Health Monitoring and Remaining Useful Life Estimation of Lithium-Ion Aeronautical Batteries

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1 Health Monitoring and Remaining Useful Life Estimation of Lithium-Ion Aeronautial Batteries José Affonso Moreira Penna Instituto Tenológio de Aeronáutia ITA - Praça Marehal Eduardo Gomes, 5 CEP São José dos Campos, São Paulo Brasil zeaffonso@gmail.om Cairo Lúio Nasimento Júnior Instituto Tenológio de Aeronáutia ITA - Praça Marehal Eduardo Gomes, 5 CEP São José dos Campos, São Paulo Brasil airo@ita.om Leonardo Ramos Rodrigues EMBRAER S.A. Avenida Brigadeiro Faria Lima, 27 Putim, São José dos Campos, São Paulo, Brasil, leonardo.ramos@embraer.om.br Abstrat Batteries are essential omponents of any airraft eletrial system. They are used to start the airraft propulsion engines and to provide power during eletrial emergenies. As is the ase with most airraft omponents, batteries exhibit aging and health degradation during operation. Therefore, the orretly estimation of the battery state-of-health (SoH) and of the remaining useful life () is important to airraft operators. Failure to do so an result in underutilization of the equipment (if it is removed before the end of its life yle) or unpredited failure events during operation (when the battery SoH is overestimated). The onsequenes an range from inreased operation osts to redued flight safety. This artile first presents the life yle of lithium-ion aeronautial batteries. Then a method is proposed to generate disharge, apaity and health monitoring models during the battery life yle. It is shown how these models are used to estimate the battery SoH and. The method is validated using data from the NASA Ames Prognostis Data Repository. The models are implemented using MATLAB/Simulink and used to simulate a typial battery in different operational onditions. TABLE OF CONTENTS. INTRODUCTION LITHIUM-ION BATTERIES DISCHARGE AND CAPACITY MODELS HEALTH MONITORING MODEL MODELS SIMULATION ESTIMATING REMAINING USEFUL LIFE CASE STUDY CONCLUSIONS... REFERENCES... BIOGRAPHIES.... INTRODUCTION PHM (Prognostis and Health Management) is a systems engineering disipline in proess of maturation and therefore does not have a researh methodology established and universally aepted. In the last deade, groups that studied the system s reliability have begun to fous on fundamental priniples of failures with the purpose of understanding how omplex systems age and thus predit when they might fail. The emerging siene that onnets the study of failure mehanisms to the management of system life yle is alled PHM []. Therefore, the PHM projet inludes a health monitoring omponent and the use of this health monitoring to predit the failure, enabling ations to better perform a maintenane task. The siene of prognostis is prediated on four fundamental notions []: () All eletromehanial systems age as a funtion of use, passage of time, and environmental onditions; (2) Component aging and damage aumulation is a monotoni proess that manifests itself in the physial and hemial omposition of the omponent; (3) Signs of aging (either diret or indiret) are detetable prior to overt failure of the omponent (i.e., loss of funtion); (4) It is possible to orrelate signs of aging with a model of omponent aging and thereby estimate remaining useful life of individual omponents. MTBF (Mean Time Between Failures) is used in many appliations as a referene value in order to estimate when a omponent will fail. However, degradation is a omplex funtion that an affeted by many aspets suh operational profile, time and environmental onditions. Thus, the omponent an be repaired or replaed with a positive or the failure an ours before the appropriate maintenane intervention. A preise estimation requires ontinuous monitoring and analysis of environmental onditions in whih the omponent operates (e.g., temperature, humidity, pressure, aeleration, speed, vibration). Furthermore, it is important to use the appropriate metris for the estimation of life (e.g., disharge/reharge yles for lithium-ion batteries, flight hours for engines, number of landings/takeoffs for brakes and gears, number of pressurization yles to strutural fatigue). The estimation of an be based on data reorded from the airraft (Data-Driven Methods) or based on models (Model-Based Methods). In first option, the hallenge is to /2/$ IEEE

2 apture and analyze multi-dimensional and noisy data ontaining a large number of variables related to omponent degradation. In many ases, the olletion, storage and analysis are ostly. Given that the future health of the omponent depends on future operating and environmental onditions, the management of unertainty is an inherent element in this method. Another approah to estimation is the model-based approah. The model-based approah involves development of first-priniples models of omponent use and damage aumulation, and the use of operational data to fine-tune model parameters. There are few examples of model-based methods in omparison with the data-driven methods. This reflets the fat that model-based prognostis are a more involved proess than data-driven prognostis. Depending on the fidelity of the model, model-based prognostis typially result in more aurate and preise estimation. Model-based prognostis also have advantages in validation, verifiation, and ertifiation sine the model response an be orrelated with laws of nature. A modelbase method to estimate the of lithium-ion batteries using PHM tehniques is presented in []. 2. LITHIUM-ION BATTERIES Lithium-ion batteries are omposed of an anode, a athode and an eletrolyte substane [2][]. The athode is made of grains of oxides of transition metal ion (e.g., LiCoO 2 ) whih have high energy density and good stability. The anode uses lithium metal, graphite or lithium alloy ompounds. Graphite spheres have the greatest ability to perform this funtion [3]. The eletrolyte substane an be liquid or solid [4]. When manufatured, the battery is disharged. Disharge: Reharge: LiCoO Li 2 6C Li x CoO2 + LixC6 + () xcoo2 + LixC6 LiCoO2 6C + (2) Lithium-ion batteries have a high initial apaity and a good onservation of harge after repeated yles of disharges and reharges. Additionally, these batteries are easily made beause all lithium atoms neessary to support the reation ell an be inorporated in the athode, whih, unlike most of the anodes, is relatively stable to air in its state of lithium (i.e., disharged). Lithium is a highly reative material, and very lightweight in omparison to the materials used in other batteries. Thus, the lithium-ion battery has a higher gravimetri energy density, as shown in Figure. Figure Comparative of the Energy Density of Different Batteries The lithium-ion battery has the advantage of a low selfdisharge rate, whih allows the battery to remain in stok for 2 months without maintenane. On the other hand, lithium is a very reative material, and requires a speial iruit to ontrol the harging and disharge, avoiding exeed the limits. If a voltage above the safe limit is applied, there may be a atastrophi failure (i.e., explosion), resulting in damage to the operating loation. In addition, a hole penetrating the eletrode or a negative eletrode ontating water are also situations that lead to atastrophi failure with a spontaneous ombustion. The expetation of the life yle of a lithium-ion battery is approximately 5 yles or more. Its storage when fully harged and at high temperature leads to a signifiant degradation of apaity. With the harateristis of being lightweight, having a good life in stok, a long yle life, wide temperature range for operation, high voltage per ell, no periodi maintenane requirement and a low self-disharge rate, lithium-ion beomes a good option for aeronautial appliations. Its relatively high ost is due mainly the ost of the protetions neessary for the operation of the battery. A ost study should be onduted to verify the feasibility of its use in an airraft projet. The performane of a lithium-ion battery is dependent on temperature and operating voltage. The diagram in Figure 2 shows that the battery should operate with voltage and temperature within the limits indiated by the green square. This is a very important harateristi of the lithium-ion batteries that, ompared to other aeronautial batteries, has more severe onsequenes when used outside their operating limits. When used outside these limits, permanent damage to the ell may result [5]. The effets of voltage and temperature in the battery failure tend to be evident immediately, but their effet during the life yle is less obvious. As mentioned, the use of the battery outside the reommended limits may ause an irreversible loss of battery apaity. The umulative effet of this degradation affets the lifetime of the ell and in the worst ase auses a sudden failure when it exeeds a ertain 2

3 limit. The yle of life mentioned in the manufaturers speifiations usually assume operations at room temperature, whih may be unrealisti for most appliations. Curves that reflet the life yle as a funtion of operating temperature are rarely provided by manufaturers. Another relevant fator is the battery s operating at different temperatures. Degradation ours at different rates whih are aumulated over the life of the battery. Prognostis CoE at NASA Ames [6], the battery apaity (C) through number of yles was alulated: C Tfinal I()dt t = (3) With this information, and applying a model for disharge, it was possible to simulate the disharge urve. To simulate the disharge urve, the model proposed by PAATERO [7] and by SPERANDIO [8] was used. The model ontemplates two omponents, the open iruit voltage (U OC ) and the over potential voltage (U OP ): U OC ( SoC) + T ( x + x ( SoC) ) = x + x (4) U OP + ( SoC) x( SoC) x3t [( x + x2 ) ( + x4 ) I ] + x = x 5 5 e tanh + x 6 T + x ( x ( SoC) + x ) 6 7 e 7 + x 8 x I + I (5) Figure 2 Lithium-ion Cell Operating Window The use of batteries in the aeronautial industry requires strit maintenane tasks. This is beause the battery is onsidered the last resoure used in the event of eletrial failure of the main soures of eletriity (e.g., generators) and alternative soures (e.g., ram air turbine). Thus, in today's airraft maintenane senario, maintenane tasks are assigned based on fixed times (hard times) or, in some ases, inspetion tasks that inlude the diagnosis of battery health (on ondition). In both situations, maintenane ations have diret and indiret osts, ontribute to the derease in the dispath of the airraft, produe insuffiient data to predit failure and represent a signifiant degradation in flight safety. Therefore, it is useful to employ methods of prognosis of battery health. Although in use sine 99, the development of aurate, safe, and with low ost eletroni ontrols for the operation of lithium-ion batteries, as well as ertifiations and produt regulations, have made lithium-ion tehnology attrative for the aviation industry, offering many benefits. The voltage at the terals of the battery (U) is defined as U = (6) U OC U OP The State of Charge (SoC) is defined as SoC C t ( t ) = SoC( t ) I()dt t t Using the first disharge of five different experiments, representing the disharge urve of the batteries in the new state and for eah one of the operational profiles (I,T), the parameters for the disharge model were alulated using the Matlab funtion fsearh, whih implements the least-squares algorithm, and the polynomial funtions that approximate the original data of the five disharge urves. (7) 3. DISCHARGE AND CAPACITY MODELS Using a data repository ontaining data of harges and disharges at different temperatures, provided by the 3

4 Table - Batteries Seleted to Disharge Model Battery I (A) T(ºC) B48 4 B B B B The disharge battery model provides a good fit for the polynomial funtions whih are used to approximate the original battery data. Figure 3 shows a omparison between the original data and the model data, with an error mean of.565 V and an error variane of.58 V 2. Table 2 - Disharge Model Parameters The apaity model parameters were defined using the data obtained from the apaity through the life yle of five batteries. The batteries were seleted with different disharge profiles (I, T) and with the same V = 2.2V (voltage at the end of the disharge, when the test iruit is opened), exept for battery B53 (V = 2.V). This battery was used beause of the better quality of the data if ompared with B54 (V = 2.2V). Table 3 - Batteries seleted to apaity model Battery I (A) T(ºC) B46 4 B B B B Parameters Value x x + x x +2 x x + x x -3 x 5 7,229 x +2 x x + x x +2 x x + x x -5 x x - x -3.3 x -3 x x - x x +2 x x + x x +2 x x + x x + Figure 3 Disharge Model Data x Repository Data 4

5 Table 4 - Capaity Model Parameters Based on the visual harateristis of the urve Capaity versus number of yles, a linear model for apaity was assumed. The parameters y y of the apaity model were alulated using the Matlab funtion fsearh. With these parameters and the respetive oeffiients, it was possible to obtain a good fit of the model, as shown on Figure 4 (error mean of.324 Ah and error variane of.35 A 2 h 2 ). C n + = (8) 3 2 ( T ) y + ( T I ) y2 + ( T I ) y3 + ( I ) y4 5 + = (9) y 3 2 ( T ) y6 + ( T I ) y7 + ( T I ) y8 + ( I ) y9 + = () y Parameters Value y 4.32 x - y x -2 y x -2 y x -7 y 5.52 x -7 y x + y x - y x -4 y x -4 y x +2 With the apaity model, it was possible to find the orrelation of temperature and eletrial urrent with the degradation through the life yle of the battery, shown in Figure 5 and Figure 6. Figure 5 Capaity Degradation x Eletrial Current Figure 4 Capaity Model x Repository Capaity Figure 6 Capaity Degradation x Temperature 5

6 In Figure 5, the onlusion is that with a smaller eletrial urrent, the initial apaity is higher, but the apaity's degradation is more aentuated. In Figure 6, the onlusion is that with a higher temperature, the initial apaity is higher, but the apaity's degradation is more aentuated. This relationship was until now unknown. Remaining Useful Life The estimated useful life remaining, alulated from the battery state of health (SoH). Provides information of the remaining number of yles that the battery an operate up to a threshold value of health (SoH), onsidering failure of the omponent from this limit. 4. HEALTH MONITORING MODEL To model the state of health battery, some basi onepts [9] were introdued: State of Health The state that represents the health of the battery throughout its useful life. When new, the battery has a life of % (i.e., SoH = ). After a yle, the value of SoH redues aording to the operating profile (I, T) in whih the disharge yle ours. 5. MODELS SIMULATION The disharge model, apaity model and health monitoring model, were implemented in Matlab & Simulink R2b in order to simulate a lithium-ion battery at airraft eletrial operations. The battery apaity was evaluated by the blok shown in Figure 7. SoH ( t ) SoH ( t ) DeltaHealth = () Delta Health Degradation of the health at eah battery disharge (or yle). This value is alulated from the apaity model and varies depending on the disharge profile (I and T): DeltaHealt h = (2) n ( = ) Figure 7 Simulink Diagram Used to Evaluate the Battery Capaity The State of Charge (SoC) of the battery was evaluated by the blok shown in Figure 8. ( ) n = ± error = (3) DeltaHealth = + error (4) Figure 8 Simulink Diagram Used to Evaluate SoC Relative Number of Cyles (rn) Represents the number of yles that the battery should perform in a ertain ondition of I and T to obtain a speifi value of SoH. This parameter is used when the battery operates in different operating profiles. For a given SoH, the battery may get different relative numbers of yles, aording to the parameters I and T: C SoC SoH ± error = (5) rn + = SoH ± error (6) ( SoH ) rn ± error = (7) Figure 9 Simulink Diagram Used to Evaluate the Battery Voltage during Disharge The battery voltage (U) was evaluated by the blok shown in Figure 9. These three diagrams represent the battery, and are assoiated like show in Figure. 6

7 Figure Simulink Battery Diagram To detere the operating profile of the battery (I,T) was used the blok shown in Figure. Using this blok the profile an be hanged in the same yle or during the life yle of the battery, depending on the set of the first swith. Figure 3 Simulink Diagram of the Health Monitoring System The SoH evaluation onsists in the implementation of the equations of the health monitoring model, shown in Figure 4, Figure 5 and Figure 6. Figure Simulink Diagram of the Profile Soure Figure 4 Simulink Diagram of the Overall SoH Evaluation The health monitoring blok together with the soure blok and the battery blok is shown in Figure 2. Figure 2 Simulink Diagram of the Lithium-ion Health Monitoring System Figure 5 Simulink Diagram of Delta Health and rn Evaluation The health monitoring blok onsists of the implementation of the health monitoring model. The apaity model s error is inorporated using a gaussian noise generator, shown in Figure 3. Figure 6 Simulink Diagram of SoH Evaluation 7

8 Figure 8 Estimation Figure 7 Example of SoH, rn, Delta Health Evaluation The oeffiients b and b and BINT matrix (2x2) are alulated by the REGRESS funtion: [ B BINT ] REGRESS( Y, X ), = (8) Figure 7 shows an example of the evaluation of SoH, delta health and nr at deterate operation profile throughout the life of the battery. At the yle 2 the disharge profile hange from I=4A and T=43 C to I=2A and T=24 C. b B = ; BINT b b = b MIN MIN b b MAX MAX (9) 6. ESTIMATING REMAINING USEFUL LIFE Using the SoH data evaluated with the health monitoring of the battery disharges, a method with the objetive to estimate the remaining useful life of the battery has been proposed. It onsists of () A linear regression of the SoH data available to date using the funtion REGRESS (Matlab R2b); (2) Evaluation of the yle number at whih the battery reahes the imum threshold of SoH (SoH) by extrapolating the line obtained by linear regression; (3) Addition of the unertainty of the model and of the future operating profile to be performed. The result is an estimated interval omprehended between the and max. Figure 8 shows the basis of the method. Extrapolation evaluates the estimated yle of the battery failure: n failure The an be evaluated by SoH b b = (2) = (2) n failure n atual and max are evaluated by SoH b max error = mean n atual b (22) max 2 max SoH b = b + error mean 2 n atual (23) 8

9 7. CASE STUDY Two ases were simulated. The first ase (Case A) is a simulation of the eletrial starting of the engines using the battery. The eletrial urrent was an exponential deay represented by Figure 2 shows the effet on disharge urve and SoC urve at the degraded battery after a few yles. It is observed that the disharge urve is omplete with the degraded battery and the SOC reahes zero. Figure 2 Degradation Effet Figure 9 Disharge profile (Case A) The threshold (SoH) was alulated by the number of yles that the battery annot exeute an emergeny yle that onsists of a 5 utes disharge of I=4A at T=43ºC (worst ase). With the simulation, the failure ourred when SoH=.6. With the result of the simulation, we have the failure ourring at yle number 495. Even of the battery an exeute the starting profile until yle number 77, the battery annot omply with the requirement to perform the emergeny yle after yle 495, as shown in Figure 2. In this ase the failure of the battery is delared on yle 495. Table 5 Estimation (Case A) Cyle Estimated Failure max Figure 2 Case A Simulation 9

10 The failure that was expeted to our at yle 3 is antiipated to our at yle 59, as shown in Figure 24. Figure 22 Estimation (Case A) Applying the estimating method was provided the urve shown in Figure 22 and the values showed on Table 5. With the small hange in the disharge profile, oasioned by the ambient temperature alteration along the year, the results present a good auray and preision (approximately 34 yles). At yle 47 the airraft operator an make a maintenane task plan. At yle 49 the method estimates the failure of the battery at yle 495, equal to the result obtained with the simulation. Figure 24 Case B Simulation Applying the estimating method, the urve shown in Figure 25 and the values showed on Table 6 were provided. With the inrease of the degradation rate during 25 yles, the method reognized this hange of degradation rate and gradually dereased the estimated number of yles that the battery an perform, after the yle 24. After the disharge profile had returned to the noal profile, the algorithm gradually reovers the estimation to the initial value us the number of yles that was degraded during the inrease in temperature. The response of the method, in this ase, ensures its appliability when there is a dynamial hange of disharge profile, I or T, and verifies the use of historial profiles to evaluate the estimation. Figure 23 Inrease of Degradation Rate The seond ase (Case B) is a simulation of a nonantiipated degradation when the battery operates with a noal operation of I=4A and T=24ºC. The inrease of the degradation rate is generated by an inrease on the ambient temperature (T=43ºC) and is shown by the red line in the Figure 23. Figure 25 Estimation (Case B)

11 Cyle Table 6 Estimation (Case B) Estimated Failure max CONCLUSIONS This paper presented a model based methodology to evaluate the state of health and estimate the remaining useful life of aeronautial batteries. A publi battery database was used in order to generate the models. Future investigation ould extend the work presented in this paper by onsidering the effets of depth of disharge in the battery model. REFERENCES [] UCKUN, S.; GOEBEL, K.; LUCAS, P. J. Standardizing researh methods for prognostis. In: INTERNATIONAL CONFERENCE ON PROGNOSTICS AND HEALTH MANAGEMENT, 28, Denver. Proeedings... Pisataway: IEEE, 28. [2] Mark N OBROVAC e Jeffrey R. DAHN. Lithium-ion batteries. 23. United States patent US 23/393 A, 3 Feb. 23. [3] GOLD PEAK INDUSTRIES LTD. Lithium-ion tehnial handbook. De., 2. Available in: < Aessed in: 4 aug. 2. [4] HARDING ENERGY, INC. Harding battery handbook for Quest rehargeable ells and battery pak. De., 28. Available in: < 2of%2Appliations.pdf >. Aessed in: 4 ago. 2. [5] ELECTROPAEDIA. Lithium battery failures. 25. Woodbank Communiations Ltd. Available in: < Aessed in: 4 aug. 2. [6] SAHA, B.; GOEBEL, K. Battery data set. 27. NASA Ames Prognostis Data Repository. Available in: < >. Aessed in: 4 aug. 2. [7] J. Paatero, A mathematial model for flooded nikel admium battery, Helsinki University of Tehnology, Department of Physis, Teh. Rep., 997. [8] G. S. Sperandio, Nikel-admium batteries model for disharge simulation, (in Portuguese) Professional Master Dissertation, Instituto Tenológio de Aeronáutia, São José dos Campos, Brazil, 2. [9] J. A. M. Penna, Health monitoring and remaining useful life estimation of lithium-ion aeronautial batteries (in Portuguese) Professional Master Dissertation, Instituto Tenológio de Aeronáutia, São José dos Campos, Brazil, 2. The ase studies ertified that the method an be applied to different disharge profiles and to dynamial hanges of profile during the yle or over the life of the battery.

12 BIOGRAPHIES José Affonso Moreira Penna reeived the B.S. degree in Eletrial Engineering from the Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil, in 28, and a Master Degree in Aeronautial Engineering from the Instituto Tenológio de Aeronáutia (ITA, 2), São José dos Campos, São Paulo, Brazil. Sine 2, he has worked as ivil aviation regulation speialist in the Continuous Airworthiness Superintendene of the Brazilian National Ageny of Civil Aviation (ANAC). Cairo L. Nasimento Jr. reeived the B.S. degree in Eletrial Engineering from the Universidade Federal de Uberlândia (UFU), Uberlândia, Brazil, in 984, the M.S. degree in Eletronis Engineering from the Instituto Tenológio de Aeronáutia (ITA), São José dos Campos, Brazil, in 988, and the PhD degree in Eletrial Engineering from the University of Manhester (UMIST), Control Systems Centre, Manhester, UK, in 994. Sine 986, he has been a leturer with the Division of Eletronis Engineering, ITA, and has supervised or osupervised 6 Ph.D. and 24 M.S./Prof.M. students. He is the o-author of a book on intelligent systems and was the hairman for the 999 Fourth Brazilian Conferene on Neural Networks. His urrent researh interests are the appliation of artifiial intelligene tehniques to Prognostis and Health management (PHM), intelligent mobile robotis, and the development of internet-based remote-aess laboratories for engineering eduation. Dr. Nasimento Jr. is an IEEE and SBA (Brazilian Soiety of Automatis) member. Leonardo Ramos Rodrigues holds a bahelor s degree in Eletrial Engineering from Universidade Federal do Espírito Santo (UFES, 23), Brazil, and a Master Degree in Aeronautial Engineering from Instituto Tenológio de Aeronáutia (ITA, 28), São José dos Campos, São Paulo, Brazil. He is with EMBRAER S.A., São José dos Campos, São Paulo, Brazil, sine 26. He works as a Development Engineer in an R&T group at EMBRAER perforg researh on PHM tehnology for appliation to aeronautial systems. His urrent researh interests are the appliation of health monitoring tehniques for eletroni omponents and the usage of PHM information for inventory optimization. 2