DE10328055A1 - State quantity and parameter estimators with several partial models for an electrical energy storage - Google Patents

Abstract

The invention relates to a state variable and parameter estimator (1) for determining state variables and parameters of a mathematical energy storage model, in particular a battery model, which consists of operating quantities (U¶Batt¶, I¶Batt¶, T¶Batt¶) of an energy store (3) State variables (Z) and parameters (P) of the mathematical energy storage model are calculated. A particularly simple estimation of the state variables and parameters can be carried out if the state quantity and parameter estimator (1) comprises several mathematical sub-models (4, 5) which apply to different working and / or frequency ranges of the energy store (3).

Description

The invention relates to a method for determining state variables and Parameters of a mathematical energy storage model, in particular a battery model, according to the preamble of claim 1, and a state quantity and parameter estimator according to the preamble of claim 9.

In electrical networks, such as Vehicle electrical systems, are usually several electrical consumers from an electrical energy storage, e.g. a battery with Power supplied. To carry out of energy and consumer management, in which consumers can be switched on and off automatically as required knowledge of performance of energy storage is essential. With knowledge of capacity of the energy store, in particular the charge that can still be removed until the required minimum capacity is undershot e.g. For an engine start, can still measures to reduce consumption or increase performance before an undersupply occurs, such as switching off certain consumers, initiated and thus a failure of the electrical supply can be prevented.

To estimate the performance of the energy store, it is known to use mathematical models that describe the electrical properties of the energy store. With the aid of the mathematical models, the performance of the energy store can be estimated, taking into account current operating parameters of the energy store, such as, for example, a current battery voltage U _Batt , the current battery current I _Batt and the current battery temperature T _Batt . A device known from the prior art for determining the charge which can be removed from an energy store is shown in 1 shown.

1 shows a device for determining the charge that can be removed from an energy store, in particular from a vehicle battery, up to a predetermined discharge termination criterion. The device comprises a state quantity and parameter estimator 1 , as well as a charge predictor 2 , in which the mathematical energy storage model is stored. The state quantity and parameter estimator 1 is used to calculate state variables Z and / or parameters P from the current operating variables of the battery, namely the battery voltage U _Batt , the battery current I _Batt and the battery temperature T _Batt , on the basis of which the charge predictor 2 calculates the desired information, such as the charge Q _e that can be taken from the battery, or other variables, such as the time t _e until a discharge criterion is reached or the state of charge SOC. The charge predictor 2 A discharge current _profile I _{Batt, Entl} and a temperature profile T _{Batt, Entl can also be} supplied.

In this description, state variables Z apply in particular internal voltages U resulting from the respective equivalent circuit diagram of the energy store or the underlying mathematical model result. The parameters mentioned are constant Values such as resistors R and capacities C in the equivalent circuit or mathematical energy storage model.

The charge predictor 2 The charge calculation carried out is based on the current state of the energy store. The one in the charge predictor 2 stored mathematical models are therefore initially initialized to the current operating state of the energy store. The state variable and parameter estimator provides this 1 the corresponding initial values. A known Kalman filter, for example, can be used as the state variable and parameter estimator. Based on the initialization state, the charge predictor 2 For example, calculate the charge Q _e that can be taken from the energy store for a given discharge current and a current battery temperature.

2 shows an example of an equivalent circuit diagram for the discharge operation of a lead accumulator (I _Batt <0A, U _Dp <0V, U _Dn <0V). The individual equivalent circuit diagram sizes are as follows, from left to right:
R (U _C0 , U _e , T _Batt ) Ohmic internal resistance, depending on the open circuit voltage U _C0 , the electrolyte voltage U _e and the acid temperature T _Batt
U _Ri ohmic voltage drop
C ₀ acid capacity
U _C0 open circuit voltage
R _k (U _C0 , T _Batt ) acid diffusion resistance, depending on the open circuit voltage U _C0 (degree of discharge) and the acid temperature T _Batt
tau _k = R _k · C _k (time constant of acid diffusion) is assumed to be constant in the order of 10 minutes
U _k concentration polarization
U _e = Uc _C0 + U _k (electrolyte voltage)
U _D (I _Batt , T _Batt ) Stationary passage polarization at the positive electrode of the battery (U _Dp ) and the negative electrode (U _Dn ), depending on the battery current I _Batt and the acid temperature T _Batt
U _Batt terminal voltage of the battery

The individual equivalent circuit diagram sizes are attributed to different physical effects of the battery, the expert from the relevant Literature are known.

The following relationship can be used for the ohmic internal resistance R _i : R i (U C0 , U e , T Batt ) = R i0 (T Batt ) · (1 + R I, fakt · (U C0max - U C0 ) / (U e - U e, cross- )), R i0 (T Batt ) = R I025 / (1 + TK Lfact ) * (T Batt - 25 ° C)) are:
R _i025 ohmic internal resistance at full charge and T _Batt = 25 ° C
TK _Lfact Temperature coefficient of the battery _conductance
R _Ifakt map _parameters
U _C0max maximum open circuit voltage of the fully charged battery
U _{e, limit} electrolyte voltage at the end of discharge ( _depending on age)

For other equivalent circuit diagram sizes (eg U _D , U _k ), the charge predictor includes 2 accordingly other suitable mathematical approaches. The mathematical model of the energy store comprises mathematical approaches at least for the internal resistance R _i , the acid diffusion resistance R _k and a passage polarization U _D.

The state variables provide information about the energy content of a system's energy stores. In the equivalent circuit diagram, they correspond to the voltages at the capacitors, i.e. U _C0 and U _k . In addition to the state variables, the model parameters must also be known for the model-based determination of the performance of the energy store. In particular, parameters that vary greatly in age, such as parameters R _i025 and U _{e, must be adapted to} the characteristic of the ohmic internal resistance.

The state quantity and parameter estimator 1 Determined state variables Z and parameters P can be used, for example, to determine the state of charge of the battery, a current or future performance, and for example the charge that can be removed from the energy store.

Conventional predictors, such as the one in 1 charge predictor shown 2 , usually include very complex models with many state variables and parameters that cover the behavior of the energy storage over a large working area. The calculation of the state variables and parameters is accordingly complex and complex. Other predictors, on the other hand, include simple models with few state variables and parameters, which, however, only describe the behavior of the energy store at certain operating points or at certain frequencies.

It is therefore the task of the present Invention, a simple and quick method for estimating State variables and / or Parameters for to create a mathematical energy storage model that is essentially about the entire working range and frequency range of the energy storage is valid.

This object is achieved according to the invention by the in the claims 1 and 9 specified features. Further refinements of the invention result from the subclaims.

The main idea of the invention consists in the state quantity and Parameter estimator several mathematical sub-models to estimate state variables and / or To provide parameters for different work and / or Frequency ranges of the energy storage apply. The working and / or The frequency ranges of the individual sub-models can overlap. Overall, the sub-models essentially cover the entire frequency and working area of the energy storage.

Thus, a continuous estimate of State variables and parameters possible in the entire working and frequency range of the energy storage. By the use of the partial models according to the invention can the number of estimates State variables and Parameters kept small and thus the risk of ambiguous estimate be minimized. Furthermore, due to the division into sub-models more efficient use of processor performance possible: "Slow" sub-models with large time constants can be used independently of "fast" sub-models be processed at a lower sampling rate.

A current (I _Batt ) or a voltage (U _Batt ) of the energy store is preferably supplied to the sub-models, the current (I _Batt ) or the voltage (U _Batt ) being restricted by a filter to the frequency range valid for the respective sub-model. The sub-models can thus be preceded by high-pass, low-pass or band-pass filters.

According to a preferred embodiment of the invention, an error between an operating variable (U _Batt , I _Batt ) of the energy store and an operating variable (U _{Batt ^} , I _{Batt ^} ) calculated by a partial model is determined and fed back into the respective partial model (self-feedback). Through self feedback the state variables and parameters to be calculated can be adapted to the actual state of the energy store.

Optionally, the error can also be found in another partial model fed back become (external feedback). Through external feedback can the state variables and Parameters calculated by several sub-models at the same time be compared against each other.

The mistakes made by a sub-model through self-feedback or external feedback supplied are preferably weighted with a weighting factor. In this way, the sensitivity of a sub-model to different Errors can be set.

State variables and / or parameters that estimated from a sub-model were and are also included in another sub-model preferably also fed to the other sub-model. There you can use it as a starting value, as Fixed value or as a correction value for the estimation serve.

According to a preferred embodiment The invention provides a stimulation device with which one supplied to the sub-models Company size (electricity or tension) into one for the submodel is valid Working or frequency range can be brought.

The invention is illustrated below the attached Exemplary drawings closer explained. Show it:

1 a device known from the prior art for calculating the charge that can be removed from an energy store.

2a an equivalent circuit diagram for a lead accumulator during a discharge process at low frequencies;

2 B an equivalent circuit diagram for a lead accumulator at high frequencies;

3a the structure of a state quantity and parameter estimator with several partial models according to a first embodiment of the invention and 3b according to a second embodiment of the invention;

4 a flowchart showing the function of a stimulator; and

5 the construction of a state quantity and parameter estimator for calculating the internal resistance of a battery.

Regarding the explanation of the 1 and 2a reference is made to the introduction to the description.

3a shows the basic structure of a state variable and parameter estimator 1 according to a first embodiment of the invention. As can be seen, the state variable and parameter estimator includes 1 several sub-models 4 . 5 which only apply in a certain frequency and / or working range (f1, A1 or f2, A2) and which can therefore be kept very simple. The sub-models 4 . 5 In their entirety, however, they cover the entire frequency and working range of the energy store 3 from.

The frequency ranges f1, f2, ... as well as the working ranges A1, A2, ... can partially overlap. The entirety of the sub-models 4 . 5 In the best case scenario, it should cover the entire, at least the largest possible working range A and frequency range f of the energy store.

The working area of a sub-model 4 . 5 is determined by predetermined conditions for the battery current I _Batt , the battery voltage U _Batt , the battery temperature T _Batt . State variables Z and battery parameters P defined.

Individual state variables Z and parameter P can be used in several sub-models at the same time 4 . 5 occur and be valued.

The in 1 shown state quantity and parameter estimators 1 receives continuously measured battery values at its input, in the present case the battery current I _Batt (optionally the battery voltage U _Batt can also be supplied) and the battery temperature T _Batt The battery current I _Batt is determined by suitable low-pass, high-pass or band-pass filters 6 . 7 . 8th . 9 each limited to the frequency range f1, f2 in which the respective sub-model 4 . 5 is valid. A partial model 4 . 5 (e.g. the sub-model 4 ), which is valid, for example, in a frequency range f1 of more than 1 kHz, has an upstream high-pass filter in the present case 6 , The sub-model 5 can, for example, a low pass filter 7 . 9 be upstream. Covers a sub-model 4 . 5 the entire frequency range f, the input filter 6 . 9 for current and voltage.

The sub-models 4 . 5 calculate a battery state variable (I _{Batt ^} or U _{Batt ^} ) from the quantities supplied. The corresponding actual value (I _Batt or U _Batt ) becomes the state variable and parameter estimator 1 supplied as a measured value from outside. The estimated values U _{Batt , 1 ^} U _{Batt, 2 ^} or quantities derived therefrom (error signals) are included in the respective sub-model 4 . 5 fed back.

The state quantity and parameter estimator 1 includes difference nodes 17 . 18 , at which an error (difference signal) is formed from the estimated battery state variable U _{Batt , 1 ^} , U _{Batt, 2 ^} and the battery state variable U _{Batt , 1} , U _{Batt, 2} measured in each case. The errors determined (U _{Batt , 1} - U _{Batt, 1 ^} , U _{Batt, 2} - U _{Batt, 2 ^} , ...) then each become a weighting unit 10 . 12 fed and at adding nodes 14 . 15 directed.

In the case of error feedback, a distinction can be made between self-feedback and external feedback. In the former case, the estimation error of a partial model ( 4 ) the same sub-model ( 4 ), otherwise the estimation error of a partial model ( 4 ) another sub-model ( 5 ) fed. At the adding node 14 . 15 an overall error is generated from the individual (weighted) estimation errors and the respective sub-model 4 . 5 fed.

External feedback is preferred only realized if certain state variables Z or parameter P are in parallel occur in several sub-models. In this case, the State variables Z and Parameter P can be compared with the other sub-models.

The following difference equation results for a state variable Z _{1, j} in the j-th sub-model, which also occurs in the sub-models i = j + 1, ..., j + n:

Here, f (Z _{j, k} , P _{j, k} , I _{Batt, j, k} , T _{Batt, k} ) is the right-hand side of a state difference equation for the state variable Z _{1, j of} the jth sub-model with the input variables: Filtered battery current I _{Batt, j, k} and battery temperature T _{Batt, k} as well as the parameter vector P _{j, k} in the k-th time step.

For a constant parameter P _{1, j} in the jth sub-model, which also occurs in the sub-models i = j + 1, ..., j + n, the following results:

The gains k _{i, j of} the weighting units 10-13 can with a partial model 4 . 5 corresponding to a Luneberger observer by means of pole specification and when using a Kalman filter for the partial models 4 . 5 by minimizing a quality criterion, such as the minimal estimation error variance.

If the current working range and / or frequency range is outside the valid working and / or frequency range of a sub-model 4 . 5 error feedback from such a partial model (e.g. partial model 5 ) to another sub-model. In such a case, therefore, the weighting factors k _{i, j of} the corresponding weighting units (for example weighting unit 11 ) set to zero. That is, k _{i, j} = 0 if the working area of the i-th sub-model is left.

At the in 3a arrangement shown is the state quantity and parameter estimator 1 the battery current Isatt supplied. According to another embodiment 3b can the sub-models 4 . 5 a (filtered) battery voltage U _{Batt can also} be supplied as an input variable. The sub-models 4 . 5 would estimate a battery current I _{Batt ^} in this case. The sub-models are compared via the battery voltage U _{Batt, 1} , U _{Batt, 2} , ..., via the battery currents I _{Batt, 1} , I _{Batt, 2} , ... if the battery voltage is the input variable and the battery current is the output variable Sub-models is defined.

State variables and / or parameters derived from a partial model ( 4 ) were estimated and also in another sub-model ( 5 ) are preferably included in the other sub-model ( 5 ) fed. There are connecting lines for this 30 . 31 intended. In the other sub-model ( 5 ) the values can serve as a starting value, as a fixed value or as a correction value for the estimate.

The sub-models 4 . 5 supply not only the state variables Z and parameters P but also the error variances (var ₁ , var ₂ , ...) of the variables. This can be used, for example, to assess whether the accuracy of the estimated variables Z, P is sufficient for subsequent calculations of the state of charge, the performance and / or the charge that can be drawn from the battery.

In a further variant, the sub-models are additionally compared via the battery voltages U _{Batt, 1} , U _{Batt, 2} , ..., ie the structure according to 3a or 3b is used twice at the same time, once with sub-models based on the battery voltage and once with partial models after the battery current. The simultaneously estimated state variables and parameters from the individual partial models of the two structures can then, for example, be weighted and linked with their error variance to form an estimated variable, in accordance with the manner already described for linking the variables estimated in parallel in different partial models.

For optimal use of all sub-models 4 . 5 should be the operating sizes of the battery 3 in the course of the calculation, all working and frequency ranges of the sub-models 4 . 5 run through. Returns the electrical network to which the battery is connected 3 connected, too few suggestions (e.g. load fluctuations), the sizes cannot be estimated precisely enough. If the excitations in the network are low, the internal resistance R _{i of} the battery, for example 3 can only be estimated very imprecisely. If there is little excitation over a longer period of time, problems can arise, particularly in safety-critical applications, since no precise statement can be made about the performance of the battery.

The state quantity and parameter estimator 1 therefore includes a stimulator 16 who is able to actively intervene in the electrical network and the working and / or frequency range of the battery 3 or the network in the desired manner. The stimulator 16 intervenes actively in the electrical network if the error variance var of predefined state variables Z or parameter P is too large for a predefined period of time. The stimulator 16 are those of the individual sub-models 4 . 5 Calculated variances fed as input variables.

Intervention in the electrical network by the stimulator 16 takes place, for example, by specifying a new generator set voltage U _{Gen, set} (in the case of a vehicle generator), a load response time constant tau _{Gen of} a generator regulator and / or by means of suitable consumer connection or disconnection. In this way, a battery current _profile I _Batt , voltage profile U _Batt and / or frequency profile suitable for estimating the respective state variable Z or the respective parameter P can be impressed. Ideally, the desired battery current curve I _Batt (or a voltage curve U _Batt ) is specified so that it is the battery 3 transferred to a working area A and excited in a frequency range f in which one of the sub-models (e.g. sub-model 5 ) that contains the estimate, is particularly accurate and thus the estimate can be determined very precisely. The distance from this new work area to the current work area A of the battery must of course be used 3 and the maximum permissible amplitudes of the control variables U _{Gen, should} , tau _Gen , I _Last and the maximum permissible duration of the control intervention are taken into account.

How the stimulator works 16 of 1 is exemplary in 4 shown. The method begins in step 20 with the initialization of the times t _p and t _stim to the values t _p = 0, t _stim = 0. Here, t _p denotes a time in which a parameter P is monitored, and t _stim a stimulation time.

In step 22 it is checked whether the error variance var _{p is} greater than a maximum error variance var _{p , mam} . If no (N), the stimulator remains 16 disabled. If the error variance var _p remains greater than var _{p, max} for a period of time t _p greater than t _{p, max} (step 23), a current profile I _{Batt, soll, p} assigned to the parameter P _is impressed (steps 24 and 26). This is done until the variance var of the parameter P _p less than or equal to the maximum variance var _{p, max} of this parameter P is or the stimulation period t _stim greater than a predetermined maximum duration t _{stim, max} (check in step 27). The variable t _stim for the stimulation _duration is increased iteratively in step 25 by one sampling period T _Ab each.

5 shows a special embodiment of a state quantity and parameter estimator 1 for determining the ohmic internal resistance R _{i of} a lead accumulator 3 , The internal resistance R _{i of} the battery 3 is a decisive factor in determining a battery condition, such as the performance of the battery 3 or the still removable charge.

The state quantity and parameter estimator 1 comprises two mathematical sub-models 4 . 5 , of which the first is valid in the entire frequency range and the second sub-model 5 is only valid for frequencies greater than or equal to 1 kHz. Corresponds to the first sub-model 4 no filter and the second sub-model 5 a high pass filter 7 upstream.

The first sub-model 4 includes a mathematical model description of the equivalent circuit diagram of 2a , In contrast, the second sub-model includes 5 a mathematical description of the equivalent circuit diagram of 2 B , which essentially only from the internal resistance R _{i of} the battery 3 consists. If you restrict yourself to a frequency range of the order of 1 kHz and consider only high-frequency alternating components of current I _Batt and voltage U _Batt , the capacities of the equivalent circuit diagram of 2a are considered short-circuited. The only remaining component in this case is the internal resistance R _{i of} the battery.

The first sub-model 4 has only validity for the discharge operation in the following case, since the internal resistance R _{i of} the battery 3 in the charging operation is difficult to estimate from the few measured variables current I _batt , voltage U _batt and temperature T _batt .

For the first partial model 4, to which the estimation errors U _Batt - U _{Batt ^} or U _Batts - U _{Batts ^ are} applied, the following applies: R i, k + 1 = R i, k + k 11 (U Batt - U Batt ^ ) + k 21 (U Batt ~ - U Batt ~ ^ )

For the second sub-model 5 applies: R i, k + 1 = R i, k

The one from the first sub-model 4 calculated value for the internal resistance R _{i of} the battery 3 becomes the second sub-model 5 supplied and can be used there as a starting value, for example. The weighting units for the second sub-model 5 with the weighting factors k ₂₂ and k ₁₂ can be omitted in this case. The weighting units 10 . 11 for the feedback of errors in the partial model 4 remain on the other hand.

It should be noted that the weighting factor k ₁₁ must be set to zero in the loading mode, since the first partial model 4 is not valid in charging mode. The weighting factors k ₁₁ and k ₂₁ can be determined, for example, using an observer design according to Luenberger or Kalman.

1

State variables and parameter estimates

2

charge predictor

3

battery

4

first submodel

5

second submodel

6-9

filter

10-13

weighting units

14.15

adding node

16

stimulator

17.18

adding node

20-27

steps

30.31

interconnectors

Claims (14)

Method for determining state variables and parameters of a mathematical energy storage model, in particular a battery model, with the aid of a state variable and parameter estimator ( 1 ), which consists of operating variables (U _Batt , I _Batt , T _Batt ) of an energy store ( 3 ) calculates the state variables (Z) and parameters (P) of the mathematical energy storage model, characterized in that the state variables and parameter estimator ( 1 ) several mathematical sub-models ( 4 . 5 ) includes, for different working and / or frequency ranges of the energy storage ( 3 ) be valid. A method according to claim 1, characterized in that the partial models ( 4 . 5 ) a current (I _Batt ) or a voltage (U _Batt ) of the energy store ( 3 ) is supplied, the current (I _Batt ) or the voltage (U _Batt ) through a filter ( 6 . 7 ) for a partial model ( 4 . 5 ) valid frequency range is restricted. Method according to Claim 1 or 2, characterized in that an error between an operating variable (U _Batt , I _Batt ) of the energy store and one of a partial model ( 4 . 5 ) calculated operating size (U _{Batt ^} , I _{Batt ^} ) determined and into the respective sub-model ( 4 . 5 ) is fed back. Method according to one of the preceding claims, characterized in that the error between an operating variable (U _Batt , I _Batt ) of the energy store ( 3 ) and that of a partial model ( 4 . 5 ) calculated farm size (U _{Batt ^} , I _{Batt ^} ) in another sub-model ( 5 ) is fed back. A method according to claim 3 or 4, characterized in that the error is weighted using a factor (k). Method according to one of the preceding claims, characterized in that one of a partial model ( 4 . 5 ) calculated state variable (Z) and / or a calculated parameter (P) of another partial model ( 5 ) is supplied. A method according to claim 6, characterized in that the state variables (Z) or weighted parameter (P) fed back become. Method according to one of the preceding claims, characterized in that a stimulator ( 16 ) is provided in order to measure the current (I _Batt ) or the voltage (U _Batt ) that the submodels ( 4 . 5 ) is brought into a desired working range or frequency range. State quantity and parameter estimators ( 1 ) for determining state variables (Z) and parameters (P) of a mathematical energy storage model, in particular a battery model, which is made up of operating variables (U _Batt , I _Batt , T _Batt ) of an energy store ( 3 ) calculates the state variables (Z) and parameters (P) of the mathematical energy storage model, characterized in that the state variables and parameter estimator ( 1 ) several sub-models ( 4 . 5 ) includes, for different working and / or frequency ranges of the energy storage ( 3 ) be valid. State quantity and parameter estimators ( 1 ) according to claim 9, characterized in that at least one of the partial models ( 4 . 5 ) a filter ( 6 . 7 ) is connected upstream by which the submodel ( 4 . 5 ) supplied operating size (U _Batt , I _Batt ) of the energy store ( 3 ) on the for the sub-model ( 4 . 5 ) valid frequency range zuschränken. State quantity and parameter estimators ( 1 ) according to claim 9 or 10, characterized in that the operating variable and parameter estimator ( 1 ) is designed such that an error between an operating variable (U _Batt , I _Batt ) of the energy store ( 3 ) and one of a partial model ( 4 . 5 ) calculated operating size (U _Batt , I _Batt ) determined and into the respective sub-model ( 4 . 5 ) is fed back. State quantity and parameter estimators ( 1 ) according to one of claims 9 to 11, characterized in that the operating variable and parameter estimator ( 1 ) is designed in such a way that an error between an operating variable (U _Batt , I _Batt ) of the energy store ( 3 ) and one of a partial model ( 4 . 5 ) calculated farm size (U _{Batt ^} , I _{Batt ^} ) in another sub-model ( 5 ) is fed back. State quantity and parameter estimator according to one of Claims 9 to 12, characterized in that a device ( 10 - 13 ) is provided for weighting the feedback error. State quantity and parameter estimators ( 1 ) according to one of claims 9 to 13, characterized in that a stimulator ( 16 ) is provided to determine the current or voltage curve (I _Batt , U _Batt ) that corresponds to the submodels ( 4 . 5 ) is brought into a desired working or frequency range.