Automatic method for estimating the entropy change of a battery cell

Abstract

Automatic method for estimating the entropy change of a battery cell. This method comprises: - a calibration phase (130) including: • a measurement step (132) of the cell's state of charge, internal cell temperature, and current through the cell and / or voltage across the cell terminals, for different cell charge states, and • the determination (134), from the measurements taken, of the coefficients βj of a polynomial model that relates a value ΔSk2 of the entropy change at time k2 to a value SOCk2 of the cell's state of charge at that time k2, and - during an operational phase, the estimation (116) of the value ΔSk2 of the cell's entropy change using the polynomial model. Fig. 3

Description

Title of the invention: Automatic method for estimating the entropy change of a battery cell

[0001] The invention relates to an automatic method for estimating the entropy change of a battery cell. The invention also relates to a recording medium and an electronic battery management system for implementing this method. The invention further relates to a motor vehicle incorporating this battery management system.

[0002] The entropy change of a cell is an important parameter for determining the operating state of a battery cell. For example, the entropy change of a cell is used to determine the cell's "State of Health".

[0003] Several methods for estimating the entropy change of a cell are known. For example, such a method is described in application WO2020064959A1. However, under certain cell operating conditions, the accuracy of the entropy change estimated by these known methods degrades. Thus, the robustness of the known methods for estimating the entropy change is not satisfactory.

[0004] The invention aims to remedy this drawback by proposing a method for estimating the entropy variation of a cell which is more robust.

[0005] The invention therefore relates to an automatic method for estimating the entropy variation of a battery cell by an electronic battery management system, this method comprising:

[0006] - during an exploitation phase, at each instant k of a temporal succession at times {0; 1; 2; ...; k; k+1; ...}, the measurement of the current intensity passing through the cell and then the estimation of the SOCk value of the cell's state of charge at time k from the measured intensity,

[0007] in which:

[0008] - this process also includes a first calibration phase, this first calibration phase including:

[0009] • a first step of measurements, for different cell charge states, of the values ​​of the cell's state of charge, internal cell temperature, and current intensity through the cell and / or voltage across the cell terminals, and

[0010] • the determination, based on the readings taken during the first reading stage, coefficients of a first polynomial model that relates the entropy variation at a time k2 in the state of charge of the cell at that time k2, this first polynomial model being defined by the following relation:

[0011] [Math.l] s / - &

[0012] where:

[0013] - ASk2 is the value of the entropy change at time k2,

[0014] - ml is a predetermined integer greater than five,

[0015] - j is an integer that varies between zero and ml,

[0016] - [3j are the coefficients of the first polynomial model, and

[0017] - SOCk2 is the value of the state of charge estimated at an instant k equal to instant k2 or immediately preceding instant k2, and

[0018] - the exploitation phase also includes, at each instant k2 of a succession temporal of instants {0; 1; 2; ...; k2; k2+l; ...}, the estimation of the value ASk2 of the entropy variation of the cell using the first polynomial model in which the coefficients [3j have the values ​​determined during the first calibration phase and the value SOCk2 is equal to the value of the estimated charge state for the instant k equal to the instant k2 or immediately preceding the instant k2.

[0019] Embodiments of this process may have one or more of the following characteristics:

[0020] 1) During the first calibration phase, the coefficients [3j] are estimated in using a first predetermined relationship which directly links the values ​​of the coefficients [3j] to the internal temperature of the cell and to the intensity of the current flowing through the cell and / or to the voltage between the terminals of the cell so that the values ​​of the coefficients [3j] are estimated without using an estimate of the entropy change.

[0021] 2) The first relation is chosen from the group consisting of the following relations:

[0022] [Math.2] <777 I 77 ii T*—fî. * dt " F | f '

[0023] and

[0024] [Math.3] ■ : v nrF »- IV P T mX.— — l:V~OCV?+--. 7 p s * *5OCr +n <A.Xa-ïïi ■ dt ? F fe J '

[0025] where:

[0026] - m is the mass of the cell,

[0027] - Cp is the heat capacity of the cell,

[0028] - dTi / dt is the first derivative of the internal temperature of the cell with respect to the time,

[0029] - Ro is the internal resistance of the cell,

[0030] - i is the intensity of the current flowing through the cell,

[0031] - Ti is the internal temperature of the cell,

[0032] - F is the Faraday constant,

[0033] - SOC is the state of charge of the cell,

[0034] - h is the heat exchange coefficient of the cell with the external environment,

[0035] - A is the area of ​​the cell in contact with the external environment, and

[0036] - Ta is the ambient temperature,

[0037] - V is the voltage between the terminals of the cell,

[0038] - OCV is the open-circuit voltage of the cell.

[0039] 3) The first calibration phase is performed in parallel with the phase operating.

[0040] 4)

[0041] - the method comprises a second calibration phase, this second phase of calibration including:

[0042] - a second recording step, for different cell charge states, of the values ​​of the cell's state of charge, the current flowing through the cell, and the voltage across the cell terminals, and

[0043] - the determination, based on the readings taken during the second reading stage, of the coefficients of a second polynomial model which relates the open-circuit voltage of the cell at a time kl to the state of charge of the cell at that time kl, this second polynomial model being defined by the following relation:

[0044] [Math.4] U3.3. x * ^° c w r

[0045] where:

[0046] - OCVki is the open-circuit voltage value at time kl,

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] - m2 is a predetermined integer greater than five, - u is an integer that varies between zero and m2, - are the coefficients of the second polynomial model, and - SOCki is the value of the estimated state of charge at a time k equal to or immediately preceding time kl - the exploitation phase also includes, at each instant kl of a temporal succession of instants {0; 1; 2; ...; kl; kl+1; ...}, the estimation of the value OCVki of the open-circuit voltage of the cell using the second polynomial model in which the coefficients au have the values ​​determined during the second calibration phase and the value SOCki is equal to the value of the state of charge estimated for the instant k equal to the instant kl or immediately preceding the instant k. 5) During the second calibration phase, the au coefficients are estimated using a second predetermined relationship which directly links the values ​​of the au coefficients to the intensity of the current flowing through the cell and to the voltage between the terminals of the cell so that the values ​​of the au coefficients are estimated without using open circuit voltage estimation. 6) The second relation is chosen from the group consisting of the following relations: [Math.5] ¥-Y a J And [Math.6] : ■ V " zL CÇ * [SOC f + R » V, + +V r And [Math.7] c Or : - SOC is the state of charge of the cell,

[0061] - Vs is the voltage across the terminals of an RC circuit number s connected in series with the internal resistance Ro, and

[0062] - Cs and Rs are, respectively, the capacitance and resistance of RC circuit number s.

[0063] 7) The second calibration phase is performed in parallel with the phase operating.

[0064] 8) The exploitation phase also includes a step of estimating the state of cell health based on ASk2 values ​​of the entropy change estimated for that cell.

[0065] The invention also relates to an information recording medium readable by an electronic computer, which includes instructions for the execution of the above estimation process, when these instructions are executed by the electronic computer.

[0066] The invention also relates to an electronic battery management system equipped with at least one cell, this system comprising an electronic computer programmed to execute an automatic process for estimating the entropy variation of this cell, in which the computer is programmed to execute the above automatic process for estimating the entropy variation of a cell.

[0067] The invention also relates to a motor vehicle comprising:

[0068] - at least one drive wheel,

[0069] - an electric motor capable of rotating this drive wheel to move the motor vehicle,

[0070] - a battery comprising at least one cell capable of storing electrical energy and, alternately, to return electrical energy to power the electric motor, this cell having two terminals through which it is electrically connected to the electric motor,

[0071] - a voltmeter electrically connected between the terminals of the cell to measure the voltage between these terminals,

[0072] - an ammeter connected in series with the electrical cell to measure the current of the current that flows through this cell,

[0073] - a thermometer capable of measuring the internal temperature of the electrical cell, and

[0074] - the above battery management system connected to the voltmeter, the ammeter and the thermometer, this management system includes a programmable electronic calculator capable of estimating the entropy variation of the battery cell from the measurements of the thermometer, voltmeter and ammeter.

[0075] The invention will be better understood upon reading the following description, given solely by way of non-limiting example and made with reference to the drawings in which:

[0076] - Fig. 1 is a partial schematic illustration of a motor vehicle equipped of an electric battery,

[0077] - [Fig. 2] is a schematic illustration of an arrangement of estimators used to estimate the state of charge and the entropy change of a cell in the vehicle's battery [Fig. 1],

[0078] - [Fig. 3] is a flowchart of a method for estimating the state of charge and the entropy variation of a cell using the estimators of [Fig.2];

[0079] - [Fig. 4] is a graph illustrating the evolution over time of the estimation of the state of charge of a cell by implementing the process of [Fig.3].

[0080] In this description, the terminology, conventions, and definitions of the terms used in this text are introduced in Chapter I. Next, a detailed example of an embodiment is described in Chapter II with reference to the figures. In Chapter III, variants of this embodiment are presented. Finally, the advantages of the different embodiments are specified in Chapter IV.

[0081] Chapter I: Definitions, terminology and conventions:

[0082] In the remainder of this description, the well-known characteristics and functions of a person skilled in the art are not described in detail.

[0083] A cell is one of the elements of a battery capable of storing electrical energy. A battery typically comprises several cells electrically connected in series and / or in parallel.

[0084] The capacity, denoted Capa, of a cell represents the maximum amount of electrical energy that can be stored in that cell. This capacity is expressed in Ah (Ampere-hour).

[0085] The internal resistance Ro of a cell is the value of the internal resistance of that cell. The internal resistance of a cell is a physical quantity found in most electrical models of an electrical cell. As the cell ages, typically, the internal resistance increases.

[0086] The open-circuit voltage (OCV) of a cell is the open-circuit voltage of that cell. The OCV is also known as the "open-circuit voltage." The OCV is the measurable voltage across the cell terminals after the cell has been electrically isolated from any electrical load for several hours. The OCV varies depending on the cell's state of charge.

[0087] The state of charge of a cell represents the percentage of energy that is stored in that cell. The state of charge is often referred to by the acronym SOC (State of Charge). It is equal to 100% when the amount of electrical energy stored in the cell is at its maximum. It is equal to 0% when the amount of energy stored in the cell is zero, that is, when no more electrical energy can be extracted from the cell to power an electrical load.

[0088] The health state of a cell represents its current state compared to its initial state. The health state is often referred to by the acronym SOH (State of Health). The health state is equal to 100% when the cell's capacity is equal to its initial capacity, that is, before any use of the cell. Here, the SOH health state is defined by the following relationship: SOH = 100*Capa / Capaini, where:

[0089] - Capa is the current capacity of the cell, and

[0090] - Capaini is the initial capacity of the cell.

[0091] The definitions of the state of charge and the state of health of a battery are identical to the corresponding definitions given in the case of a cell except that in these definitions, the term "cell" is replaced by the term "battery".

[0092] The term "internal temperature" refers to the temperature at the core of the cell. If the temperature inside the cell is relatively uniform, the internal temperature is close to the temperature measurable on the external surface of that battery cell. Thus, the internal temperature also refers to the temperature of the cell's external surface.

[0093] Application FR230012 refers to the French patent application filed on January 5, 2023 by the company Entroview.

[0094] The symbol “.” or “*” denotes scalar multiplication.

[0095]

[0096] Chapter II: Example of an embodiment

[0097] Figure 1 represents an electrically powered motor vehicle 2, more commonly known as an "electric vehicle." Electric vehicles are well known, and only the structural elements necessary to understand the remainder of this description are presented. Vehicle 2 comprises:

[0098] - an electric motor 4, capable of rotating drive wheels 6 to make drive vehicle 2 on roadway 8, and

[0099] - a battery 10 which supplies electrical energy to the motor 4.

[0100] The battery 10 has two electrical connection terminals 12, 14 and several Electrical cells are connected between terminals 12 and 14. Terminals 12 and 14 are connected to the electrical loads to be powered. Here, they are therefore connected, in particular, to electric motor 4.

[0101] To simplify [Fig. 1], only four electrical cells 18 to 21 are shown. Typically, these electrical cells are grouped into several tiers, and these tiers are connected in series between terminals 12 and 14. Here, only two tiers are shown. The first tier comprises cells 18 and 19, and the second tier comprises cells 20 and 21. Each tier has several branches connected in parallel. Each branch of a tier comprises one or more electrical cells in series. Here, the first tier has two branches, and each branch comprises a single electrical cell. The second stage is structurally identical to the first stage in the example shown in [Fig.1].

[0102] Here, all the cells of the battery 10 are structurally identical except for manufacturing tolerances. Therefore, only cell 18 is now described in more detail.

[0103] 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 commonly called a "pack" of cells. The cell 18 is capable of storing electrical energy when it is not being used. 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.

[0104] The cell 18 is a cell of a known type, for example, it is an LFP (Lithium Iron Phosphate) cell or a Lithium-ion cell.

[0105] The cell 18 is characterized in particular by a nominal capacitance Capa, an internal resistance Ro, and an open-circuit voltage OCV. Here, to simplify the description of this embodiment, the internal resistance Ro is considered to be constant over time.

[0106] The Capaini parameters and the initial value R0>0 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 made on this cell.

[0107] Battery 10 also comprises, for each cell:

[0108] - a voltmeter that measures the voltage between the terminals of this cell,

[0109] - an ammeter that measures the intensity of the current flowing through this cell, and

[0110] - a thermometer that measures the internal temperature of the cell.

[0111] To simplify [Fig. 1], only a voltmeter 34, an ammeter 36, and a thermometer 38 of cell 18 are shown. Hereafter, the term "voltage V" refers to the voltage measured by the voltmeter 34. The term "current i" refers to the current measured by the ammeter 36. The term "temperature Ti" refers to the internal temperature measured by the thermometer 38.

[0112] Here, to measure the internal temperature of cell 18, the thermometer 38 is in direct thermal and mechanical contact with the outer envelope of cell 18. The thermometer 38 is directly fixed on cell 18.

[0113] Finally, the battery also includes a sensor 39 that 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, sensor 39 is a thermometer housed between an outer casing of battery 10 and the outer casings of the various cells 18 to 21.

[0114] The vehicle 2 includes an electronic battery management system 40, better known by the acronym BMS (Battery Management System). The function of this system 40 is, in particular, to determine 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. Here, the system 40 is also configured to estimate the entropy change of each cell as well as the health status of each cell.

[0115] To carry out these different estimations, the system 40 is electrically connected to each sensor of the battery 10 to acquire the measurements from these sensors.

[0116] Here, the system 40 comprises a memory 42 and a programmable electronic computer 44, capable of executing instructions stored in the memory 42. To this end, the memory 42 contains the instructions necessary for the execution of the process in [Fig. 3]. This memory 42 also contains the initial values ​​of the various parameters necessary for the execution of this process.

[0117] Figure 2 represents a first embodiment of an arrangement of estimators 60, 62, 64, 66, 68 and 70 implemented in the system 40 to estimate the state of charge of cell 18, the voltage OCV, the entropy change AS and the health state SOH of cell 18. Each of these estimators 60 to 70 is implemented in the form of an estimation algorithm executed by the computer 40. Thus, we will subsequently refer to both "execution of an estimator" and "execution of an estimation algorithm".

[0118] Estimator 60 estimates the state of charge (SOC) of cell 18 from measurements taken by sensors 34 and 36. For example, here, estimator 64 is executed at each time k of a time sequence of times {0; 1; 2; ...; k; k+1; ...}. Here, these times k are repeated at a constant frequency f. The duration of the constant interval between two immediately consecutive times k and k+1 is denoted At. The duration At is equal to 1 / f. For example, the duration At is between 0.2 s and 1 min.

[0119] Subsequently, the value of the state of charge SOC estimated at time k is denoted SOCk. For example, here, the value SOCk is estimated using the Coulomb model defined by the following relation:

[0120] [Math.8] soc. =soc

[0121] where:

[0122] - tini is the instant when the SOCini value of the state of charge was measured, and

[0123] - At is the time interval between two immediately consecutive instants k, k-1.

[0124] Typically, to have a precise SOCini value, the tini instant corresponds to an instant when the cell is completely discharged.

[0125] Estimator 62 estimates the values ​​of the OCV voltage. Estimator 60 is executed at each time step kl of a time sequence of time steps {0; 1; 2; ...; kl; kl+1; ...}. Here, these time steps kl repeat at a constant frequency fi. The duration of the constant interval between two immediately consecutive time steps kl and kl+1 is denoted Atl. The duration Atl is equal to l / fp. The duration Atl is typically between 0.1 s and 60 s and, preferably, between 0.1 s and 10 s. Here, the duration Atl is equal to 0.2 s. For example, here, the set of time steps kl is a subset of the set of time steps k. Between any two successive time steps kl and kl+1, there are therefore several time steps kl.

[0126] Subsequently, the value of the voltage OCV estimated at time kl is denoted OCVki. In this embodiment, the value OCVk[ is estimated using a polynomial model MOCV defined by the following relation:

[0127] [Math.9] OCV,

[0128] where:

[0129] - OCVki is the open-circuit voltage value at time kl,

[0130] - m2 is a constant integer greater than five,

[0131] - u is an integer that varies between zero and m2,

[0132] - at are predetermined coefficients of the MOCV polynomial model, and

[0133] - SOCk[ is the value of the state of charge SOC estimated at time k equal to time kl or immediately preceding the instant kl.

[0134] Preferably, m2 is between five and seven.

[0135] Estimator 64 estimates the entropy change AS of cell 18. Estimator 64 is run at each time k2 of a time sequence of times {0; 1; 2; ...; k2; k2+l; ...}. Here, these times k2 repeat at a constant frequency f2. The duration of the constant interval between two immediately consecutive times k2 and k2+l is denoted At2. The duration At2 is equal to l / f2. The entropy change AS varies more slowly than the voltage OCV. Thus, typically, the frequency f2 is chosen to be equal to the frequency fi or smaller than the frequency fb. For example, here, the duration At2 is equal to 5 s. For example, the set of times k2 is a subset of the set of times kl. Between any two successive times k2 and k2+l, there are therefore several times kl.

[0136] Subsequently, the value of the entropy change AS estimated at time k2 is denoted ASk2. In this embodiment, the value of ASk2 is estimated using a polynomial model MAS defined by the following relation:

[0137] [Math. 10] * ^OG /

[0138] where:

[0139] - ASk2 is the value of the entropy change at time k2,

[0140] - ml is a constant integer greater than five or ten,

[0141] - j is an integer that varies between zero and ml,

[0142] - [3j are predetermined coefficients of the MAS polynomial model, and

[0143] - SOCk2 is the value of the estimated state of charge at time k equal to time k2 or immediately preceding instant k2.

[0144] Preferably, ml is between fifteen and twenty.

[0145] Estimator 66 estimates the SOH (health state of health) of cell 18. Estimator 66 is run at each time k3 of a time sequence of times {0; 1; 2; ...; k3; k3+l; ...}. Here, these times k3 repeat at a constant frequency f3. The duration of the constant interval between two immediately consecutive times k3 and k3+l is denoted At3. The duration At3 is equal to l / f3. The SOH generally varies more slowly than the entropy change. Thus, typically, the frequency f3 is chosen to be equal to or less than the frequency f2. For example, here, the duration At3 is equal to 1 h. In this case, the set of times k3 is a subset of the set of times k2. Between any two successive times k3 and k3+l, there are therefore several times k2. Subsequently, the value of the health status SOH estimated at time k3 is noted SOHk3.

[0146] For example, estimator 66 is implemented as described in application WO2020064959A1. Thus, estimator 66 estimates the health state SOH from different ASk2 values ​​of the entropy change estimated for different OCVki values ​​of the OCV voltage.

[0147] Estimator 68 estimates the coefficients au of the MOCV model. The coefficients au vary at approximately the same rate as the state of health SOH. Thus, estimator 68 is run at a slower frequency than the frequency f3. For example, estimator 68 is run once a day, once a week, or once a month. Here, estimator 68 estimates the coefficients au using the following relation (1.1) which relates these coefficients au to the state of charge SOC, the voltage V, and the current i:

[0148] [Math. 11] 2 * ISOCJ+IUL ÿ-' ij ■. ; .-J?-■

[0149] where Vp, SOCp and ip are the values, respectively, of the voltage V, the state of charge SOC and the current i at a time p.

[0150] By recording the values ​​of Vp, SOCP and ip for a large number of times p, the estimator 68 is then able to estimate the values ​​of the coefficients at

[0151] Equation (1.1) was obtained by replacing the term "OCV" in an electrical model of cell 18 with its expression in the form of a polynomial in which the variable is the state of charge SOC. Here, the electrical model of cell 18 used for this purpose is as follows:

[0152] [Math. 12] where OCVp is the value of the OCV voltage at time p.

[0153] Estimator 70 estimates the [3j] coefficients of the MAS model. The [3j] coefficients also vary at approximately the same rate as the state of health SOH. Thus, estimator 70 is run at a slower frequency than the frequency f3. For example, estimator 70 is run once a day, once a week, or once a month. Here, estimator 70 estimates the [3j] coefficients using the following relation (2.1) which relates the [3j] coefficients to the intensity i, the state of charge SOC, and the temperatures Ti and Ta:

[0154] [Math. 13] , / 77 i TJ f M po fl ■■ y? Or :

[0155] - m is the mass of cell 18,

[0156] - Cp is the heat capacity of cell 18,

[0157] - dTiq / dt is the first derivative of the internal temperature Ti of cell 18 by relation to time at instant q,

[0158] - Ro is the internal resistance of cell 18,

[0159] - iq is the intensity of the current passing through cell 18 at time q,

[0160] - Tiq is the value of the internal temperature Ti of cell 18 at time q,

[0161] - F is the Faraday constant,

[0162] - SOCq is the value of the state of charge SOC at time q,

[0163] - h is the heat exchange coefficient of cell 18 with the external environment,

[0164] - A is the area of ​​cell 18 in contact with the external environment, and

[0165] - Taq is the value of the ambient temperature Ta at time q.

[0166] The products m.Cp and hA generally vary little over time. Thus, in 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 data provided by the manufacturer of cell 18 or measured experimentally during an initialization phase. Subsequently, the values ​​of the products m.Cp and hA are stored in memory 42 and are not estimated by the estimator 70.

[0167] By recording the values ​​Tiq, Taq, SOCq and iq for a large number of times q, the estimator 70 is then able to estimate the values ​​of the coefficients [3j.

[0168] Equation (2.1) was obtained by replacing the term “AS” in a thermal model of cell 18 with its expression in the form of a polynomial in which the variable is the state of charge SOC. Here, the thermal model of cell 18 used for this purpose is as follows:

[0169] [Math. 14] JTî ■> i 7ï mr. C,„■ ••••• ■ = R.. f. AS f h. AJ 7b - 7 !ï dt : > F This thermal model is particularly accurate because it takes into account the heat exchanges between the cell and the external environment, the creation of heat within the cell by Joule effect, and the variation in entropy caused by the movement of ions such as lithium ions.

[0170] The operation of the system 40 will now be described using the method of [Fig.3] and in the particular case of estimating the state of charge of cell 18.

[0171] The process begins with a phase 100 of initializing the values ​​of the various parameters SOCini, Capa of the Coulomb model and the coefficients [3j, au of relations (1.1) and (2.1). For example, these parameters and coefficients are initialized from the values ​​of these parameters and coefficients obtained after a previous use of the system 40 or, if this is the first use, from the use of a system similar to the system 40 with a similar cell or from calibration phases carried out in the laboratory and similar to those described later.

[0172] Once the initialization phase 100 is completed, a phase 102 of system 40 operation begins. During phase 102, the system 40 estimates the state of load SOC and the entropy variation AS of cell 18 during its use within vehicle 2. In particular, during phase 102, vehicle 2 is used normally for movement. Therefore, during phase 102, cell 18 is charged and, alternately, discharged according to charge / discharge sequences that are unknown and, in part, unpredictable.

[0173] During a measurement phase 110, at each instant k, the voltmeter 34, the ammeter 36, the thermometer 38, and the sensor 39 measure, respectively, the voltage V, the current i, and the temperatures Ti and Ta. The measured values ​​Vk, ik, Tik, and Tak are immediately acquired by the system 40 and stored in the memory 42. Phase 110 is repeated at each instant k.

[0174] In parallel with phase 110, during a step 112, at each instant k, the estimator 60 estimates the state of charge SOC at instant k of the cell 18. For this, it uses the Coulomb model. Thus, at each instant k, the estimator 60 delivers a value SOCk of the state of charge SOC obtained from the measurements of the intensity i.

[0175] In parallel with step 112, during a step 114, at each instant kl, the estimator 62 estimates the value OCVki of the voltage OCV using the MOCV model. For this, it uses the value SOCki of the state of charge SOC. Here, since the instants kl are a subset of the instants k, the value SOCH is equal to the value SOCk for k = kl.

[0176] In parallel with steps 112 and 114, during step 116, at each instant k2, the estimator 64 estimates the value ASk2 of the entropy change AS of cell 18 using the MAS model. For this, it uses the value SOCk2 of the charge state SOC. Here, since the instants k2 are a subset of the instants k, the value SOCk2 is equal to the value SOCk for k = k2.

[0177] Finally, during a step 118, at each instant k3, the estimator 66 estimates the SOHk3 value of the SOH health state from, in particular, the ASk2 and OCVki values ​​estimated during steps 114 and 116.

[0178] In parallel with the operating phase 102, during a calibration phase 120, the estimator 68 estimates the coefficients au. To do this, during a step 122, the estimator 68 records, at certain instants p, the SOCP value delivered by the estimator 60 and the Vp and ip values ​​measured by sensors 34, 36 at the same instant. The estimator 68 repeats this recording Np times. The number Np is a predetermined number greater than m2 and, preferably, ten or one hundred times greater than m2. Here, during step 122, the estimator 68 triggers a new recording only if the state of charge SOC value has substantially changed since the last recording. For example, to do this, the estimator 68 triggers a new recording of the SOCP, ip, and Vp values ​​only if the following condition is met:

[0179] [Math. 15] SOQ - SOC B SOC^ Or

[0180] - SOCk is the current value of the state of charge SOC delivered by the estimator 60,

[0181] - SOCP i is the last SOC state of charge value recorded during step 122, and

[0182] - x is a predetermined positive constant generally between 0.05 and 0.2 and most often between 0.01 and 0.1.

[0183] For example, step 122 stops when the number Np of readings is reached.

[0184] Once the number Np of readings is reached, in a step 124, the estimator 68 determines the values ​​of the coefficients au that minimize the system of equations formed by the Np relations (1.1) in each of which the values ​​Vp, SOCP, and ip are those recorded in step 122 and the coefficients au are the unknowns. For example, in step 124, the values ​​of the coefficients au are determined by implementing any known algorithm for solving such a system of equations, such as a linear regression algorithm or a multiple linear regression algorithm.

[0185] Once the new values ​​of the coefficients at have been determined, these are transmitted to the estimator 62 which uses them in place of the previous values ​​of the coefficients at.

[0186] Phase 120 is repeated, for example at regular intervals, when using cell 18 within vehicle 2. The execution of phase 120 can also be triggered in response to the occurrence of a particular event.

[0187] Also in parallel with the operating phase 102, during a calibration phase 130, the estimator 70 estimates the coefficients [3j]. To do this, during a step 132, the estimator 70 records, at certain instants q, the SOCq value delivered by the estimator 60 and the iq, Tiq, and Taq values ​​measured at that instant q by sensors 36, 38, and 39, respectively. The estimator 70 repeats this recording Nq times. The number Nq is a predetermined number greater than ml and, preferably, ten or one hundred times greater than ml. During step 132, the estimator 70 preferably triggers a new recording only if the SOC state of charge value has substantially changed since the last recording. For example, to achieve this, estimator 70 triggers a new reading of the SOCq, iq Tiq and Taq values ​​only if the following condition is met:

[0188] [Math.16] ISOQ.-S.OC, J>x,SOC\ . Or

[0189] - SOCk is the current value of the state of charge SOC delivered by the estimator 60,

[0190] - SOCq i is the last SOC state of charge value recorded during step 132, and

[0191] - x is a predetermined positive constant generally between 0.05 and 0.2 and most often between 0.01 and 0.1.

[0192] For example, step 132 stops when the number Nq of readings is reached.

[0193] Once the number Nq of readings is reached, in a step 134, the estimator 70 determines the values ​​of the coefficients [3j] that minimize the system of equations formed by the Nq relations (2.1), in each of which the values ​​iq, Tiq, SOCq, and Taq are those recorded in step 132, and the coefficients [3j] are the unknowns. The value of the derivative dTiq / dt is approximated, for example, using the following relation: (Ti k - Tik_i) / At, for k = q. Preferably, in step 134, equation (2.1) is written in the following form to avoid division by zero when the recorded value iq is zero:

[0194] [Math. 17] Or :

[0195] [Math.18] dTï, y~. Q ~ K,.. / ; “ h. AJ is ~77. [Math 19]

[0196] [Math. 19] The values ​​of the variables Yq and Xq>j are calculated from the values ​​recorded during step 132.

[0197] For example, in step 134, the values ​​of the coefficients [3j are determined by implementing any known algorithm for solving such a system of equations such as a linear regression algorithm or a multiple linear regression algorithm.

[0198] Once the new values ​​of the coefficients [3j] have been determined, these are transmitted to the estimator 64 which uses them in place of the previous values ​​of the coefficients [3j].

[0199] Phase 130 is repeated, for example at regular intervals, when using cell 18 within vehicle 2. The execution of phase 130 can also be triggered in response to the occurrence of a particular event.

[0200] Figure 4 is a graph representing the evolution of the AS entropy variation of cell 18, estimated using different methods as a function of the cell 18's state of charge, expressed as a percentage. On this graph, curve 150 represents the evolution of the AS entropy variation of cell 18 measured in the laboratory. This laboratory measurement is considered to be the one that best approximates the actual value of the entropy variation. However, the methodology used to make this estimation in the laboratory cannot be implemented when cell 18 is in operation within a vehicle 2.

[0201] Curve 152 represents the evolution of the variation of the entropy AS estimated using the method of [Fig.3] and therefore using both estimators 64 and 70.

[0202] Curve 156 represents the evolution of the variation of the entropy AS estimated using the demand method WO2020064959A1.

[0203] Comparing curves 152 and 156 with curve 150 shows that the method in [Fig. 3] provides a better estimate of the entropy variation AS than that obtained using conventional methods. In particular, the phase changes occur simultaneously on curves 152 and 150; that is, curves 152 and 150 vary at the same time.

[0204]

[0205] Chapter III: Variants:

[0206] Variants of the coefficient calibration phase [3 j

[0207] Equation (2.1) can be replaced by another relation that links the internal temperature Ti of cell 18 to the coefficients [3j]. For example, the following relation (2.2) can be used instead of relation (2.1):

[0208] [Math.20] jTïi î TTi i > mC = y -ocv^—dy B ; * * to F f ' j When relation (2.2) is used, during the calibration phase, the values ​​of the voltages V and OCV at each time q must also be recorded. For example, the OCVq value of the voltage OCV at time q is provided by estimator 62 when the coefficients au have been determined beforehand. Alternatively, the OCVq value is determined using an additional estimator dedicated to this task and which operates independently of estimator 62. For example, this additional estimator is implemented as described in application WO2020064959A1. This additional estimator can also be implemented as a Kalman filter such as, for example, the one described in application US2017146608A1.

[0209] Equation (2.1) can also be replaced by the following relation (2.3):

[0210] [Math.21] OCV.-OCV, , A.—X—« ^OC,J f S ' ' where A is a predetermined constant or determined at the same time as the values ​​of the coefficients [3j.

[0211] When relation (2.3) is used, the values ​​OCVq and OCVq i are obtained as in the case of relation (2.2). Moreover, when relation (2.3) is used, the ambient temperature Ta does not need to be measured to estimate the coefficients [3j and the sensor 39 can be omitted.

[0212] In another embodiment, relation (2.1), or any other relation obtained by replacing the entropy change AS in a thermal model with its expression as a function of the coefficients [3j] and the state of charge SOC, is not used. Instead, for example, at each instant q, a value AScq of the entropy change is estimated. For this purpose, the thermal model that relates the entropy change AS to the internal temperature Ti and to the current i and / or the value V of the voltage is used. This thermal model is typically identical to one of those presented above, except that the entropy change AS appearing in this model is not replaced by its expression in the form of a polynomial model. At each instant q, the value SOCq of the state of charge is also recorded. For example, at each instant q of the calibration phase, the AScq and SOCq values ​​are estimated by implementing the method described in application FR2300123. Next, the estimation of the coefficients [3j] consists of determining the values ​​of coefficients [3j] that minimize the following cost function:

[0213] [Math.22] Or :

[0214] - Nq is the number of pairs of estimated AScq and SOCq values,

[0215] - Aseq is the estimated value, at time q, of the entropy change of the cell at using the MAS polynomial model, that is, using the following relationship:

[0216] [Math.23] .“31 5: * me JX;' AMMS f Z" The different variants described in application FR2300123 for estimating the value of the entropy variation at a given instant from a thermal model of the cell can then be implemented to estimate the AScq values ​​of the entropy variation.

[0217] Alternatively, the calibration phase 130 is executed at each time k or k2. In this case, the algorithm used to determine the values ​​of the coefficients [3j] is, preferably, the recursive least squares algorithm better known by the acronym RLS (“Recursive Least Squares”).

[0218] In the case where a recursive algorithm such as the RLS algorithm is implemented, steps 132 and 134 are executed in parallel. Indeed, at each new time q, new values ​​of the coefficients [3j] are determined.

[0219] In a simplified embodiment, the calibration phase 130 is performed outside of the operating phase 102. For example, phase 130 is performed only once during the initialization phase 100 of the battery management system 40. In this case, typically, the calibration phase 130 is carried out in the laboratory by placing the cell 18 on a test bench that allows its state of charge to be varied in a known manner. During these variations in its state of charge, its internal temperature Ti, the ambient temperature Ta, the current i, and the voltage V are measured. Then, the coefficients [3j] are determined as described previously and then stored in the memory 42. From then on, the operating phase can begin. Indeed, the system 40 is capable of estimating the entropy variation AS using the polynomial model. MAS. However, the system 40 is unable to perform a new calibration phase 130 of the coefficients [3j] during the operating phase. In this case, the thermometer 38, the sensor 39 and the estimator 70 can be omitted in the vehicle 2. In such an embodiment, if the coefficients [3j] need to be recalibrated, the cell 18 must be removed from the vehicle 2 and placed back on the test bench to perform a new calibration phase 130.

[0220] Variants of the calibration phase of the coefficients at ;

[0221] Equation (1.1) can be replaced by another relation that links the current intensity i and the voltage V to the coefficients au. For example, other relations can be obtained by replacing the term OCV in another electrical model of cell 18 with its expression in the form of a polynomial. For example, alternatively, the electrical model is a "Thévenin model" or "Electrical lumped parameter model" which includes one or more parallel RC circuits connected in series between a terminal of the DC voltage source and terminal 30 of the cell. In this case, relation (1.1) can be replaced by the following relation (1.2):

[0222] [Math.24] < A a •• XJ i.. .' t [Math 25]

[0223] [Math.25] to R..Q where:

[0224] - Vs is the voltage across RC circuit number s,

[0225] - Cs and Rs are, respectively, the capacitance and resistance of RC circuit number s.

[0226] In another embodiment, relation (1.1) or any other relation obtained by replacing the voltage OCV in an electrical model of cell 18 with its expression as a function of the coefficients au and the state of charge SOC, is not used. For this, for example, at each instant p, an open-circuit voltage value OCVcp is estimated. For this purpose, the electrical model that relates the voltage OCV to the current i and the voltage V is used.This electrical model is typically identical to one of those presented above, except that the OCV voltage appearing in this electrical model is not replaced by its expression in the form of a polynomial model. At each time p, the SOCP value of the state of charge is also estimated. For example, at each time p of the calibration phase, the OCVcp and SOCP values ​​are estimated by implementing the method described in application FR2300123. Then, the estimation of the coefficients consists of determining the values ​​of the coefficients that minimize the following cost function:

[0227] [Math.26] Thcw. ~ocwj i I — where:

[0228] - Np is the number of pairs of estimated OCVcp and SOCP values,

[0229] - OCVep is the estimated value, at time p, of the OCV voltage of the cell using the polynomial model MOCV, that is, using the following relation:

[0230] [Math.27] a, p & ! ÿ.The various variants described in application FR2300123 for estimating the value of the OCV voltage at a given instant from an electrical model of the cell can then be implemented to estimate the OCVcp values ​​of the OCV voltage.

[0231] Alternatively, the calibration phase 120 is executed at each instant k or kl. In this case, the algorithm used to determine the values ​​of the coefficients au is preferably the recursive least squares algorithm.

[0232] In the case where a recursive algorithm such as the RLS algorithm is implemented, steps 122 and 124 are executed in parallel. Indeed, at each new instant p, new values ​​of the coefficients au are determined.

[0233] Similar to what has been explained for phase 130, alternatively, calibration phase 120 is performed, during initialization phase 100, only in the laboratory using a test bench.

[0234] In another embodiment, the MOCV polynomial model is not used. In this case, at times kl, the OCVH value is obtained directly from the electrical model. For example, at each time kl, the OCVki value is obtained as described in one of the following applications: FR2300123, WO2016083754A1, and US2017146608A1. In this case, only the MAS polynomial model is used.

[0235] Variants of the operating phase:

[0236] Other embodiments of the estimator 60 are possible. For example, the SOCk value of the state of charge of cell 18 is obtained by implementing any one of the methods described in paragraphs 86 to 88 of application US2017146608A1.

[0237] Alternatively, the k2 instants are as frequent as the k or kl instants.

[0238] The state of charge estimation method described here in the particular case of a battery cell also applies to a battery which 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 one another.

[0239] Other variants:

[0240] The thermometer 38 can be housed inside the casing of the cell 18.

[0241] The sensor 39 can be placed outside the outer casing of the battery 10.

[0242] What has been described here applies to any cell technology. For example, it also applies to a LiPB (Lithium-ion Polymer Battery) or Li-IP or other cell.

[0243] Alternatively, the internal resistance Ro is not considered to be constant over time. In this case, the value R0jk4 of the internal resistance Ro at each instant k4 of a time succession of instants {0; 1; 2; ... ; k4 ; k4+l ; ...}, is estimated. For example, the value R0jk4 is estimated using a Kalman filter dedicated to this task.An example of a Kalman filter designed to estimate the value of R0jk4 is described in application WO2016083754A1 or in Chapter 4.2.1 of article Plett2004.

[0244] The value of R0jk4 can also be estimated from a model that relates the value of the resistance Ro to the state of charge SOC of the cell. For example, in such a model, the value of the resistance Ro varies, as a decreasing exponential function of the state of charge SOC.

[0245] The value of the resistance Ro can also be related to the state of charge SOC by a polynomial MRO model. This polynomial MRO model is defined by the following relation:

[0246] [Math.28] xt ( * *4' 11 51 “'•î-

[0247] where:

[0248] - R0,k4 is the value of the internal resistance at time k4,

[0249] - m3 is a constant integer greater than two or three,

[0250] - w is an integer that varies between zero and m3,

[0251] - yw are the coefficients of the polynomial MRO model, and

[0252] - SOCk4 is the value of the state of charge estimated at a time k equal to time k4 or immediately preceding time k4.

[0253] When the polynomial MRO model is used to estimate the value R0>k4 of the internal resistance, then, during a calibration phase, the coefficients yw are estimated from measurements of the current i and the voltage V, an estimate of the voltage OCV, and using a relationship (3.1) which directly links the values ​​of these coefficients yw to the measured intensities and voltages.This calibration phase is typically carried out in a similar manner to what has been described for calibration phases 120 and 130. For example, relation (3.1) is as follows: .

[0254] [Math.29] [ "O 1 V.^QCV^ y y. * tocTLL •' ' $ AnmoÎ f w !, ! ; t “I- where Vr, OCVr, ir and SOCr are the values, recorded at times r, respectively, of the voltage V, the voltage OCV, the current i and the state of charge SOC.

[0255] To determine the coefficients yw using relation (3.1), the value OCVr of the voltage OCV is that delivered by the estimator 62 at time r or estimated by any other method of estimating this value OCVr.

[0256] Alternatively, the Capa capacity can also be estimated. An example of a method for estimating the value of the Capa capacity is described in Chapter 4.2.2 of Plett2004, Part 3. Another example is described in application WO2016083754A1.

[0257] 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 also applies to used cells and batteries as well as new cells and batteries.

[0258] Several of the variants described above can be combined in the same embodiment.

[0259]

[0260] Chapter IV: Advantages of the embodiments described:

[0261] In what has just been described, during calibration phase 130, what is estimated These are the values ​​of the [3j] coefficients of the MAS polynomial model. The values ​​of the [3j] coefficients depend primarily on the cell's SOH health status. However, the cell's SOH health status changes much more slowly than the AS entropy change. It is considered that this is why the estimation of the [3j] coefficient values ​​is more accurate and robust, and therefore why the estimation of the AS entropy change value from the MAS polynomial model is also more accurate. robust and more accurate than when the value of the entropy change is directly provided by the thermal model.

[0262] Furthermore, the MAS polynomial model provides reliable values ​​even for state-of-charge (SOC) values ​​that fall outside the range of state-of-charge values ​​used during calibration phase 130. Thus, the estimator 64 remains capable of providing an accurate estimate of the entropy change AS even when calibration phase 130 is run during normal use of cell 18, where, typically, cell 18 is not fully discharged and / or fully charged. It is therefore possible to run calibration phase 130 more frequently during normal use of cell 18. This maintains the reliability of the estimated values ​​for the entropy change AS even if cell 18 degrades and its properties change during use.

[0263] The fact that no estimate of the entropy change is used to estimate the coefficients [3j] makes the AS entropy change estimation method even more robust and reliable.

[0264] Using relation (2.1) or relation (2.2) to estimate the values ​​of the coefficients [3j during the calibration phase 130 increases the accuracy and reliability of the entropy variation estimation.

[0265] By proceeding in a similar way to estimate the OCV voltage of the cell, the estimates of the OCVki values ​​are more reliable than if the electrical model is directly used during the operating phase to obtain them.

Claims

Demands

1. An automatic method for estimating the entropy change of a battery cell by an electronic battery management system, this method comprising: - during an operating phase, at each time k of a temporal succession of times {0; 1; 2; ...; k; k+1; ...}, the measurement (110) of the current intensity through the cell and then the estimation (112) of the value SOCk of the cell's state of charge at time k from the measured intensity, characterized in that: - this process also includes a first calibration phase (130), this first calibration phase comprising: - a first step (132) of measurements, for different cell states of charge, of the values ​​of the cell's state of charge, the internal temperature of the cell and the current intensity through the cell and / or the voltage between the cell terminals, and - the determination (134), from the measurements taken during the first measurement step, of the coefficients of a first polynomial model which relates the entropy variation at time k2 to the cell's state of charge at that time k2, this first polynomial model being defined by the following relation: [Math.30] where: - ASk2 is the value of the entropy change at time k2, - ml is a predetermined integer greater than five, - j is an integer that varies between zero and ml, - [3j are the coefficients of the first polynomial model, and - SOCk2 is the value of the state of charge estimated at a time k equal to time k2 or immediately preceding time k2, and - the exploitation phase also includes, at each time k2 of a time succession of times {0; 1; 2; ...; k2; k2+l; ...}, the estimation (116) of the value ASk2 of the entropy change of the cell using the first polynomial model in which. the coefficients [3j have the values ​​determined during the first calibration phase and the value SOCk2 is equal to the value of the estimated state of charge for the time k equal to the time k2 or immediately preceding the time k2.

2. A method according to claim 1, wherein, during the first calibration phase (130), the [3j] coefficients are estimated using a first predetermined relationship which directly links the values ​​of the [3j] coefficients to the internal temperature of the cell and to the intensity of the current through the cell and / or to the voltage between the terminals of the cell so that the values ​​of the [3j] coefficients are estimated without using an estimate of the entropy variation.

3. A method according to claim 2, wherein the first relation is chosen from the group consisting of the following relations: [Math.31] — JT iï. * iSOCJj+h.AJÎb-lr ; FJJ and [Math.32] c? f ; i Fi / s mC. —-J? â-. * ? dt F 1 J where: - m is the mass of the cell, - Cp is the heat capacity of the cell, - dTi / dt is the first derivative of the internal temperature of the cell with respect to time, - Ro is the internal resistance of the cell, - i is the current flowing through the cell, - Ti is the internal temperature of the cell, - F is the Faraday constant, - SOC is the state of charge of the cell, - h is the heat transfer coefficient of the cell with the external environment, - A is the area of ​​the cell in contact with the external environment, and - Ta is the ambient temperature, - V is the voltage between the terminals of the cell, - OCV is the open circuit voltage of the cell.

4. A method according to any one of the preceding claims, wherein the first calibration phase (130) is carried out in parallel with the operating phase.

5. A method according to any one of the preceding claims, wherein: - the method comprises a second calibration phase (120), this second calibration phase comprising: - a second step (122) of recording, for different cell charge states, the values ​​of the cell charge state, the current intensity through the cell and the voltage between the cell terminals, and - the determination (124), from the readings taken during the second reading step, of the coefficients of a second polynomial model which relates the open-circuit voltage of the cell at a time kl to the cell charge state at that time kl, this second polynomial model being defined by the following relation: [Math.33] * |socÀSf U where: - OCVki is the open-circuit voltage value at time kl, - m2 is a predetermined integer greater than five, - u is an integer that varies between zero and m2, - au are the coefficients of the second polynomial model, and - SOCki is the value of the state of charge estimated at a time k equal to time kl or immediately preceding time kl - the operating phase also includes, at each time kl of a time succession of times {0; 1; 2; ...; kl; kl+1; ...}, the estimation (114) of the value OCVki of the open-circuit voltage of the cell using the second polynomial model in which the coefficients au have the values ​​determined during the second calibration phase and the value SOCki is equal to the value of the state of charge estimated for time k equal to time kl or immediately preceding time k.

6. A method according to claim 5, wherein, during the second calibration phase (120), the au coefficients are estimated using a second predetermined relationship which directly relates the values ​​of the au coefficients to the current intensity through the cell and to the voltage across the cell terminals so that the values ​​of the au coefficients are estimated without using open-circuit voltage estimation.

7. A method according to claim 6, wherein the second relation is chosen from the group consisting of the following relations: [Math.34] V-XX * !50Ci“+V and [Math.35] <t v : A h et [Math.36] dvs j __ ys & cs où : - SOC est l’état de charge de la cellule, - Vs est la tension aux bornes d’un circuit RC numéro s raccordé en série avec la résistance interne Ro, et - Cs et Rs sont, respectivement, la capacité et la résistance du circuit RC numéro s.

8. A method according to any one of claims 5 to 7, wherein the second calibration phase (120) is carried out in parallel with the operating phase.

9. A method according to any one of the preceding claims, wherein the exploitation phase also comprises a step (118) estimating the health status of the cell from the ASk2 values ​​of the entropy change estimated for that cell.

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

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

12. A 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 delivering electrical energy to power the electric motor, this cell comprising two terminals (30, 32) through 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 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, ammeter and thermometer,this management system comprising a programmable electronic computer (44) capable of estimating the entropy variation of the battery cell from measurements of the thermometer, voltmeter and ammeter, characterized in that the battery management system (40) conforms to claim 11.

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