Model-based internal resistance determination of a vehicle battery

Abstract

The invention relates to a method for generating a mathematical model for the relationship between state variables (3) of a battery (1) and its internal resistance (5), comprising the steps of: carrying out (S1) a test of the battery (1) by varying state variables (3); determining (S2) an internal resistance (5); transforming (S3) the detected state variables (3) and / or the internal resistance (5) by a forward transformation (7) so that a relationship that is as linear as possible is obtained; applying (S4) a linear modeling method (11) based on the state variables (3) and the associated values ​​of the internal resistance (5) to create a preliminary mathematical model (9);Back-transforming (S5) the preliminary mathematical model (9) by means of a back-transformation (13) to a mathematical model (15) usable for the operation of the vehicle, which model receives the state variables (3) as input variables in order to determine the internal resistance (5) as an output variable;

Description

The invention relates to a method for generating a mathematical model of a relationship between state variables of a battery of a battery-electric vehicle and an internal resistance of the battery, to a system for a vehicle for executing the model, and to a vehicle having such a system.The internal resistance of a battery of a battery-electric vehicle decisively determines the electrical power consumption and power output of the battery. It is therefore potentially known for many possible applications what internal resistance the battery of a battery-electric vehicle currently has during operation. If a current flow through the battery is present, the current intensity and the electrical voltage can be measured and the internal resistance can be deduced therefrom. However, if no current flow is present, this is generally not possible by electrical measurement. In addition, such estimates of the internal resistance are related to specific operating points, such as a current state of charge, a current temperature of the battery, an aging state and others. Methods are therefore known in the prior art for estimating the internal resistance, and this to a defined set of operating points or continuously.DE 10 2018 127 530 A1 relates in this connection to a method for calculating a maximum current and for predicting a capacity of a battery pack in a system, the method comprising: determining an open circuit voltage of the battery pack via a controller; measuring a voltage and a current during a charging or discharging process of the battery pack; calculating an internal resistance of the battery pack from the measured voltage and the measured current; calculating the maximum current of the battery pack from the open circuit voltage and the internal resistance; selecting a lower value of: an absolute value of the calculated maximum current and an absolute value of a predefined current limit; predicting the capacity of the battery pack using the selected lower absolute value; and controlling a state of the system using the calculated capacity.DE 10 2017 103 377 A1 further relates to a vehicle comprising: a battery; and a controller programmed to charge and discharge the battery based on a health indicator output from a model describing changes in internal resistance of the battery over time identified from a plurality of different representative battery usage aggressive drive cycles and changes in internal resistance of the battery derived from a state of charge, temperature and current associated with the battery.The invention results from the features of the independent claims. Advantageous refinements and refinements are the subject matter of the dependent claims.A first aspect of the invention relates to a method for generating a mathematical model of a relationship between state variables of a battery of a battery-electric vehicle and an internal resistance of the battery, comprising the steps:performing testing of a battery by varying and detecting state variables of the battery;determining, based on measurements, values of an internal resistance of the battery during the testing, while assigning the detected state variables;transforming the detected state variables and / or the values of the internal resistance by a forward transformation, so that a relationship which is as linear as possible is obtained between a change in one of the state variables and a change in a value of the internal resistance;applying a linear model forming method based on the state quantities obtained after the transformation and the associated values of the internal resistance to produce a preliminary mathematical model;retransforming the preliminary mathematical model by means of a reverse transformation to a mathematical model usable for the operation of the vehicle, which contains the state variables as input variables in order to ascertain the internal resistance as output variable, wherein the reverse transformation is the reversal of the forward transformation.In a first step, a real battery or a sufficiently realistic calculation model of a real battery for a battery-electric vehicle is used in order to carry out a system identification thereon. In this case, a relationship between state variables of the battery and an internal resistance is identified.For this purpose, state variables of the battery are deliberately and intentionally varied in order to be able to determine the influence on the resulting internal resistance of the battery. This results in a data record of individual measurement tuple, i.e. the respective relationship at individual measurement points.Since this relationship is generally nonlinear, the data set obtained is transformed in the further step by a forward transformation in order to be able to use the linear modelling methods which are more available than nonlinear ones. In this case, for example, a linear regression method is used in order to be able to generate a linear modeled relationship of the transformed state variables with respect to the internal resistance (which may likewise be transformed).The forward transformation can be realized in particular by a mathematical mapping, for example the input of a series of varied state variables into a mathematical function such as a logarithm. Its function value is used in the transformed quantities to apply a linear modelling method.The aim of the linear model formation method is to map the pseudo-linear relationship between the state variables and the internal resistance in a mathematical model. The mathematical model can be expressed in the form of an analytical function which has the number of input variables which corresponds exactly to the number of relevant state variables. However, the mathematical model can also be present as an interpolation function, so that individual support values in the later real operation of a similar or structurally identical battery can be used using the mathematical model to determine current intermediate values between the support values, in particular by linear interpolation.Since a provisional mathematical model is first generated that is still under the influence of the forward transformation and is thus not yet ready for an application in the real operation of the battery, a reverse transformation is applied in order to be able to remap the actual nonlinearity in the mathematical model. The mathematical model obtained from this is usable with the battery during operation of the vehicle in order to reliably estimate a current internal resistance from current state variables of the battery even if no electrical power flows to or flows from the battery, i.e. if a current intensity of zero is present at the battery poles. The method is not a direct resistance estimation method, but a postprocess method requiring a data preparation and resistance estimation method.The battery may be a single battery cell, or a battery pack having a plurality of battery cells. This depends on the unit for which an actual estimate of an internal resistance is desired in the vehicle. In order to obtain a higher resolution and a more accurate estimate, for example, a temperature detection of a state of charge detection of each battery cell of a battery pack can be carried out individually in order to estimate individual internal resistances of the respective battery cells in order subsequently to determine an overall internal resistance of the battery pack from the individual internal resistances.The method is preferably used for lithium ion cells, but can in principle also be used for other battery chemistries. Preferred state variables are a temperature of the battery and a current state of charge of the battery, i.e. which energy amounts have already been emitted or are still available from the total energy amount potentially to be emitted.By executing the final model used in the vehicle, scenarios during the driving operation can be evaluated or predictions can also be concluded by ascertaining the internal resistance. Further possible applications are the delivery of a performance prediction, the generation of information regarding the aging of the battery, regarding a temperature development and regarding cell properties of battery cells of the battery.According to an advantageous embodiment, the linear model formation method is a linear regression method.According to a further advantageous embodiment, the linear regression method is applied recursively.An advantage of the recursive application of the regression method is the economy with respect to the required data sets from carrying out the testing of the battery. The regression method can be carried out by its recursive nature up to an abort condition which specifies a quality of the mathematical model in comparison with the test results determined in the testing.According to a further advantageous embodiment, the linear regression method is applied recursively until a quality parameter meets a predefined limit condition, wherein the quality parameter specifies a deviation of the usable mathematical model from a determination of the actual internal resistance based on measurement.According to a further advantageous embodiment, the state variables comprise at least one or a combination of: temperature of the battery, current state of charge of the battery.According to a further advantageous embodiment, the forward transformation comprises one of the following: polynomial function, in particular root function, exponential function, logarithm.The forward transformation serves to form particularly non-linear relationships as linearly as possible. The suitable forward transformation results in particular from preliminary experiments and measurements in the developments. For example, power or logarithm functions are appropriate. The data can thus be formulated recursively as efficiently as possible.According to a further advantageous embodiment, when detecting state variables during the testing of the battery, a selection of state variables takes place, the change of which results in a change of the internal resistance above a predefined threshold.State variables in question, in addition to the temperature and the state of charge of the battery, can be the current intensity, the energy throughput and the time. In addition to this test criterion as to whether a changed state leads to a significantly changed value in the internal resistance, further test criteria can be used, for example as to whether the internal resistance estimate is of sufficiently high quality.A further aspect of the invention relates to a system for a vehicle, which is designed to execute a mathematical model which specifies a relationship between state variables of a battery of a battery-electric vehicle and a value of an internal resistance, and wherein the system is designed to ascertain current state variables of the battery, to feed them to the mathematical model and to ascertain therefrom a current value of the internal resistance of the battery, wherein the mathematical model comprises an analytical function or a look-up table.The mathematical model described in this system for a vehicle is one that is finally obtained from the method described above and below as being usable in a vehicle having such a battery.According to a further advantageous embodiment, the state variables comprise a state of charge of the battery and a temperature of the battery.Advantages and preferred refinements of the proposed system result from an analogous and analogous transfer of the statements made above in connection with the proposed method.A further aspect of the invention relates to a vehicle having a system as described above and below.Further advantages, features and details are evident from the following description, in which--possibly with reference to the drawing--at least one exemplary embodiment is described in detail. Identical, similar and / or functionally identical parts are provided with the same reference numerals.The following are shown: FIG. 1 : a method for generating a mathematical model of a relationship between state variables of a battery and its internal resistance according to an exemplary embodiment of the invention. FIG. 2 : shows an exemplary result of a test in the method of FIG. 1. FIG. 3 : shows an exemplary result of a forward transformation of the data of FIG. 2 according to an exemplary embodiment of the invention. FIG. 4 : An exemplary result of the modelling based on the data of FIG. 3.The representations in the figures are schematic and not to scale.FIG. 1 shows a method for generating a mathematical model of a relationship between state variables 3 of a battery 1 of a battery-electric vehicle and an internal resistance 5 of the battery 1. measured data 3 such as temperature and state of charge and calculated variables such as the internal resistance 5 are acquired and recursively guided into a learning segmented model if these data 3 meet certain predetermined restrictions. For this purpose, a test of a battery 1 is carried out by intentionally applying a variation of state variables 3 of the battery 1. First, all measurable and relevant quantities of the battery 1 are checked for suitability in a preliminary process compiled. In this case, firstly the estimation accuracy of the internal resistance 5 is checked and secondly the state variables 3 to be used are selected. The ascertainment S 2, based on measurements, of values of an internal resistance 5 of the battery 1 during the testing with assignment of the detected state variables 3 follows. a data record is thus obtained which assigns different values to the internal resistance 5 via different state variables 3. Such a relationship is shown for a first state variable, the state of charge 3 SOC of the battery 1 and for a second state variable, the temperature 3 T of the battery. In the direction of the arrow, values which become larger are displayed. The state variables 3 can be evaluated by recursive correlation analysis or can be defined by preliminary examinations. The greatest correlation is shown for the battery 1 used with regard to the temperature and the state of charge. It can be seen in FIG. 2 that the dependence with respect to the temperature 3 T is significantly greater than the dependence of the state of charge 3 SOC. Furthermore, it can be seen here that there is a clearly nonlinear relationship, in particular between the temperature 3 T and the internal resistance 5 of the battery 1. by logarithmizing the two state variables 3 and, in addition, logarithmizing the value of the internal resistance 5, all detected values are transformed S 3. The application of the respective logarithm function is a forward transformation 7; the result can be seen in FIG. 3. While a perfectly linear mapping over non-linear state variables 3 to the internal resistance 5 is not yet obtained, tangents and tangential planes over further regions of the mapping describe the actual relationship as still in the mapping in FIG. 2. the aim is to generate a plane largely (in the optimum case globally) in order to utilize the properties of linearity. Once this has been done, a linear modelling method 11 can then be applied by carrying out a recursive regression method S4. In this case, the logarithmized state variables 3 and the logarithmized internal resistance 5 are used as the data basis. The application is therefore recursive in that each formation of a preliminary mathematical model 9 also determines a quality parameter which evaluates the quality of the mathematical model 9 obtained in this way in comparison with the measurements from steps S 1 and S 2. If the quality parameter is sufficiently high, the recursion can be terminated. This advantageously leads to a typically significantly reduced memory requirement when performing the recursive regression compared to a conventional recursion. The recursive regression method is to be divided into two sections: First, an initialization of auxiliary variables is carried out, then a recursive onboard data processing. Initialization is necessary whenever basic relationships change which make the previously determined mathematical model invalid. This is required, for example, by increasing the aging of the battery 1. By further steps in the application of the regression, namely the calculation of the initial states, a cumulation, the calculation of mean square deviations, a cross cumulation, a cross cumulation with weighting of the mean square deviation, the difference of cross cumulation and the weighted cross cumulation, and with the conditioning of the mathematical model, an evaluation of the learning procedure of the regression model can be carried out and finally the provisional mathematical model 9 can be obtained. Since this provisional mathematical model 9 still contains the logarithmic transformation function, a inverse transformation S 5 of the provisional mathematical model 9 follows, by means of an inverse transformation 13, a mathematical model 15 which can be used for the operation of the vehicle and which receives the state variables 3 as input variables in order to ascertain the internal resistance 5 as output variable. This usable mathematical model 15 is shown by way of example in FIG. 4. The inverse transformation 13 is the inverse of the forward transformation 7, i.e. the exponential function inversely related to the logarithm. If a battery 1, which is comparable to the tested battery 1, is installed in a battery-electric vehicle and is used there in its operation, then with the aid of the mathematical model 15 only the measurement of a state of charge 3 SOC of the battery 1 and a temperature 3 T of the battery 1 is sufficient to infer the internal resistance 5 of the battery 1. It is not necessary here for the battery 1 to be in operation, i.e. for a current intensity not equal to zero to be present at the connection poles of the battery 1.Although the invention has been illustrated and explained in more detail by preferred exemplary embodiments, the invention is not restricted by the disclosed examples and other variations can be derived therefrom by the person skilled in the art without departing from the scope of protection of the invention. It is therefore clear that a large number of possible variations exist. It is also clear that embodiments mentioned by way of example represent only examples which are not to be understood in any way as limiting, for example, the scope of protection, the possible applications or the configuration of the invention. Rather, the preceding description and the description of the figures enable the person skilled in the art to implement the exemplary embodiments in concrete terms, wherein the person skilled in the art, knowing the disclosed inventive concept, can make various changes, for example with regard to the function or the arrangement of individual elements mentioned in an exemplary embodiment, without departing from the scope of protection defined by the claims and their legal equivalents, such as further explanations in the description.List of reference characters1 Battery 3 State variables 5 Internal resistance 7 Forward transformation 9 Provisional mathematical model 11 Model formation method 13 Inverse transformation 15 Mathematical model S 1 usable in later operation S 2 Ascertaining S 3 Transforming S 4 Applying S 5 Inverse transformationReferences included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedDE 10 2018 127 530 A1

[0003] DE 10 2017 103 377 A1

[0004]

Claims

Method for generating a mathematical model of a relationship between state variables (3) of a battery (1) of a battery electric vehicle and an internal resistance (5) of the battery (1), having the steps: - carrying out (S1) a test of a battery (1) by varying and detecting state variables (3) of the battery (1); - determining (S2), based on measurements, values of an internal resistance (5) of the battery (1) during the test, with assignment of the detected state variables (3); - transforming (S3) the detected state variables (3) and / or the values of the internal resistance (5) by a forward transformation (7) so that a relationship which is as linear as possible is obtained between a change in one of the state variables (3) and a change in a value of the internal resistance (5); applying (S4) a linear model formation method (11) on the basis of the state variables (3) obtained after the transformation and the associated values of the internal resistance (5) to produce a provisional mathematical model (9); and retransforming (S5) the provisional mathematical model (9) by means of a retransformation (13) to a mathematical model (15) which can be used for the operation of the vehicle and which receives the state variables (3) as input variables in order to determine the internal resistance (5) as output variable, wherein the retransformation (13) is the inverse of the forward transformation (7).The method according to claim 1, wherein the linear modeling method (11) is a linear regression method.The method of claim 2, wherein the linear regression method is applied recursively.Method according to claim 3, wherein the linear regression method is applied recursively until a quality parameter satisfies a predefined limit condition, wherein the quality parameter specifies a deviation of the usable mathematical model from a determination of the actual internal resistance (5) based on measurement.Method according to one of the preceding claims, wherein the state variables (3) comprise at least one of: temperature of the battery (1), current state of charge of the battery (1).Method according to one of the preceding claims, wherein the forward transformation (7) comprises one of the following: polynomial function, in particular root function, exponential function, logarithm.Method according to one of the preceding claims, wherein, when detecting state variables (3), a selection of state variables (3) takes place during the testing of the battery (1), the change in said state variables resulting in a change in the internal resistance (5) above a predefined threshold.System for a vehicle, which is designed to execute a mathematical model (15) which specifies a relationship between state variables (3) of a battery (1) of a battery-electric vehicle and a value of an internal resistance (5), and wherein the system is designed to ascertain current state variables (3) of the battery (1), to feed them to the mathematical model (15) and to ascertain therefrom a current value of the internal resistance (5) of the battery (1), wherein the mathematical model (15) comprises an analytical function or a look-up table.The system according to claim 8, wherein the state variables (3) comprise a state of charge of the battery (1) and a temperature of the battery (1).Vehicle comprising a system according to one of claims 8 to 9.

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