Different methods for determining the state of charge and operability of electric energy accumulators, in particular lead acid batteries customary in the automatic industry, are known from the related art. In most of the methods, the state of charge of lead acid batteries is determined from the open-circuit voltage measured in the idling state, since the open-circuit voltage is proportional to the acid density in a broad range of states of charge (open-circuit voltage method). For the purpose of estimating the operability or load capacity of the energy accumulator with regard to a predetermined current consumption or power consumption, the internal resistance, which in starter batteries is ideally computed from the difference between the measured voltage values divided by the difference between the measured current values during the high current load at engine start, is needed in addition to the open-circuit voltage or the state of charge. A method used for determining the battery charge in that manner is known from German Published Patent Application No. 198 47 648 for example.
Continuous information and the state of charge and the operability of energy accumulators is required when safety-critical electrical consumers are used in motor vehicles, e.g., steer-by-wire or brake-by-wire systems, but also for battery systems and consumer management systems, so that the open-circuit voltage and the state of charge must also be determined during charging and/or discharging phases, and the internal resistance also without high current load. For this purpose, the state of charge is mostly extrapolated via the current integral using charge balancing and the internal resistance is mostly extrapolated via fixed predefined characteristic curves as a function of state of charge and battery temperature. However, during extended operation of the energy accumulator without idle phases or high current load, as well as due to the aging effects not taken into account in the characteristic curves, this method results in errors in the estimation of the state of charge and operability.
To prevent these errors, the related art describes model-based estimation methods which constantly adjust the state variables and parameters of a mathematical model of the energy accumulator to the real state variables and parameters by continuously measuring voltage, current, and temperature. Such model-based estimation methods are known from German Published Patent Application No. 199 59 019 for example. In the known methods, state of charge and operability of the energy accumulator are calculated from state variables and parameters so determined. The disadvantage of these methods is the fact that in order to cover the entire operating range of the energy accumulator with regard to discharging-/charging current range, state of charge, temperature, as well as aging effects, a complex, and as a rule non-linear, model of the energy accumulator is required, having many state variables and parameters to be estimated and which may only be analyzed at a great expense.
Alternatively simpler models covering only individuals operating points of the battery, e.g., only the discharging operation, have advantages; however, they allow an accurate determination of state of charge and operability only at these operating points. Such simple models are described in German Published Patent Application No. 100 56 969 for example.
An object of the present invention is to make the most accurate determination of the state of charge and the operability of a charge accumulator possible over a large operating range without great expense. By using a weighted correction of the state variables and parameters estimated from at least two methods that are active at two different operating points via continuous measurement of voltage, current, and temperature, the method according to the present invention makes a more accurate estimation of the current and future state of charge and operability of the energy accumulator, in particular a motor vehicle lead battery, possible over a large operating range compared to the individual methods.
The method according to the present invention combines the advantage of the open-circuit voltage methods, i.e., the accurate determination of the open-circuit voltage, i.e., the state of charge in phases of the battery without load and the internal resistance at high current load (e.g., engine start), and the advantage of simple model-based estimation methods using which open-circuit voltage and internal resistance, as well as other optional state variables and parameters may be estimated, even during operation without idling or high current loads, thereby, compared to the individual methods, enabling a more accurate determination of the state of charge and the operability of the battery over a large operating range without complex battery models.
For calculating the state of change and the operability, the minimum required variables open-circuit voltage and internal assistance, as well as other optional state variables and parameters, are calculated in an advantageous manner from the values of the individual methods by weighted correction, their weighting being selected according to their reliability at the current operating point of the battery.
Predictions of the future operability are possible via extrapolation of the currently estimated state variables and parameters for state of charge and temperature to a later point in time, so that, the example, the capability of the battery to start a vehicle parked for several days may also be estimated.
State variables z(e.g., open-circuit voltage U00) and parameters p(e.g., internal resistance Ri) required for determining the state of charge and the operability of the battery are obtained from continuous measurement of battery voltage UBatt, battery current IBatt, and battery temperature TBatt by the state and parameter estimating system. The state of charge calculation determines state of charge soc from vector z of the state variables and from the instantaneous battery temperature TBatt, while the instantaneous operability of the battery is estimated via voltage response UBatt,pred(t) of a battery model initialized using state vector z and parameter vector p to a predefined load current profile ILoad(t).
If the operability of the battery at a future point in time is of interest, e.g., the starting capability is queried after the vehicle was parked for several days, then instantaneous variables z and parameters p, as well as instantaneous battery temperature TBatt are extrapolated to values z′, p′, and TBatt′ to be expected at the future point in time. In order to pre-estimate the reduction in the state of charge as a function of the parking time of the vehicle, the variation of closed-circuit current IRest(t) in the parked vehicle must be known.
Using method A, here referred to as open-circuit voltage method, open-circuit voltage U00 is determined during no-load phases of the battery and internal resistance R1 of the battery is determined during a high current load (e.g., engine start). In addition, further variables, e.g., (acid) capacity Q0 may be derived from measured variables current IBatt, voltage UBatt, and temperature TBatt, or calculated variables U00 and Ri. The state variables determined by method A are combined in state vector zA, and the parameters are combined in vector pA. Method B is model-based and also estimates at least open-circuit voltage U00 and internal resistance Ri, however, compared to method A, also in other or additional operating stages of the battery (e.g., discharge). The state variables determined by method B are combined in state vector zB, and the parameters are combined in vector pB.
In each calculation step k, state vector zk+1 is calculated by using weighted differences zA,K−zk, zB,k−zk and parameter vector pk+1 is calculated by using weighted differences pA,k−pk, pB,k−pk starting with starting values zk=0=z0 and pk=0=p0:
zk+1=zk+Gz,A*(zA,k−zk)+Gz,B*(zB,k−zk)
pk+1=pk+Gp,A*(pA,k−pk)+Gp,B*(pB,k−pk)
Weighting matrixes Gz,A, Gz,B, Gp,A, and Gp,B are square diagonal matrixes whose main diagonal elements gz,A,i=1 . . . n, gz,B,i=l . . . n, gp,A,j=1 . . .m, gz,B,j=l . . . m specify the degree of correction of the n state variables and the m parameters and must fulfill the following requirements, so that the sequences zk=0,zk=1,zk=2 . . . and pk=0,pk=1,pk=2 . . . converge:
gz,A,i+gz,B,i≦1, i=1 . . . n
gp,A,j+gp,B,j≦1, j=1 . . . m
The weightings are selected in such a way that state variables and parameters which at the instantaneous operating point are more accurately determined by using one method than the other, contribute more to the correction. For example, the estimated variables of the model-based method may flow into the correction only when the estimating algorithm has become stable, when the estimated variables are uniquely identifiable (observability), and when the battery operates at points which are also described by the underlying model (e.g., discharge). In all other cases the corresponding weightings must be set gz,B,i and gp,Bj=0.
An example of a particular variant of an embodiment of the battery state of charge detection for predicting the operability of lead batteries in motor vehicles is described in the following:
Predictor Model
For estimating the operability of a lead battery under short-time load (on the order of 10 sec) using currents on the order of ILoad≦−100A (counting direction I<0A for discharge) as it typically occurs, e.g., in the operation of electric braking and steering systems, as well as at engine start in motor vehicles. The following simple predictor model, illustrated in
Using the equivalent diagram components:
Formula determined from measurements:
UD(ILoad,UD0)=UD0*1n(ILoad/(−1A)),ILoad<0A
using the temperature-dependent crossover parameter:
UD0(TBatt)=4.97e−7*(TBatt/° C.)3−4.87e−5*(TBatt/° C.)2+1.82e−3*(TBatt/° C.) . . . −131e−1
UBatt,pred=U00+Ri*ILoad+UD(ILoad,UD0)=predicted voltage response for battery current ILoad
The following prerequisites must be met for the applicability of the predictor model:
These prerequisites are met for the described load in the state of charge range of soc>approximately 30% and for battery temperatures of TBatt>approximately 0° C., as well as soc>approximately 50% and TBatt>approximately 0° C.
State variables and parameters are determined on the basis of the following considerations:
State variable U00, as well as parameters Ri and UD0 of the predictor model, are determined by using two different methods:
Method A determines U00,A from measurements of the idling voltage an unloaded battery and Ri,A by analyzing the quotient of differences of the voltage and current values measured at engine start, while crossover parameter UD0,A is not estimated by method A but rather calculated via the above-mentioned characteristic curve.
In addition, method A determines the battery (acid) capacity from two open-circuit voltage determinations U00,A1 and U00,A2, as well as the current integral (charge balance)q=∫IBatt(t)dt:
Q0,A=q*(U00,max(25° C.)−U00,min(25° C.)/(U00,A,2(25° C.)−U00,A,1(25° C.)
where U00,max=open-circuit voltage of the fully charged battery and U00,min=open-circuit voltage of the empty battery at TBatt=25° C.
Using Q0,A, current charge balance qk, and current battery temperature TBatt,k, method A tracks open-circuit voltage UD0,0, determined during the idle phase, during operation in each time step k:
U00,A,k(25° C.)=U00,A,0(25° C.)+qk/Q0,A*(U00,max(25° C.)−U00,min(25° C.)
U00,A,k=U00,A,k(25° C.)+TkU00*(TBatt,k−25° C.), TkU00=1.38e−6V/° C.
Internal resistance Ri,A,0, determined at the start, is tracked in a similar manner during operation via a characteristic curve as a function of current open-circuit voltage U00,A,k and instantaneously measured battery temperature TBatt,k:
Ri,k=f(Ri,A,0,U00,A,k,TBatt,k)
By adjusting a suitable battery model in discharge range (IBatt<0A), method B estimates open-circuit voltage U00,B, internal resistance Ri,B, as well as crossover parameter UD0,B, and battery capacity Q0,B. The variables needed for determining the state of charge and operability are calculated from the state variables and parameters determined by methods A and B using a weighted correction; a constant sampling rate of 0.01 sec has been assumed for the individual time steps.
U00,k+1=U00,k+gU00,A*(U00,A,k−U00,k)+gU00,B*(U00,B,k−U00,k)
where
U00,0=U00,A,0, gU00,A=1−|qk|/Q0, gU00,B=|qk|/Q0
i.e., with an increasing absolute value of charge balance |qk|, starting value U00,0=U00,A,0 determined by method A from an idle phase is corrected to an increasing degree by value U00,B,k determining by method B during vehicle operation.
Ri,k+1=Ri,k+gRi,A*(Ri,A,k−Ri,k)+gRi,B*(Ri,B,k−Ri,k)
where
Ri,0=Ri,A,0, gRi,A=0, gRi,B=1.e−3
i.e., starting value Ri,0=Ri,A,0 determined by method A at engine start is corrected during vehicle operation to value Ri,B,k determined by method B using constant weighting gRi,B=1.e−3.
UD0,k+1=UD0,k+gUD0,A*(UD0,A,k−UD0,k)+gUD0.B*(UD0,B,k−UD0,k)
where
UD0,0=UD0,A,0, gUD0,A=0, gUD0,B=1.e−3
i.e., crossover parameter UD0,A predefined by method A via characteristic curve UD0(TBatt) is corrected to value UD0,B,k estimated by method B during vehicle operation using constant weighting gUD0,B=1.e−3.
Capacity Q0 is not really needed for the prediction of operability; however, value Q0,A,0 determined from idle phases by method A may be improved by values Q0,B,k estimated by method B during vehicle operation. Since the accuracy of Q0,B,k increases with increasing absolute value of charge balance |qk|, the weighting was selected proportional to this value
Q0,k+1=Q0,k+gQ0,A*(Q0,A,k−Q0,k)+gQ0,B*(Q0,B,k−Q0,k)
where
Q0,0=Q0,A,0, gQ0,A=0, gQ0,B=5.e−4*|qk|/Q0,k
Calculation of the Instantaneous State of Charge:
Relative state of charge soc is calculated from instantaneously determined open-circuit voltage U00 (state variable) and instantaneous battery temperature TBatt(measured variable):
soc=(U00(25° C.)−U00,min(25° C.))/(U00,max(25° C.)−U00,min(25° C.))
where
U00(25° C.)=U00=TkU00*(TBatt−25° C.), TkU00=1.38e−6V/° C.U00,max(25° C.)=
maximum value of the open-circuit voltage at room temperature and fully charged battery U00,min(25° C.)=minimum value of the open-circuit voltage at room temperature and empty battery (after removal of charge Q0).
Calculation of the Instantaneous Operability
The instantaneous operability is determined by battery voltage UBatt,pred under predefined load current ILoad calculated by using the predictor model, and the instantaneously estimated state variables and parameters (U00, Ri, UD0):
UBatt,pred=U00+Ri*ILoad+UD(ILoad,UD0)
As the absolute measure for the operability of the energy accumulator (SOH=State of Health), the distance of the minimum value of the predicted battery voltage to a lower limit voltage UBatt,limit at which the energy accumulator just about generates the power required for the considered user (e.g., electric steering and brake systems, starter, . . . ) may be used:
SOHabs=min(UBatt,pred)−UBatt,limit
The relative measure is obtained by relating SOHabs to the difference obtained in the most favorable case, i.e., for a new, fully charged battery and at high temperatures:
SOHrel=(minUbatt,pred)−Ubatt/limit)/(UBatt,pred,max−Ubatt,limit)
Calculation of Future Operability
Future operability may be estimated by inserting the state variables (U00′) and parameters (Ri′, UD0′), extrapolated to the future point in time with regard to battery temperature and state of charge, into the prediction equation. Temperature TBatt′ to be expected may be determined by averaging the battery temperatures over the previous 10 to 14 days. For worst case scenarios, 10K are once more subtracted from this value.
Open-circuit voltage U00′ to be expected after x days of parking of the vehicle is determined via the drop in the state of charge based on the discharge due to closed-circuit current IRest:
U00(25° C.)′=U00(25° C.)+IRest*x*24h/Q0*(U00,max(25° C.)−U00,min(25° C.))
U00′=U00(25° C.)′+TkU00*(TBatt′−25° C.),TkU00=1.38e−6V/° C.
Internal resistance Ri′ is extrapolated by using characteristic curve Ri′=f(Ri,U00′,TBatt′), while crossover parameter UD0′ is calculated via characteristic curve UD0(TBatt′).
Number | Date | Country | Kind |
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101 31 297 | Jun 2001 | DE | national |
102 13 810 | Jan 2002 | DE | national |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCTDE02/02053 | 6/6/2002 | WO | 00 | 6/23/2003 |
Publishing Document | Publishing Date | Country | Kind |
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WO0300505 | 1/16/2003 | WO | A |
Number | Name | Date | Kind |
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5629604 | Sengupta et al. | May 1997 | A |
5825218 | Colli et al. | Oct 1998 | A |
5883497 | Turnbull | Mar 1999 | A |
Number | Date | Country |
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198 47 648 | Apr 2000 | DE |
199 59 019 | Jun 2001 | DE |
100 56 969 | May 2002 | DE |
Number | Date | Country | |
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20040032264 A1 | Feb 2004 | US |