METHOD FOR CONTROLLING A BATTERY CURRENT BASED ON A LITHIUM CONCENTRATION CALCULATED BY A FINITE ELEMENT MODEL

Abstract

The present invention relates to a method for controlling the current of a battery system (1) comprising a lithium-ion type electrochemical element (10), the method comprises the steps of estimating a lithium concentration at the surface of an electrode of polarity calculated from a finite element model according to calculation steps for a discretized grain volume of the structure of the electrode comprising a predetermined surface volume and at least one internal volume and controlling the current of the electrochemical element (10) comprising providing a first current setpoint (IDC1) when the lithium concentration is lower than a maximum authorized level and providing a second current setpoint (IDC2) when the lithium concentration is equal to or higher than the maximum authorized level. Figure 1.

Description

Title of the invention: METHOD FOR CONTROLLING A BATTERY CURRENT AS A FUNCTION OF A LITHIUM CONCENTRATION CALCULATED BY A FINITE ELEMENT MODEL

[0001] The field of the invention relates to a method for controlling the current of a battery system, in particular of an electrified vehicle.

[0002] Power battery systems, particularly for electrified vehicles, conventionally comprise a set of electrochemical cells connected in series and / or parallel in the system. The term energy storage element refers to an electrochemical cell or an assembly of cells that can be connected in series and / or in parallel. Conventionally, in electromobility applications, the energy storage elements are lithium-ion type electrochemical cells. In operation, these cells are likely to degrade if they are not used under nominal operating conditions, i.e. within the thermal, current and voltage limits defined by the cell manufacturers.Indeed, if the temperature is too low or if currents are too high, the electrodes of a cell can become saturated with lithium atoms on the surface, which can lead to the formation of dendrites causing internal short circuits. The management of the cell charge and discharge currents must be carried out under safe conditions while ensuring optimal energy management and the least restrictive use of the battery possible, particularly in terms of charging time and driving range.

[0003] Lithium transport in a negative graphite electrode is generally slower than in positive electrodes and, consequently, is the limiting phenomenon of the charging current. This phenomenon is called lithium deposition or lithium plating, also referred to as "Lithium Plating" in English. Too high a lithium concentration can lead to the formation of dendrites and cause an increase in internal resistance, or even a short circuit. During charging, lithium ions are reduced to lithium metal on the surface of the graphite structure during the exchange of electrons. The oxidation-reduction rate of the lithium ions is proportional to the current and diffusion in the graphite structure follows the diffusion laws. The diffusion rate depends on the lithium metal concentration gradient and a diffusion coefficient, which depends on the state of charge, temperature and aging of a cell.Fick's law governs the diffusion of lithium ions into the various components of the battery, such as the electrolyte and electrodes. This law is well . known to those skilled in the art in the field of batteries. For example, the following bibliographic reference describing principles of application of Fick's law in the field of lithium-ion cells may be cited: "Wu Musheng, Xu Bo, Ouyang Chuying. Physics of electron and lithium-ion transport in electrode materials for Li-ion batteries. Chinese Physics B, 2016, 25(1): 018206". Further, patent document EP-A1-2266181 may be cited describing an adaptive charging method based on a technique for estimating a diffusion time and a surface lithium concentration from the diffusion time, the cell capacity and the measured charging current. Then, from the concentration, a charging current is calculated. This document teaches measuring the diffusion time during a relaxation phase from the measurement of an open-circuit voltage following the application of a direct current for a fixed duration.This technique for estimating the surface lithium concentration concerns charges connected to the terminal, commonly called "Plug-in" charges. This technique is therefore not applicable to regenerative braking due to the driving dynamics and the impossibility of imposing cell relaxation, particularly in the case of a vehicle with a fully electric motor.

[0004] However, to improve energy management, the majority of electrified vehicles are equipped with a regenerative braking system in order to optimize the energy management of the vehicle. The management of the powertrain is then provided on the one hand to promote regenerative electric braking and on the other hand to control maximum charging current values ​​specific to braking situations while respecting the electrochemical and safety constraints linked to lithium-ion storage cells.

[0005] Document WO-A1-2022237476 is known from the state of the art, which teaches a solution for calibrating charging current pulse tables from electrochemical and thermal models established experimentally. These electrochemical models also include a law of diffusion coefficient of lithium ions at the electrodes. This document teaches a principle of control by current pulse of a given duration, for example 10 seconds, of which a stopping condition can be dependent on the cell voltage relative to a high voltage threshold, an electrode potential value between the negative electrode and the separator or a cell temperature. These pulse tables are intended to control maximum currents respecting the electrochemical constraints of the cells, in particular with regard to the lithium deposition.

[0006] Patent document WO-A 1-2022032460 is also known, describing a solution comprising a method for detecting lithium plating on a battery cell electrode comprising determining a potential value in real time of the negative electrode and in which, if this potential becomes less than or equal to a threshold of zero volts, the method detects a lithium plating. This document teaches the use of an embedded model in a vehicle to determine this potential as a function of the charging current, state of charge and temperature. This document teaches a principle of controlling the charging current aimed at reducing the current value as a function of this potential. The disadvantage of a real-time calculation model is that it is particularly energy-intensive.

[0007] Patent document EP-A1-3806270 also discloses a device and method for charging a battery consisting of estimating a lithium ion concentration on the surface of an anode using a model order reduction technique in order to reduce the computational complexity of the calculations.

[0008] In the state-of-the-art documents, the current control tables provide information on values ​​that can be applied from an estimation of the instantaneous state of charge and the temperature of a cell, generally for a relaxed state of the cell. However, although the estimation of the state of charge of a cell can be considered as the image of the lithium saturation level of the core of the graphite structure of the electrode, the saturation level of the surface area of ​​the electrode is not always identical to that of the core of the graphite structure, particularly during the rolling phase during which the dynamics of the electrical stresses during charging and discharging modify the concentration level of the lithium atoms on the surface.This implies that, following an electrical charge in regenerative braking, the surface may be at an already critical saturation level, higher than that estimated from the cell's state of charge (SOC) or, following a discharge, may be at a level lower than that estimated from the state of charge. In the first case, there is a risk of lithium deposition if the current resulting from the table obtained experimentally is applied. In the second case, the opportunity for energy recovery is limited.

[0009] There is therefore a need to optimize current control solutions for the charging and discharging phases of a battery.

[0010] One objective of the invention is to overcome the aforementioned problems. Another objective of the invention is to propose a lithium concentration estimator requiring suitable computing resources for an on-board computer of a motor vehicle. Another objective of the invention is to implement an optimized current control solution increasing the opportunities for controlling the maximum charging current, in particular in the regenerative braking phases, while limiting the risk of lithium deposition.

[0011] More specifically, the invention relates to a method for controlling a battery system comprising a lithium-ion type electrochemical element, the method being implemented by a control unit of said battery system and comprising the measurement of instantaneous electrical parameters of the electrochemical element comprising the temperature, the current and the voltage of said electrochemical element.

[0012] According to the invention, the method further comprises the following steps:

[0013] - the estimation of a lithium concentration on the surface of an electrode of polarity calculated from a finite element model according to calculation steps for a discretized grain volume of the electrode structure comprising a predetermined surface volume and at least one internal volume, the estimate comprising at each calculation step:

[0014] a) a first sub-step of calculating a reduced quantity of lithium for the surface volume under the action of a current, noted Nredox(t), calculated from a predetermined redox equation as a function of the measured electrical parameters,

[0015] b) a second sub-step of calculating a diffused quantity of lithium from the surface volume towards the internal volume, noted Ndiff(t), calculated from a predetermined diffusion equation as a function of the measured electrical parameters,

[0016] c) a third sub-step of calculating said surface lithium concentration calculated according to the following relation: CLiZl(t) = CUZl(tl) + / Nredoxtf) - Ndiffit) \ CLiZl(tl) being the concentration of \ vzi; surface of the previous calculation step and VZ1 being the surface volume,

[0017] - controlling the current of the electrochemical element comprising providing a first current setpoint when the lithium concentration is below a maximum permitted level and the provision of a second current setpoint when the lithium concentration is equal to or above the maximum permitted level.

[0018] The method according to the invention may include the following additional characteristics, alone or in combination:

[0019] - The lithium oxidation-reduction equation is based on a quantity of electricity measured during the current calculation step and the Faraday constant according to the following relationship: Nredox(j) - W™6, where Nredox (t) is the reduced quantity expressed in mol for the current calculation step, I(t) is the measured instantaneous current, Pdc is the predetermined duration of the calculation step expressed in seconds and F the Faraday constant expressed in coulombs per mol.

[0020] - The quantity diffused from the surface volume to the internal volume is calculated according to the following lithium diffusion equation: j - r ~ ...((CD'Zl(f-ï)-CLiZ2(tl))*Pdc) Ndiff (t) = D*------............ where Ndiff is the quantity diffused expressed in mol during the predetermined duration Pdc of the calculation step, D is the diffusion coefficient determined from a table recorded in the memory of the control unit as a function of the measured electrical parameters and expressed in pm2 per second, CliZl(tl) is the lithium concentration of the surface volume for the previous calculation step expressed in mol / pm3, CLiZ2(tl) is the lithium concentration of the internal volume for the previous calculation step expressed in mol / pm3, Ldiff is a predetermined diffusion distance expressed in pm representative of a distance between the surface volume and the internal volume.

[0021] - The value of the second setpoint is calculated at each calculation step and corresponds at a current value for which the quantity of lithium diffused is equal to the reduced quantity of lithium for the surface volume when the lithium concentration of the surface volume reaches the maximum permitted level.

[0022] - The method further comprises, at each calculation step:

[0023] - a sub-step of calculating simulated lithium concentration values ​​at a end time of a simulated command of a constant current profile having a predetermined application duration for, respectively, the first setpoint and a third current setpoint whose value is between the first setpoint and the second setpoint,

[0024] - a sub-step of selecting the highest current value from at least the first and third instructions whose simulated concentration value is less than or equal to the maximum authorized level.

[0025] - Current control also includes, at each calculation step:

[0026] - a sub-step of calculating simulated lithium concentration values ​​at a end time of a gradual current transition ramp from the value of the measured instantaneous current to the second setpoint, said simulated values ​​being calculated as a function of the current of the transition ramp,

[0027] - and a sub-step of activating the transition ramp when one of the values simulated reached the maximum authorized level.

[0028] - The first instruction is a direct current value applicable during a fixed predetermined duration delivered by a current table recorded in the memory of the control unit dependent on the instantaneous electrical parameters.

[0029] Further provided according to the invention is a battery system comprising a lithium-ion type electrochemical element and a control unit configured specifically for implementing the current control method according to any one of the preceding embodiments.

[0030] There is further provided a vehicle with an at least partially electrified powertrain comprising such a battery system.

[0031] The invention further provides a control unit comprising means specifically configured to implement the current control method according to the invention, a computer program comprising instructions which, when the program is executed by the control unit, cause the latter to implement any one of the embodiments of the current control method, and a computer-readable recording medium comprising instructions which, when executed by a computer, cause the latter to implement the current control method according to the invention.

[0032] The invention is a software solution implementing a lithium concentration estimator on the surface of an active material structure of an electrode of an electrochemical energy storage element. The estimator executes a finite element calculation model where the calculations of the lithium concentration of the electrode structure are discretized into volumes of homogeneous concentration during the duration of each calculation step. This estimator improves the control of the battery current and increases the opportunities for recharging in regenerative braking while effectively protecting against the risks of lithium deposition.

[0033] Other characteristics and advantages of the present invention will appear more clearly on reading the detailed description which follows, comprising embodiments of the invention given as non-limiting examples and illustrated by the appended drawings, in which:

[0034] [Fig.l] schematically represents a battery system according to the invention adapted for the implementation of the finite element model for calculating the lithium concentration.

[0035] [Fig.2] schematically represents an electrode structure illustrating the principle redox and diffusion of lithium ions through the active material of the electrode structure.

[0036] [Fig.3] shows graphs of current curves and simulated values ​​of lithium concentration for constant current profiles according to the invention.

[0037] [Fig.4] shows graphs of current curves and simulated values ​​of lithium concentration for a current transition ramp according to the invention.

[0038] [Fig.5] represents the current control method according to the invention.

[0039] [Fig.6] represents an electrified vehicle intended for the implementation of the method of current control according to the invention.

[0040] The invention applies to an energy storage system comprising a lithium-ion type electrochemical element and more precisely to a current control method. The invention finds an application in the field of vehicles comprising an at least partially electrified, fully electric powertrain. or hybrids, preferably motor vehicles, but not only such as aircraft, tractors, bicycles, ships.

[0041] [Fig.l] schematically represents an energy storage system 1 comprising an energy storage element 10 comprising at least one electrochemical cell 11 in accordance with the invention. The storage element 10 may comprise a plurality of cells 11 or group of cells (also called a cell cluster) electrically connected in parallel and / or in series.

[0042] An electrochemical cell is an electrical energy accumulator having two terminals and presenting a voltage of a few volts, most often between 2.3V and 4.2V, approximately. The cells are of the Lithium-ion type (a lithium Nickel Manganese Cobalt oxide NMC or a lithium iron phosphate LFP can be cited as examples of positive electrode active materials). More precisely, a Lithium-ion cell is composed mainly of a porous positive electrode, a porous negative electrode, a separator and an electrolyte (which can be liquid, polymeric or solid). The operating principle of a Lithium-ion cell is based on the reversible exchange of lithium ions between the two porous electrodes.

[0043] The storage system 1 further comprises means for measuring, estimating or sensing electrical parameters P, including at least one current sensor 12 capable of measuring or estimating a current value ICR in real time passing through the storage element 10, a voltage sensor and a temperature sensor for cells 11 or each cell 11 of the energy storage element 10. The storage system 1 further comprises a control unit 13 (also called ECU for “Electronic Control Unit” or BMS for “Battery Management System”).

[0044] The control unit 13 comprises calibration information for direct current tables for a fixed duration, taking as input electrical parameters including the state of charge and the temperature of an energy storage element, a cell or a group of cells. These direct current tables deliver current values ​​applicable for a fixed duration. An experimental protocol carried out on cells under controlled conditions may be a numerical modeling from the lithium concentration equations described above. Another experimental protocol may be the measurement of a reference potential of the negative electrode corresponding to a voltage measured between the negative electrode and a so-called reference electrode, generally made of lithium, connected to the electrolyte. During a charge, when this voltage reaches 0 volts, this condition indicates that the saturation level has been reached.

[0045] A first table provides values ​​of a first continuous charging current applicable for the first duration at most as a function of measured electrical parameters. The current values ​​are applicable until reaching a saturation level of lithium deposition on the surface of a negative electrode of said storage element at the end of the first duration. The measured parameters include the state of charge and the temperature of a storage element, for a range of [0%, 100%] in charge points and for a temperature range [-20°C, 60°C] for example. It is envisaged to obtain several first tables for different applicable durations, for example durations between 10 seconds and 180 seconds, for example a table for a duration of 10 seconds, another table for a duration of 30 seconds and another table for a duration of 180 seconds. These are current tables intended for a dynamic charging situation while a vehicle is running, such as regenerative braking for example.

[0046] Thus, with reference to [Fig.l], the control unit 13 comprises, recorded in memory, at least one first direct current table 18 IDC1. The control unit may comprise at least two direct current tables 18 and 19 IDC1 and IDC3 respectively. For example, table 18 records direct current values ​​associated with an application duration of 10 seconds, and table 19 records direct current values ​​associated with an application duration of 30 seconds.

[0047] Another current table may be provided for controlling a direct current for an application duration greater than tables 18 and 19, i.e. greater than several minutes, possibly between several minutes and several hours. The direct current value delivered by the second table corresponds to a lithium oxidation-reduction rate close to that of the diffusion of atoms in the core of the electrode structure. This second current may be controlled constantly, i.e. until the voltage limit of a cell corresponding to the so-called “Cut-off voltage” is reached without the lithium deposition phenomenon appearing. These are current values ​​suitable for charging at a terminal, for example.This table provides current values ​​applicable without risk of lithium deposit depending on the state of charge and temperature parameters of a storage element, for a range of [0%, 100%] in charge points and for a range of [-20°C, 60°C] for example.

[0048] It will be noted that the second table can be replaced as a variant by a module 161 for calculating a direct current IDC2 based on the calculation of the lithium concentration in real time implemented by the invention. This calculation module 161 is described in more detail in the remainder of the description.

[0049] Conventionally, the control unit 13 of the battery system further comprises an estimator 14 of the aging state of the cells providing an SOH parameter representative of the aging state expected to operate a current correction factor as a function of the aging parameter SOH. The current correction factor is provided to correct a value of the current IDC1, IDC3 delivered by the first and second tables 18 and 19 respectively. The aging state parameter is a value representative for example of a number of charge and discharge cycles, a number of hours of use of the battery, a mileage, or a model depending on a combination of factors. The control unit 13 further comprises an estimator 17 of the instantaneous state of charge of the battery 10 as a function of the parameters P. For example, the estimator determines a state of charge value as a function of the measured no-load voltage, for example when starting the vehicle.

[0050] An objective of the invention is to control maximum currents temporarily in the charging phase and for this it is necessary to know an estimate of the lithium concentration of the surface of the structure of a polarity electrode. The invention is based on a principle of modeling the mechanism of diffusion of lithium through the structure of an electrode, in particular Fick's law applied to lithium cells.

[0051] For this purpose, the control unit 13 is provided with an integrated circuit computer and electronic memories, the computer and the memories being configured to execute the current control method according to the invention. But this is not obligatory. Indeed, the computer could be external to the battery control unit, while being coupled to the latter. The control unit 13, according to the invention, can be produced in the form of software modules (or computer modules (or even "software")), or electronic circuits (or "hardware"), or even a combination of electronic circuits and software modules.

[0052] The invention proposes a current control method based on the physical properties of lithium oxidation-reduction at the surface of a polarity electrode and lithium diffusion within the internal structure of the electrode. More specifically, the method implements an estimator 15 of a lithium concentration at the surface of a polarity electrode calculated from a finite element model according to calculation steps for a discretized grain volume of the structure of the electrode comprising a predetermined surface volume and at least one internal volume. The model may comprise at most two internal volumes.

[0053] The calculations are carried out, for example, in steps of approximately 0.1 seconds, for example. The discretized grain volume corresponds to a grain volume representative of the structure of the active material. The grain volume is discretized into a cubic volume comprising a surface volume having a wall S of surface exposure to the oxidation-reduction of lithium and a lithium ion insertion length L1 and an internal volume having a wall S and a lithium ion insertion length L2. The volumes are separated by an ion diffusion length.

[0054] As an example of model calibration, S is a value representative of the cumulative surface area of ​​the graphite grains, proportional to the capacity, equal to 1.6.107cm2, L1 is equal to 0.055pm and L2 is equal to 10pm. A diffusion length Ldiff is considered equal to 3.2pm.

[0055] The finite element model allows to reduce the computational resources required for the estimation so that it can be implemented by an on-board computer of a battery system. It allows to simplify the calculation of the lithium concentration at the surface of the graphite particle structure. In addition, it is assumed that the estimation of the diffusion mechanism in the individual grain structure is representative of the diffusion mechanism in the total structure of the active material.

[0056] In this embodiment, the estimator 15 is configured to calculate a reduced quantity of lithium for the surface volume under the action of a current, noted Nredox, calculated from a module 151 implementing a predetermined redox equation as a function of the measured electrical parameters P.

[0057] More precisely, the lithium redox equation is based on a quantity of electricity measured during the current calculation step and the Faraday constant according to the following relationship: ^re^Ox(t) - : where Nredox (t) is the reduced quantity expressed in mol for the current calculation step, I is the measured instantaneous current, Pdc is the predetermined duration of the calculation step expressed in seconds and F is the Faraday constant expressed in coulombs per mol equal to 96485 A / mol.

[0058] Furthermore, the estimator 15 is further configured to calculate a diffused quantity, denoted Ndiff, of lithium ion from the predetermined surface volume to the internal volume.

[0059] More precisely, the quantity diffused from the surface volume to the internal volume is calculated from a module 152 implementing a lithium diffusion equation according to the following relationship:

[0060] Ndiff ( t ) = D*--—---------- Ldiff

[0061] where Ndiff is the quantity diffused expressed in mol during the predetermined duration Pdc of the calculation step, D is the diffusion coefficient determined from a table recorded in the memory of the control unit as a function of the measured electrical parameters P and expressed in pm2 / s, CliZl(tl) is the lithium concentration of the surface volume for the previous calculation step expressed in mol / pm3, CLiZ2(tl) is the lithium concentration of the internal volume for the previous calculation step expressed in mol / pm3, Ldiff is a predetermined diffusion distance expressed in pm representative of a distance between the surface volume and the internal volume.

[0062] More precisely, the diffusion coefficient D is delivered by a table recorded in the memory of the control unit taking as input the value of the measured current, the state of charge parameter SOC, and the aging state SOH of the battery. In particular, the aging state can be used to apply a correction factor.

[0063] It will be noted that in the case where the discretized volume comprises two or more internal volumes, the quantity of lithium diffused is expressed according to the same formula between each internal volume.

[0064] The estimator 15 is configured to further calculate the surface lithium concentration from a module 153 according to the following relationship:

[0065] CLiZ 1 ( £ ) = CUZ1 ( t -1 ) + (j, CLiZ 1 (t-1 ) being the surface concentration of the previous calculation step and VZ1 being the surface volume with VZ1=S*L1.

[0066] It is considered that at the first calculation step t=Os, CliZl(O) is determined as a function of the instantaneous state of charge of the battery. Thus, at the instant of initialization of the estimator 15, for example when starting the vehicle, the value of the concentration CliZl(0) is delivered by a table recorded in the memory of the control unit as a function of the state of charge and the temperature of the cells, and possibly a correction dependent on the aging state of the battery. This table is configured to deliver a concentration value as a function of the value of the state of charge provided by the estimator 17.

[0067] Similarly, at the time of initialization of the estimator 15, the value of CliZ2(0) is determined from the same table stored in the memory of the control unit. CliZl(O) =CLiZ2(0).

[0068] Then, the diffusion equation makes it possible to estimate at each calculation step the value of the lithium concentration of the internal volume from a module 154 according to the following relation:

[0069] cuzit] = CUZ^t-1) +

[0070] CLiZ2(tl) being the surface concentration of the previous calculation step, and VZ2 being the internal volume with VZ2=S*L2.

[0071] Finally, at each calculation step of a predetermined period Pdc, the estimator 15 estimates the lithium concentration value at the surface volume from the difference between the quantity of lithium resulting from the oxidation-reduction mechanism and the quantity diffused from the surface volume to the internal volume, and possibly between internal volumes. The estimator 15 makes it possible to estimate the evolution of the surface state of an active electrode material structure in highly dynamic transition phases such as a regenerative braking situation during which the charging current is likely to increase the lithium ion insertion speed more faster than the diffusion speed within the structure. The model improves current control and electrical safety.

[0072] In [Fig.2] is schematically illustrated the mechanism of redox and diffusion of lithium in the electrode structure implemented by the finite element model according to the invention. The surface structure and the internal structure are modeled respectively by the surface volume having a volume VZ1, defined by the surface S and the length L1, and a homogeneous concentration of lithium ion and further, by the internal volume having a volume VZ2, defined by the surface S and the length L2, and a homogeneous concentration of lithium ion. The redox flux Jredox operates according to the quantity of lithium ion reduced at the surface and the diffusion flux Jdiff operates between the two volumes according to a diffusion distance Ldiff is between these two volumes. The surface state is estimated by calculating the difference between the redox flux and the diffusion flux.

[0073] The lengths of the discretized volumes L1 and L2, and the diffusion length Ldiff are calibrated and fixed values ​​or can be values ​​delivered by tables recorded in the memory of the control unit taking as input the parameters of state of charge SOC and aging state SOH. In particular, the aging state can be used to apply a correction factor.

[0074] Returning to [Fig.l], the control unit 13 comprises a current controller 16 comprising a control function delivering current control information CCI, the control of which is a function of the estimation of the lithium concentration at the surface of the electrode structure CLiZl. The information CCI may be a current setpoint value, a maximum current value authorized at a given time or an electrical power value authorized for charging or discharging.

[0075] The current controller 16 comprises a module 161 delivering the CCI information configured to provide a first current setpoint when the lithium concentration is lower than a maximum authorized level and the provision of a second current setpoint when the lithium concentration is equal to or higher than the maximum authorized level. The maximum level is a predetermined lithium concentration corresponding to a state of charge of the battery between 90% and 100% of SOC, for example 95% or 100%.

[0076] The CCI information is delivered through communication means to other electrical systems consuming and / or generating energy, for example voltage converter, electric motor, charger.

[0077] The first current setpoint is the value of the current IDC1 delivered by the table 18. It may be provided that the current control 16 is configured to provide a third current setpoint corresponding to the value of the current IDC3 delivered by the table 19 when the lithium concentration is lower than the maximum authorized level.

[0078] The second current setpoint is delivered by a direct current table stored in the memory of the control unit delivering a current value dependent on the state of charge and the temperature. Alternatively, the second current setpoint is delivered by the module 162 delivering a current value IDC2 calculated from the surface concentration CLiZ1. More precisely, the module 162 is configured to calculate the value of the second setpoint at each calculation step and corresponds to a current value for which the quantity of lithium diffused is equal to the reduced quantity of lithium for the surface volume when the lithium concentration of the surface volume reaches the maximum authorized level. More precisely, in this situation Nredox(t)=Ndiff(t) for a lithium concentration of the internal volume CliZ2 equal to the saturation level reported at 100%, with: [°° 79 1 N n dox(t) 100801 Ndiff(t) =

[0081] Thus, the value of the second current setpoint IDC2 is obtained according to the following relationship:

[0082] IDC2(t) =

[0083] Furthermore, according to variants of the invention, the estimator 15 may comprise modules for calculating simulated lithium concentration values ​​in order to produce concentration projections for battery usage situations. These projections improve current control.

[0084] A first simulated usage situation is the application of direct currents for a fixed duration. These projections make it possible to verify that it is possible to apply current values ​​for a fixed duration without reaching a deposition of lithium on the electrode surface, in particular to carry out regenerative braking without changes in braking torque. For this purpose, the estimator comprises a module 155 configured to implement, at each calculation step, the calculation of simulated values ​​SCLil of lithium concentration at an end time of a simulated command of a constant current profile having a predetermined application duration. The calculation of the simulated values ​​is executed for, respectively, the first value setpoint IDC1 and the third value setpoint IDC3 whose value is between the first setpoint and the second setpoint.Furthermore, the current control 16 is configured to select the highest current value IDC1 and IDC3 from at least the first and third setpoints whose simulated concentration value is less than or equal to the maximum authorized level.

[0085] Thus, at the instant of triggering a current, the current control ensures that this constant maximum value can be applied for the duration associated with this value. This avoids an undesirable or unexpected drop in braking torque during a regenerative braking phase. The driving pleasure of a vehicle is improved.

[0086] In [Fig.3], a graph represents the simulated concentration values ​​as a function of three projections dependent on three distinct DC current values. The upper graph represents a current control situation where, on the y-axis, the instantaneous values ​​of the current Ib are represented by a solid line up to a time t1 and simulated values ​​of different DC currents IDC1, IDC3 and IDC4 are represented by dotted lines. For example, IDC1, IDC3 and IDC4 represent current values ​​applicable for a fixed duration of 10s ending at time t2. The constant current IDC2 is permanently applicable without reaching surface saturation and is represented by a double line.

[0087] The lower graph represents the lithium concentration values ​​CLi_IDCl, CLi_IDC3 and CLi_IDC4 for the surface volume calculated according to the concentration estimator implemented by the invention, for respectively each current value IDC1, IDC3 and IDC4. At time t1, it can be observed that among the simulated values ​​calculated for time t2 of finalization of the predetermined application duration of 10s, the value CLi_IDCl is greater than the maximum authorized level CLi_sat. This current value cannot therefore be retained for the CCI setpoint. The value CLi_IDC3 and the value CLi_IDC4 are both less than the maximum authorized level CLi_sat, the current control function is configured to select the associated current IDC3 of greater value.

[0088] A second simulated usage situation is the application of a gradual current transition ramp from the first setpoint to the second current setpoint, also called a “derating” ramp in English. This ramp aims to secure the transition from the first setpoint to the second setpoint so as to prevent a risk of lithium deposition. For this purpose, the estimator comprises a module 156 configured to implement, at each calculation step, simulated values ​​of lithium concentration SCLi2 at an end time of a gradual current transition ramp from the value of the instantaneous current to the second setpoint, said simulated values ​​being calculated as a function of the current of the transition ramp. Furthermore, the current control 16 is configured to activate the transition ramp when one of the simulated values ​​reaches the maximum authorized level.

[0089] In [Fig.4], a graph schematically represents in the upper part two current control situations Iba and Ibb for which a transition ramp from the instantaneous current Iba or Ibb, towards the second setpoint IDC2. The constant current IDC2 is applicable permanently without reaching the saturation of the surface and is represented by a double line. In the lower part, the lithium concentration values ​​for the surface volume calculated according to the concentration estimator implemented by the invention, respectively for the current Iba and the current Ibb, are represented by the curves CLi_Iba and Cli_Ibb. After time tl, the dotted line curves represent the transition ramp from the instantaneous current to the second setpoint, the IRPa ramp for the current Iba and the IRPb ramp for the current Ibb. The simulated values ​​CLi_RPa and CLi_RPb of the lithium concentration for the surface volume associated respectively with the IRPa and IRPb ramps are also represented by a dotted line.

[0090] For the IRPa ramp, the simulated lithium concentration values ​​CLI_RPa do not reach the maximum authorized level CLi_sat at any time. The current control for this situation does not trigger the transition ramp. For the IRPb ramp, the simulated lithium concentration values ​​Cli_RPb calculated at time t1 reach the maximum authorized level CLi_sat at the projected time t2. The current control of the battery system is then configured to activate the transition ramp at time t1. This configuration of the current control makes it possible to prevent lithium deposition during the operation of the transition ramp.

[0091] A variant is provided combining the simulated values ​​SCLil and SCLi2 calculated by the modules 155 and 156 of the estimator 15 in which the simulated values ​​of concentration of the ramp are calculated following the end time of each constant current profile. This variant aims to guarantee the execution of the transition between the constant current profile and the second setpoint IDC2.

[0092] In [Fig.5], the current control method according to the invention is represented. The current control method is implemented by the control unit of the energy storage system of an electrified vehicle as described in detail in [Fig.l]. This method applies during the driving phase of an electrified vehicle when it is moving at non-zero speed or in a situation of electrical recharging of the battery by electrical connection to a charging station.

[0093] In a first step E1, the control unit is started and initialized. The control unit measures the electrical parameters of the battery, the temperature, the no-load voltage and the current in particular. These measurements make it possible to determine a state of charge of the battery. The control unit initializes the finite element model at a first initial calculation step, triggered for example by the detection of the “KEY-ON” information from the vehicle. More precisely, the lithium concentration value of each discretized volume of the finite element model implemented by the estimator of the control unit is determined from the table of values ​​stored in the memory of the control unit and configured for this purpose. The table delivers a value concentration as a function of temperature and state of charge for the predetermined surface volume CLiZl(O) and for the internal volume CLIZ2(0).

[0094] Then, the method comprises a second step E2 of measuring or estimating the electrical parameters P of the storage element of the battery, the parameters comprising at least the temperature, the voltage of each storage element of the battery, the exchanged current I(t), a charge state parameter, an aging state parameter, in particular. The measurement is carried out periodically during operation of the battery, and at least at each calculation step.

[0095] Then, the method comprises a third step E3 of estimating a lithium concentration CLiZl on the surface of a polarity electrode calculated from the finite element model according to calculation steps for a discretized grain volume of the structure of the electrode comprising the predetermined surface volume and at least the internal volume.

[0096] More precisely, the method comprises for each calculation step a first sub-step E31 of calculating a reduced quantity of lithium for the surface volume under the action of a current, denoted Nredox(t), calculated from the predetermined redox equation as a function of the measured electrical parameters. The lithium redox equation is based on a quantity of electricity measured during the current calculation step Pdc and the Faraday constant according to the following relationship: |W-' 7 I Nr e dox(t)=!^

[0098] The method further comprises for each calculation step a second sub-step E32 of calculating a quantity of lithium diffused from the surface volume to the internal volume, denoted Ndiff(t), calculated from the predetermined diffusion equations as a function of the measured electrical parameters. The lithium diffusion equation is implemented according to the following relationship:

[0099] Acuz . Ldiff

[0100]

[0101] It is further recalled that the concentration of the internal volume CLiZ2(t) is calculated according to the following relation CLiZmj = CLiZ2^-lj + ..... / The method further comprises for each calculation step a third sub-step of calculating said surface lithium concentration CLiZl(t) calculated according to the following relationship:

[0102] cUZl(t) = CUZlÇt-1)

[0103] Then, at each calculation step, the method comprises, for the current control of the battery system, a verification step E4 of the value of the lithium concentration CLiZl in relation to the maximum authorized level CLi_sat. The maximum level allowed can be a value corresponding to a state of charge between 90% and 100% of the battery state of charge, for example 95% or 100%.

[0104] Then, the method comprises a step of controlling the current E5 of the electrochemical element of the battery comprising the supply of the first current setpoint when the lithium concentration is lower than the maximum authorized level CLi_sat and the supply of the second current setpoint when the lithium concentration is equal to or higher than the maximum authorized level CLi_sat. The first current setpoint is a constant current IDC1 delivered by a direct current table associated with a fixed duration, for example the current IDC1 for a duration of 10 seconds or the direct current IDC3 for a fixed duration of 30s. The second current setpoint is the current IDC2, either delivered by a current table depending on the state of charge and the measured temperature, or calculated as a function of the concentration CLiZl as described previously for the module 162.

[0105] Preferably, the method provides for the application of a current transition ramp, when it is detected that the concentration Cli_Zl becomes equal to or greater than the maximum authorized level.

[0106] According to variants of the method, it is provided that the method comprises steps of calculating the simulated lithium concentration values ​​for the constant current profiles IDC1, IDC3 and IDC4 described previously according to the example of [Fig. 3], and / or for the transition ramp when the current limitation is triggered. These concentration simulation steps make it possible to prevent a lithium deposition situation.

[0107] According to these latter variants, the current control is able to select the currents of the highest value and which have the advantage of avoiding the deposition of lithium. In addition, these concentration simulations make it possible to ensure the operation of the current transition ramp before reaching the maximum authorized level of lithium concentration.

[0108] In [Fig. 6], an electrified vehicle 100 comprising a battery system 103 according to the invention is schematically represented. The vehicle may be a hybrid or fully electric vehicle, it comprises at least partially electrified traction. The vehicle 100 comprises an electric prime mover 101 intended to move the vehicle and powered by the battery system 103. Some or all of the functions of the vehicle 100 are controlled by a control unit 102. The control unit 102 may comprise at least one processor that executes instructions stored in a computer-readable medium such as non-volatile memory. The control unit 102 may also be multiple computing devices that control individual components or subsystems of the vehicle 100 in a distributed manner. The processor may be any any conventional processor, such as a commercially available central processing unit. Alternatively, the processor may be a dedicated device such as an application-specific integrated circuit (ASIC) or other hardware processor.

[0109] The prime mover 101 and the battery system 103 can be controlled in regenerative braking operation. The battery system comprises a control unit 104 comprising a computer and memories configured for implementing the current control method according to the invention. In particular, the memories have a recorded program comprising instructions which, when the program is executed by the control unit of the battery system, cause the latter to implement any one of the embodiments of the control method according to the invention.

[0110] Furthermore, the control unit 104 is connected in communication with vehicle computers by means of an on-board communication bus 108, for example of the CAN (Control Area Network) type, to deliver the current control information determined from the method according to the invention. The control unit 104 informs, for example, the powertrain of a maximum authorized current determined as a function of the lithium concentration value calculated from the finite element model in accordance with the invention.

[0111] The maximum authorized current is, for example, the charge current that can be controlled in regenerative braking or a discharge current to power the electric machine. The current value is a direct current that is associated with a maximum authorized fixed duration. The vehicle further comprises a voltage converter 105 of the DC / DC or AC / DC type. The vehicle further comprises an electrical relay or switch 106 provided for selectively disconnecting and connecting the battery system 103 from the vehicle's electrical systems and, possibly, from a charging box 107. The charging box is an interface allowing the connection of a charging cable to an external energy source connected to an extended electrical supply network operating at alternating voltage.

[0112] The invention is described in the above by way of example. It is understood that the person skilled in the art is able to produce different variant embodiments of the invention by associating, for example, the different characteristics above taken alone or in combination, without departing from the scope of the invention.

Claims

Claims

1. Method for controlling the current of a battery system (1) comprising a lithium-ion type electrochemical element (10), the method being implemented by a control unit (13) of said battery system (1) and comprising the measurement (E2) of instantaneous electrical parameters (P) of the electrochemical element comprising the temperature, the current and the voltage of said electrochemical element, the method being characterized in that it further comprises the following steps: - the estimation (E3) of a lithium concentration at the surface of an electrode of polarity calculated from a finite element model according to calculation steps for a discretized grain volume of the structure of the electrode comprising a predetermined surface volume and at least one internal volume, the estimation comprising at each calculation step: a) a first sub-step (E31) of calculating a reduced quantity of lithium for the surface volume under the action of a current, denoted Nredox(t),calculated from a predetermined redox equation as a function of the measured electrical parameters, b) a second sub-step (E32) of calculating a diffused quantity of lithium from the surface volume to the internal volume, denoted Ndiff(t), calculated from a predetermined diffusion equation as a function of the measured electrical parameters, c) a third sub-step (E33) of calculating said surface lithium concentration calculated according to the following relationship: CUZIW = CLiZl(tl) being the surface concentration of the previous calculation step and VZ1 being the surface volume, - the control (E5) of the current of the electrochemical element (10) comprising the supply of a first current setpoint (IDC1) when the lithium concentration is lower than a maximum authorized level and the supply of a second current setpoint (IDC2) when the lithium concentration is equal to or higher than the maximum authorized level.,

2. The method of claim 1 wherein the lithium redox equation is based on an amount of electricity measured during the current calculation step and Faraday's constant according to the following relationship: Nredox(t} - : where Nredox (t) is the reduced quantity expressed in mol for the current calculation step, I(t) is the measured instantaneous current, Pdc is the predetermined duration of the calculation step expressed in seconds and F is the Faraday constant expressed in coulombs per mol.

3. A method according to claim 1 or 2 wherein the amount diffused from the surface volume to the internal volume is calculated according to the following lithium diffusion equation: »• z> / • / . — u((C£iZKM)-CLtZ2(tl))*P <Zc), NdlffW-D* Uiff où Ndiff est la quantité diffusée exprimé en mol pendant la durée prédéterminée Pdc du pas de calcul, D est le coefficient de diffusion déterminé à partir d’une table enregistrée en mémoire de 1‘unité de commande en fonction des paramètres électriques mesurés et exprimé en pm2 par seconde, CliZl(t-l) est la concentration en lithium du volume de surface pour le pas de calcul précédent exprimée en moFpm3, CLiZ2(t-l) est la concentration en lithium du volume interne pour le pas de calcul précédent exprimée en mol / pm3 , Ldiff est une distance de diffusion prédéterminée exprimée en pm représentative d’une distance entre le volume de surface et le volume interne.

4. Method according to any one of claims 1 to 3 in which the value of the second setpoint is calculated at each calculation step and corresponds to a value of the current for which the quantity of lithium diffused is equal to the reduced quantity of lithium for the surface volume when the lithium concentration of the surface volume reaches the maximum authorized level.

5. Method according to any one of claims 1 to 4 further comprising, at each calculation step: - a sub-step of calculating simulated lithium concentration values ​​(Cli_IDCl, Cli_IDC3) at an end time of a simulated command of a constant current profile having a predetermined application duration for, respectively, the first setpoint (IDC1) and a third current setpoint (IDC3) whose value is between the first setpoint (IDC1) and the second setpoint (IDC2), - a sub-step of selecting the highest current value from at least the first and third setpoints (IDC1, IDC3) whose simulated concentration value is less than or equal to the maximum authorized level (CLi_sat).

6. Method according to any one of claims 1 to 5 in which the current control further comprises, at each calculation step: - a sub-step of calculating simulated lithium concentration values ​​(CLi_RPb) at an end time of a gradual current transition ramp from the value of the measured instantaneous current to the second setpoint, said simulated values ​​being calculated as a function of the current of the transition ramp, - and a sub-step of activating the transition ramp (IRPb) when one of the simulated values ​​reaches the maximum authorized level (CLi_sat).

7. Method according to any one of claims 1 to 6 in which the first setpoint is a direct current value (IDC1) applicable for a fixed predetermined duration delivered by a current table (18) recorded in the memory of the control unit dependent on the instantaneous electrical parameters (P).

8. Battery system (1) comprising a lithium-ion type electrochemical element (10) and a control unit (13) configured specifically for implementing the current control method according to any one of claims 1 to 7.

9. Vehicle (100) with at least partially electrified powertrain comprising a battery system (103) according to claim 8.

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