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 battery- driven 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 lead-
dioxide (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) H2SO4 + H2O ! HSO4 + H3O
Discharge RX at negative electrode : Pb + HSO - !Dissolution ! !! " Pb2+ + SO 2# + 2e# + H+ 4 14 4 2 4 4 43 (2) $ Deposition PbSO 4
Discharge RX at positive electrode : PbO + HSO - + 2e- + 3H+ !Dissolution ! !! " Pb2+ + SO 2# + 2H O 2 4 14 4 2 4 4 43 2 (3) $ Deposition PbSO 4
Overall RX : (4) Pb + PbO2 + 2H2SO4 ! 2PbSO4 + 2H2O 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 2+ 2# PbSO4 ! ! !! " Pb + SO4 (5) 2+ 2# + # - Pb + SO4 + H + 2e " Pb + HSO4
Primary charge RX at positive electrode : Dissolution 2+ 2# PbSO4 ! ! !! " Pb + SO4 (6) 2+ 2# - - + Pb + SO4 + 2H2O " PbO2 + HSO4 + 2e + 3H
Overall Primary RX : (7) 2PbSO4 + 2H2O ! Pb + PbO2 + 2H2SO4
Oxygen evolution RX at positive electrode : + - (8) 2H2O ! O2 + 4H + 4e
Oxygen recombination RX at negative electrode : + - (9) O2 + 4H + 4e ! 2H2O
Hydrogen evolution RX at negative electrode : + - (10) 2H + 2e ! 2H2
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].
RT ! aH SO $ E = E 0 + ln 2 4 (11) F # a & " H 2O %
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, a is the H 2 SO4
activity of the sulfuric acid in the electrolyte and a is the activity of the water in the H 2O electrolyte. The chemical ‘activity’ can be approximated by concentrations. With a
known battery chemistry and temperat ure, 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 open- circuit 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.
E0 = 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 !V R = (13) diff !I
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 (14) dt R1 "C1 C1
Vbatt = !Vc ! R0 " I + E0 (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 ‘open- circuit’ 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.
1 SOC = SOC ! "SOC = SOC V ! I # dt (16) 0 0( oc ) Ah $
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 + PbO2 + 2H2SO4 ! 2PbSO4 + 2H2O (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 lead- sulfate 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 lead- alloys 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 ! " PbO2 and ! " PbO2 crystals when the battery is new to only ! " PbO2 when the battery has been extensively cycled is best seen in the scanning electron micr oscope 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 V0 ! Vmin Rcrank = (17) Imax ! I0
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 amp- hours 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).
!V Voc " Vp1_ avg Rp1 = = (18) !I I p1_ avg
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 time- period 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)) (19) i=1
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.
Capacity R0 R1 Tau 1 RMS error Cycle Total Ah (Ah) (Ohms) (Ohms) C1 (F) (sec) (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
Capacity R0 R1 Tau 1 RMS error Cycles Total Ah (Ah) (Ohms) (Ohms) C1 (F) (sec) (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.
Ah_dis Tau RMS Error E0 (V) (Ah) SOC R0 R1 C1 (F) (sec) (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 (15-
16V) 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 amp- hours 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 open- circuit 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; 10-
100Hz 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.
V0 ! Vmin_avg Rcrank = (20) Imax_avg ! I0
Qest = ! "Qcyc + # "Qpe + $ "Q%V (21)
Qest ! Ahdis SOCest = (22) Qest
where
! + " + # = 1 (23)
Ah (dV /dt) + Ah (dV /dt) Q = Ah (V ) + remain _ ub remain _ lb (24) !V dis oc 2
Qpe = f (P) (25)
Q = f I " dt (26) cyc (! )
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
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[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
80 s p A
t n e r 60 r u c constant parameter at each step r(I,SOC,T) 40 2I /N max steps
20 1I /N max steps initial rest inter pulse rest
SOC = 5% change 0 0 50 100 150 200 250 300 time s
116 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 " 6 m A 80 ! 5 t n e 60 r r ! 4 u c 40 ! 3 2 20 ! ! 1
0 0 50 100 150 200 250 300 350 time s
Step Discharge Current (A)
1 10
2 20
3 30
4 50
5 75
6 100
119
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 30-
70000 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 # R0 R1 C1 Time Constant RMS error (V) Peak error (V) Step 1 0.0194 0.0239 537.6 12.85 0.0082 0.1141 Step 2 0.0117 0.02 285.1 5.70 0.0064 0.0382 Step 3 0.0112 0.0152 270 4.10 0.0076 0.0221 Step 4 0.0085 0.0123 210 2.58 0.0105 0.0217 Step 5 0.0079 0.0091 250.04 2.28 0.0133 0.0259 Step 6 0.0079 0.0057 70000 399.0 0.0157 0.0427 Recovery 0.0134 0.901 10.97 9.9 0.0098 0.0952 75% SOC: Step 1 0.0127 0.0359 186.02 6.68 0.005 0.0369 Step 2 0.0085 0.0235 70.01 1.65 0.0062 0.0164 Step 3 0.0098 0.0154 60 0.92 0.008 0.0181 Step 4 0.0081 0.0111 70 0.78 0.0114 0.0234 Step 5 0.0082 0.0076 196.7 1.49 0.0143 0.0277 Step 6 0.0076 0.0064 2100 13.4 0.017 0.0418 Recovery 0.0188 1.3328 5.37 7.2 0.0145 0.1264 60% SOC: Step 1 0.0125 0.0337 223.9 7.55 0.0071 0.0365 Step 2 0.0134 0.0191 380 7.26 0.0067 0.0342 Step 3 0.0107 0.0157 580 9.11 0.0068 0.0186 Step 4 0.0103 0.0102 1100 11.22 0.0089 0.0285 Step 5 0.0099 0.0078 6000 46.80 0.0105 0.0367 Step 6 0.0084 0.0548 50000 2740.0 0.0109 0.0253 Recovery 0.0185 1.658 6 9.9 0.0131 0.1225
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