A battery ageing model used in stand alone PV systems
A.Cherif *,M.Jraidi,A.Dhouib
Laboratoire d'Energe
Âtique ENIT,Engineering Institute of Tunis,BP 37,Le Belve Âde Áre,1002Tunis,Tunisia Received 17J anuary 2002;received in revised form 15May 2002;accepted 27May 2002
Abstract
The authors present a new model for the ageing of a lead-acid battery which is based on the initial model of Shepherd.The proposed model
allows to predict temporal variations of the Shepherd coef®cients and to control the deterioration of the battery parameters and performances.The model validation has been realised by the recursive least square (RLS)algorithm by using long-term measurements under several solicitations.This study will improve the storage section of stand-alone photovoltaic systems and reduce overloads and deep discharges.#2002Elsevier Science B.V .All rights reserved.
Keywords:Shepherd model;Recursive least square algorithm;Less battery storage system
1.Introduction
The electrochemical storage section constitute the weak point of photovoltaic stand alone PV plants due to their maintenance,life period and breakdowns.Thus,the improv-ing and the conception of new storage strategies constitute a promising research area of PV applications.
In fact,we have presented in a previous study [1]two alternatives of PV systems.The ®rst one is the less battery storage system (LBSS)in which the electrical storage is substituted by hydraulic,thermal,eutectic or latent storage.Among its main applications,we can note PV pumping,desalination and refrigeration.These plants,which work to the thread of the sun,require more favourable climatic conditions and high ef®ciency of dc±dc and dc±ac converters.The second PV system is the battery storage system which uses a lead-acid battery,a dc±dc converter and a ®xed frequency self commutated inverter.These systems,which are,used in rural electri®cation and grid connected PV plants require optimal battery regulation and control by reducing the overloads and the high discharges.2.The storage battery model
Thanks to their sturdiness and stability,the lead-acid batteries are the most used in rural PV electri®cation.Such
battery is mainly characterised by the following three rela-tions:
the relation between the state of charge (Q )and the charging current (I )[2,3],
the variation of the voltage (V )according to the current and the state of charge (Q ),
the capacity variation (C )in function of the current [4].The synoptic diagram of the battery model is presented in Fig.1.
2.1.Presentation of the battery model
The simulation model,which predicts the charge±dis-charge phenomena,is that proposed by Shepherd [5].This model presents the relation between voltage,current and the battery state of charge Q as follows:in discharge (I <0):
U t U d Àg d It C R d I 1 M d It
C 1 C d ÀIt
(1)
in charge (I >0):U t U c Àg c 1ÀIt C R c I 1 M c It
CC c ÀIt
(2)
where U is the battery output voltage,g the coef®cient with
characterise D U f (Q ),C the capacity,R the internal resistance,I the current,t the time,T the temperature,M the slope of the U f (t ,I ,Q )characteristic,SOC the state of charge (1À(Q /C )),DOD the deep of discharge (Q /C )and c ,d are the indices of charge and discharge,
respectively.
Journal of Power Sources 112(2002)49±53
*
向华强北京挨打Corresponding author.Tel.: 216-1-874700;fax: 216-1-872729.E-mail addresses:adnen2fr@yahoo,adnane.u.tn (A.Cherif).
0378-7753/02/$±see front matter #2002Elsevier Science B.V .All rights reserved.PII:S 0378-7753(02)00341-5
2.2.Experimental tests and results
To validate the model of Shepherd,we have proceeded experimentally to the tests of charge and discharge of the battery with ®xed currents.The measured values enabled us to determine the model parameters (G d ,R d ,M d ,C d ,C c ,g c ,R c ,M c ,C c )relating to discharge and charge processes [6].The two parameters U d and G d are calculated according to the measured linear characteristic U f (t )obtained for I 0and 4.5A (Figs.2and 3).The discharge resistance R d is obtained for the origin value (t 0),as:R d U I 0 ÀU I 0 I À1
(3)
The parameters C d and M d can be deduced with the choice of experimental points.The model para
meters of the charge process are computed with the same method.
These parameters are deduced from empirical expressions obtained from a Tunisian battery,type ASSAD/TV90(12V/90Ah)which is the most used in the photovoltaic applica-tions in Tunisia (such as PV electri®cation,pumping,refrig-eration,...).The measured values of the Shepherd parameters relatives to a battery element are presented in the following Table 1.
3.Modelling of the battery ageing
The main reasons for the ageing process are the corrosion of the positive grid,the degradation of the active material and the sulfatation during long periods in low states of charge [6].These procedures increase the internal resis-tance,decrease the capacity and reduce the battery life period.However,the Shepherd model given by expressions (1)and (2)does not represent the ageing of the main parameters in function of the time.In order to take into account the dynamic behaviour of the battery,we will identify the temporal model of each parameter by using experimental input/output measurements under several soli-citations (I 0,1,4.5A,...)and state of charge Q (new,1month old,3months old,1year old,...).3.1.Procedure and experimental results
From the measured results,we have calculated the para-meters values of the Shepherd model for ea
ch state of ageing.As application,we have operated tests of charge and discharge to the same type of the battery ASSAD 12V/90Ah for four various states of its ageing:new,4,13and 30months old.
The obtained curves are presented by the Figs.2±4for the discharge and Figs.5±7for the charge.Table 2repre-sents the values of the same parameters for the other states of
ageing.
Fig.1.Synoptic diagram of the battery
model.
Fig.2.Discharge characteristic U f (t )with I 0A for four states of ageing (battery ASSAD 12V/90
Ah).
Fig.3.Discharge variation U f (t )with I 4:5A for four states of ageing (battery ASSAD 12V/90Ah).
Table 1
Experimental values of the Shepherd model parameters relatives to discharge and charge of the battery ASSAD 12V/90Ah (new state)Parameters Values U d (V) 2.175g d (V)0.21R d (O )0.0053M d 0.065C d
À0.005U c (V) 2.205g c (V)0.25R c (O )0.011M c 0.55C c
1.15
50 A.Cherif et al./Journal of Power Sources 112(2002)49±53
3.2.Presentation of the model of ageing
Thus,the obtained model of ageing is the following [6]:in discharge:
U U d Àg d It C R d I 1 M d It
C 1 C d ÀIt
(4a)
C d À0:005À0:0012t
(4b)U d 2:175À0:0001D 2
À0:036log 0:25t 1 (4c)M d 0:065 0:011log 0:75t 1 (4d)g d 0:210 0:0473log 0:33t 1
(4e)
R d 0:0053 0:0008D 20À0:5D 20À0:5D 2Àt 2q 0
B @1
C
A
(4f)
in charge:U U c Àg c
1ÀIt C
R c I 1
M c It CC c ÀIt
(4a H )
C c 1:15 0:0004t t 30
(4b H )U c 2:01 0:00013D 2 0:0266t log t 1 (4c H )M c 0:55 0:053log 0:25t 1
(4d H )g c 0:250À0:078log 0:125t 1
(4e H )R c 0:011 0:001D exp
Àt
t À20 0:5D
(4f H )
where D is the battery age (in months),t the time variable (in hours).The values at origin (t 0)indicate the new state of the battery.
3.3.The life time reduction
The lifetime reduction depends on the daily cycles,the deep of discharge,the sulfatation and corrosion process.Hence,the lifetime reduction due to sulfatation can be expressed by the empirical expression [7]:X s C 0:6 0:1C
(5)
Fig.4.Variation of discharge resistance R d f (t )for four states of ageing (battery ASSAD 12V/90
Ah).
Fig.5.Charge characteristic U f (t )with I 0A for four states of ageing (battery ASSAD 12V/90
Ah).
Fig.6.Charge variation U f (t )with I 4:5A for four states of ageing (battery ASSAD 12V/90
Ah).Fig.7.Variation of the charge resistance R c f (t )for four states of ageing (battery ASSAD12V/90Ah).
A.Cherif et al./Journal of Power Sources 112(2002)49±5351
Table 2
Effect of the ageing on the battery parameters (battery ASSAD 12V/90Ah)Months U d (V)g d (V)
R d (O )
M d C d U c (V)麦克杰克逊的歌曲
g c (V)
R c (O )
M c C c
4 2.150.1700.0080.080À0.01 2.1670.230.0140.58 1.1713 2.120.1300.0140.092À0.02 2.1300.170.0190.62 1.2530
2.10
0.0970.0250.100
À0.04
2.1150.130.030
0.65
1.80
Fig.8.The validation
algorithm.
Fig.9.Configuration of a photovoltaic
plant.
Fig.10.Comparison between measured and simulated energetic efficiency
(with and without battery ageing PV 55Wcr,B 90
Ah).Fig.11.Comparison between measured and simulated Ah efficiency (with and without battery age
ing PV 55Wcr,B 90Ah).
52 A.Cherif et al./Journal of Power Sources 112(2002)49±53
Yet,the life period resulting from corrosion is:X c C 0:88 13:3C À3:4
(6)
The battery capacity for a discharge current (I )can be given by:
C I C 01:66
1 0:66 I =I 0 0:9
!
1 0:005D T (7)where D T T b ÀT a (battery cell temperature Àambient temperature)and I 0 4:5A (discharge current with remark-able solicitation)(DOD 80%).3.4.Results
The capacity of the battery is the most sensitive parameter to ageing since its slope is raised and remarkable.The other parameters U d ,G d ,U c ,g c ,R d and R c decrease according to logarithmic,
exponential and linear laws.C c and C d have an in¯uence on the speed of the end of charge and discharge processes,respectively.4.Validation
To validate the model of the battery ageing,we have used the recursive least square algorithm of Fig.8which was integrated in the software environment (INSEL [8]).The experimental and simulated values are compared in order to minimise the quadratic error [9].Besides we have compared in Figs.9±11the measured and simulated ef®ciency and satis-faction rate of a domestic PV rural electri®cation system.This hardware platform which is illustrated by Fig.9is constituted by:
a domestic PV electrification system fed by a 55power peak panel,a 90Ah battery and a load of 350WH per day (lighting 20W TV30W);
a data acquisition system MODAS (16inputs)which collect the experimental voltages,currents,efficiencies,temperatures,solar radiation,....For example,we presented in the Figs.11and 12the experimental and simulated variation of the satisfaction rate and the energetic ef®ciency.These parameters were simu-lated by considering two cases of the battery behaviour with ageing and without ageing.
We can observe how the ageing factor affects not only the battery parameters but also the PV syste
主角爱我m performances especially the satisfaction rate.
5.Conclusion
In this paper,we have identi®ed the temporal model of a lead-acid battery.Moreover,we demonstrated how the battery ageing affects all parameters of the Shepherd model.This variation is most remarkable with dynamic solicitations (in current and load consumption).However,in nominal functioning conditions,the ageing affects slightly the output voltage and is not signi®cant before the ®rst year.
To protect the battery from deep discharges and irrever-sible sulfatations,the load request and the power consump-tion must be limited and controlled.To avoid deep discharge,the voltage output must be ®xed in function of the discharge current.
Finally,the battery regulator in insuf®cient to reduce ageing consequences and thus must be assisted by an optimal management and monitoring of the PV plant.References只是太爱你
[1]A.Cherif,in:Proceedings of the Renewable Energy Congress on the
Evaluation of Less Battery Storage System in Stand Alone PV Plants,Florenze,1998.
[2]F.W.Anthony,Modelling and simulation of lead-acid batteries for
photovoltaic systems,Ph.D.Thesis,1983.
[3]J.R.Wood,Mobil Solar Corp.,Personal Communication,Waltham,
Mussachusetts,1980.
Solar Energy Conference,Athens,1983.
[5]C.M.Shepherd,Design of primary and secondary cells,Anequation
describing battery discharge,J.Electrochem.Soc.112(1965).
[6]M.Jraõ
Èdi,Contribution a Ála caracte Ârisation et a Ála mode Âlisation des syste
Ámes photovoltaõÈques,DEA Thesis,ENIT,Tunis,1993.[7]F.Al Chenlo,in:Proceedings of the 12th EPSEC on Life Time
and Sizing of Batteries in Stand Alone PV Plants,Amsterdam,1994.
[8]H.G.Bloos,On the validation of programs for the simulation of
PV-battery systems,Master Thesis,University of Oldenbourg,1989.
[9]A.Cherif,Mode
Âlisation dynamique d'une unite Âde refrigeration solaire,Doctorate Thesis,Tunis,
1997.
大家一起来 孙悦Fig.12.Comparison between measured and simulated satisfaction rate (with and without battery ageing PV 55Wcr,B 90Ah).
A.Cherif et al./Journal of Power Sources 112(2002)49±5353
发布评论