Method for estimating the maximum current value to be applied to a battery cell to reach an operating limit condition related to the estimation of the maximum available power

Abstract

Method for estimating a maximum current value to be applied to a battery cell to achieve at least one operating boundary condition, the method comprising the iterative steps of: Initializing a first estimate of the maximum current value to a predefined value assumption, Executing (201) a first instance of a cell state prediction model to estimate a voltage value across the cell terminals obtained at the end of a given time horizon, from the temperature measurement and the first estimate of the maximum current value, Calculating (202) a voltage difference between a voltage boundary value, corresponding to an operating boundary condition, and the predicted voltage value, Calculating (204) a first current difference corresponding to said voltage difference, from a first characteristic curve of the cell, At the next iteration,correct the first estimate of the maximum current value of said first current deviation. Figure 2,

Description

Title of the invention: Method for estimating a maximum current value to be applied to a battery cell to reach an operating limit condition related to the estimation of the maximum available power

[0001] The invention relates to the field of electric batteries and more specifically to algorithms for estimating the maximum available power or the maximum current value to be applied to a battery cell to reach a limit condition of battery operation which conditions the maximum available power.

[0002] An electric battery is composed of several rechargeable elementary cells connected in series and / or in parallel between two main voltage supply terminals.

[0003] A battery is generally associated with a management device connected to the terminals of the elementary cells of the battery and / or to the main terminals of the battery and which can implement functions of balancing the charge of the cells in particular.

[0004] To this end, the management device implements various algorithms which aim to characterize the internal state of each cell through various indicators such as the state of charge, also called SoC (from the English "State of Charge"), the state of health, also called SoH (from the English "State of Health") or the state of available power, also called SoAP (from the English "State of Available Power").

[0005] The present invention aims more specifically to propose a method allowing the estimation of the available power, this maximum calculated power being able to be at the charge or discharge.

[0006] This indicator aims to provide an estimate of the power available to a battery at the end of a given time horizon. This information cannot be determined directly using sensors and must be estimated via a model or algorithm.

[0007] An accurate estimation of the available power is important in order to prevent in particular overcharging (in the case of regeneration) or over-discharging (leading to critical conditions from the point of view of premature aging of the battery for example).

[0008] The state of available power (SoAP) can be defined as the ratio between the peak power and the nominal power of the battery. The peak power is the maximum power that the battery can receive or transmit over a predefined time horizon.

[0009] The power available at the output of the battery depends on various parameters such as the state of charge, temperature, capacity or even the aging conditions of the battery.

[0010] Various methods exist in the prior art for estimating the state of available power. These methods are generally based either on characterizations via tables or on models of battery operation.

[0011] Table-based methods have the advantage of being simple to implement and quick to execute. However, they are not robust to dynamic changes, particularly those due to aging, and require storing a large amount of information in memory. Furthermore, these methods are not very specific to each battery and are affected by safety margins that can be significant. Finally, establishing these tables requires a large number of preliminary laboratory characterizations.

[0012] Conversely, there are methods based on equivalent electrical circuit models of the cell, or on physical models (also called electrochemical models). US patent application 2010174500 describes an example of such a method using an equivalent electrical circuit model. Reference [1] describes another example of a two-dimensional pseudo-2D physical model, also called a Doyle-Fuller-Newman model. This model provides information on the internal states of a cell and its physical behavior. Some of the methods identified in the literature that use an electrochemical model implement machine learning techniques to provide an estimate of the state of available power (SoAP). Reference [2] gives an example of such a method, which has the disadvantage of a long execution time, incompatible with real-time execution and an embedded solution.Indeed, the various indicators of a battery's state must be provided in real time in order to best adjust cell usage at any time.

[0013] One objective of the invention is to provide a new method for estimating the power available for each cell of a battery. More specifically, the method aims to estimate the maximum value of constant applicable current over a given time horizon for battery operation during charging or discharging.

[0014] In a particular embodiment, the method is based on the use of a two-dimensional multi-particle Doyle-Fuller-Newman model of a cell and an iterative approach to estimate the maximum current value that allows compliance with a limit constraint of battery operation from characteristic curves of cell operation.

[0015] In a particular embodiment, the method further implements a Bayesian filter, for example a UKF or S3-UKF Kalman filter.

[0016] The invention relates to a method for estimating a maximum current value to be applied to a battery cell to reach at least one operating limit condition, the method comprising the iterative steps of: - Initialize a first estimate of the maximum current value to a predefined value assumption, - Execute a first instance of a cell state prediction model to estimate a voltage value across the cell terminals obtained at the end of a given time horizon, based on temperature measurements and the first estimate of the maximum current value, - Calculate the voltage difference between a voltage limit value, corresponding to an operating limit condition, and the predicted voltage value. - Calculate a first current deviation corresponding to said voltage deviation, from a first characteristic curve of the cell, - In the next iteration, correct the first estimate of the maximum current value of said first current deviation.

[0017] In one embodiment, the method further comprises the application of a first Proportional Integral Derivative regulator to the voltage difference before determining the first current difference.

[0018] According to a particular aspect of the invention, the battery is in a discharged state, the voltage limit value is a minimum value.

[0019] In one embodiment, the method further comprises the steps of: - Initialize a second estimate of the maximum current value to a predefined value assumption, - Execute a second instance of a cell operating model to estimate a value for the electrical potential difference of the cell's negative electrode, based on temperature measurement, lithiation rate estimation, and a second estimate of the maximum current value. - Calculate the difference in electrical potential difference between a limiting value of electrical potential difference, corresponding to an operating limit condition, and the estimated value of electrical potential difference. - Calculate a second current deviation corresponding to said electrical potential difference deviation, from a second characteristic curve of the cell, - In the next iteration, correct the second estimated value of the maximum current value of said second current deviation.

[0020] In one embodiment, the method further includes the application of a second Proportional Integral Derivative regulator to the electrical potential difference gap before determining the second current gap.

[0021] According to a particular aspect of the invention, the battery is in a state of charge, the voltage limit value is a maximum value and the lower value is retained between the first estimated current value or the second estimated current value.

[0022] According to a particular aspect of the invention, the cell state prediction model is an equivalent electrical circuit model configured to estimate a cell charge state and several voltage estimates relative to each RC sub-circuit of the model.

[0023] In one embodiment, the method further comprises the steps of: - Execute multiple instances of the cell state prediction model, the model acting as a state model of a nonlinear Bayesian filter, - Execute a correction step of the nonlinear Bayesian filter to predict a state vector comprising a prediction of a cell charge state and several voltage estimates relative to each RC subcircuit of the model from the outputs of the model executed for all instances, - Determine, from the state vector, a state matrix comprising several modified vectors obtained by transformations of the state vector, - Provide each modified vector as input to the model at a subsequent iteration,

[0024] According to a particular aspect of the invention, the cell operating model is an electrochemical model, for example a Doyle-Fuller Newman model, which further receives as input an estimate of the lithiation rate of at least one electrode of the cell.

[0025] According to a particular aspect of the invention, the electrochemical model receives as input a temperature measurement taken on the cell.

[0026] According to a particular aspect of the invention, the cell is provided with two electrodes, each electrode being spatially discretized according to a predefined spatial mesh, the estimation of the lithiation rate being provided for each electrode of the cell and each point of the spatial mesh.

[0027] In one embodiment, the method further includes a step of receiving, at the given time, a measurement of the current applied to the cell and in which the estimation of the lithiation rate is obtained by means of the execution of an instance of the cell state prediction model to estimate the lithiation rate from the current and temperature measurements.

[0028] In one embodiment, the method further comprises the steps of: - receive, at the given moment, a voltage measurement across the cell terminals, and in which the estimation of the lithiation rates is obtained by means of the execution of the sub-steps of: i. Execute multiple instances of the cell state prediction model to estimate the cell voltage and lithiation rates of each electrode for each point of the spatial mesh, based on current measurements, temperature measurements, and a prediction made in a previous iteration of the lithium concentration of each electrode. The model acts as a state model of a nonlinear Bayesian filter. ii. Execute a nonlinear Bayesian filter correction step to predict a state vector including a prediction of the corrected lithiation rate for each point of the spatial mesh and for each electrode from the voltage measurement and the outputs of the model executed for all instances, iii. Determine, from the state vector, a state matrix comprising several modified vectors obtained by transformations of the state vector, iv. Provide each modified vector as input to the model at a subsequent iteration, v. Provide the state vector as an estimate of the lithiation rate.

[0029] According to a particular aspect of the invention, the nonlinear Bayesian filter is a UKF or S3-UKF type Kalman filter.

[0030] In one embodiment, the method further includes a step of calculating the maximum available power by multiplying the maximum current value by the voltage value estimated by the model at the end of said time horizon for said maximum current value.

[0031] The invention also relates to a device for managing the state of charge of a battery comprising a processing unit configured to implement the steps of the method according to the invention.

[0032] The invention has the advantage of being both precise and of low complexity, which makes it compatible with real-time applications.

[0033] Other features and advantages of the present invention will become more apparent from the following description in relation to the following accompanying drawings.

[0034] [Fig. 1] represents a diagram of an electric battery management system adapted to implement the invention,

[0035] [Fig.2] represents a synoptic diagram of a method for estimating the available power of an electric battery cell according to a first embodiment of the invention corresponding to the operation of the cell in discharge,

[0036] [Fig.3] represents a variant embodiment of the method of [Fig.2],

[0037] [Fig.4] represents a time diagram illustrating the operating rhythm of the different steps of the method of [Fig.3],

[0038] [Fig.5] represents a method for estimating lithiation rates according to a variant embodiment of the invention,

[0039] [Fig.6] represents a synoptic diagram of a method for estimating the available power of an electric battery cell according to a second embodiment of the invention corresponding to cell operation under load, and considering two physical operating limits,

[0040] Fig. 1 schematically represents a system comprising an electric battery BAT and an electronic management device GES configured to implement a method for estimating the available power of the battery according to the invention.

[0041] The battery BAT may be a single battery cell or comprise several individual cells connected in series and / or parallel. The GES management device includes a SENS measuring device with one or more sensors adapted to measure one or more physical quantities of the battery, for example, the current in the battery and / or the voltage across the battery terminals and / or the battery temperature. The GES management device further includes a PROC processing unit, for example, a microprocessor, which receives the data measured by the SENS measuring device and calculates an estimate of the available power in order to prevent the battery from being used outside its intended area of ​​use.

[0042] The BAT battery provides information to the GHG management system via the SENS measuring device. The BAT battery is also controlled and its status is monitored by the GHG management system.

[0043] Figure 2 represents a diagram of a method for estimating the available power of a cell in an electric battery according to a first embodiment of the invention corresponding to the operation of the cell in discharge.

[0044] The method aims to determine the maximum current value Imax to be applied to the cell to reach a limiting operating condition after a predefined time thorizon. From this current value, the maximum power available at the end of this time can be deduced as P = U.Imax. The voltage U used to calculate the power P can be an estimate of the voltage at the end of the horizon. temporal horizon or the current voltage measurement or the maximum voltage under load or the minimum voltage under discharge.

[0045] Method 200 is schematically illustrated in [Fig. 2]. It consists of running at least one instance of a model 201 for predicting the cell state. Model 201 is, for example, a two-dimensional, multi-particle electrochemical model of the cell, such as a Doyle-Fuller Newman model. At each iteration with a time clock at rate Tr2, model 201 receives as input a vector x comprising estimates of the lithiation rates of the two cell electrodes. The lithiation rates are expressed for all nodes of the volume of an electrode according to a predefined 2D spatial mesh. Typically, an electrode is modeled by a number Nx of particles along an axis normal to the principal plane of the cell. Each particle is discretized into a number Nr of points along a radial direction. The lithiation rates and the lithium concentrations in the solid phase are therefore matrices of dimension Nx * Nr.Without departing from the scope of the invention, the spatial discretization parameters of an electrode may be identical or different between the two electrodes of the same cell. It also receives a temperature measurement T and an estimate of the lithium concentration in the electrolyte C2 discretized according to a mesh in the normal direction.

[0046] Model 201 also takes as input a current assumption to be applied to the cell. Initially, this current assumption is fixed at a priori value. In subsequent iterations, this current assumption is that resulting from the last calculation.

[0047] At output, the model 201 produces an estimate of the voltage U across the cell terminals, for the current assumption considered. Optionally, the model also provides at output an estimate of an electrical potential difference of at least the negative electrode, ddpneg.

[0048] Other estimates of physical quantities characterizing the cell can be produced as output from the model.

[0049] The Doyle-Fuller-Newman model used is, for example, that described in reference [1]. Other models may be considered insofar as they take into account a 2D spatial discretization of the electrode volume and provide an estimate of the same physical quantities.

[0050] Without departing from the scope of the invention, the model used may be any type of electrochemical model including a single-particle electrochemical model taking into account a spatial discretization in one direction.

[0051] In an alternative embodiment, the model used may also be an equivalent electrical circuit model, for example that described in reference [4].

[0052] Such a model is composed of several RC sub-circuits each parameterized by a resistance R and a capacitance C. In this variant, the equivalent electrical circuit model does not provide an estimate of the lithiation rate, but an estimate of the state of charge and the voltages of the RC sub-circuits which serve as the basis of the equivalent electrical circuit model.

[0053] The model is executed over a duration thorizon so as to estimate the voltage value obtained at the end of this duration Tr2+ thorizon from the model inputs received at the initial time Tr2. In other words, the model itself operates iteratively to provide an estimate of the future behavior of the cell if the current is kept constant and equal to the input value for the duration thorizon.

[0054] At the first iteration, the current is initialized to a predefined value.

[0055] In step 202, the difference between the estimated output voltage of the model and a The minimum value Umin below which the cell can no longer operate in discharge mode without damaging the cell. This minimum value is typically provided by the battery manufacturer.

[0056] Optionally, a PID controller or regulator for "Proportional Integral Derivative" is applied in step 203 to this voltage difference in order to improve the performance of the control achieved by the method.

[0057] The equivalent bandwidth of this PID control filter defines the stability and robustness of the estimator with respect to the dynamics of current evolution.

[0058] In step 204, a current deviation corresponding to the voltage deviation is then calculated from a characteristic curve of the cell dI=f(dU). This curve depends on at least one parameter, including the initial voltage applied across the cell, the age of the battery, and the battery temperature. The curve gives the current deviation dl to be applied as a function of the voltage deviation across the cell. This current deviation corresponds to the correction to be applied to the current assumption in the previous iteration in order to reach the setpoint voltage Umin. This characteristic curve of the cell is obtained, for example, by varying the current intensity at the input of the model and recording the evolution of the voltage at the output of the model. The shape of this curve, and in particular the derivative at the origin, influences the accuracy and robustness of the estimation with respect to the dynamics of the current evolution.

[0059] In the next iteration, the current I supplied at the input of the model 201 is corrected for the current difference dl supplied at the output of step 204.

[0060] After a convergence phase, the current I at the input of the model corresponds to the maximum value of current Imax to be applied to reach the operating limit condition at the end of the duration thorizon.

[0061] In a particular embodiment of the invention described in [Fig. 3], the vector x containing the lithiation rates of the two electrodes is estimated, in step 205, by running a first instance of the multi-particle model taking as input a current measurement I applied to the cell and the associated temperature measurement. Step 205 is run at a different time rate Tri than the execution rate Tr2 of step 201. Typically, Tri is strictly less than Tr2, as shown in the example in [Fig. 4].

[0062] In this example, step 205 is executed at the rate Tri producing a new estimate of the electrode lithiation rates every time period At. Step 201, on the other hand, produces outputs at the rate Tr2 and models, at each execution, the behavior of the cell over a time horizon thorizon which is typically equal to several time periods At.

[0063] In another embodiment of the invention described in [Fig.5], step 205 consists of the combined execution of the cell state prediction model and a step of correcting the model outputs by a Bayesian filter which aims to produce a state vector x containing corrected lithiation rate values.

[0064] The Bayesian filter correction step can be executed at an intermediate rate between Tri and Tr2 or be executed at the rate of Tri or Tr2.

[0065] Figure 5 shows a diagram of an example embodiment of step 205 which aims to provide an estimate of the lithiation rates for the two electrodes from the combined execution of a cell state prediction model and a Bayesian filter. More specifically, model 500 is executed as a state model of a Bayesian filter to determine a first a priori prediction of the lithiation rates. Then, a correction step 503 using the Bayesian filter is applied to determine a second a posteriori prediction of the lithiation rates.

[0066] In the example of [Fig. 5], the method is based on the execution of a two-dimensional multi-particle 500 model of the cell, for example the Doyle-Fuller Newman model, which is executed from the measurement of current I, the measurement of temperature T and predictions of lithium concentration values ​​of each electrode, Clposet Clneg and in the electrolyte, C2. The model provides as output an estimate of the voltage across the cell terminals U, the respective lithiation rates of each electrode and a lithium concentration in the electrolyte C2 which loops back to the input of the model.

[0067] The model also provides as output an average lithiation rate of each electrode xlipos, xLineg which can be calculated from the lithiation rates of all points of the spatial mesh.

[0068] Optionally, the model also provides as output an estimate of an electrical potential difference of each electrode, ddppos, ddpneg.

[0069] Other estimates of physical quantities characterizing the cell can be produced as output from the model.

[0070] Model 500 is executed as a state model of a Bayesian Observer-type estimator to provide a priori prediction of lithiation rates. The Bayesian Observer-type estimator is, for example, a nonlinear Bayesian filter.

[0071] The method is further based on the execution of a correction step by a nonlinear Bayesian filter 503, for example a UKF (Unscented Kalman Filter) or S3-UKF (Scaled Spherical Simplex Unscented Kalman Filter) type Kalman filter. A complete description of an S3-UKF (also called S3F) Kalman filter is given in reference [3].

[0072] The correction step 503 takes as input certain outputs from the model 500, in particular the voltage U, the lithiation rates of each electrode, and a measurement of the voltage across the cell terminals Uceii. Optionally, the electrical potential differences of the two electrodes are also provided as input to the correction step 503.

[0073] Thus, the nonlinear Bayesian filter consists of the sequence of step 500 of a priori prediction using a state model of the cell and step 503 of correction of the a priori predictions to provide a posteriori predictions, and step 504 where the state matrix is ​​generated.

[0074] The correction step 503 also takes as input an estimate of the total amount of lithium nLi, which is calculated 502 from the average lithiation rates of each electrode xLipos, xLiJneg. The total amount of lithium is, for example, expressed as a total mass of lithium or as a number of moles. This total amount is provided as input to the filter as a constraint in the observation vector y. This is a virtual measurement. The total amount of lithium is considered constant if cell aging phenomena are ignored, or this phenomenon can be taken into account, in which case a cell aging model allows the evolution of the total amount of lithium over time to be considered. This constraint is respected by the filter when calculating its a posteriori predictions.

[0075] The correction step 503 allows the calculation of a new corrected a posteriori prediction of the lithiation rates of the two electrodes in the form of a state vector x.

[0076] More specifically, correction step 503 aims to determine the state vector x from several input data sets obtained by executing several instances of the same model 500. For each instance, model 500 receives the same current and temperature measurements as input, but different versions of lithium concentrations (derived from lithiation rates).

[0077] These different versions are determined from the state vector x by constructing a state matrix X, each column of which corresponds to a slight modification of the state vector, obtained via a predefined mathematical transformation. The determination of the state matrix X is carried out using equations specific to the type of Kalman filter used. For a UKF type Kalman filter, the state matrix has dimension N by 2N+1, where N is the size of the state vector, which is equal to the number of variables in the state vector, for example, equal to the sum of all the nodes in the mesh of at least one electrode.

[0078] In one embodiment, the number of operations to be performed by the Kalman filter can be further reduced by taking into account, in the state vector, the lithiation rates estimated for a single electrode. The predicted lithiation rates for the second electrode are then determined from those predicted for the same electrode in the previous iteration, those predicted for the first electrode, and a total quantity of lithium from both electrodes, assumed to be constant over a given time interval or provided by an aging model that takes into account cyclable lithium losses.

[0079] For a Kalman filter of type S3-UKF, the state matrix is ​​of dimension N by N +2. Thus, the S3-UKF filter has the advantage of requiring fewer executions of the 500 model.

[0080] The state matrix X contains, like the state vector x, assumptions about lithiation rates. A conversion step 507 can be applied to convert the lithiation rates into lithium concentration. This step 507 consists of applying a ClpOS îmax or Clnegmax.

[0081] Thus, several instances of the 500 model are executed in parallel (2N+1 for a UKF filter, N+2 for an S3-UKF filter).

[0082] The set of outputs of the model 500 obtained for all execution instances are provided as input to the correction step 503 which therefore determines a corrected state vector x from a voltage measurement Uceii, the virtual measurement of total quantity of lithium nLi and several sets of quantities estimated by the model (voltage and lithiation rate).

[0083] The Kalman filter is driven by a set of input parameters PAR and involves the calculation of several internal variables VAR calculated iteratively such as innovation, Kalman filter gain or state covariance matrix S which can be used as output.

[0084] The Kalman filter also produces an observation vector y at its output, which includes the estimated voltage. Optionally, the filter can also provide predictions of the electrical potential differences of the two electrodes: ddp*pos and ddp*neg.

[0085] One advantage of using a nonlinear Bayesian filter is to improve the accuracy of the lithiation rate estimates provided as input to the model in step 201 to calculate the maximum values ​​of current available over a given time horizon.

[0086] In the case where the 500 model used is an equivalent electrical circuit model, it can also be combined with a nonlinear Bayesian filter. In this case, the equivalent circuit model outputs an estimate of the cell's state of charge as well as an estimate of the voltage for each RC sub-circuit of the model. The state vector of the Bayesian filter then comprises a corrected estimate of the cell's state of charge as well as several corrected estimates of the voltage for each RC sub-circuit. The remainder of the operation described in [Fig. 5] is similar in the case of an equivalent circuit model.

[0087] Fig. 6 represents a diagram of a variant embodiment of the method described in Fig. 2 for cell operation under load.

[0088] The operating limits of the cell differ depending on whether it is operating during charging or discharging. During discharging, the voltage across the cell must not fall below a minimum value Umin. Conversely, during charging, the voltage across the cell must not exceed a maximum value Umax.

[0089] In addition, a second operating limit condition can be defined for the charging phase with respect to the electrical potential difference of the negative electrode ddpneg which cannot fall below a minimum value close to 0 in order to avoid the aging phenomenon known under the English term "lithium plating".

[0090] Thus, in the charging phase, the operating limit condition is defined by at least one or both of the limit values ​​of voltage and electrical potential difference.

[0091] When only the voltage value is used, the operation of the method for a cell under load is identical to the operation under discharge with the sole difference that the current deviation (step 602) of [Fig.6] is calculated between the estimated output voltage of the model and a maximum value Umax above which the cell can no longer operate under load without risk.

[0092] The PID control steps 604 and 605 and the current deviation calculation steps 606 and 607 are identical to steps 203,204 of [Fig.2].

[0093] When the value of the electrical potential difference is used in addition to the voltage value, the operation of the method is described in [Fig.6].

[0094] The 601 model produces at output an estimated voltage U across the cell terminals and an estimated electrical potential difference of the negative electrode of the cell ddpneg.

[0095] More specifically, two instances of the 601 model are run in parallel for two different input current values ​​IbI2. For each instance, the 601 model provides as output a pair of voltage and electrical potential difference values.

[0096] For the first instance, corresponding to the current Ib, only the voltage Ui is used at the output to calculate a voltage difference 602.

[0097] For the second instance, corresponding to the current I2, only the electrical potential difference ddpneg2 is used at the output to calculate a potential difference gap 603 between the value of electrical potential difference ddpneg2 and a minimum limit value which is a value close to 0, for example a positive value corresponding to a tolerance margin with respect to the zero value.

[0098] Optionally, a PID controller or regulator for "Proportional Integral Derivative" is applied in step 605 to this potential difference deviation.

[0099] In step 607, a current deviation corresponding to the potential difference deviation is then calculated from a characteristic curve of the cell dl=f(du). This curve depends on at least one parameter, including the initial voltage applied to the cell terminals, the age of the battery, and the battery temperature.

[0100] At the next iteration, the first current L supplied at the input of model 601 is corrected for the current deviation dh supplied at the output of step 606 and the second current I2 supplied at the input of model 601 is corrected for the current deviation dl2 supplied at the output of step 607.

[0101] The final maximum current value Imax to be applied to the cell to comply with the two cell operating limit conditions at the end of thorizon is determined in step 608 as being the minimum value between the two absolute current values ​​IbI2.

[0102] The variants for estimating lithiation rates described in Figures 3 and 5 apply identically to implement the method of [Fig.6].

[0103] In an alternative embodiment not shown in [Fig.6], additional limit operating conditions may be added in addition to voltage and electrical potential difference.

[0104] For example, an additional maximum temperature condition may be added in addition to or instead of the operating limit conditions in voltage and electrical potential difference.

[0105] In this case, the 601 model implements a prediction of future temperature values ​​based on a current assumption and a temperature measurement at the time considered. The iterative operation described for voltage and electrical potential difference predictions is identical for temperature; namely, at each iteration, a difference is calculated between the temperature estimate provided by the model and a maximum temperature value. This temperature difference is then used to determine a current difference from a cell characteristic. A PID controller can be used to filter the temperature difference.

[0106] To obtain the maximum power available over a given time horizon, an additional calculation step is performed by multiplying the maximum current value by a voltage value. This value is, for example, the last voltage prediction available at the end of the time horizon for the limiting condition, the current voltage measurement, the maximum voltage under load, or the minimum voltage under discharge.

[0107] The method according to the invention can be implemented as a computer program comprising instructions for its execution. The computer program can be stored on a storage medium readable by a processor. It can be executed by the PROC processing unit of a battery management device.

[0108] Although the invention has been described for estimating the maximum available power of a cell in a battery, it can be extended to estimate the same quantity for a group of cells in a similar way. References

[0109] [1] Doyle, M., Fuller, T. & Newman, J. (1993), Modeling of Galvanostatic Charge and Discharge of the Lithium / Polymer / Insertion Cell. Journal of The Electrochemical Society, Volume 140, Number 6, DOI 10.1149 / 1.2221597

[0110] [2] Li, W., Fan, Y., Ringbeck, F., Jôst, D., & Sauer, DU (2022). Unlocking electrochemical model-based online power prediction for lithium-ion batteries via Gaussian process regression. Applied Energy, 306, 118114. doi:10.1016 / j. apenergy.2021.118114 [OUI] [3] Papakonstantinou, K., Amir, M., & Warn, G. (2022). A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and équivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy. Mechanical Systems and Signal Processing, 163,107433.

[0112] [4] Plett, G.L. (2004). Extended Kalman filtering for battery management Systems of LiPB-based HEV battery packs. Part 3. State and parameter estimation. Journal of Power Sources, 134, 277-292. doi:10.1016 / j.jpowsour.2004.02.033

Claims

Demands

1. A method for estimating a maximum current value to be applied to a battery cell to achieve at least one operating boundary condition, the method comprising the iterative steps of: - Initializing a first estimate of the maximum current value to a predefined value assumption, - Executing (201,601) a first instance of a cell state prediction model to estimate a voltage value across the cell terminals obtained at the end of a given time horizon, from the temperature measurement and the first estimate of the maximum current value, - Calculating (202,602) a voltage difference between a voltage boundary value, corresponding to an operating boundary condition, and the predicted voltage value, - Calculating (204,606) a first current difference corresponding to said voltage difference, from a first characteristic curve of the cell, - At the next iteration,correct the first estimate of the maximum current value of said first current deviation.

2. Method of estimating a maximum current value according to claim 1 further comprising applying (203,604) a first Proportional Integral Derivative regulator to the voltage deviation before determining the first current deviation.

3. Method for estimating a maximum current value according to any one of claims 1 or 2 in which the battery is in a discharged state, the voltage limit value is a minimum value.

4. A method for estimating a maximum current value according to any one of claims 1 or 2, further comprising the steps of: - Initializing a second estimate of the maximum current value to a predefined value assumption, - Executing (601) a second instance of a cell operating model to estimate a value of the electrical potential difference of the negative electrode of the cell, from the temperature measurement, the estimation of the lithiation rate and the second estimated value of the maximum current, - Calculate (603) a difference in electrical potential difference between a limit value of electrical potential difference, corresponding to a limit condition of operation and the value of electrical potential difference, - Calculate (607) a second current difference corresponding to said difference in electrical potential difference, from a second characteristic curve of the cell, - At the next iteration, correct the second estimated value of the maximum current of said second current difference.

5. Method for estimating a maximum current value according to claim 4 further comprising applying (605) a second Proportional Integral Derivative regulator to the electrical potential difference deviation before determining the second current deviation.

6. Method for estimating a maximum current value according to any one of claims 4 or 5 wherein the battery is in a state of charge, the voltage limit value is a maximum value and the lower of the first estimated current value or the second estimated current value is retained (608).

7. Method for estimating a maximum current value according to any one of the preceding claims wherein the cell state prediction model is an equivalent electrical circuit model configured to estimate a cell charge state and several voltage estimates relative to each RC subcircuit of the model.

8. A method for estimating a maximum current value according to claim 7, further comprising the steps of: - Executing several instances of the cell state prediction model, the model acting as a state model of a nonlinear Bayesian filter, - Executing a correction step of the nonlinear Bayesian filter to predict a state vector comprising a prediction of a cell charge state and several voltage estimates for each RC subcircuit of the - Determine, from the outputs of the model executed for all instances, a state matrix comprising several modified vectors obtained by transformations of the state vector, - Provide each modified vector as input to the model at a subsequent iteration.

9. Method for estimating a maximum current value according to any one of claims 1 to 6 wherein the cell operating model is an electrochemical model, for example a Doyle-Fuller Newman model, which further receives as input an estimate of the lithiation rate of at least one electrode of the cell.

10. Method for estimating a maximum current value according to claim 9 wherein the electrochemical model receives as input a temperature measurement taken on the cell.

11. Method for estimating a maximum current value according to any one of claims 9 or 10 wherein the cell is provided with two electrodes, each electrode being spatially discretized according to a predefined spatial mesh, the estimation of the lithiation rate being provided for each electrode of the cell and each point of the spatial mesh.

12. Method for estimating a maximum current value according to claim 11 further comprising a step of receiving, at the given time, a measurement of the current applied to the cell and in which the estimation of the lithiation rate is obtained by means of the execution (205) of an instance of the cell state prediction model to estimate the lithiation rate from the current and temperature measurements.

13. A method for estimating a maximum current value according to claim 12, further comprising the steps of: - receiving, at the given time, a voltage measurement across the cell terminals, and wherein the estimation of the lithiation rates is obtained by means of performing the substeps of: i. Executing (500) several instances of the cell state prediction model to estimate The voltage across the cell and the lithiation rates of each electrode for each point of the spatial mesh are derived from current measurements, temperature measurements, and a prediction made at a previous iteration of the lithium concentration of each electrode. The model acts as a state-space model of a nonlinear Bayesian filter. ii. Execute (503) a nonlinear Bayesian filter correction step to predict a state vector including a prediction of the corrected lithiation rate for each point of the spatial mesh and for each electrode from the voltage measurement and the outputs of the model executed for all instances, iii. Determine (504), from the state vector, a state matrix comprising several modified vectors obtained by transformations of the state vector, iv. Provide each modified vector as input to the model at a subsequent iteration, v. Provide the state vector as an estimate of the lithiation rate.

14. Method for estimating a maximum current value according to claim 13 wherein the nonlinear Bayesian filter is a UKF or S3-UKF type Kalman filter.

15. Method for estimating a maximum current value according to any one of the preceding claims further comprising a step of calculating the maximum available power by multiplying the maximum current value by the voltage value estimated by the model at the end of said time horizon for said maximum current value.

16. Battery state of charge management (GES) device comprising a processing unit (PROC) configured to implement the steps of the method according to any one of the preceding claims.

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