Method for automatically estimating the state of charge of a cell of a battery

Abstract

The invention relates to a method comprising a phase (116) of estimating the state of charge of the cell at a time k based on an estimated entropy change ΔS, this phase (116) comprising, for a physical quantity chosen from among the group consisting of an internal temperature of the cell and a voltage across the terminals of the cell, the following steps: - calculating (118) an estimate of this physical quantity using an electrical model if the physical quantity is the voltage across the terminals of the cell and using a thermal model if the physical quantity is the internal temperature, then calculating (122) a difference between this estimate of the physical quantity and a measurement of this physical quantity, and then - constructing (122) the estimate of the state of charge at time k using the calculated difference.

Description

Automatic method for estimating the state of charge of a battery cell [1] The invention relates to an automatic method for estimating the state of charge of a battery cell as well as a recording medium and an electronic battery management system for implementing this method. The invention also relates to a motor vehicle comprising this battery management system. [2] Application W02020064959A1 describes a method for estimating the state of charge SOC of a cell of a battery from estimates of the entropy variation AS and the enthalpy variation AH of the cell of this battery. More precisely, the state of charge SOC is estimated using the following relationship: SOC = a. AS + p.AH + y, where a, [3 and y are constants predetermined during a calibration phase. The enthalpy variation AH of the cell is estimated using the following relationship: AH = - F. OCV - Ti. AS, where: - OCV is the open circuit voltage of the battery cell, - Ti is the measured internal temperature of the battery cell, and - F is Faraday's constant. [3] To estimate the open circuit voltage OCV, application W02020064959A1 uses an electrical model of the battery. To estimate the entropy variation AS, application W02020064959A1 uses a thermal model of the battery. The method described in application W02020064959A1 is advantageous in that it can be implemented during normal use of the cell and therefore in an electronic battery management system. These battery management systems are better known by the acronym BMS (“Battery Management System”). [4] It was noted by the inventors that the use of the entropy variation AS to estimate the state of charge of a cell of a battery should make it possible to obtain a much more precise estimate of this state of charge, particularly in the case of a battery cell whose open circuit voltage varies little as a function of its state of charge. Such cells whose open circuit voltage varies little as a function of its state of charge are notably used in LFP (“Lithium Iron Phosphate”) or Li-IP (Lithium Iron Phosphate) batteries. Indeed, in LFP battery cells, the variation in entropy AS of the cell varies significantly depending on its state of charge, which should make it possible to obtain greater precision in estimating its state of charge. However, in practice, this expected advantage has not been clearly obtained using the method described in application W02020064959A1. [5] The invention aims to overcome this drawback by proposing an automatic method for estimating the state of charge of a battery cell that is more precise than that described in application WO2020064959A1 while retaining its advantages. [6] The invention is set forth in the attached set of claims. [7] The invention will be better understood on reading the description which follows, given solely as a non-limiting example and made with reference to the drawings in which: - figure 1 is a partial schematic illustration of a motor vehicle equipped with an electric battery, - Figure 2 is a schematic illustration of an electrical model of a battery cell of the vehicle of Figure 1; - Figure 3 is a schematic illustration of an arrangement of estimators used to estimate the state of charge of a cell of the battery of the vehicle of Figure 1, - Figure 4 is a flowchart of a method for estimating the state of charge of a cell using the estimators of Figure 3; - Figure 5 is a graph illustrating the evolution over time of the estimation of the state of charge of a cell by implementing the method of Figure 4. [8] In this description, in a first chapter, the terminology and conventions used in this text are defined. In a chapter II, a detailed example of an embodiment is described with reference to the figures in the particular case where the cell whose state of charge is estimated is a cell of a battery of an electric vehicle. Then, in a chapter III, variants of these embodiments are introduced. Finally, the advantages of the different embodiments are specified in a chapter IV. [9] Chapter I: Terminology and convention:

[0010] In the figures, the same references are used to designate the same elements. In the remainder of this description, the characteristics and functions well known to those skilled in the art are not described in detail.

[0011] In this description, "computing power" refers to the number of operations to be performed by an electronic computer. Thus, reducing computing power means reducing the number of operations to be performed to achieve the same result or a result of the same nature.

[0012] The term "internal temperature" refers to the temperature at the heart of the cell. If the temperature inside the battery is relatively uniform, the internal temperature is close to the temperature measurable on the outer surface of the battery cell. Thus, the internal temperature also refers to the temperature of the outer surface of the cell.

[0013] In this description, the symbol " T » denotes the mathematical transpose operation. The multiplication operation is represented by the operator “.”.

[0014] Chapter: Example of implementation mode

[0015] Figure 1 represents a motor vehicle 2 with electric traction, better known as an “electric vehicle”. Electric vehicles are well known and only the structural elements necessary to understand the rest of this description are presented. The vehicle 2 comprises: - an electric motor 4, capable of rotating drive wheels 6 to make the vehicle 2 roll on a roadway 8, and - a battery 10 which supplies electrical energy to the motor 4.

[0016] The battery 10 has two electrical connection terminals 12, 14 and several electrical cells electrically connected between these terminals 12 and 14. The terminals 12 and 14 are connected to the electrical loads to be supplied. Here, they are therefore connected in particular to the electric motor 4.

[0017] To simplify Figure 1, only four electrical cells 18 to 21 are shown. Typically, these electrical cells are grouped into several stages and these stages are connected in series between terminals 12 and 14. Here, only two stages are shown. The first stage has cells 18 and 19, and the second stage has cells 20 and 21. Each stage has several branches connected in parallel. Each branch of a stage has one electrical cell or several electrical cells in series. Here, the first stage has two branches, and each branch has a single electrical cell. The second stage is structurally identical to the first stage in the example shown in Figure 1.

[0018] Here, all cells of battery 10 are structurally identical within manufacturing tolerances. Therefore, only cell 18 is now described in more detail.

[0019] The cell 18 has two electrical connection terminals 30, 32 which electrically connect it to the other cells and to the terminals 12 and 14 of the battery 10. The cell 18 is also mechanically fixed, without any degree of freedom to the other cells of the battery 10 to form what is frequently called a "pack" of cells. The cell 18 is capable of storing electrical energy when it is not in use. This stored electrical energy is then used to power the motor 4, which discharges the cell 18. At other times, the cell 18 can also receive electrical energy which charges it.

[0020] Cell 18 is a known cell type, for example, it is an LFP cell.

[0021] The cell 18 is characterized in particular by a nominal capacity Capa, an internal resistance Ro, and an open circuit voltage OCV. The capacity Capa is the capacity of the cell 18. The capacity of a cell represents the maximum quantity of electrical energy that can be stored in this cell. This capacity is expressed in Ah (Ampere-hour). Here, to simplify the description of this embodiment, the capacity Capa is considered to be constant over time.

[0022] The internal resistance Ro is the value of the internal resistance of cell 18. The internal resistance of a cell is a physical quantity found in most electrical models of an electric cell. As the cell ages, the internal resistance typically increases. At time k, the value of the internal resistance Ro of cell 18 is denoted Ro,k.

[0023] The OCV voltage is also known as the "open circuit voltage." The OCV voltage is the measurable voltage between terminals 30 and 32 after the cell 18 has been electrically isolated from any electrical load for several hours. The OCV voltage varies depending on the cell's state of charge.

[0024] The state of charge at time k of cell 18 is denoted SOCk. The state of charge represents the filling rate of cell 18. It is equal to 100% when the quantity of electrical energy stored in cell 18 is equal to its capacity Capa. It is equal to 0% when the quantity of energy stored in cell 18 is zero, that is to say that no more electrical energy can be extracted from cell 18 to power an electrical load.

[0025] The parameters Capa and the initial value Ro,o of the internal resistance Ro are known parameters of the cell 18. For example, they are given by the cell manufacturer or are determined experimentally from measurements carried out on this cell.

[0026] Battery 10 also includes for each cell: - a voltmeter which measures the voltage between the terminals of this cell, - an ammeter which measures the intensity of the current which passes through this cell, and - a thermometer that measures the interior temperature of the cell.

[0027] To simplify Figure 1, only a voltmeter 34, an ammeter 36 and a thermometer 38 of cell 18 have been shown.

[0028] Here, to measure the internal temperature of the cell 18, the thermometer 38 is in direct thermal and mechanical contact with the external casing of the cell 18. The thermometer 38 is directly fixed to the cell 18.

[0029] Finally, the battery also includes a sensor 39 which measures a physical quantity representative of the ambient temperature Ta. The ambient temperature Ta is the temperature of the external environment in which the cell 18 is immersed. For example, here, the sensor 39 is a thermometer housed between an external envelope of the battery 10 and the external envelopes of the different cells 18 to 21.

[0030] Unlike the various parameters of the cell 18 introduced previously, the state of charge SOC of the cell 18 is not directly measurable. It must therefore be estimated. For this purpose, the vehicle 2 comprises an electronic system 40 battery management system 10 better known by the acronym BMS (“Battery Management System”). This system 40 has the particular function of determining the state of charge of the battery 10. To determine this state of charge, the system 40 is capable of estimating the state of charge of each cell of the battery 10.

[0031] To carry out these different estimations, the system 40 is electrically connected to each sensor of the battery 10 to acquire the measurements necessary for estimating the state of charge of each cell.

[0032] Here, the system 40 comprises a memory 42 and a programmable electronic computer 44, capable of executing instructions recorded in the memory 42. For this purpose, the memory 42 comprises the instructions necessary for executing the method of figure 4. This memory 42 also comprises the initial values ​​of the different parameters necessary for executing this method.

[0033] Figure 2 represents an electrical model 50 of cell 18. This model is known as the “First Order Thévenin Model” or “Electrical Lumped Parameter Model”. It comprises successively, connected in series from terminal 32 to terminal 30: - a 52 generator of the no-load voltage OCV, - a parallel RC circuit 54, and - the internal resistance Ro.

[0034] Circuit 54 comprises a capacitor of capacity Ci connected in parallel with a resistor of value Ri. Subsequently, it is considered that these two parameters Ci and Ri of model 50 are known and constant over time. The voltage across circuit 54 is noted Vi. The voltage between terminals 30 and 32 of cell 18 is noted V and the intensity of the current flowing through cell 18 is noted i. The value of the voltage OCV at time k is noted OCVk.

[0035] Figure 3 represents a first embodiment of an arrangement of estimators 60, 62 and 64 implemented in the system 40 to estimate the state of charge of the cell 18. Each estimator 60, 62 and 64 is implemented in the form of an estimation algorithm executed by the computer 40. Thus, we will subsequently speak of both “execution of an estimator” and “execution of an estimation algorithm”.

[0036] The estimator 60 estimates the values ​​of the parameters Ro and OCV of the electrical model 50 from the measured values ​​of the voltage V and the intensity i of the current flowing through the cell 18. The estimator 60 is executed at each instant k1 of a temporal sequence of instants {0; 1; 2; ...; k1; k1 +1; ...}. Here, these instants k1 are repeated at a constant frequency fi. The duration of the constant interval between two immediately consecutive instants k1 and k1 +1 is noted At1. The duration At1 is equal to 1 / fi. The duration At1 is typically between 0.1 s and 60 s and, preferably, between 0.1 s and 10 s. Here, the duration At1 is equal to 0.2 s.

[0037] Subsequently, the values ​​of the parameters Ro and OCV estimated at time k1 are denoted Ro,ki and OCVki. The measured values ​​of the voltage V and the current i at time k1 are denoted Vrriki and irriki. The estimator 60 is implemented here as described in application W02020064959A1. It therefore executes, at each time k1, a recursive least squares algorithm to determine the value OCVki and the values ​​bo.ki, bi,ki and ba,ki of the coefficients of the following relation (1) from the measurements Vrriki and irriki acquired between times k1 and k1 -Ni: Vm k l = b 0tk l .im kl +b l tk l . im k l- L +b 2t kl . (OCV k l - l -Vm k l-l )+OCV k l

[0038] Relation (1) follows from the electrical model 50. Ni is an integer greater than two and, preferably, greater than one hundred or one thousand.

[0039] The values ​​bo.ki, bi,ki and ba.ki of the coefficients of relation (1) are related to the values ​​of the parameters of model 50 by the following relations: bo,k1 = Ro,k1 bi ,ki = -Ro,ki + ( At1 / Ci) + ( At1 .Ro,ki / (Ci.Ri)) b2,ki = At1 / (Ci.Ri) - 1

[0040] Thus, at each instant k1, the estimator 60 delivers new values ​​Ro.ki and OCVki for the parameters, respectively, R0 and OCV of the model 50.

[0041] Estimator 62 estimates the entropy variation AS of cell 18 from the measured values ​​of voltage V, intensity i of the current flowing through cell 18, internal temperature Ti and ambient temperature Ta. Estimator 62 is executed at each instant k2 of a temporal sequence of instants {0; 1; 2; ...; k2; k2+1; ...}. Here, these instants k2 are repeated at a constant frequency f2. The duration of the constant interval between two immediately consecutive instants k2 and k2+1 is denoted At2. The duration At2 is equal to 1 / f2. The temperature of the cell 18 varies more slowly than the voltage and the current. Thus, typically, the frequency f2 is chosen equal to the frequency fi or smaller than the frequency fi. For example, here, the duration At2 is equal to 5 s. In this case, the set of instants k2 is a subset of the set of instants k1 . Between two successive instants k2 and k2+1 , there are therefore several instants k1.

[0042] Subsequently, the value of the entropy variation AS estimated at time k2 is denoted ASk2. The measured values ​​of the voltage V, the current i and the temperatures Ti and Ta at time k2 are denoted, respectively, Vrrik2, irrik2, Tir and Tar. The estimator 62 is also implemented here as described in application W02020064959A1. The estimator 62 therefore uses the following thermal model of the cell 18: Or : - m is the mass of cell 18, - C P is the heat capacity of cell 18, - dTi / dt is the first derivative of the temperature Ti with respect to time, - F is the Faraday constant, - h is the heat exchange coefficient of cell 18 with the external environment, - A is the area of ​​cell 18 in contact with the external environment, and - Ta is the room temperature.

[0043] This thermal model is particularly accurate because it takes into account thermal exchanges between the cell and the external environment, the creation of heat within the cell by the Joule effect, and the variation in entropy caused by the movement of ions such as lithium ions.

[0044] At each instant k2, the estimator 62 executes a recursive least squares algorithm to determine the values ​​ao,k2, ai,k2 and aa,k2 of the coefficients of the following relation (2) from the measurements Vrrik2, irrik2, Tir and Tarrik2 acquired between instants k2 and k2-N2:

[0045] Relation (2) follows from the thermal model presented above. N2 is an integer greater than two and, preferably, greater than ten or fifty or one hundred. In relation (2), the value OCVk2 is the value of the OCV parameter estimated by the estimator 60 at time k1 equal to time k2 or to time k1 which precedes time k2 and is closest to time k2.

[0046] The values ​​ao,k2, ai,k2 and aa,k2 are related to the values ​​of the parameters of the thermal model by the following relations: ao,k2 = At2 / (m.Cp) ai,k2 = At2. ASk2 / (m.Cp.F) a2,k2 = At2.hA / (m.Cp).

[0047] Thus, the estimator obtains an estimate of the values ​​of the parameters of the thermal model using the following relations: m.Cp = At2 / ao,k2 ASk2 = ai,k2.F / ao,k2 hA = a2,k2 / ao,k2.

[0048] Thus, at each instant k2, the estimator 60 delivers a new value ASk2 of the parameter AS of the thermal model. On the other hand, the products m.Cp and hA generally vary little as a function of time. Thus, in this embodiment, the products m.Cp and hA are considered constant. The values ​​of these products m.Cp and hA are for example determined from the data provided by the manufacturer of the cell 18 or measured experimentally during a calibration phase. Then, the values ​​of the products m.Cp and hA are recorded in the memory 42 and are no longer estimated by the estimator 62.

[0049] Estimator 64 estimates the state of charge SOC of cell 18 from the entropy variation AS estimated by estimator 62.

[0050] Estimator 64 is executed at each instant k of a temporal sequence of instants {0; 1; 2; ...; k; k+1; ...}. Here, these instants k are repeated at a constant frequency f. The duration of the constant interval between two immediately consecutive instants k and k+1 is denoted At. The duration At is equal to 1 / f. Typically, the duration At is between 0.2 ss and 1 min. For example, here, the frequency f is equal to the frequency fi and the duration At is equal to the duration At1. Thus, here, the set of instants k and the set of instants k1 are identical.

[0051] Subsequently, the value of the state of charge SOC estimated at time k is denoted SOCk. The measured values ​​of voltage V, current i and temperatures Ti and Ta at time k are denoted, respectively, Vrrik, irrik, Tirrik and Tarrik.

[0052] Estimator 64 compensates for the errors introduced by the use of the electrical and thermal models by estimators 60 and 62 to improve the accuracy of the SOC state of charge estimation. For this purpose, estimator 64 estimates the SOCk value of the SOC state of charge by additionally taking into account the following deviations: - a Vek-Vrrik gap, where Vek is the estimate, at time k, of the voltage V between terminals 30 and 32 obtained using model 50, and - a Tiek-Tirrik gap, where Tiek is the estimate, at time k, of the temperature Ti obtained using the thermal model of estimator 62.

[0053] For this purpose, the estimator 64 is implemented here in the form of a Kalman filter. The thermal model is nonlinear. Because of this, the estimator 64 implements the extended version of the Kalman filter, better known by the acronym EKF (Extended Kalman Filter). The implementation and operation of an extended Kalman filter are well known to those skilled in the art. For example, the implementation and operation of an extended Kalman filter are described in detail in the following article: L. Plett, et al.: “Extended Kalman filtering for battery management systems of Li PB-based H EV battery packs”, Journal of Power Sources, 2004, pages 252-292. Hereinafter, this article is referred to by the abbreviation “Plett 2004”. Thus, subsequently, only the state and observation models of the Kalman filter of estimator 64 are described.

[0054] In this exemplary embodiment, the state vector Xk is equal to [SOCk, Tik, Vik] T. The Kalman filter uses a state representation that allows obtaining a prediction Xk / ki of the state vector Xk at time k only from the measurements made between times 0 to k-1 and from the previous state vector Xk-1. This state representation is constructed from the electrical and thermal models used by estimators 60 and 62. Thus, this state representation uses the same parameters as those used by the electrical and thermal models previously described. For example, here, the state representation is defined by the following relation (3): - the index k / k-1 indicates that it is a prediction obtained at time k and made by taking into account only the measurements made between times 0 and k-1, - the index k-1 / k-1 indicates that it is the estimate obtained at time k-1 taking into account all the measurements made between times 0 and k-1, - irrik is the measure of the intensity of current i at time k, - Ro,k is the estimate of the internal resistance Ro provided by the estimator 60 at time k1 equal to time k or immediately preceding time k, - Tarrik is the measurement of the ambient temperature at time k, - ASk is the value of the entropy variation AS provided by the estimator 62 at time k2 equal to time k or immediately preceding time k, and - Vi, k / ki and Vi ,ki / ki are, respectively, the predicted value of voltage Vi at time k and the predicted and corrected value of voltage Vi at time k-1.

[0055] The observation model used in this Kalman filter is defined by the following relation (4): Or : - Tiek and Vek are the estimates of the measurements, respectively, Tirrik and Verrik, at time k, - OCVk and Ro,k are the estimates, respectively, of the OCV voltage and the internal resistance Ro provided by the estimator 60 at time k1 equal to time k or immediately preceding time k.

[0056] The operation of the system 40 will now be described using the method of FIG. 4 and in the particular case of estimating the state of charge of the cell 18.

[0057] The method begins with a phase 100 of initializing the values ​​of the various parameters of the electrical and thermal models. For example, the parameters are initialized from the values ​​of these parameters obtained following a previous use of the system 40 or from a use of a system similar to the system 40 with a similar cell. Phase 100 also includes the initialization of the covariance matrices Û64 and R64 necessary to execute the estimator 64. The matrix Û64 expresses the uncertainties in the model used. For example, the various coefficients of the matrix Û64 are obtained from the square of the error originating from the modeling of the cell. For this, a usable method is to compare, over a certain given time range, the actual state of charge, measured in the laboratory, at a time t and the level of charge predicted by the model at this time t knowing the actual state of charge at the previous time.The mean square error between the predictions and the actual state of charge over the given time range provides an estimate of the error inherent in the model.

[0058] The RÔ4 matrix expresses the uncertainties in the measurements used. For example, the different coefficients of the RÔ4 matrix are obtained from the square of the standard deviation of the Gaussian noise on each measurement.

[0059] Subsequently, the covariance matrices Û64 and RÔ4 are considered to be constant. These matrices Û64 and RÔ4 are pre-recorded in the memory 42.

[0060] Once the initialization phase 100 is complete, a phase 102 of using the system 40 to estimate the state of charge of the cell 18 during its operation within the vehicle 2 can begin.

[0061] During a measurement phase 1 10, at each instant k, the voltmeter 34, the ammeter 36 and the thermometer 38 and the sensor 39 measure, respectively, the voltage V, the current i and the temperatures Ti and Ta. These measurements Vrrik, irrik, Tik and Tak are immediately acquired by the system 40 and recorded in the memory 42. Phase 1 10 is repeated at each instant k. Since the instants k2 are a subset of the instants k, phase 1 10 also makes it possible to obtain the measurements Vrrik2, irrik2, Tik2 and Tak2.

[0062] In parallel, at each instant k1, the estimator 60 executes a phase 112 of estimation of the values ​​Ro.ki and OCVki of the parameters Ro and OCV of the electrical model 50. For this, the estimator 60 uses the Ni measurements of the voltage V and the intensity i acquired following the Ni previous iterations of the measurement phase 1 10. The phase 112 is carried out as described in the application W02020064959A1. Thus, the phase 1 12 is not described in more detail.

[0063] In parallel with phases 110 and 112, at each instant k2, the estimator 62 executes a phase 114 of estimating the value ASk2 of the variation in entropy AS of the cell 18. For this, the estimator 62 uses the N2 measurements of the voltage V, of the intensity i and of the temperatures Ti and Ta acquired at the instants k between the current instant k2 and k2-N2. Phase 1 14 is carried out as described in application W02020064959A1. Thus, phase 114 is not described in more detail.

[0064] In parallel, phases 1 10, 1 12 and 114, at each instant k, the estimator 64 executes a phase 1 16 of estimation of the state of charge at instant k of the cell 18.

[0065] For this, during a step 118, the estimator 64 calculates the prediction Xk / k-1 of the state vector Xk using the state representation defined by the relation (3). The prediction Xk / k-1 is calculated from: - irrik and Tarrik measurements acquired by system 40 at time k, - estimates Tik-i / ki and Vi,ki / ki, respectively, of the temperature Ti and the voltage V1 obtained by the estimator 64 at the end of the execution of phase 114 for the instant k-1.

[0066] In a step 120, the estimator 64 also calculates a prediction Pk / k-1 of an estimation error covariance matrix on the state vector Xk. Typically, this is achieved using the following relationship: Pk / k-1 = Fk-i Pk-i / k-iFk-i T +Q64, where: - Pk-i / ki is the estimate of the covariance matrix Pk-1 of the error at time k-1 obtained by taking into account all the measurements acquired up to time k-1, and - Pk / k-1 is the prediction of the covariance matrix Pk at time k obtained by taking into account only the measurements acquired up to time k-1.

[0067] The matrix Fk-1 is the state matrix. It is obtained from relation (3). For example, for this, here relation (3) is linearized in the neighborhood of the vector Xk using a Taylor series expansion in the neighborhood of the vector Xk. Then we neglect the contributions of the derivatives from the second order. The matrix Fk-1 is thus defined here by the following relation: In this matrix Fk-1, the derivative dASk / dSOCk-i is for example calculated using the following relation: dASk / dSOCk-i = (ASk2-ASk2-i) / (SOCk2-SOCk2-i), where: - the instant k2 in this relation is the most recent instant k2 at which the estimate of the entropy variation AS was updated by the estimator 62, and - SOCk2 and SOCk2-i are the charge states of cell 18 determined by estimator 64 for the times k closest, respectively, to times k2 and k2-1.

[0068] In a step 122, the estimator 64 corrects the prediction Xk / k-1 of the state vector to construct the corrected state vector Xk / k. The corrected vector Xk / k is constructed as a function of a difference lk between: - a vector Zk of the estimates of the physical quantities at time k, and - a vector Zk of measurements of these same physical quantities at time k.

[0069] The deviation lk is known as "innovation". Here, the physical quantities measured are the temperature Ti and the voltage V. The vector Zk is therefore equal to [Tirrik, Vrrik] T Innovation lk is calculated using the following relationship: lk = Zk - â. Innovation lk is therefore defined by the following relationship: J where the Tiek and Vek estimates are those obtained using the observation model defined by relation (4).

[0070] Typically, in step 122, the estimator 64 corrects the prediction Xk / k-1 by adding the innovation lk multiplied by the Kalman gain Kk. The gain Kk is calculated using the following relationship: Kk = Pk / k-iHk T (HkPk / k-iHk T + F i)' 1 , Or : - the RM matrix is ​​the covariance matrix of the noise on the measured physical quantities, and - Hk is an observation matrix.

[0071] The observation matrix Hk is obtained from relation (4).

[0072] Then, the state vector Xk / k is constructed using the following relation: Xk / k = Xk / k-1 + Kklk.

[0073] The updated error covariance matrix at time k is calculated using the following relation: Pk / k = (I - KkHk)Pk / ki, where I is the identity matrix.

[0074] The matrix Pk / k expresses the margins of error on the estimates SOCk / k, Tik / k and Vi,k / k. The SOCk value of the state of charge estimate at time k is equal to SOCk / k.

[0075] Figure 5 is a graph that represents the evolution over time of the state of charge of the cell 18 estimated using different algorithms. On this graph, curve 150 represents the evolution of the state of charge of the cell 18 measured in the laboratory. This laboratory measurement is considered to be the one that best approaches the real value of the state of charge. However, the methodology implemented to make this estimation in the laboratory cannot be implemented when using the cell 18 in operation within a vehicle 2.

[0076] Curve 152 represents the evolution of the state of charge estimated using the method in Figure 4 and therefore using both the Vek-Vrrik and Tiek-Tirrik deviations.

[0077] Curve 156 represents the evolution of the state of charge estimated using a process identical to that of figure 4 except that only the Vek-Vrrik difference is taken into account to correct the SOCk / ki estimate.

[0078] Curve 158 represents the evolution of the state of charge estimated using a conventional method known by the English term “Coulomb Counting”.

[0079] It can be seen (curve 156) that correcting the SOCk / ki prediction using the Vek-Vrrik gap already allows us to obtain a much better estimate than that obtained using the conventional method (curve 158).

[0080] It can also be seen (curve 152) that the best estimate is obtained by correcting the SOCk / ki prediction using both the Vek-Vrrik gap and the Tiek-Tirrik gap.

[0081] Finally, although not shown in Figure 5 to improve its readability, it is emphasized that correcting the SOCk / ki prediction using only the Tiek-Tirrik gap allows to obtain a better estimate than that obtained using only the Vek-Vrrik gap but less good than that obtained by implementing the method of figure 4.

[0082] Chapter: Variants:

[0083] Electric model variants:

[0084] Other electrical models can be used. For example, as a variant, the electrical model has several parallel RC circuits connected in series between one terminal of the DC voltage source and terminal 30 of the cell. In this case, the number of parameters to be estimated from the electrical model is greater. However, as before, the values ​​of these additional parameters can be estimated by implementing a recursive least squares method.

[0085] Alternatively, the parameters Ri and Ci are not considered constant. In this case, for example, they are estimated at each time k1 in a similar way to what is described for the parameters Ro and OCV of the electrical model.

[0086] In a simplified embodiment, the value of the parameter Ro is considered to be constant over time. In this case, the value Ro.ki is not estimated at each instant k1.

[0087] Algorithms other than the recursive least squares algorithm can be used to estimate the values ​​of the electrical model parameters. For example, the Ro.ki and OCVki values ​​can also be estimated using an additional Kalman filter dedicated to this task. An example of an additional Kalman filter designed to estimate the Ro.ki value is described in application WO2016083754A1 or in chapter 4.2.1 of the article Plett2004. An example of using a Kalman filter to estimate the value of the OCV parameter is also described in application US2017146608A1.

[0088] Variants of the thermal model:

[0089] Other thermal models are possible. For example, the thermal model used by estimator 62 can also be the one defined by the following relationship:

[0090] In another embodiment, the thermal model used to estimate the entropy variation AS is that of equation (5) of application US2017146608A1. In this case, the thermal model relates the entropy value Sk2 to its value ASk2-i and to the values ​​Tik2, Tik2 -1, OCVk2 and OCVk2-i. In this case, the ambient temperature is not used to estimate the entropy variation AS and the sensor 39 can be omitted.

[0091] Alternatively, the value of the product m.Cp and / or the value of the product hA are not considered constant. In this case, the values ​​of these products are estimated at each time k2, for example, by implementing the recursive least squares algorithm.

[0092] The physical quantity Ta representing the ambient temperature can be different from a temperature. For example, when the battery is equipped with a cell cooling system, the physical quantity Ta can be the control of this cooling system. Indeed, the greater the cooling control, the higher the ambient temperature of the cell.

[0093] The ASk2 value of entropy can be estimated by implementing a method other than the recursive least squares method. For example, alternatively, the ASk2 value is estimated using a Kalman filter dedicated to this task.

[0094] Alternatively, the instants k2 are as frequent as the instants k or k1 .

[0095] Variants of state of charge estimation:

[0096] In a simplified variant, only the Vek-Vrrik gap or only the Tiek-Tirrik gap is used to correct the SOCk / ki prediction of the state of charge. In this case, the lk innovation has only one gap.

[0097] In the given example of Fk-i matrix, the derivative dASk / dSOCk-i can be calculated differently. For example, during a calibration phase, a polynomial approximation of the evolution of the AS entropy variation as a function of the SOC charge state is constructed. Then, the value of the derivative dASk / dSOCk-i is taken equal to the value of the derivative of the polynomial constructed at the abscissa equal to SOCk-i.

[0098] Estimator 64 can be implemented using other Kalman filter forms than the EKF form.

[0099] In another variant, the estimator 64 is not implemented as a Kalman filter but in some other form. For example, the estimator 64 is implemented in the form of a learning machine which, after a learning phase on a database, associates a SOCk value as a function of the imk and Vrrik measurements and the Vek-Vrrik and Tiek-Trrik deviations. For this, the database includes, for a large number of instants k, a SOCk value measured experimentally at instant k associated with the imk, Vrrik measurements and the Vek-Vrrik and Tiek-Trrik deviations calculated for the same instant k using the electrical and thermal models. The estimator 64 can also be implemented using a first and a second learning machine. The first learning machine is configured to generate the Vek-Vrrik and Tiek-Trrik deviations from the imk, vrrik, Tirrik and Tarrik measurements and the ASk2 value of the AS entropy variation estimated at instant k2 closest to instant k.Then, the second learning machine is configured to provide the estimated value SOCk of the state of charge of the cell 18 from the Vek-Vrrik and Tiek-Trrik deviations generated by the first learning machine and the estimated value ASk2.

[0100] Alternatively, k times are less frequent than k1 times.

[0101] The method for estimating the state of charge described here in the particular case of a battery cell also applies to a battery that contains a pack of several cells. In this case, the battery is treated as if it were a single cell. In other words, what has been described here applies to the case of a battery itself formed of several cells electrically connected to each other.

[0102] Other variants:

[0103] The thermometer 38 can be housed inside the cell casing 18.

[0104] The sensor 39 can be placed outside the outer casing of the battery 10.

[0105] What has been described in the specific case of an LFP cell applies to any cell technology. For example, it also applies to a LiPB (Lithium-ion Polymer Battery) or Li-IP cell or other.

[0106] Alternatively, the cell's capacitance Capa is not constant and changes over time. In this case, the value of the capacitance Capa can also be estimated. An example of a method for estimating the value of the capacitance Capa is described in chapter 4.2.2 of the article Plett2004, part3. Another example is described in the application WO201 6083754A1.

[0107] The teaching given here in the specific case of a cell and battery of an electric vehicle applies to all cells and batteries whether or not they are used in an electric vehicle. This applies equally to used cells and batteries as to new cells and batteries.

[0108] Several of the variants described above can be combined in a single embodiment.

[0109] Chapter III: Advantages of the embodiments described:

[0110] Estimating the state of charge SOC of the cell from the variation AS of entropy makes it possible to increase the accuracy of the estimation of the state of charge, in particular when the OCV voltage does not vary much depending on the state of charge SOC. In addition, calculating the SOCk value as a function of at least one of the Vek-Vrrik and Tiek-Tirrik deviations makes it possible to compensate for the errors caused by the use of the electrical and thermal models by the estimators 60 and 62. Thanks to this, the SOCk value thus calculated is more precise, in particular, for example, with respect to the method proposed in application W02020064959A1.

[0111] Correcting the SOCk value estimate using both the Vek-Vrrik deviation and the Tiek-Tirrik deviation increases the accuracy of the estimated state of charge.

[0112] Using a thermal model that takes into account the intensity i of the current flowing through the cell and a measurement of the ambient temperature, makes it possible to increase the precision of the estimation of the AS variation of entropy and therefore to increase the precision of the estimation of the state of charge.

[0113] Using a Kalman filter to estimate the SOCk value can speed up the execution of the SOCk value estimation process.

Claims

Claims 1. Automatic method for estimating the state of charge of a battery cell by an electronic battery management system, this method comprising: - a first phase (112) of estimating the internal resistance and the open circuit voltage of the cell using an electrical model linking a voltage V between terminals of the cell and the intensity i of the current flowing through the cell, this electrical model comprising a parameter Ro which corresponds to the internal resistance of the cell and a parameter OCV which corresponds to the open circuit voltage of the cell, - a second phase (114) of estimating a variation AS of entropy of the cell using a thermal model of the cell, this thermal model linking a variation of the internal temperature of the cell to the variation AS of entropy, this thermal model comprising a parameter chosen from the group composed of the parameters Ro and OCV and the value of which was estimated during the first estimation phase, - at each instant k of a temporal succession of instants {0; 1; 2; ...; k; k+1; ...}, a third phase (116) of estimation of the state of charge of the cell at instant k from the variation AS of entropy estimated during the second estimation phase, characterized in that the third estimation phase (116) comprises, for at least one physical quantity chosen from the group composed of the internal temperature of the cell and the voltage between the terminals of the cell, the following steps: - the calculation (118) of an estimate of this physical quantity using the electrical model if the physical quantity is the voltage between the terminals of the cell and using the thermal model if the physical quantity is the internal temperature, then the calculation (122) of a difference between this estimate of the physical quantity and a measurement of this physical quantity, then - the construction (122) of the estimate of the state of charge at time k using the calculated difference.

2. Method according to claim 1, in which the third estimation phase comprises: - the calculation (118) of an estimate Vek of the voltage between the terminals of the cell at time k using the electrical model, then the calculation (122) of a first difference between the estimate Vek and the measurement Vrrik, and - the calculation (118) of a Tiek estimate of the internal temperature of the cell at time k using the thermal model, then the calculation (122) of a second difference between the Tiek estimate and the Tirrik measurement, and - the construction (122) of the estimation of the state of charge using the first and second deviations calculated to compensate for the errors introduced by the use of the electrical and thermal models during the estimations of the parameters Ro, OCV and the variation AS of entropy.

3. Method according to any one of the preceding claims, in which the thermal model also links the variation of the internal temperature of the cell: - the intensity of the current flowing through the cell, and - at the ambient temperature of the medium in which the cell is stored.

4. Method according to any one of the preceding claims, in which the estimation of the state of charge is obtained by implementing a Kalman filter in which the innovation comprises the first and second deviations.

5. Method according to claim 4, in which the state representation used by the Kalman filter to predict the state Xk / k+i of the state variables is defined by the following relation: - Xk / ki is the estimate of a state vector obtained at time k and made by taking into account only the measurements made between times 0 and k-1, - SOCk / k-1 is the prediction of the state of charge obtained at time k and made by taking into account only the measurements made between times 0 and k-1, - SOCk-i / ki is the estimate of the state of charge obtained at time k-1 and made by taking into account all the measurements carried out between times 0 and k-1, - Tik / k-1 is the prediction of the internal temperature obtained at time k and made by taking into account only the measurements made between times 0 and k-1, - Tik-i / ki is the estimate of the internal temperature obtained at time k-1 and made by taking into account all the measurements made between times 0 and k-1, - Vi,k / ki is the prediction of a voltage Vi at the terminals of an RC circuit of the electrical model obtained at time k and made by taking into account only the measurements carried out between times 0 and k-1, - Vi,ki / ki is the estimate of the voltage Vi obtained at time k-1 and made by taking into account all the measurements made between times 0 and k-1, - At is the time elapsed between two immediately consecutive instants k and k-1, - Capa is the value of the cell's capacity, - irrik is the measure of the intensity of the current flowing through the cell at time k, - Ro,k is the estimate of the internal resistance Ro obtained at the end of the first estimation phase carried out at a time k1 equal to time k or immediately preceding time k, - m is the mass of the cell, - C P is the heat capacity of the cell, - h is the heat exchange coefficient of the cell with an external environment, - A is the area of ​​the cell in contact with the external environment, - Tarrik is the measurement of the ambient temperature of the external environment at time k, - ASk is the value of the entropy variation AS obtained at the end of the second estimation phase executed at a time k2 equal to time k or immediately preceding time k, - F is Faraday's constant.

6. Method according to any one of the preceding claims, in which the first estimation phase comprises: - at each instant k1 of a temporal succession of instants {0; 1; 2; ...; k1; k1 +1; ...}, the acquisition (110) of a measurement Vrriki of the voltage between the terminals of the cell and of a measurement irmu of the intensity of the current which crosses the cell, the index k1 identifying the instant k1 at which the measurements Vm ki and irriki are acquired, then - from the voltage and current measurements acquired between times k1 and k1 - Ni, where Ni is a predetermined integer greater than three, the estimation of the values ​​Ro.ki and OCVki, respectively, of the parameters Ro and OCV of the electrical model of the cell by implementing a Recursive Least Squares algorithm.

7. Method according to claim 6, in which the values ​​Ro,ki and OCVki of the parameters Ro and OCV of the electrical model are estimated using the following relationship: Or : - Vrriki and Vrriki-i are the measurements of the voltage between the terminals of the cell at times k1 and k1 -1, respectively, - irriki and irriki-i are the measures of the intensity of the current flowing through the cell at times k1 and k1 -1 respectively, - OCVki-i is the value of the OCV parameter estimated at time k1 -1, - bo.ki , bi,ki and b2,ki are the values ​​of the coefficients of the electrical model updated at time k1 , the value Ro,ki of the parameter Ro at time k1 being equal to the value bo.ki .

8. Method according to any one of the preceding claims, in which the second estimation phase comprises: - at each instant k2 of a temporal succession of instants {0; 1; 2; ...; k2; k2+1; ...}, the acquisition of a measurement Virrik2 of the voltage between the terminals of the cell, of a measurement of the intensity irrik2 of the current which crosses the cell, of a measurement Timk2 of the internal temperature of the cell and of a measurement Tarrik2 of a physical quantity representative of the ambient temperature of the medium in which the cell is immersed, the index k2 identifying the instant k2 at which the measurements Virrik2, irrik2, Tir and Tar are acquired, then - from measurements of the voltage between the terminals of the cell, the intensity of the current passing through the cell, the internal temperature and the physical quantity representative of the ambient temperature acquired between times k2 and k2-N2, where N2 is a predetermined integer greater than two, and from a value of the internal resistance or a value of the open-circuit voltage obtained at the end of the execution of the first estimation phase, the estimation of a value ASk2 of the variation AS of entropy by implementing a Recursive Least Squares algorithm.

9. Method according to claim 8, in which the value ASk2 of the variation AS of entropy is estimated using the following relation: Or : - Tirrik2 and Tir -i are the values ​​of the internal temperature of the cell measured, respectively, at times k2 and k2-1, - Irrik2 is the value of the current intensity which crosses the cell measured at time k2, - Tarrik2 is the value of the physical quantity representative of the ambient temperature measured at time k2, - OCVk2 is the value of the OCV parameter obtained at the end of the execution of the first estimation phase at a time equal to or immediately preceding time k2, - ao,k2, ai,k2 and a2,k2 are the values ​​of the thermal model coefficients updated at time k2, the value ASk2 of the AS variation of entropy at time k2 being equal to ai,ki.F / ao,k2, where F is the Faraday constant.

10. Information recording medium (42) readable by an electronic computer, characterized in that it comprises instructions for the execution of an estimation method in accordance with any one of the preceding claims, when these instructions are executed by the electronic computer.

11. Electronic system for managing a battery equipped with at least one cell, this system comprising an electronic computer (44) programmed to execute an automatic method for estimating the state of charge of a cell of a battery, characterized in that the computer (44) is programmed to execute the automatic method for estimating the state of charge in accordance with any one of claims 1 to 9.

12. Motor vehicle comprising: - at least one drive wheel (6), - an electric motor (4) capable of rotating this drive wheel to move the motor vehicle, - a battery (10) comprising at least one cell (18-21) capable of storing electrical energy and, alternately, of restoring electrical energy to power the electric motor, this cell comprising two terminals (30, 32) via which it is electrically connected to the electric motor, - a voltmeter (34) electrically connected between the terminals of the cell to measure the voltage between these terminals, - an ammeter (36) connected in series with the electric cell to measure the intensity of the current flowing through this cell, - a thermometer (38) capable of measuring an internal temperature of the electric cell, and - a battery management system (40) connected to the voltmeter and the ammeter, this management system comprising a programmable electronic computer (44) capable of estimating the state of charge of the battery cell from the measurements of the voltmeter and the ammeter, characterized in that the battery management system (40) conforms to claim 11.

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