entire vehicle electrical system. Alternator activation, and subsequent
battery charging, would take place primarily during vehicle braking or overrun and when
the battery’s state of charge drops below a predefined minimum threshold. The reduction
4
of parasitic engine loading during normal operation by implementing this technique
results in fuel economy improvements of approximately 4% [3].
More aggressive
improvements can be realized with the inevitable transition from the current 14V
electrical system to a higher voltage system (36-42V), which will result in less ohmic
losses in the distribution system and the electromechanical actuators themselves. The
additional electric power that could be provided by a 42V battery also allows for the
possibility of mild powertrain hybridization as well, enabling engine-turn off during idle
(start-stop) and more energy recuperation during braking (‘regen’) [1]. Lead-acid is
likely to remain the battery chemistry of choice for this new high-voltage system
configuration due to its superior cost advantage over other electrical energy storage
technologies.
In the near future, automotive lead-acid batteries will be required to maintain their power
and energy performance for longer periods despite their more active role as a supply in
the vehicle electrical system.
These challenges must be addressed not only by
improvements in battery design, but also through onboard control, monitoring and
diagnosis capabilities that simply do not exist in vehicles today.
5
1.3 Battery Terminology
Prior to a detailed treatment of battery components and characteristics, a basic overview
of terminology used to describe battery state or operation will be given in this section.
Capacity
Battery capacity simply refers to the total amount of charge that can be drawn from a
fully charged battery until it is depleted. The rated capacity of a battery is typically given
in units of amp-hours (Ah) for a specified temperature and discharge current. It is
important to note that the battery’s actual available capacity is highly dependent on these
conditions, and if the battery is discharged at a different current or temperature, the
effective capacity under these conditions will not be the same. The reasons for this are
explained later in this chapter. Furthermore, discharge currents for a particular battery
are often denoted in terms of the battery’s nominal Ah capacity (‘C’). For example, a
60Ah battery discharged at 3A is said to be discharged at the C/20 rate. The procedure
for capacity tests is given in Chapter 4.
State of Charge
A battery’s state of charge (SOC) denotes amount a battery has been discharged with
respect to its nominal capacity. A fully charged battery will therefore have an SOC of
100%, and a fully discharged battery will have an SOC of 0%. Knowledge of a battery’s
SOC is important for a number of reasons. From a modeling perspective, the battery’s
dynamic characteristics change with SOC.
From a diagnostics perspective, more
irreversible damage can be incurred if a battery is operated or stored at low SOC.
6
Aging
Aging refers to the gradual loss of a battery’s rated electrical performance. After a
battery is produced it undergoes a number of irreversible chemical reactions that cause its
internal resistance to increase and its rated capacity to decrease. There are a number of
different physical and chemical processes that can be responsible for aging, however,
battery usage and storage conditions will largely determine the rate of aging and the
dominant aging mechanism.
State of Health and End of Life
In general, there is no universal definition of battery state of health (SOH), and its
meaning is largely application-dependant. However, in all cases battery SOH quantifies
the extent a battery’s performance has been reduced, and it is usually expressed in terms
of a percentage. A new battery would therefore have a SOH of 100%, and a battery that
has reached its minimum level of acceptable performance, or end-of-life (EOL), could be
said to have a SOH of 0%. In stationary and hybrid-vehicle applications capacity is often
the primary metric of interest, and so SOH will refer to the amount of capacity loss a
battery has experienced and EOL will identify the minimum allowable capacity before
the battery is said to have failed. For starter batteries where peak power output is the
most important battery characteristic, SOH could be defined in terms of increases in
internal resistance.
7
1.4 General Battery Background
Despite the criticality of batteries to modern electrical devices and systems, there is
minimal formal treatment of battery technology and operation within the electrical
engineering academic community. This section seeks to go beyond the traditional ‘black
box’ representation of batteries, and to establish a more complete understanding of the
underlying chemical processes responsible for the dynamic electrical behavior observed
during charge and discharge operation.
The basic functionality of a battery can be described by the reactions that occur within
the battery’s cells. The arrangement of a cell’s components can be seen in Figure 1.3.
Figure 1. 3: Basic Battery Cell Configuration
8
A battery cell stores electrochemical energy in the active materials bonded to its metallic
positive and negative electrode grids. When a conductive external circuit is connected to
the electrodes, electrons are transferred from one active material to the other as their
chemical compositions change. At the same time, the electrolyte also participates in the
reaction by shuttling ions between active materials. These electrochemical reactions
allow the battery to provide electrical energy to a connected load during discharge, or
accept electrical energy from a connected source during charging.
In the case of lead-acid batteries, the positive active material (PAM) is a paste of leaddioxide (PbO2), the negative active material (NAM) is a porous sponge lead (Pb), and the
electrolyte is an aqueous solution of sulfuric acid (H2SO4). The chemical reactions that
occur between these materials during discharge can be summarized as follows:
Sulfuric Acid Hydration :
(1)
H 2SO 4 + H 2O ! HSO 4 - + H 3O +
Discharge RX at negative electrode :
Pb + HSO 4 - ! ! !!" Pb 2+ + SO 4 2# + 2e # + H +
1442443
Dissolution
(2)
$ Deposition
PbSO 4
Discharge RX at positive electrode :
Dissolution
PbO 2 + HSO 4 - + 2e - + 3H + ! ! !!" Pb 2+ + SO 4 2# + 2H 2O
1442443
(3)
Overall RX :
Pb + PbO 2 + 2H 2SO 4 ! 2PbSO 4 + 2H 2O
(4)
$ Deposition
PbSO 4
9
The first reaction identifies what happens to the dilute electrolytic solution of sulfuric
acid and water during battery assembly/production. The highly dipolar nature of water
enables it to break off one of the sulfuric acid’s H+ ions, causing it to transform into H3O+
or hydronium, and leaving an ionic form of the sulfuric acid (HSO4-). This hydration
reaction also occurs at the negative electrode during discharge. As sponge lead reacts
with sulfuric acid ions to form lead sulfate (PbSO4), water molecules in the vicinity
capture the remaining highly reactive H+ ions to form hydronium [4]. Hydronium acts as
carrier for H+ ions, which are consumed during both charge and discharge reactions. The
electrons liberated in the NAM discharge reaction pass through the negative electrode
grid and externally connected circuit to arrive at the positive electrode grid where they
react with the positive active mass and electrolyte. The PAM combines with sulfate ions
from the incoming HSO4-, and hydrogen ions from the incoming H3O+ and electrons to
form PbSO4 and water.
The entire process at either electrode begins with the
electrochemical dissolution reaction, which involves electron transfer, followed by the
precipitation of solid lead-sulfate.
10
Figure 1. 4: Diagram of ion and electron flows in a discharging lead-acid cell
Figure 1. 5: Diagram of Lead Acid Discharge Reactions at NAM [5]
11
The overall discharge reaction creates non-conducting solid PbSO4 on both electrodes by
breaking down sulfuric acid and producing water at the positive electrode, making the
electrolyte much more dilute than it was originally (particularly around the positive
electrode). As one might imagine, as the discharge reactions proceed and the SOC is
depleted, the abundance of primary reactants (Pb, PbO2 and HSO4-) dwindles, causing an
increase in the battery’s internal resistance that is a result of increased current densities
within the active mass and decreased active surface area.
Knowing the reactions and reactants that must be present at each active mass surface for
current to flow is very important in understanding the dependence of battery performance
on operating conditions. Furthermore, the morphological structure and availability of the
active materials themselves will also play a large role in battery electrical behavior.
The active materials are not simply thin coatings on the conductive electrode grids, but
they are actually complex, porous structures with a thickness that is designed by the
manufacturer to suit the application of the battery being produced. Adding thickness to
the active material can have the beneficial effects of increasing capacity and cycle-life by
virtue of the fact that there are now more reactants in the battery.
12
Figure 1. 6: Schematic of basic structural elements of PAM [6]
Figure 1. 7: Scanning electron micrograph (SEM) of formed PAM [12]
The active material structure, and its associated conductivity, can have a profound impact
on battery parameters like capacity and resistance. Certain additives to the sponge lead
and lead dioxide pastes can create a more conductive skeletal structure for these active
13
materials, increasing the efficiency of charge and discharge. Active mass pore size and
abundance impact both active surface area and electrolyte diffusion rate into the active
mass interior. This, in turn, affects the usability of the interior region during charge and
discharge, and thus the battery’s effective capacity. Curing and formation during battery
manufacture and cycling during battery use all contribute to the evolution of the active
material’s crystallographic structure [1].
As was stated in the previous section, battery parameters like capacity and internal
resistance will be highly dependent on the operating conditions of the battery at the time
of the test. For example, higher temperatures have the effect of increasing ion energy and
mobility, allowing a greater surface area to participate in reactions and thus lowering one
aspect of the battery’s internal resistance. Current magnitude has the effect of changing
the distribution of the active materials that are utilized in reaction. High discharge
currents can require more electrochemical reactions than the interior active material is
able to support due to the low rate of HSO4- diffusion. This causes a higher percentage of
the reactions to take place at the surface where the active material directly contacts the
bulk electrolyte [6].
14
(a)
(b)
Figure 1. 8: Top view of NAM utilization under (a) low discharge rate, (b) high
discharge rate [7]
The formation of lead-sulfate on the surface of the active material during discharge can
also hinder further HSO4- diffusion due to the large volume of PbSO4 particles relative to
the active material they replace (pore clogging). Despite the large number of factors that
determine discharge reaction dynamics, this operational regime is substantially less
complicated than the charging process of valve-regulated lead-acid batteries.
Unlike discharge chemical reactions, the charging of VRLA batteries consists of both
primary reactions and secondary reactions. These secondary reactions consume some of
the charging current while not contributing to the actual transformation of lead-sulfate
back into the active materials, and thus decrease the charging efficiency. Like the section
on discharge processes, the treatment of battery charging will be limited to the extent that
15
we use this information for diagnostic purposes so as not to overwhelm the reader. The
chemical reactions that take place during charging can be seen in equations (5)-(10)
below.
Primary charge RX at negative electrode :
Dissolution
PbSO 4 ! ! !!" Pb 2+ + SO 4 2#
(5)
Pb2+ + SO 4 2# + H + + 2e # " Pb + HSO 4 Primary charge RX at positive electrode :
Dissolution
PbSO 4 ! ! !!" Pb 2+ + SO 4 2#
(6)
Pb2+ + SO 4 2# + 2H 2O " PbO 2 + HSO 4 - + 2e - + 3H +
Overall Primary RX :
2PbSO 4 + 2H 2O ! Pb + PbO 2 + 2H 2SO 4
Oxygen evolution RX at positive electrode :
2H 2O ! O 2 + 4H + + 4e Oxygen recombination RX at negative electrode :
O 2 + 4H + + 4e - ! 2H 2O
Hydrogen evolution RX at negative electrode :
2H + + 2e - ! 2H 2
(7)
(8)
(9)
(10)
The charge reactions taking place at the negative and positive active materials in (5) and
(6) are simply the reverse of discharge equations (2) and (3).
Each start with a
dissolution reaction of solid lead-sulfate into ionic lead and sulfate. At the PAM, these
16
ions react with nearby water molecules to reform lead-dioxide and sulfuric acid. In this
deposition process, the 2 electrons produced are transported through the external circuit
to the NAM lead-sulfate sites. These locations are then transformed back into sponge
lead and sulfuric acid via dissolution and deposition reactions.
The oxygen
recombination reaction (9) that takes place at the negative electrode is what allows
VRLA (‘sealed’) batteries to be ‘maintenance free’ unlike their flooded predecessors
which vented oxygen and hydrogen gas during the recharge process and thus required
the periodic addition of water to the electrolyte.
The onset of gas-producing secondary reactions (8) and (10) occur when the supplied
charging current cannot be supported due to the shrinking availability of water or H+ ions
within the active material’s interior. The NAM structure typically is more open and
porous, facilitating more rapid acid and water transport than in the PAM. For this reason
oxygen evolution occurs first at the PAM, typically at ~70-80% SOC, followed by
hydrogen evolution much later (if at all) above 90% SOC. [1]
The absorptive glass-mat (AGM) separator is a porous sheet of insulating glass fibers that
immobilizes the liquid electrolyte and isolates the two active materials from one another.
This essential component of a VRLA battery enables the efficient transport of oxygen
from the PAM to the NAM by way of gas channels, thus allowing recombination to take
place at the NAM. These channels allow oxygen diffusion to take place at rates 104 times
17
greater than that in liquid electrolyte, and form naturally as a result of float charge or
cycling [1].
Figure 1. 9: AGM separator SEM image [8]
Figure 1. 10: Diagram of AGM Separator gas channels [1]
18
The kinetics of oxygen reduction are quite fast, and this enables the overpotential at the
negative electrode to remain low [9]. This region of charging corresponds to domain I in
Figure 1.11.
Figure 1. 11: Overpotential at negative and positive electrodes during constant
current charging at high SOC [9]
However, one result of the recombination reaction is the formation of a thin film of water
on top of the NAM near the gas channel outlet. The thickness of this film limits the rate
of recombination due to oxygen’s slow diffusion in liquids.
If the rate of oxygen
production at the PAM (controlled by the constant current charging rate), exceeds what
can be reduced at the NAM, an overpotential will be developed at the negative electrode.
This transition can be observed as a steep increase in cell voltage, corresponding to
domain II in Figure 1.11.
Hydrogen evolution (10) takes place when the negative
19
electrode overpotential exceeds a value that is determined by the NAM chemical
composition. The H2 gas formed in this reaction will quickly diffuse to the top of the
battery, and will not recombine at the PAM. This causes the battery’s internal pressure to
increase until the safety valve at the top of the battery opens to prevent case deformation
or destruction (the ‘valve’ in a VRLA).
Measurements of voltage during charge, discharge, or open-circuit stand can be used to
help ascertain a battery’s SOH or SOC. The open-circuit voltage that exists between the
positive and negative cell electrodes is dependent on cell temperature and the chemicals
that comprise the active materials and electrolyte. For a lead-acid cell, this relationship
can be approximately quantified by the Nernst equation [4].
E = E0 +
RT ! aH SO $
ln
F #" aH O &%
2
(11)
4
2
In the Nernst equation (11), E0 is a constant due to the potential difference between the
active materials, T is the cell temperature, R is the universal gas constant, aH
2
SO 4
is the
activity of the sulfuric acid in the electrolyte and aH O is the activity of the water in the
2
electrolyte. The chemical ‘activity’ can be approximated by concentrations. With a
known battery chemistry and temperature, an open-circuit voltage measurement may
therefore serve as an indicator of electrolyte ion concentration. In the case of a lead-acid
cell, the acid in the electrolyte is actually broken down during discharge.
By
transforming sulfuric acid into lead-sulfate and water, the electrolyte becomes diluted as
20
the SOC is depleted. This results in a nearly linear relationship between rested opencircuit voltage and battery SOC for a given temperature. More on this topic is revealed in
the next chapter on battery modeling.
Nominally, the open circuit voltage of a lead-acid cell is approximately 2V. An
automotive battery combines six of these cells together in series to obtain a 12V potential
difference between its terminals. The physical arrangement of cells within an automotive
battery depends on the manufacturer, but typically flat and ‘spirally wound’ geometries
are the most common.
(a)
(b)
Figure 1. 12: Typical Automotive Lead-Acid Battery Architectures, (a) Prismatic
[2], (b) Spirally wound [10]
21
1.5 Conclusion
This chapter provided the reader an introduction to automotive lead-acid battery history,
terminology and electrochemistry. This background establishes a motivation for battery
health monitoring, and an understanding of the principles governing battery dynamic
electrical behavior that will be important in identifying aging mechanisms and their
impact on battery performance.
22
2 BATTERY MODELING
2.1 Introduction
This chapter describes lead-acid battery modeling within the context of state of health
diagnosis.
Development of battery models that can predict the battery’s electrical
behavior while in use is important, because subtle changes in this behavior can indicate
the progression of battery aging and subsequent performance reduction.
Static and
dynamic model types will be examined and evaluated based on the tradeoff between
accuracy, ease of implementation, and potential usefulness in SOH monitoring.
Physicochemical significance will be assigned to battery parameters in order to
appreciate how these parameters will be changed due to different aging mechanisms.
2.2 Basic Electrical Model
Often times electrical circuit diagrams will represent batteries as ideal voltage or current
sources.
As has been demonstrated in the previous chapter, this is a drastically
oversimplified representation of a battery’s electrical characteristics, and consequently,
not very accurate. A battery’s terminal voltage is not a fixed value, and will change
based on the current magnitude, current directionality, SOC, SOH, temperature and a
number of other factors. The most simplistic electrical battery model should therefore
23
include both an internal ‘ideal’ DC voltage source, and a internal resistance (Thevenin
equivalent circuit).
Figure 2. 1: Basic Battery Electrical models [11]
The open-circuit voltage parameter E0 from the circuit model in Figure 2.1 can be related
to chemical phenomenon as described in the previous chapter. This potential difference
is particularly sensitive to changes in electrolyte acidity that occur after discharge (acid
consumption, decrease in SOC) and charge (acid production, increase in SOC). As
reactions proceed, the local acidity of the electrolyte will vary due to the slow ionic rate
of diffusion, especially near the active materials themselves [13]. For example, from the
set of discharge equations (1)-(4) we note that during discharge water is produced at the
positive electrode, causing the solution to be locally more dilute around this electrode.
Once the external circuit is disconnected, electrochemical reactions cease, and diffusion
allows the electrolyte to regain a more homogeneous mixture. This is the reason the
24
open-circuit voltage of a battery that has recently been discharged will be initially lower
than its final value.
(a)
(b)
Figure 2. 2: Open-circuit voltage settling: battery (a) current, and (b) voltage
A similar phenomenon occurs during charging, except now the electrolyte concentration
around the electrodes is more acidic than the bulk. Upon disconnection of the external
circuit, the open-circuit voltage will initially be higher than the final (rested) value.
Lead-acid batteries will typically arrive within ~50mV of their final settled voltage within
4 hours [27]. The modeled battery rested open-circuit voltage E0 can be thought of as
this steady-state or equilibrium value that changes with SOC and temperature.
E 0 = f (SOC,T)
(12)
25
Lookup tables of E0 vs SOC can be found at different temperatures for a new battery,
allowing a simple measurement of a battery’s rested open-circuit voltage to reveal the
battery’s SOC. It should be noted that these curves only truly represent the battery’s
actual SOC when it has not succumbed to capacity loss via aging. More on this will be
revealed in the next chapter on aging.
Figure 2. 3: VOC (E0) vs SOC map for 20°C
A battery has internal resistance due to a number of factors that depend largely on battery
state and temperature, including: ohmic resistance due to the electrode grids and active
material skeletal structure, active material availability, electrolyte composition, ionic
mobility/diffusion rates, and secondary reactions. In the simplistic ‘static’ battery model
shown in Figure 2.1, all of these resistance terms are lumped into one parameter that is
26
valid under a certain set of operating conditions (SOC, T, etc). The general structure of
the battery electrical model uses current as the input and terminal voltage as the output.
The dynamic performance of this model in estimating the battery’s voltage response to a
step change in load is poor at best as seen in Figure 2.4. However, if the accuracy of the
model is only important for a small window of time under a given set of conditions, there
could be some value in this type of measurement from a diagnostics perspective.
(a)
(b)
Figure 2. 4: Measured vs Static Model Response: (a) load, (b) voltage
In the above example, the static battery model would be accurate in the range of thirty
seconds after the constant load is applied. In general, a differential resistance parameter
could be easily calculated from a simple Ohm’s Law calculation:
27
Rdiff =
!V
!I
(13)
This simplistic means of calculating an instantaneous or ‘differential’ internal resistance
is not uncommon in battery state estimation algorithms and management schemes [1]. If
these same operating conditions (SOC, T, I) are frequently encountered throughout the
life of the battery, changes in this parameter could be used to identify battery
performance degradation.
2.3 Dynamic battery models
To obtain an electrical model that accurately reproduces the battery’s voltage response
over time, a dynamic model is needed. Expanding from the very basic static circuit
model developed in the previous section is the Randle electrical model, which adds n sets
of parallel R-C components as seen in Figure 2.5. The time constants associated with
these RC pairs help shape the battery’s dynamic voltage response.
28
Figure 2. 5: General form of Randle battery model
Ideally, the behavior of an electrochemical system can be described by a distributed
parameter model through partial differential equations. However, it is well understood
that lumped parameter models like the Randle can provide a good approximation to this
system. While increasing model complexity can more accurately replicate a plant’s
dynamics, the solution often loses its uniqueness, with multiple parameter sets in a high
order model producing a similar result. This is especially problematic in a diagnostics
application where system identification is used to identify parameter fluctuations that can
indicate SOH. Furthermore, assigning even a basic physical significance to parameters in
high-order models can be next to impossible. The step response performance of first and
second order Randle models can be seen in Figures 2.6 and 2.7.
29
Figure 2. 6: Measured vs First Order Randle Model Response
30
Figure 2. 7: Measured vs Second Order Randle Model Response
From Figures 2.6 and 2.7, it can be observed that both first and second order Randle
models produce excellent results: the RMS error between measured and modeled
voltages for each being 0.0043V and 0.0035V, respectively. It has been found that the
second order model typically adds a very small time-constant, on the order of 0.1sec, to
better approximate the faster dynamics in the response. However, the added accuracy
offered over this short time-period comes at the price of trying to estimate an additional
two parameter values. Estimating 5 parameter values for a system that can be almost
completely characterized in 3 often produces erroneous results.
In a diagnostics
application where parameter variations are the key to understanding system deterioration,
this compromise is unacceptable. Therefore, in this example a first order model would be
31
selected to represent a lead-acid battery for the purpose of state of health assessment.
The dynamic response test, and in particular the battery’s step response over periods
ranging from 5-40 seconds, is one of the diagnostic techniques that is discussed in
Chapter 4.
Figure 2. 8: Randle First order battery electrical model
Kirchhoff’s voltage and current laws define the behavior of the Randle model. The
equations for the first order model shown in Figure 2.8 are provided in (14) and (15).
dVc
1
1
=!
"Vc +
"I
dt
R1 " C1
C1
(14)
Vbatt = !Vc ! R0 " I + E 0
(15)
The current in this model is positive when leaving the positive electrode (discharging),
and negative when entering the positive electrode (charging). The physicochemical
significance of parameters R0, R1 and C1 can be broadly described from the
32
electrochemical background on lead-acid batteries developed in the previous chapter.
The resistance term R0 is often referred to as the ‘high-frequency’ resistance, as it is the
only impedance to current/ion flow that will be encountered under high frequency loads.
This resistance is always present, and can be attributed to ohmic losses in the electrode
grid, the conductive interface between the active material and grid (also known as the
corrosion layer) and active material skeletal structure. On the other end of the spectrum,
the steady-state resistance that is encountered under DC conditions after the initial
transient subsides is the sum of R0 and R1. Therefore, R1 can be thought of as an
additional equilibrium resistance associated with: charge-transfer processes, ionic
diffusion, electrolyte concentration gradients, and active material abundance.
Capacitance term C1 defines the onset of resistance term R1, and as such can be linked to
many of the same electrochemical processes.
Chemical and structural changes occurring within the battery during operation make
parameters R0, R1 and C1 of the proposed model functions of: current directionality, SOC,
temperature and SOH. Sensors can provide measurements for temperature and current,
but not SOC or SOH. As mentioned earlier in this chapter, an estimation of initial SOC
can be obtained from a rested open-circuit voltage measurement. Onboard a vehicle,
however, there are always parasitic loads active on key-off that provide ~0.3W [1]. This
current draw is on the order of tens of milliamps, and will therefore not have a major
impact on the electrolyte diffusion that causes voltage settling. If the pseudo ‘opencircuit’ voltage vs SOC maps are created under these loading conditions, this method can
33
still be applied onboard a vehicle to generate an initial estimation of battery SOC prior to
vehicle operation.
During vehicle operation and subsequent battery charge and
discharge, the measured battery current can be integrated to track changes from the initial
estimate.
SOC = SOC0 ! "SOC = SOC0 (Voc ) !
1
I # dt
Ah $
(16)
In this expression, Ah is the battery capacity and the measured battery current I is positive
during discharge. From the background on lead-acid battery operation provided in the
previous chapter, we can deduce that ∆SOC calculated via amp-hour counting in this
estimation algorithm will be more accurate at low SOC and during discharge operation.
This is due to the fact that battery charging at high SOC can involve a number of
secondary reactions that, while consuming current, do not increase the battery’s SOC.
For the purpose of diagnosis, a battery model with accuracy under all possible operating
conditions is not necessary. Instead, it is more important to identify model parameter
values at several frequently encountered operating points (defined by T, SOC and
sign(I)). As the battery ages, changes in these parameter values can provide an indication
of a battery’s SOH. More on lead-acid battery diagnostic techniques will be described in
Chapter 4.
34
2.4 Conclusion
The parameters that define the behavior of the battery models described in this chapter
play an important role in battery diagnosis. Throughout a battery’s life, these resistance
and capacitance values change as the battery’s performance deteriorates. State of health
estimation is therefore highly reliant on making the connection between the calculated
electrical model parametric changes and subsequent loss of capacity or peak power
output.
In the next chapter, the reader will be introduced to the primary aging
mechanisms that afflict lead-acid batteries.
35
3 AGING MECHANISMS
3.1 Introduction
This chapter provides an overview of the primary aging mechanisms that lead-acid
batteries are susceptible to.
These chemical and morphological changes result in
decreased battery capacity and peak power output, eventually causing battery
performance to be reduced to its end-of-life criteria. A knowledge of the electrical
signatures of these internal changes and the usage conditions that accelerate them can
lead to more accurate state of health estimations and predictions. This chapter will
conclude with an overview of accelerated aging experiments conducted on a set of
automotive VRLA batteries at the Ohio State University’s Center for Automotive
Research.
3.2 Background
Throughout its life, a battery will undergo a number of irreversible chemical reactions
that cause its electrical performance to decrease. The primary means by which this
“aging” is typically quantified is in terms of an increase in internal resistance, causing the
peak power output to drop, and a decrease in battery capacity. The environmental and
usage history of the battery will determine the dominant aging mechanism, and
consequently the type and extent of performance loss that can be expected. To introduce
36
these aging mechanisms, it would first be instructive to analyze a battery’s components,
and isolate those that are most vulnerable to deterioration. A diagram of the principle
components of a valve-regulated lead-acid battery is shown in Figure 3.1 below.
Figure 3. 1: Diagram of VRLA components
From Figure 3.1, we can identify six major components of a VRLA battery: positive and
negative electrode grids, positive and negative active masses, electrolyte and AGM
separator. The AGM separator is composed of glass fibers that isolate the electrodes
from one another to prevent internal short-circuits. It does not participate in reaction or
break-down over time, and therefore is not considered subject to aging. The electrolyte
housed inside the separator pores, however, is an active material that participates in
electrochemical reactions, making its presence and abundance critical to proper battery
37
function.
In older flooded lead-acid batteries, water from the electrolyte would
decompose into hydrogen and oxygen gas that is lost during recharging, forcing the user
to periodically add water to the battery to retain its functionality. Valve-regulated (also
called ‘sealed’) lead-acid batteries, on the other hand, have internal gas channels through
the separator that allow oxygen formed at the positive electrode to recombine back into
water at the negative electrode. Under the constant voltage charging that takes place in a
vehicle, this oxygen recombination cycle largely prevents the water loss that occurred in
flooded batteries and electrolyte dry-out is not typically considered a principle cause of
performance loss in VRLA batteries. The remaining battery components: the electrode
grids and active materials, are the most vulnerable to degradation that will cause capacity
loss and peak power reduction. These aging mechanisms will be discussed in detail for
the remainder of the chapter.
3.3 Hard Sulfation
Hard sulfation is one of the most frequently cited causes of reduced battery performance.
In a lead-acid battery, lead sulfate (PbSO4) forms on both electrodes as a natural product
of the discharge chemical reaction (4):
Pb + PbO 2 + 2H 2SO 4 ! 2PbSO 4 + 2H 2O
(4)
The problem occurs when this PbSO4 crystallizes into a form that is no longer
electrochemically active, a process referred to as irreversible or ‘hard’ sulfation. Upon
38
recharging, this crystallized lead sulfate does not break down as it should, but remains on
the electrodes. This presents a number of problems, the first of which is the fact that
some of the active materials are locked away inside the inactive lead-sulfate, causing a
decrease in available capacity. Secondly, lead-sulfate is substantially larger than the
active materials it replaces.
This causes pores within the active material to clog,
inhibiting electrolyte diffusion into the active material and resulting in more capacity loss
[14].
Figure 3. 2: Large Lead-sulfate crystals on NAM surface [15]
In VRLA batteries, hard sulfation has been found to be more of a problem at the negative
active mass than the positive. The exact physicochemical processes responsible for the
formation of hard lead-sulfate is still an active area of research, however, it is commonly
held that the principle catalyst of this aging mechanism is battery storage and operation at
39
low SOC for prolonged periods of time [16]. It has been widely reported that larger leadsulfate crystals have a tendency to form at low acid concentrations (low SOC), where the
solubility of Pb2+ is higher, allowing the crystal to reshape itself and grow [17].
Allowing lead-sulfate to stand in these conditions can cause it to re-crystallize into a form
that has a lower activity, making it more difficult to break down on recharge [18].
(a)
(b)
Figure 3. 3: Atomic Force Microscope (AFM) Image of lead-sulfate crystal formed
(a) immediately after discharge, and (b) after open-circuit stand [18]
40
Figure 3. 4: Diagram of PbSO4 formation [18]
It has also been shown that high discharge currents contribute to the build-up of
irreversible sulfation on the surface of the negative active mass exposed to the bulk
electrolyte [7,15]. Elevated temperatures [19] and battery undercharging caused by low
charging voltages also have the reputation of promoting hard sulfation as well [16].
The occurrence of this chemical change in the active mass may be detectible through
electrical measurements. For example, the removal of sulfate ions from the electrolyte
causes the maximum achievable rested open-circuit voltage to drop [16]. This is a direct
result of the decrease in the concentration of sulfuric acid in the electrolyte.
41
Figure 3. 5: Changes in maximum SOC for a battery with 18% sulfation
The assumption in Figure 3.5 is that no significant amount of water has been lost from
the electrolyte. Water loss increases the concentration of sulfuric acid in the electrolyte,
possibly negating the appearance of sulfation in an open-circuit voltage measurement.
Gassing, or water lost through electrolysis during recharging, is unlikely to occur in
automotive batteries due to the relatively low (~14V at 20°C) constant voltage charging
employed by alternators. However, under elevated temperatures water may be lost by
evaporation or diffusion of water vapor through the battery container walls [16].
Water is also consumed during corrosion, however, there are ways of detecting corrosion
as will be demonstrated in the next section.
42
Increases in charging resistance or the reduction of peak charging current, particularly at
high SOC, could also serve as an indication of sulfation. Capacity loss could result from
the formation of large lead-sulfate crystals that cause pore-clogging and a general
disruption of contact between NAM and sulfuric acid. It is also conceivable that some
permanent sulfation could occur with no noticeable reduction in capacity or increase in
internal resistance. This would occur in the situation where the battery is manufactured
with an overabundance of NAM and sulfuric acid, making the PAM the limiting reagent
in electrochemical reactions. This is not uncommon in VRLA batteries sold today [20].
3.4 Positive Grid Corrosion
The positive and negative electrode grids of a battery provide a low resistance conduit for
electrons traveling to/from the external circuit to the active material during charge and
discharge reactions. Corrosion occurs when water from the electrolyte oxidizes some of
the grid’s lead-alloy into PbO2.
43
Figure 3. 6: Corrosion reaction during charging [16]
The positive grid has been identified as being particularly susceptible to corrosion due to
its contact with lead dioxide, a thermodynamically unstable arrangement [16]. Both
charging and open-circuit stand conditions facilitate corrosion reactions.
Numerous
advances in positive grid alloys have been made in the last 40 years, and modern leadalloys contain: calcium, tin, silver, and other additives to drastically reduced the rate of
corrosion.
44
Figure 3. 7: Corrosion during open circuit conditions [16]
At first glance, one might believe that this type of reaction occurring at the positive
electrode is not a bad thing, since it potentially increases capacity by adding more PAM.
However, the replacement of highly conductive grid alloy with a substantially more
resistive lead-oxide causes a battery’s internal resistance to increase. This also decreases
battery capacity to varying extents. Furthermore, corrosion-born lead-oxide takes up
considerably more volume than the lead-alloy it replaces, causing mechanical stress to
the grid that can eventually cause it to fracture and break apart.
45
Figure 3. 8: Corroded positive plate of a starter battery after 5 years of service [16]
Higher temperatures cause more frequent water transport through the active layer of
PbO2, resulting in accelerated corrosion. Larger charging voltages and charging currents
will also result in accelerated corrosion rates [16].
Due to advances in grid alloys,
corrosion has been retarded to such an extent that it is rarely the primary failure mode of
modern automotive VRLA batteries. However, even under the most ideal conditions, all
lead-acid batteries will eventually succumb to corrosion on long time scales.
The location of the corrosion layer in the electron path between the PAM and positive
grid results in an increase in ohmic resistance that would most likely be characterized by
an increase in parameter R0 in a first order Randle electrical model.
46
3.5 Positive Active Mass Degradation
Positive active mass degradation occurs when the particles of PbO2 begin losing their
attraction to one another, or to the grid itself. Eventually, complete loss of contact
occurs, at which point the PbO2 no longer participates in charge/discharge reactions.
This process is also known as the “softening” or “shedding” of the positive active
material. Unlike the other two aging mechanisms studied so far, this transformation is
morphological in nature, not chemical.
The principle cause of PbO2 softening is thought to be due to the expansion and
contraction this active mass undergoes as it makes its transformation to higher volume
PbSO4 during discharge, then back to PbO2 during charging. This process has the
consequence of changing the bonding structure between PbO2 particles, causing them to
transition away from the skeletal agglomerate bonding with neighboring particles and
expand outward into single-crystal structures that eventually lose their coherence with
each other and with the grid itself [21]. This morphological change in the PAM from the
initial mix of ! " PbO 2 and ! " PbO 2 crystals when the battery is new to only ! " PbO 2
when the battery has been extensively cycled is best seen in the scanning electron
microscope images in Figure 3.9.
47
Figure 3. 9: SEM images of PAM when: (a) new (α & β ), and (b) after failure ( β
only) [12]
Figure 3. 10: Positive Grid with substantial loss of active mass (PbO2) after serving 6
months as a starter battery in a city bus [16]
48
As softening progresses and the mechanical connection between PbO2 particles begins to
weaken, it is likely that vibrations present during vehicle travel will accelerate this aging
process. However, charging at higher currents [22,23] and temperatures [16] has been
found to suppress PAM degradation and extend cycle life. Furthermore, it has been well
established that this phenomenon can be greatly slowed with higher compression on the
PAM, as is often achieved in spiral-wound cells [23,24].
The most obvious effect of positive active mass degradation is an increase in electrical
resistance at PbO2 sites that are cycled often. This, in turn, causes a loss of capacity as
the softened sites’ resistance increases to a point where they are no longer participate in
electrochemical reactions.
Furthermore, as mentioned in the previous chapter, the
positive active mass is the limiting reagent in VRLA batteries sold today. Therefore, the
increase in PAM resistance automatically results in a decrease in capacity.
Due to the fact that this type of aging mechanism is a direct result of charge and
discharge operation, simple amp-hour counting could be used to track changes in
capacity. However, establishing a correlation between this ‘amp-hour life’ and capacity
decrease would require the collection of a considerable amount of empirical data. To
achieve an accurate SOH estimate, this open-loop approach would need to supplemented
with feedback through some measured electrical quantities. Diagnostic SOH tests that
could provide this information are reviewed in the next chapter. In a first order Randle
electrical model of the battery, it is likely that the PAM morphological changes inherent
in this aging mechanism would be manifested in fluctuations in parameters R1 and C1.
49
3.6 VRLA Battery Aging Experiments Conducted at CAR
The dominant aging mechanism and subsequent performance loss a lead-acid battery
experiences is largely determined by its usage history. The previous sections provided a
qualitative examination of these internal changes, and the operating conditions that
accelerate them. In order to more fully characterize the damage inflicted by automotive
duty cycles, a set of accelerated battery aging experiments was conducted at the Center
for Automotive Research (CAR).
As identified in Chapter 1, traditional automotive VRLA batteries are primarily
responsible for supplying power to start the engine, and energy to electrical loads when
the engine is off or when demand exceeds the alternator’s maximum output. This latter
condition is occurring more and more often as additional consumers are added to new
vehicle electrical systems. One consequence of this duty cycle is battery operation under
so-called ‘partial state of charge’ conditions, where the battery is maintained at an SOC
of 75% or less and is rarely, if ever, fully recharged. Another condition that may be
encountered is the complete discharge of the battery when an electrical load is
accidentally left on for an extended period of time while the engine is off. To explore the
impact of these different operating modes, two duty cycles were created to age two 60Ah
(C/24 rate) automotive VRLA batteries.
The first duty cycle was designed to simulate the complete discharge of a battery at a
moderate rate. Starting at a rested open circuit voltage of 12.7V (~75% SOC on a new
battery), this ‘Energy Cycle’ consisted of a sustained 30A (C/2) discharge until a terminal
50
voltage of 10.5V was reached, at which point constant current recharging was initiated at
a 10A rate (C/6) until a terminal voltage of approximately 14V was reached. This
roughly returned the battery to the same initial SOC for the next cycle. An Agilent
N3301A DC electronic load was used to apply this profile.
Figure 3. 11: Energy Cycle Load Profile
The second duty cycle was designed to simulate the effect of repeated engine cranking.
As such, the battery was connected to low resistance loads that drew 300-400A for a
period of 5 seconds, followed by a rest period of 10 seconds. Starting at a rested open
circuit voltage of approximately 12.7V, this ‘Power Cycle’ was repeated 40 times, at
which point the battery was recharged using the same procedure as the Energy Cycle.
51
Figure 3. 12: Power Cycle Load Profile
Two 12V 60Ah AGM Exide automotive VRLA batteries, which we will refer to as N1
and N2, were aged using the energy and power cycles, respectively. Both batteries were
cycled at a constant ambient temperature of 45°C in a TestEquity Model 140 temperature
chamber. Periodically, cycling would be interrupted and the batteries were brought to
room temperature (24°C) and subjected to a series of nondestructive diagnostics tests to
evaluate their electrical performance. This process of cycling and testing was continued
until the batteries failed to supply sufficient cranking power to start an engine. At this
point, the batteries are said to have reached their end-of-life criteria. The next chapter
provides descriptions of the diagnostic tests and the results of the aging experiments.
52
4 BATTERY DIAGNOSTIC TECHNIQUES
4.1 Introduction
This chapter examines both traditional and unconventional lead-acid battery diagnostic
tests that may be used to characterize battery state of health. Data collected from the
aging experiments introduced in the previous chapter is used to evaluate the effectiveness
of each of these techniques in estimating performance metrics like capacity and internal
resistance. Online battery state estimation algorithms could be used to warn the driver of
declining battery performance and the need for replacement prior to failure.
4.2 Automotive Battery Performance Specifications
The performance of a new automotive lead-acid battery is typically specified in terms of
cranking amps (‘CA’), cold cranking amps (‘CCA’), and ‘Reserve Capacity’. As the
names imply, the CA and CCA are the amount of current the battery can provide to crank
an engine under low-temperature conditions (typically 32°F and 0°F, respectively). The
reserve capacity, as defined by the Society of Automotive Engineers (SAE), is the
number of minutes the battery can be discharged at a 25A rate until a terminal voltage of
10.5V is reached [19]. Together, these power and energy metrics roughly define a
battery’s ability to act as an electrical energy supply onboard a vehicle. End-of-life
53
conditions are also often specified in terms of either capacity or power output. The next
sections elaborate on traditional methods of determining these fundamental battery
qualities.
4.3 Cranking Resistance Tests
Above all else, engine starting is the primary functional requirement of an automotive
battery. The electrical power needed to achieve this event is highly temperature
dependent. At lower temperatures the engine’s internal friction is much higher, and thus
more power is required by the battery to rotate this mass. This condition is particularly
challenging, because, as we have learned in Chapter 1, at lower temperatures the battery’s
internal resistance is higher due to the lower energy of reactants and lower diffusion rates
of sulfuric acid. Automotive batteries are often designed to optimize peak power output
under these abusive conditions. As mentioned in the previous section, vehicle batteries
often specify their power output indirectly in ‘CA’ and ‘CCA’ ratings at low
temperatures.
A more accurate means of tracking the battery’s ability to provide
cranking power is by looking at the differential resistance during the cranking event. In
this thesis, cranking resistance Rcrank is defined as the differential resistance measured
during engine cranking at the time instance corresponding to the minimum voltage and
the maximum current.
54
Rcrank =
V0 ! Vmin
Imax ! I0
(17)
In (17), V0 and I0 are the battery voltage and current just prior to the cranking event, and
Vmin and Imax are the minimum voltage and maximum current during the event. This
value is, of course, highly dependent on both temperature and SOC. For a given T and
SOC, changes in this parameter can be indicative of battery aging, and large increases
will eventually cause the battery to fail to supply sufficient power for engine cranking.
Figure 4. 1: Voltage and Current during Engine Cranking
55
Even in a new battery there may be a situation where an electrical load is left on by
accident after the vehicle has been turned off, and the battery’s SOC is consequently
depleted to the point where it is no longer is able to provide sufficient power to start the
engine. For the purposes of this thesis, this type of condition will not be considered a
battery failure, since recharging the battery will restore its ability to supply cranking
power. In accordance with the sponsors of the lead-acid battery aging experiments
conducted at CAR, battery failure is defined as the inability to crank an engine at room
temperature (75°F) at a rested open-circuit voltage of 12.7V (roughly 75% SOC for a
new battery). The protocol by which the cranking tests take place is defined below.
The battery is first brought to a constant temperature of 75°F (24°C) over a period of 16
hours using the TestEquity temperature chamber described in the previous chapter. The
battery is then charged so that its rested (>8hr period) open-circuit voltage is brought to
12.7V.
The engine that is started is a 4 cylinder diesel engine that resides in a
dynamometer test cell at CAR. The ambient temperature in the test cell is maintained
approximately between 65-80°F year-round. To ensure engine cranking occurs under
‘cold start’ conditions, cranking tests begin at least 12 hours after the last time the engine
was operational. The voltage and current measurements used in calculating cranking
resistance are as described in (17) and shown in Figure 4.1.
56
Figure 4. 2: Cranking Resistance of N1 and N2 vs Total Amp-hours
Figure 4.2 shows a plot of the cranking resistance of batteries N1 and N2 as aging
progresses. Since the cycles have their own characteristic profile with distinct current
magnitudes and depth of discharge, cranking resistance for N1 and N2 were plotted under
the more absolute quantity ‘Total Amp-hours’, which is simply an integration of the
absolute value of the measured current during the aging cycles.
As can be seen in Figure 4.2, there is very little increase in cranking resistance as N1 and
N2 are cycled. However, after 4,497Ah of cycling, the power cycle battery (N2) was
unable to provide cranking power, as can be seen in its final cranking resistance
measurement, which is over twice its initial ‘new’ value. A theory for the failure of N2 is
57
provided in section 4.5, although it is believed that this mechanism is atypical for
automotive batteries.
The primary reason for the relatively static Rcrank may be the fact that cranking utilizes a
relatively small quantity of active material. A cranking event draws 300-800A over a
period of less 2 seconds, meaning only 0.4Ah, or 0.67% of the total 60Ah, worth of
active material is needed for this event. However, the distribution of the reaction sites
used does impact current densities in the AM skeletal structure, and therefore Rcrank.
Cranking resistance tests are therefore somewhat representative of the ‘healthy’ active
material surface area. At some critical value, the internal resistance will be high enough
to prevent engine cranking.
Due to the fact that cranking events occur all the time in vehicle operation, simple
measurements of voltage and current lend this particular diagnostic technique to onboard
implementation.
4.4 Capacity Tests
A standard capacity test discharges a fully charged battery at a fixed rate until the
terminal voltage drops below some predefined minimum threshold.
For lead-acid
batteries, this minimum voltage is usually around 1.67-1.75V/cell, or 10-10.5V on a 12V
battery. The purpose of this test is to determine the maximum amount of useful electrical
energy that can be extracted from the battery. In so doing, this test also indirectly
58
determines the maximum amount of useful active material within the battery. In this
context, “useful” refers to active material that does not have a prohibitively resistive path
between the reaction site and the grid.
As mentioned in the preceding section,
automotive lead-acid batteries often denote the SAE reserve capacity in minutes of
discharge at 25A and 25°C. In general, battery manufacturers specify capacity in terms
of amp-hours (Ah), typically at a 20-hour discharge rate (C/20) [25] and at temperatures
greater than or equal to 20°C. For example, a fully charged 12V 60Ah battery discharged
at 3A will take 20 hours to reach a terminal voltage of 10.5V.
Effective battery capacity is heavily dependent on the temperature and discharge current
during the test [1]. At higher temperatures, diffusion of the sulfuric acid from the
electrolyte into the PAM and NAM interior proceeds more rapidly, and the reactants
possess more energy. These factors lead to the utilization of a higher percentage of the
active materials and a lower internal resistance, resulting in a higher effective capacity.
Discharge current essentially specifies the required rate of reaction, and therefore the
necessary consumption rate of sulfuric acid. As discharge currents increase, the rate of
HSO4- consumption begins to overtake the rate of HSO4- diffusion from the bulk
electrolyte into the pores of the active materials at the positive and negative electrodes
[1]. Consequently, sustaining a high rate of discharge restricts electrochemical reactions
predominantly to the surface where the PAM and NAM contact the bulk electrolyte
directly [7]. This decreases the utilization of the active material interior, resulting in an
earlier onset of the exhaustion of available reactions sites that is characterized as the
‘voltage knee’.
59
Figure 4. 3: Discharge curves of a 12V, 80Ah battery at various discharge rates [1]
However, it has been demonstrated that additional capacity can be recovered from these
batteries at a lower discharge rate after a suitable rest period that allows electrolyte
concentrations to evenly distribute. Figure 4.4 presents capacity test results for a 65Ah
12V lead-acid battery discharged at 5A and 50A. The terminal voltage is plotted against
the ‘Discharged Capacity’, which is simply the discharge rate multiplied by the number
of hours that have elapsed during the test.
As expected, the 50A rate reaches the
minimum voltage long before the 5A rate due to greater ohmic losses and an earlier onset
of the ‘voltage knee’ due to the decreased utilization of AM. At the conclusion of the
50A capacity test, the battery was rested for 6 hours, and then discharged at a 5A rate. In
this way, an additional 20Ah were able to be extracted from the battery [26].
60
Figure 4. 4: Voltage vs Capacity curves at 50A and 5A discharge rates [26]
For these reasons it is important that battery capacity tests be carried out under the same
conditions.
The capacity tests performed during the lead-acid aging experiments
conducted at CAR were carried out using the protocol specified by the industry sponsor
of the project.
The battery is first brought to a constant 24°C over a period of 16 hours using the
TestEquity temperature chamber described in the previous section. A full SOC is then
achieved by charging at a constant current of 25A until an upper voltage limit of 16V is
reached. At this point, constant 16V charging takes place for the remainder of the 24
hour charging period.
After 24 hours of charging, the battery is disconnected and
allowed to rest for 4 hours. After the rest period, discharging commenced at a constant
61
rate of 2.5A (C/24 rate) until a terminal voltage of 10.5V is reached.
The initial
capacities for new batteries N1 and N2 were found to be 60.1Ah and 60Ah, respectively.
Figure 4. 5: Initial Capacity Tests for Batteries N1 and N2
Cycling under both aging profiles was periodically interrupted to perform all diagnostic
tests. The capacity test results for batteries N1 and N2 are given in Figures 4.6 and 4.7.
62
Figure 4. 6: Voltage vs Capacity of N1 for different cycles
Figure 4. 7: Voltage vs Capacity of N2 for different cycles
63
It should be noted that the rest period for the first capacity test (Cycle 0) was 24 hours,
and this is the primary reason for the difference in voltage seen between 0 and 10Ah.
The failure of battery N2 occurred shortly after cycle 151. From Figures 4.6 and 4.7,
some general observations can be made about the aging of N1 and N2. As battery
capacity is decreased due to aging, we note a similar voltage response behavior in N1 and
N2. This earlier onset of the ‘voltage knee’ as capacity decreases is similar to what we
observe when the discharge current is increased, causing a lower utilization of the active
material. However, in this case the discharge current is the same, and therefore the rapid
exhaustion of reaction sites can be attributed to the loss or destruction of some of the
useful active material. Furthermore, despite the overwhelming differences between the
two aging profiles, both N1 and N2 lose capacity at approximately the same rate with
respect to total amp-hours cycled, as seen in Figure 4.8. This is an indication that the
primary source of capacity loss in the two batteries is the same, and implies that capacity
loss is strictly related to active material cycling, a characteristic of positive active mass
degradation. Furthermore, the characteristic voltage knee is due to the exhaustion of the
limiting reagent, which is more often than not the positive material in a VRLA battery
[20]. To illustrate this point, Figure 4.9 shows the potentials of positive and negative
electrodes of a cell within a spiral-wound VRLA battery from a study conducted by T. G.
Chang, et al. The voltage knee is strictly a characteristic of the positive electrode,
identifying the PAM as the limiting reagent in this battery [23].
64
Figure 4. 8: Capacity of N1 and N2 vs Total Amp-hours
65
Figure 4. 9Figure 4.9: VRLA Cell Electrode Potentials during discharge and charge
[23]
Unfortunately, because capacity tests involve complete battery discharge, they are
unsuitable as onboard diagnostics tests. However, indicators of capacity, in the form of
other internal battery parameters like impedance are more readily calculable from
electrical measurements of voltage and current.
4.5 Analysis of Aging Data
An examination of voltage and current data collected during the aging experiments
themselves also reveals some evidence of the aging mechanisms at work in N1 and N2.
66
This information will prove to be vital in development of onboard diagnostic tests that
can be used to estimate battery SOH and possibly even advanced charging strategies that
can prolong battery life.
4.5.1 Energy Cycle Data
The ‘energy cycle’ load profile resembles a high rate of discharge capacity test (C/2 vs
C/24) that starts from a rested open-circuit voltage of approximately 12.7V (15Ah
discharged) instead of 13.1V for a fully charged battery. Immediately following this
discharge down to 10.5V, the battery is recharged at a rate of C/6 until a terminal voltage
of 14V is reached, or the charge removed during discharge was replaced. The voltage
response behavior of the battery during discharge should be similar to what is observed
during the capacity tests, which can predominantly be characterized by the early onset of
the voltage knee. However, in scrutinizing the cycling data for battery N1, a subtle
observation can be made regarding the differences in battery performance before and
after capacity tests. Figure 4.10 shows the discharge and charge behavior of battery N1
at cycles 46 and 49: before and after capacity test 6.
67
Figure 4. 10: Energy Cycles before and after Capacity Test 6
Each of the cycles shown above were the first collected on their respective days,
indicating that there was over 8 hours of rest prior to each test. Also, the initial voltage of
each cycle was within 60mV of the other, ensuring that both began at approximately the
same SOC.
The most notable changes in battery performance between cycles 46 and 49 are without
question the 82% increase in discharge duration and 70% increase in charge duration.
This type of behavior is not isolated to cycles 46 and 49, but it appears to some extent in
all cycles before and after every capacity test performed on N1. This apparent increase in
battery capacity in the cycles immediately following a set of diagnostic tests is most
likely an indication of hard sulfation occurring during successive cycles between capacity
68
tests. It is believed that the extremely aggressive charging protocol of 16V for 24 hours
to fully recharge the battery for a capacity test actually had the unintended consequence
of eliminating most of the sulfation that had built up on the NAM since the previous
capacity test. Further evidence that a temporary hard sulfation is occurring between
capacity tests can be seen in the charging behavior of cycles 46 and 49. The inability of
the highly crystalline lead-sulfate to be transformed back into active materials forces the
oxygen cycle to start much sooner than it would normally, as evident in the sudden
increase in internal resistance present in cycle 46 but largely absent in 49. The presence
of sulfation as an aging mechanism under this duty cycle is hardly surprising. The
operating conditions of the energy cycle, characterized by high temperatures, partial SOC
operation, and low charging voltages, make it an ideal environment for the growth of
large, highly structured lead-sulfate crystals that are difficult to break down during
recharging.
Looking forward over 200 cycles, a similar behavior can be observed in cycles 252 and
259, as seen in Figure 4.11. The rapid rise in recharging resistance is still present, but the
discharge capacity of the battery before and after the capacity test is largely unchanged.
This can be explained by the hypothesis proffered in the previous section: that the
primary cause of capacity loss is irreversible positive active mass degradation.
69
Figure 4. 11: Energy Cycles before and after Capacity Test 13
In cycles 46 and 49, the extent of temporary capacity loss due to sulfation, caused by pore
clogging and general blocking of NAM access to sulfuric acid, was dominant. At this
point, the permanent damage due to PAM degradation only accounted for a 27% decrease
in capacity. However, as cycling progressed, the destruction of useful positive active
mass began to eclipse the effects of sulfation, achieving an irreversible capacity loss of
63% by cycle 259. As evident in Figure 4.11, the damage due to both aging mechanisms
is not additive, since this would cause the discharge duration at cycle 259 to be
considerably higher than cycle 252. In light of the above observations and general
knowledge of the progression of chemical reactions, it can be hypothesized that it is the
limiting reagent that is almost wholly responsible for capacity loss in N1.
70
It is interesting to think of how aging would have progressed had the capacity tests
adopted a constant voltage charging protocol more representative of that utilized by
alternators onboard a vehicle, where voltages typically do not exceed 15V at
temperatures over 0°C.
Figure 4. 12: Typical ranges of voltage regulation for alternators [1]
It is reasonable to surmise that battery failure in this situation would be brought about
much more rapidly due to sulfation wrought through chronic battery undercharging and
SOC depletion.
Examination of the energy cycles directly following capacity tests reveals a voltage
response very similar to what is observed during the capacity tests themselves. From
Figure 4.13, we observe the same inward progression of the voltage knee that was evident
during the capacity tests.
71
Figure 4. 13: Energy Cycle Voltage Response on Cycles after Capacity Tests
While PAM degradation is suspected to be the principle source of capacity loss in battery
N1, a scenario in which sulfation is the primary aging mechanism would likely yield
similar discharge voltage curves to those in Figure 4.13. Support for this claim can be
found in discharge portion of the energy cycles that exhibited temporary capacity loss
between capacity tests. The onset of the voltage knee is therefore not unique to one
particular aging mechanism, but rather is symptomatic of a decreased access to ‘useful’
active material. The observable distinction between sulfation and PAM degradation can
primarily be found in the charging curve. As previously stated, hard sulfation forces
secondary reactions like the oxygen cycle to occur at lower states of charge than they
72
would normally occur, which can be observed as a rapid increase in internal resistance
during charging.
In either case, when the active materials are the source of extensive capacity loss, the
battery’s dynamic electrical behavior at high SOCs will begin to resemble its electrical
behavior at much lower SOCs. As a general observation, the voltage knee will typically
be encountered when the final 5-10Ah of extractable charge is reached. Furthermore, the
rate of voltage drop under a given load can quantify the remaining discharge capacity at a
given discharge rate.
To demonstrate the potential of this method as a diagnostic technique, each of the C/2
(30A) energy cycle curves from Figure 4.13 were examined. Working backwards from
the point where the minimum voltage threshold of 10.5V is reached, the number of amphours discharged from 1 to 15 were counted. At several points between these bounds, the
rate of voltage drop over a 100second period was measured. This process is shown for
energy cycle 84 in Figure 4.14, and then repeated for each of the other cycles shown in
Figure 4.13. The results are plotted as ‘Remaining Discharge Capacity vs Voltage drop
every 100 seconds’ in Figure 4.15.
73
Figure 4. 14: Analysis of Energy Cycle 84
Figure 4. 15: Remaining Discharge Capacity vs Voltage drop every 100sec
74
Figure 4.15 shows that there is a clear correlation between the voltage time derivative and
remaining discharge capacity.
As the voltage drop increases, the estimate of the
remaining number of amp-hours that can be discharged at the given rate becomes more
accurate. For example, if the voltage drop measured over a 100 second period is 50mV,
the remaining capacity is approximately between 6 and 10Ah. However, at a falling rate
of 100mV/100sec, or 1mv/sec, the battery can only provide an additional 2-3Ah. This
technique, combined with an estimation of the amp-hours discharged from a
measurement of the rested open-circuit voltage, has the potential to quantify the reduced
effective capacity of the battery. More details on this technique are provided in the next
chapter, which creates a lead-acid battery state-of-health estimation algorithm.
4.5.2 Power Cycle Data
The ‘power cycle’ load profile was designed to resemble a duty cycle in which engine
cranking is the only load the battery experiences. To accelerate the aging process, the
resistive load would sink approximately 6.6C (400A) for a period of 5 seconds when the
battery was connected. This discharge was followed by a short 10 second rest period,
and then this process was repeated 40 times before the battery was again recharged at a
constant C/6 to bring the SOC back to the starting point, which, like the energy cycle,
was approximately 75% SOC (Voc = 12.7V).
75
From the capacity test section, it was noted that the rate at which capacity decreased with
respect to amp-hours cycled was the same for batteries N1 and N2. This indicates that
the primary aging mechanism at work in these two batteries is the same, and likely due to
positive active mass degradation. However, the large discharge currents of the power
cycle would seem to promote the formation of irreversible sulfation on the negative
active mass surface. Like the energy cycle analysis, the power cycles occurring before
and after capacity tests were examined to determine whether the same temporary
performance decrease occurs during cycles between capacity tests. Sure enough, cycles
following capacity tests exhibited higher power outputs and a recession of the previously
encroaching voltage knee.
Figure 4. 16: Discharge voltage and current of power cycle before capacity test 3
76
Figure 4. 17: Power output before capacity test 3
Figure 4. 18: Discharge voltage and current of power cycle after capacity test 3
77
Figure 4. 19: Power output after capacity test 3
Figure 4. 20: Discharge voltage and current of power cycle before capacity test 4
78
Figure 4. 21: Power output before capacity test 4
Figure 4. 22: Discharge voltage and current of power cycle after capacity test 4
79
Figure 4. 23: Power output after capacity test 4
Like the energy cycle comparison, power cycles displayed in the above figures were the
first cycles of their respective days, and the rested open circuit voltage was within 60mV
of each other. Recall that in the energy cycles directly following capacity tests, an
increase in discharge capacity was observed when compared to the cycles occurring
between capacity tests. A similar behavior is observed in the power cycles, where higher
discharge currents are maintained throughout cycles 37 and 70, as compared to cycles 33
and 67, respectively. The peak power output in the first pulse of 37 and 70 also increases
slightly.
This indicates that the temporary sulfation built-up between power cycles
caused an increase in ‘cranking’ resistance. To quantify this reduction, a differential
resistance was calculated for the first discharge pulse in power cycles before and after
80
capacity tests. The peak current and minimum voltage values over the total 5 seconds of
pulse 1 were averaged to obtain Ip1_avg and Vp1_avg in (18).
R p1 =
!V Voc " V p1_ avg
=
!I
I p1_ avg
(18)
Figure 4. 24: 5sec average differential resistance over pulse 1
Figure 4.24 shows the differential resistance calculated in the first pulse of power cycle
occurring before and after several capacity tests throughout the aging of N2. From this
plot, it is observed that the ‘unsulfated’ (post-capacity test) cycles exhibit a steady
increase in resistance as cycling continues. The ‘sulfated’ (pre-capacity test) cycles
increase the resistance to varying extents before their effect is temporarily erased by the
aggressive charging protocol of the capacity test. Its interesting to note that this same
81
monotonic increase in resistance is not observed with the cranking tests, which, as fate
would have it, were administered after the capacity tests.
It may be that the few
milliseconds over which the cranking test differential resistance was measured is not a
sufficient discharge period to notice this trend. To verify this claim, the differential
resistance in the above cycles was recalculated over a much shorter period: the first 300
milliseconds of pulse 1. The results of this are shown in Figure 4.25 below.
Figure 4. 25: 300msec average differential resistance over pulse 1
This small, incremental increase in resistance in the ‘unsulfated’ cycles is much closer to
what is observed in the cranking resistance estimates shown in Figure 4.2. From this
observation, in using the cranking event onboard a vehicle as a diagnostic test, it is
82
advisable to calculate the differential resistance using the average minimum voltage and
maximum current of the first 1second or more of discharge, should cranking last that
long. Ironically, there is not much of a change in the differential resistance for the
sulfated cycles, indicating that if the cranking test had been performed on N2 before the
capacity test, cranking failure would have likely occurred much earlier in the cycling
process. This also may have been the case for energy cycle battery N1.
Like the energy cycles, the charging portion of power cycles between capacity tests
exhibit the same rapid increase in internal resistance that disappears in the cycles
following a capacity test. This provides further evidence that sulfation is the aging
mechanism behind the observed temporary performance decrease.
Figure 4. 26: Voltage during charging in cycles 33 and 37
83
Finally, as mentioned earlier in the chapter, power-cycle battery N2 was the first to fail
the engine cranking test. It successfully completed 158 cycles, or a total of 4,497Ah of
cycling amp-hours.
However, failure occurred quite suddenly, and can perhaps be
pinpointed to cycle 152, or diagnostic tests occurring between cycles 151 and 152, as can
be seen in Figures 4.27 through 4.32.
Figure 4. 27: Discharge Voltage and Current of Power Cycle 151
84
Figure 4. 28: Power output of Power Cycle 151
Figure 4. 29: Charging voltage of Power Cycle 151
85
Figure 4. 30: Discharge Voltage and Current of Power Cycle 152
Figure 4. 31: Power output of Power Cycle 152
86
Figure 4. 32: Charging Voltage of Power Cycle 152
It is clear from the above plots that something occurred during the diagnostic tests
conducted between cycles 151 and 152 that caused the rapid advance of the voltage knee
during discharge in cycle 152. An examination of the capacity test conducted for N2
after cycle 151 in Figure 4.7 reveals no abnormal voltage response. The condition of N2
rapidly deteriorated after cycle 152, to the point where peak power output dropped well
below 500W in the final discharge pulses of cycle 158.
87
Figure 4. 33: Discharge voltage and current for Power Cycle 158
Figure 4. 34: Power output for Power Cycle 158
88
At this point, the extremely high rate of self-discharge made it impossible to safely fully
charge N2 for a capacity test under the standard protocol. Left to stand, the battery would
discharge down to a voltage of 10.5V, indicating that a short-circuit may have formed
across one the cells. This type of failure could be explained by extreme local dilution of
the electrolyte caused by the high rate of discharge (sulfuric acid consumption). The
increased solubility of lead in an electrolyte approaching the consistency of water could
cause the dissociation of Pb2+ ions from lead-sulfate on the surface of the NAM. These
ions could migrate into the AGM separator, and form conductive pathways to the PAM,
shorting out the cell. It is believed that if this is the case for N2, this failure mode is
unlikely to occur in lead-acid batteries onboard vehicles, which do not experience
complete discharge at high rate like the power cycles.
4.6 Dynamic Response Test
Unlike the capacity and differential resistance tests examined in the previous sections, the
dynamic response test is a relatively new technique that takes a more sophisticated
approach to characterizing battery electrical behavior. The purpose of this test is to
model the battery’s dynamic voltage response to a specific load over a predefined period.
System identification techniques are used to estimate parameter values for a selected
electrical model that enable accurate reproduction of the measured voltage response of
the battery. Changes in a battery’s dynamic electrical behavior, manifested as changes in
estimated parameter values, is indicative of chemical and morphological transformations
89
occurring within the battery. A quantification of performance degradation in terms of
capacity reduction caused by these aging mechanisms may also be possible with this
diagnostic technique.
From a cranking test, a differential resistance is calculated over an extremely short timeperiod to indicate changes in the battery’s peak power potential (active material surface
area). From capacity tests and energy cycles, it was found that differential resistances or
voltages calculated over longer periods can be useful in estimating remaining discharge
capacity.
The dynamic response test fits neatly between these two extremes by
identifying subtle changes in electrical behavior over a window of time directly after the
load is applied. To maintain consistency with the other diagnostic tests, the input was
selected to be a step-change in load starting from 0A. Under this excitation, the dynamic
response test seeks to characterize the ‘voltage heel’ that results shortly after load
application.
90
Figure 4. 35: Voltage ‘Heel’ in step response
Recall from Chapter 2 that a first order Randle electrical model was found to yield
consistently accurate voltage reproduction to a step-change in load over the time-period
of interest. This leaves four circuit parameters (E0, R0, R1, C1) that need to be identified.
One way of obtaining internal voltage E0 is by allowing a suitable open-circuit rest
period, preferably between 6-8 hours, prior to the step response test.
This allows
electrolyte concentration gradients (overpotentials) built up during charge/discharge
operation to dissipate, making an open-circuit voltage measurement at the conclusion of
the rest period an accurate representation of the bulk electrolyte density. The other
parameter values, R0, R1 and C1, are then found using an offline parameter estimation
technique.
91
The dynamic response test consists of three steps: data collection, parameter estimation
and state of health assessment. As previously mentioned, if the battery has remained at
near open circuit conditions for 6-8 hours without disturbance (vehicle off), conditions
are deemed appropriate for the dynamic response test.
An open-circuit voltage
measurement collected at this point serves as an estimate of battery SOC and provides a
value for E0. Battery temperature is also measured, as the battery’s voltage response is
highly temperature dependent.
At this point, voltage and current measurements are
captured as a constant current load is switched on and the battery begins to discharge.
After discharging for the desired length of time, the load is switched off, and the test is
completed.
Figure 4. 36: Current and Voltage Captured during Dynamic Response Test
92
The collected data should then be digitally filtered to remove noise present in the
measurements. As an example, the data shown in Figure 4.36 was sampled at a rate of
1000/sec, and afterwards a low-pass first order Butterworth filter was designed with a
cutoff frequency of 50Hz, and applied using zero-phase forward and reverse filtering.
The results of this can be seen in Figure 4.37.
Figure 4. 37: Filtered Voltage and Current Data from Figure 4.36
Next, parameters R0, R1 and C1 for a first order Randle electrical model of the battery are
estimated using a nonlinear least squares minimization. This iterative process begins by
calculating the Randle model voltage output from the measured current input and an
initial guess of the parameter values for R0, R1 and C1. This model voltage output is then
compared with the measured voltage output at each time instance i by taking the sum of
squares error between the two voltages, as seen in equation (18).
93
m
(
)2
S = " Vmeasi ! Vmodeli ( R0 ,R1,C1 )
i=1
(19)
An optimization function then attempts to minimize S by refining the candidate parameter
values in an iterative fashion until a local minimum for S is found. The final set of
candidate parameter values at the end of this process is taken as the estimate for R0, R1
and C1. A diagram of this process is depicted in Figure 4.38.
Figure 4. 38: Process of Parameter Estimation
94
Figure 4. 39: Comparison between measured and modeled voltage
In the above example, Simulink was used to simulate the first order Randle model
response to the measured current input. A MATLAB script was then used to calculate
the least squares error between measured and modeled voltages. Minimization of this
cost function was achieved using the optimization function fmincon, which produced a
final set of parameter estimates.
The goal of this dynamic response test is to determine a relationship between one or more
of the estimated parameters and the battery capacity. If such a relationship can be found,
the dynamic response test could be conducted on a battery of unknown state, and the
parameter values estimated from the test’s voltage and current measurements could be
used to determine the capacity of said battery.
95
The step response tests conducted on N1 and N2 were carried out at an excitation of 5A
over a period of 32seconds. Parameter estimation occurred over a 33second window,
which spanned from one second prior to step application, to the end of the step. Voltage
and current sensor measurements were collected at a rate of 100/sec through a National
Instruments SCC-68 signal conditioning box that contained a two channel isolated analog
input module with built-in low pass filtering with cut-off frequency of 10kHz. The
current sensor used was a 225A Honeywell Hall-effect sensor. After collection, a sixth
order low-pass Butterworth filter with a cut-off frequency of 2Hz was applied to the data
using zero phase forward and reverse filtering.
The results of parameter estimation are given in the table below, and the accompanying
figures.
Cycle
Total Ah
Capacity
(Ah)
R0
(Ohms)
R1
(Ohms)
C1 (F)
Tau 1
(sec)
RMS error
(V)
0
0
60.2
0.0217
0.0202
558.2
11.3
0.0104
16
695.4
48.3
0.0341
0.026
178.6
4.6
0.0083
27
1118.3
42.2
0.0247
0.0287
297.9
8.5
0.0061
37
1368
47.4
0.0195
0.0269
354.9
9.5
0.0056
48
1693.6
43.7
0.0157
0.0315
351.4
11.1
0.0043
83
2508.6
39.2
0.0171
0.0511
173.6
8.9
0.0035
116
3139.4
32.2
0.0176
0.0406
294.2
11.9
0.0027
141
3760.7
29.3
0.0158
0.0434
263.6
11.4
0.0042
167
4447.8
27.4
0.0166
0.0417
258.8
10.8
0.0040
198
5215.1
24.8
0.0167
0.0389
254.7
9.9
0.0043
229
5759.9
23.7
0.0159
0.0431
221.3
9.5
0.0045
258
6218.2
22.1
0.0193
0.0436
198
8.6
0.0051
301
6621.5
20.6
0.019
0.0378
225
8.5
0.0051
Table 4. 1: Estimated parameters for battery N1
96
Cycles
Total Ah
Capacity
(Ah)
R0
(Ohms)
R1
(Ohms)
C1 (F)
Tau 1
(sec)
RMS error
(V)
0
0
60.1
0.022
0.0229
429.2
9.8
0.0102
21
733.7
44.8
0.0414
0.0449
131.7
5.9
0.0093
36
1190.5
42.3
0.039
0.0388
150.4
5.8
0.0039
69
2147.9
34.5
0.035
0.048
112.7
5.4
0.0038
103
3048.7
30
0.025
0.0453
258.8
11.7
0.0029
123
3579.9
28.7
0.0178
0.0418
272.6
11.4
0.0040
151
4314
28.2
0.0213
0.0411
233.3
9.6
0.0049
Table 4. 2: Estimated parameters for battery N2
Figure 4. 40: Parameter R0 estimates for N1 and N2 vs Capacity
97
Figure 4. 41: Parameter R1 estimates for N1 and N2 vs Capacity
Figure 4. 42: Parameter C1 estimates for N1 and N2 vs Capacity
98
Figure 4. 43: Parameter Tau estimates for N1 and N2 vs Capacity
From Tables 4.1 and 4.2, it can be seen that the RMS error between measured and model
voltages in all tests were very low: less than 10.5mV, implying accurate reproduction of
the voltage dynamics. Figures 4.40 through 4.43 show the estimated parameter values
plotted against the battery capacity. Parameters R0 and R1 contain significant scattering
with respect to capacity, and no clear trends are observed other than the general increase
in parameter R1 as battery capacity is reduced. Some of this scattering may have been
caused by somewhat inconsistent rest-periods prior to initiation of the step-response test.
However, parameters C1 and Tau, while containing a similar degree of scattering at
higher capacities, begin to decrease in a linear fashion starting at around 50% of the
initial capacity (30Ah). This type of behavior is similar to what is observed in the
99
dynamic behavior of a new battery that is operated at progressively lower states of
charge. Step response tests were conducted on a third new battery ‘N4’ at various states
of charge. Like the step tests on N1 and N2, the N4 step magnitude and period were 5A
and 30sec, respectively. The resting period prior to each test was a consistent 12 hours.
E0 (V)
Ah_dis
(Ah)
SOC
R0
R1
C1 (F)
Tau
(sec)
RMS Error
(V)
12.73
12.52
76.8%
0.0095
0.0325
538.2
17.5
0.0013
12.65
15.87
71.5%
0.0102
0.032
504.8
16.2
0.0014
12.58
19.2
66.9%
0.0099
0.0296
495.3
14.7
0.0015
12.46
25.38
59.0%
0.0103
0.0256
505.5
12.9
0.0016
12.34
31.47
51.1%
0.0105
0.0239
480.1
11.5
0.0017
12.2
37.59
41.9%
0.0126
0.0248
420.3
10.4
0.0021
12.07
43.66
33.33%
0.0147
0.0264
369.9
9.8
0.0027
11.93
49.66
24.11%
0.0209
0.0326
308.1
10
0.004
11.85
52.96
18.84%
0.0313
0.0473
217.8
10.3
0.0059
Table 4. 3: Parameters estimated for battery N4 at various SOC
100
Figure 4. 44: Parameter C1 estimates for N4 vs SOC
Figure 4. 45: Parameter Tau estimates for N4 vs SOC
101
It may be possible to use parameters C1 or Tau as absolute SOC indicators, not unlike the
‘dV’ test. This information, combined with knowledge of the amp-hours discharged that
can be found from the rested open-circuit voltage (indicating electrolyte density), could
provide an estimation of capacity. This technique should be explored further in future
aging experiments. Care should be taken to allow a uniform 6-8 hour rest period prior to
conducting the step test to avoid corruption of the results.
4.7 Conclusion
This chapter presented both experimental results from the aging study conducted on
batteries N1 and N2 and a number of diagnostic tests that may be used to determine a
battery’s electrical performance characteristics. In the process of examining energy and
power cycle data, it was discovered that a temporary decrease in discharge capacity and
charge acceptance occurred in cycles between capacity tests. It is suspected that the
aggressive charging protocol used to recharge the battery for a capacity test was the
source of the performance boost experienced by cycles directly following the set of
diagnostic tests. It is therefore recommended that future automotive lead-acid battery
experimental aging studies adopt a capacity test charging protocol that has a maximum
voltage closer to what is produced by the alternator (14-15V) in order to avoid corruption
of the aging results. Furthermore, based on these findings, this type of high voltage (1516V) charging strategy could be temporary instated onboard a vehicle equipped with an
externally regulated alternator to possibly regain some lost electrical performance. This
102
type of advanced charging strategy could significantly extend battery lifetime onboard a
vehicle, and should be investigated further. A new diagnostic test that measures voltage
drop over time under a known load (‘dV’ test) to determine remaining discharge capacity
was also proposed, and based on the initial findings, warrants further exploration and
validation to confirm its potential. The next chapter integrates many of the diagnostic
tests introduced in this chapter into an onboard state of health estimation calculator.
103
5 LEAD-ACID BATTERY STATE OF HEALTH ESTIMATION ALGORITHM
5.1 Introduction
This chapter introduces a lead-acid battery state of health estimation algorithm that can
be run onboard a vehicle in order to assess: battery capacity, ‘absolute’ state of charge,
and high-power resistance.
In addition, based on these estimated battery electrical
performance metrics, the algorithm can recommend a different battery charging strategy
to the system responsible for assigning alternator reference voltage in an attempt to
extend battery life. Finally, the algorithm is also capable of generating its own ‘check
engine light’ (CEL) to indicate the need of immediate battery replacement should
estimated performance drop below some predefined minimum threshold.
5.2 Battery Mapping
In order to estimate any of the aforementioned battery performance metrics, extensive
electrical characterization derived from empirical data under different conditions must be
performed on the battery of interest. One of the most fundamental and important of these
‘maps’ or tables is the relationship between battery rested open-circuit voltage and amphours discharged. Using the charging protocol specified by the battery manufacturer, the
104
battery should first be fully charged. This ensures that the maximum amount of active
material is available for reaction. After a 24 hour rest period, the first open-circuit
voltage should be recorded. At this point, the battery should be discharged at the C/20
rate for a period that would correspond to a 10% change in SOC. The battery should then
be allowed to rest for a period of 8 hours before an open circuit voltage measurement is
collected, and the process is repeated.
The selected resolution (step-duration) is
completely arbitrary, and can be as fine or course as the diagnostician requires. When the
battery has reached a loaded terminal voltage of 10.5V, the battery has reached 0% SOC
and the load should be disconnected. The data collected for new battery N4 can be seen
in Table 5.1 and Figure 5.1 below.
E0 (V)
Ah_d (Ah)
SOC
13.23
0
100%
12.88
6.24
86.70%
12.73
12.52
76.8%
12.65
15.87
71.5%
12.58
19.2
66.9%
12.46
25.38
59.0%
12.34
31.47
51.1%
12.2
37.59
41.9%
12.07
43.66
33.33%
11.93
49.66
24.11%
11.85
52.96
18.84%
Table 5. 1: Battery rested open circuit voltage vs Amp-hours discharged
105
Figure 5. 1: Battery rested open circuit voltage vs Amp-hours discharged
This process should be repeated at several different temperatures to form a
comprehensive map that will allow a rested open-circuit voltage measurement to identify
the number of amp-hours discharged.
In addition to the open-circuit voltage vs amp-hours discharged map, an amp-hour
remaining vs voltage slope map should also be developed.
Building this map first
requires selecting the desired level of discharge current to be used during the onboard
test; magnitudes between C/2 and C are recommended by the author. At this point, the
battery should be fully discharged at the selected rate down to a terminal voltage of
10.5V starting from several initial rested open circuit voltages. The slopes of these
voltage curves should be evaluated at various amp-hours away from the 10.5V intercept.
106
This process should be repeated at various temperatures to form a comprehensive map so
that a measured voltage drop over a predefined period under any SOC or T can be used to
find an approximation of remaining amp-hours.
Figure 5. 2: Remaining amp-hours vs change in voltage over 100sec period
Functional relationships or tables derived from empirical data using the same current step
should also be found to relate estimated battery parameters to capacity at various opencircuit voltages and temperatures, as described in the previous chapter.
Also, a
relationship should be developed between capacity and amp-hours cycled, similar to that
shown in Figure 4.8 for batteries N1 and N2.
107
In addition to battery mapping, upper and lower bounds should be assigned for cranking
resistance Rcrank and capacity Q, respectively. These boundaries define the minimum
acceptable level of electrical performance of the battery.
5.3 Diagnostic Tests
Two ‘tests’ are conducted onboard the vehicle in order to estimate capacity and high
power resistance.
The first test combines dynamic response and ‘delta V’ tests by
activating a step change in load. This load should be on the order of C/2 in magnitude,
and activation should occurs after the vehicle electrical system has been inactive (no
driver interaction) for a period of 8 hours. This could easily take place overnight while
the vehicle is parked. After the 8-hour rest period has expired without disturbance,
conditions are deemed appropriate for testing.
At this point, voltage, current and
temperature measurements would begin to be collected and the desired sampling rate; 10100Hz is recommended. After 30seconds of open-circuit voltage measurements, the load
is applied for a period of 220seconds.
108
Figure 5. 3: Step response test
This duration allows parameter estimation to characterize the short-term dynamics in the
first 5-40seconds of the response, and the voltage drop over the last 100seconds to
indicate the remaining discharge capacity. In the time between these two parts of the
voltage response, the ‘coup-de-fouet’ often makes an appearance, which can throw off
the results of either diagnostic technique.
The second diagnostic test utilized by the state of health algorithm is not really a test at
all, but rather a collection of voltage and current measurements when the driver cranks
the engine. This data allows a calculation of differential cranking resistance to take
place, which can indicate trends in the battery’s ability to provide the high power
required by the starter motor.
109
5.4 State of Health Calculations
Voltage and current measurements from the crank test and step test are used in
combination with the battery maps developed from the previous section and diagnostic
techniques described in the previous chapter to produce battery performance metrics:
cranking resistance Rcrank, capacity estimate Qest and absolute state of charge estimate
SOCest. Equations (20) through (26) are used to calculated these metrics.
Rcrank =
V0 ! Vmin_avg
Imax_avg ! I0
(20)
Qest = ! " Qcyc + # " Q pe + $ " Q%V
(21)
Qest ! Ahdis
Qest
(22)
SOCest =
where
! +" +# =1
Q!V = Ahdis (Voc ) +
(23)
Ahremain _ ub (dV /dt) + Ahremain _ lb (dV /dt)
2
Q pe = f (P)
Qcyc = f
(24)
(25)
(! I " dt )
(26)
110
The battery capacity estimate Qest is a weighted average of capacity estimates found from
parameter estimation Qpe, voltage slope QdV and amp-hours cycled Qcyc. The amp-hours
discharged Ahdis is found from the measured open-circuit voltage and its associated
lookup table.
Similarly, the upper and lower bounds of the remaining amp-hours,
Ahremain_ub and Ahremain_lb, are found from the measured change in voltage with respect to
time and the associated lookup table. Estimated parameter value P is also used to find an
estimate of capacity Qpe from its lookup table. Finally, a capacity estimate Qcyc is found
from the total measured amp-hours cycled and its respective map.
After Qest is
calculated, the absolute state of charge SOCest is found by subtracting Qest by Ahdis and
dividing by Qest. The cranking resistance measurement is calculated in a similar fashion
to that of the pulse 1 in the power cycle, where Vmin_avg and Imax_avg are the average
minimum voltage and maximum current over the cranking duration.
5.5 Health Assessment
In addition to the actual quantification of battery health using the metrics calculated in the
previous section, the SOH algorithm also determines whether the battery needs
replacement. If Qest is found to be below the minimum acceptable value, Qmin, or if Rcrank
is found to be above the maximum acceptable value, Rmax, the SOH algorithm will
increase the alternator voltage output to 15-16V for the next j hours of charging. If, at the
conclusion of this period, the capacity estimate is still below the minimum value, or the
cranking resistance is above the maximum acceptable value, the battery must be replaced
111
and the algorithm triggers a CEL to notify the driver. If at this point the capacity and
resistance are back within a tolerable range, the alternator output voltage returns to its
nominal value.
5.6 Conclusions and Future Work
The conceptual framework for an onboard battery state of health diagnostic algorithm has
been developed in this chapter.
It utilizes a variety of techniques that would be
constructed from extensive amounts of empirical data to calculate the desired battery
electrical performance metrics. Based on the experimental data collected from the aging
of batteries N1 and N2, many of these diagnostic tests appear to have some merit in their
ability to relate to battery capacity.
However, many more experiments need to be
conducted to fully evaluate each of these methods. Once it has been determined that
capacity and cranking resistance can be reliably estimated, future work in this area should
include development of a prognostic algorithm to predict the remaining time and mileage
prior to battery failure.
112
BIBLIOGRAPHY
[1]
D. A. J. Rand et al., Valve Regulated Lead Acid Batteries, Elsevier, New York,
2004.
[2]
Robert Bosch GmbH, Alternators and Starter Motors, Robert Bosch GmbH, 2003.
[3]
“BMW Introduces Intelligent Alternator Control with Regenerative Braking…”,
http://www.greencarcongress.com/2006/09/bmw_introduces_.html,
September
2006.
[4]
V. S. Bagotsky, Fundamentals of Electrochemistry, John Wiley & Sons, Inc.,
New Jersey, 2006.
[5]
D. U. Sauer, E. Karden, B. Fricke, H. Blanke, M. Thele, O. Bohlen, J. Schiffer, J.
B. Gerschler, R. Kaiser, J. Power Sources 168 (2007) 22-30.
[6]
M. Dimitrov, D. Pavlov, J. Power Sources 93 (2001) 234-257.
[7]
L. T. Lam, N. P. Haigh, C. G. Phyland, A. J. Urban, J. Power Sources 133 (2004)
126-134.
[8]
D. Pavlov, V. Naidenov, S. Ruevski, V. Mircheva, M. Cherneva, J. Power
Sources 113 (2003) 209-227.
[9]
A. Hammouche, M. Thele, D. U. Sauer, J. Power Sources 158 (2006) 987-990.
[10]
http://www.optimabatteries.com/home.php
[11]
http://www.exide.com/products/trans/na/automotive.html
[12]
J. H. Yan, W. S. Li, Q. Y. Zhan, J. Power Sources 133 (2004) 135-140.
113
[13]
R. Wagner, J. Power Sources 53 (1995) 153-162.
[14]
Y. Guo, M. Wu, S. Hua, J. Power Sources 64 (1997) 65-69.
[15]
M. L. Soria, J. C. Hernàndez, J. Valenciano, A. Sànchez, J. Power Sources 144
(2005) 473-485.
[16]
P. Ruetschi, J. Power Sources 127 (2004) 33-44.
[17]
D. Pavlov, G. Petkova, T. Rogachev, J. Power Sources 175 (2008) 586-594.
[18]
Y. Yamaguchi, M. Shiota, Y. Nakayama, N. Hirai, S. Hara, J. Power Sources 85
(2000) 22-28.
[19]
T. McNally, J. Klang, J. Power Sources 116 (2003) 47-52.
[20]
D. Pavlov, V. Naidenov, S. Ruevski, J. Power Sources 161 (2006) 658-665.
[21]
G. Papazov, D. Pavlov, J. Power Sources 62 (1996) 193-199.
[22]
I. M. Steele, J. J. Pluth, J. W. Richardson Jr, J. Power Sources 95 (2001) 79-84.
[23]
T. G. Chang, D. M. Jochim, J. Power Sources 91 (2000) 177-192.
[24]
K. Sawai, Y. Tsuboi, Y. Okada, M. Shiomi, S. Osumi, J. Power Sources 179
(2008) 799-807.
[25]
H. Bode, Lead-Acid Batteries, John Wiley & Sons, New York, 1977.
[26]
D. Doerffel, S. A. Sharkh, J. Power Sources 155 (2006) 395-400.
[27]
Nick Picciano
114
APPENDIX
2.2 LARGE SIGNAL RESPONSE MODELING
Large signal response modeling provided another method for refining the battery model.
This method also allows for comparison between methods, and allows for better
modeling of the battery while being operated since the EIS modeling is really only
sufficient for small signals. This modeling investigates the battery response to different
large signals, for charge and discharge, and once again tries to fit a circuit model to the
response.
2.2.1 MODIFYING ORIGINAL METHOD
The original battery model was based on this method, and the refined model is an
adaptation to this method. The large signal to be applied consisted of a staircase current
profile, which would provide a sufficient set of voltage responses to characterize the
battery. The original model, however, seemed to need adjustments to this staircase
profile, as well as, adjustments to the parameterization method.
To begin, the levels of current in the staircase are developed specifically for the size of
the battery capacity. Moreover, the time the current is to be applied depends on the
115
battery capacity. The entire staircase is to only discharge the battery approximately 5% of
its rated capacity. This constraint is due to the dependence of the parameters on the
battery’s SOC. If we limit the change of SOC, then we can effectively neglect the
dependence of parameters on SOC. Each step within the staircase is a different current
level, which will then provide a different voltage response. The parameters are then
determined at each step on the staircase by assuming constant SOC and temperature
along the step. The result is a set of responses for one staircase where a set of parameters
will characterize each step. An example staircase current profile can be found in the
figure below.
Figure 7: Staircase Profile for Large Signal Modeling
120
Posssible battery current profile
100
s
p
A
t
n
e
r
r
u
c
80
60
constant parameter
at each step r(I,SOC,T)
40
2I
20
1I
initial rest
0
50
steps
/N
max
SOC
0
/N
max
100
steps
inter pulse rest
change
= 5%
150
time s
116
200
250
300
As briefly mentioned above, this staircase profile needed to be modified to better
approximate the battery parameters. One modification for the staircase profiles is to
include more steps in the staircase to obtain more responses. Another modification
considered is to stagger the step levels. Since the battery in a vehicle is found to operate
around 20A more than any other current level, it could be advantageous to have more
current steps around the 20A level. The figures below help show these modifications.
Figure 8: Additional Steps in the Staircase
90
117
Figure 9: More Steps Concentrated around 20A
Additional modifying techniques to be done would be to superimpose noise onto the
staircase. This would then allow for better characterization at high frequencies. Since
the battery is a nonlinear system, the response to noise provides a very reasonable data set
for analysis. The final staircase for a discharge response is shown below.
118
Figure 10: Discharge Staircase
60% SOC discharging current Amps
120
100
s
p
m
A
t
n
e
r
r
u
c
!5
80
60
!4
40
!3
20
0
"6
!1
0
50
!2
100
150
200
250
300
time s
Step
Discharge Current (A)
1
10
2
20
3
30
4
50
5
75
6
100
119
350
2.2.2 STAIRCASE RESPONSE ANALYSIS
Before the parameters of each step in the staircase are identified, the data must be
preprocessed.
This process mainly includes the filtering of the data, and the
identification of the beginning and ending time for each step in the staircase. The data is
filtered through a multi-stage median filtering process before it is used in the
identification of parameters. The voltage response data is then subdivided into groups
that correspond to each step in the current discharge staircase (each of which undergoes a
separate estimation).
After the data is preprocessed in this fashion, it is ready to be used in identification. The
method for extracting the parameters is a function already located in MATLAB called
“fmincon”. This function is an ARMA based identification method. The cost function
minimized by fmincon is a least squares error between the experimental and simulation
voltage response curves. A first order Randle Model is created in Simulink and used to
identify the model elements. Since fmincon is used in the parameter estimation, the
accuracy of the estimation is highly dependent on the initial guess. This was found to be
particularly true with the initial value of the capacitor C1. In many instances, finding an
adequate fit for the experimental data was achieved after trying a number of different
initial values for C1. Ultimately, the initial values used for C1 ranged anywhere from 3070000 depending on the step under examination. A circuit diagram of the first order
120
model and a table of boundary and initial values used in parameter estimation are shown
below.
Figure 11: First Order Randle Model and Parameter Estimation bounds
R0
R1
C1
Lower Bound:
0.0001
0.0001
1
Upper Bound:
0.1
0.1
100000
Initial Value(s):
0.01
0.01
30-70000
Since the parameters depend on SOC, the staircase profiles need to be run for batteries at
different SOC. The profiles were examined at three SOC’s: 60%, 75%, and 100%. The
results for these tests can be found below.
121
Figure 12: Staircase Discharge Voltage Response and Fit for 100% SOC
122
Figure 13: Staircase Discharge Voltage Response and Fit for 75% SOC
123
Figure 14: Staircase Discharge Voltage Response for 60% SOC
124
100% SOC:
Step #
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Recovery
R0
0.0194
0.0117
0.0112
0.0085
0.0079
0.0079
0.0134
R1
0.0239
0.02
0.0152
0.0123
0.0091
0.0057
0.901
C1
537.6
285.1
270
210
250.04
70000
10.97
0.0127
0.0085
0.0098
0.0081
0.0082
0.0076
0.0188
0.0359
0.0235
0.0154
0.0111
0.0076
0.0064
1.3328
186.02
70.01
60
70
196.7
2100
5.37
0.0125
0.0134
0.0107
0.0103
0.0099
0.0084
0.0185
0.0337
0.0191
0.0157
0.0102
0.0078
0.0548
1.658
223.9
380
580
1100
6000
50000
6
Time Constant
12.85
5.70
4.10
2.58
2.28
399.0
9.9
RMS error (V)
0.0082
0.0064
0.0076
0.0105
0.0133
0.0157
0.0098
Peak error (V)
0.1141
0.0382
0.0221
0.0217
0.0259
0.0427
0.0952
6.68
1.65
0.92
0.78
1.49
13.4
7.2
0.005
0.0062
0.008
0.0114
0.0143
0.017
0.0145
0.0369
0.0164
0.0181
0.0234
0.0277
0.0418
0.1264
7.55
7.26
9.11
11.22
46.80
2740.0
9.9
0.0071
0.0067
0.0068
0.0089
0.0105
0.0109
0.0131
0.0365
0.0342
0.0186
0.0285
0.0367
0.0253
0.1225
75% SOC:
Step
Step
Step
Step
Step
1
2
3
4
5
Step 6
Recovery
60% SOC:
Step
Step
Step
Step
Step
1
2
3
4
5
Step 6
Recovery
Table 1: Parameter Extraction
As can be seen in figures 12-14 and in Table 1, parameter values found from estimation
resulted in very low error statistics between the experimental and simulation voltage
response data. However, the tendency of the optimization function fmincon to find a
local minimization (as opposed to global) of the cost function necessitated the trial of
number of different initial parameter values before obtaining satisfactory results.
125