A method for controlling a plurality of binary selectable components contributing cumulatively to an output quantity, in particular voltage, in a modular battery

Abstract

A control method for controlling a system comprising a plurality (N) of components, which can be selected in a binary fashion and called to contribute cumulatively together to an output quantity of the system, which is to match a setpoint quantity as optimally as possible, each selectable component (C k ) being put into use by a binary command u k , the method comprising repeating the following steps: - obtaining the setpoint quantity, - obtaining at least one state (SOC k ) of each selectable component, - determining a set of constraints to be respected, - determining a co-state using a Pontryagin maximum principle algorithm, with a Hamiltonian to be minimized, - determining a minimum of the Hamiltonian, while respecting the set of constraints, using a mixed-integer linear solver module, in order to obtain therefrom an optimal control vector u to be applied.

Description

[0001] The present invention relates to a control method for controlling multiple components that can be selected in a binary manner and contribute to the output of a modular battery, particularly, for example, voltage accumulation.

[0002] The output must follow a variable setpoint over time.

[0003] More specifically, the present invention relates to a method for controlling multiple electrochemical cell units that can be selected in a binary manner and contribute to the output voltage of such modular battery in an aggregate manner (in series arrangement).

[0004] The emphasis here is particularly on the fact that the batteries include switchable battery cells, which are sometimes referred to in the art by the acronym SWIBA (switchable battery).

[0005] Here, it is important to note that binary choice is not a continuous command. In fact, in possible control solutions, the command will jump between 0 and 1 over time, resulting in a discontinuous effect. Consequently, optimal computational solutions based on analytical calculations involving continuous or differentiable functions often cannot be directly used in this context.

[0006] When the number of components that can be selectively moved (correspondingly, battery cells / modules) becomes large, the number of possible combinations of choices rapidly becomes enormous, and the selection decision is no longer insignificant. In practice, if the number of components is N, the number of possible combinations evolves to 2^N. N If N > 20, the number of possible combinations exceeds one million, and if N is 32, the number of possible combinations exceeds one billion. At these scales, performing computations without involving at least one powerful computing unit is no longer reasonable, especially for real-time decision-making requirements.

[0007] A switchable battery (SWIBA, also known as a modular or configurable battery) is a battery that can change its output voltage based on whether certain battery cells in a set of available battery cells in the SWIBA are in use, and these battery cells are arranged in series.

[0008] In known embodiments, when a modular battery has a certain number of battery cells, each battery cell can be activated or deactivated. When the number of battery cells is 30 or more, it is common practice to use permutation-based decision rules, which are based on the past usage time of each battery cell or on the measured voltage or corresponding state of charge of these battery cells.

[0009] However, these rules do not take into account the actual observed state of each battery cell, such as early degradation of the battery cell.

[0010] In addition, analytical optimal control methods have been attempted, but these methods use real numbers and fail to produce good results if the results of the real numbers are rounded to integers (which is necessary for the incomplete or non-existent control of cell activation).

[0011] The inventors have sought to propose a computing solution that can be implemented on the microcontroller of an onboard computer in milliseconds or tens of milliseconds to enable the real-time execution of battery cell selection decision logic.

[0012] To address this, a control method is proposed for controlling a system comprising at least multiple components. These components can be selected and invoked in a binary manner to contribute cumulatively to the system's output. The system will then optimally match the output to the setpoint. Each selectable component is controlled via a binary command u. k Once put into use (that is, activated), the method includes a step of defining a time range, and the method is characterized in that it includes repeating the following steps in a first cycle: a) Obtain the setpoint value as the setpoint for this output value. b) Obtain at least one state for each selectable component. c) Determine a set of constraints to be followed, which in particular includes constraints that conform to the setpoint values ​​for the output. d) Use the Pontryagin maximum principle algorithm on this time range to determine the costate by constructing the Hamiltonian H. Here, it is represented as a vector ( The function Φ is a generalized cost function, which represents one or more cost functions to be minimized while adhering to this set of constraints. e) Use a mixed-integer linear parser module to determine the minimum of the Hamiltonian while adhering to the set of constraints, in order to obtain the optimal control vector. f) Apply this optimal control vector. g) Calculate the gradient of the costate of the Pontryagin maximum principle algorithm for use in subsequent iterations.

[0013] As a reminder, 'Pontryagin' is the name of a Russian scientist, also written as Понтрягин in technical documents.

[0014] With these provisions, software embodying the method can be implemented on an embedded computer microcontroller and can perform iterations of steps a) to g) in a reasonable time (i.e., typically less than 50 ms, preferably less than 10 ms) to achieve real-time execution.

[0015] It should be noted that the time frame discussed here is much larger than that of the first period. The time frame extends from time t... o (or '0') extends to time t f (or T). The time range is represented by the interval [0, T] within square brackets. For vehicles, this can be a driving cycle lasting tens or even hundreds of minutes, such as the driving cycle with the acronym WLTC, which lasts 30 minutes.

[0016] It will also be seen that, according to literature related to optimal control, a set of constraints to be followed can be written as a matrix relation (AX < b), where A is a matrix, X and b are vectors, and X represents a generalized state variable.

[0017] It should be noted that each selectable component can be in a serviced (i.e., 'invoked' or 'activated') state, or conversely, in a 'not invoked' or 'inactive' state. There is no possible intermediate state between 'activated' and 'inactive'. In other words, u k = 0 or u k = 1, and intermediate values ​​are impossible.

[0018] The Pontryagin maximum principle algorithm is known to have the acronym PMP, which will be used later in this document and in references in the technical field.

[0019] The Mixed Integer Linear Parser module is known to have the acronym MILP (Mixed Integer Linear Programming), which will be used later in this document and in reference documents in the technical field.

[0020] It should be noted that the number of selectable components N can be at least 10, at least 20, at least 30, and even greater than 30. As will be seen later, the benefits of using this method increase with the number N.

[0021] The phrase “to contribute cumulatively together” should be understood in a broad sense, which also includes “to contribute subtractively together”.

[0022] According to one aspect, the optional component is an electrochemical cell of a battery that includes switchable cell units, and the output is the voltage across the terminals of the cell, wherein the selected electrochemical cell units are arranged in series in the battery, which is designed to supply a setpoint voltage that varies over time.

[0023] Each battery cell is switchable in the sense that it is used in series with other battery cells when activated, and isolated and bypassed when not in use or deactivated. This binary selection corresponds to the representation u for battery cell k. k The command, k varies from 1 to N.

[0024] It provides a dual-switch or two logic-coupled switches for changing from an active state to an inactive state and vice versa.

[0025] Applying the optimal control vector u (u) 1 to u N This means that, for each battery cell, command u k Applied to the corresponding electrical switch T k .

[0026] On the one hand, static and non-static, or even dynamic, characteristics are assigned to each selectable component. Some characteristics can be known in advance and do not need to be measured or estimated in real time as a function of time. On the other hand, non-static characteristics must be continuously re-evaluated, that is, measured by sensors on the real system, or alternatively, acquired at the output of the dynamic behavior model.

[0027] According to one aspect, static characteristics include the nominal capacity (Qt) of a single battery cell. k ), and non-static characteristics include voltage (v) k ), State of charge (SoC) k ), capacity loss (Qloss) k ) and internal resistance (r) k ).

[0028] According to one aspect, regarding the Hamiltonian H, the generalized cost function Φ includes terms aimed at minimizing the sum of the resistances of the activated battery cells, terms aimed at minimizing the decrease in the state of charge of each battery cell and / or the entire battery, and terms aimed at minimizing the aging rate of each battery cell and / or the entire battery.

[0029] The weighting among the three criteria mentioned above can be performed using Lagrange multipliers, as is known in the technical field of optimal control computation.

[0030] It should be noted that other criteria to be minimized may be used, firstly for the case of batteries and secondly for the general case of systems that include multiple optional components.

[0031] According to one aspect, the Hamiltonian H is written as follows: in, It is the resistance of the battery cell with the order k. : is the costate associated with the state of charge of the battery cell, represented as q or SoC. : is the time derivative of the state of charge of the battery cell k. : is the costate associated with the capacity loss of the battery cell of order k. : is the time derivative of the capacity loss of the battery cell k. so QQ k It is the nominal capacity of the battery with sequence number k.

[0032] It should be understood that functions f1 and f2 can be arbitrary, and the examples given in the specification are by no means restrictive.

[0033] According to one aspect, the setpoint quantity Vreq and the output quantity Vout correspond to the following constraint form: and ,in, V min and V max It is the acceptable limit, that is to say, and , It is a parameterizable tolerance.

[0034] This expression for the constraint on the output allows for consideration of the discretization implied by the binary command and the use of selected battery cells in the incomplete-or-nothing mode.

[0035] The parameterization allows for adjustment of the desired accuracy and, consequently, the computation time required (the greater the tolerance applied, the faster the algorithm can execute).

[0036] In other words: According to one perspective, the first cycle is between 0.5 Hz and 4 Hz. As an example, the first cycle can be close to 1 Hz. For instance, the first cycle could correspond to repeating steps a) to g) once per second.

[0037] Therefore, this decision is repeated every second to determine which battery cells should participate in supplying the output voltage.

[0038] The computation time is on the order of milliseconds or tens of milliseconds; in automotive computer systems, it is typically less than 50 ms, which is standard in automotive applications.

[0039] The present invention also relates to a control system comprising: at least one battery, the at least one battery comprising switchable battery cells; and an electronic control unit in which the method described above is implemented.

[0040] The present invention also relates to a vehicle comprising: at least one battery comprising switchable battery cells; and an electronic control unit in which the method described above is implemented.

[0041] The invention will be described in more detail by way of description of non-limiting embodiments and based on the accompanying drawings, which illustrate variations of the invention, and in which: - [ Figure 1 This schematically illustrates an example of a battery structure comprising switchable battery cells connected in series, to which the method according to the invention can be advantageously applied; - [ Figure 2 This schematically illustrates an example of a generalized system with multiple components that can be selected in a binary manner, to which the method according to the invention is applicable; - [ Figure 3 This illustrates an example of a schematic flowchart in the context of applying the proposed method to batteries that include switchable battery cells; - [ Figure 4 This illustrates an example of a schematic flowchart in the context of applying the proposed method to a generalized system with multiple selectable components; - [ Figure 5 This shows an example of a functional block diagram of the method described. - [Figure 6] shows an example of a timing diagram illustrating the results obtained using the proposed method.

[0042] In the various figures, the same reference numerals denote the same or similar elements. For clarity of this disclosure, some elements are not necessarily shown to scale.

[0043] Figure 1 A battery is shown, comprising switchable battery cells and labeled 10. A battery comprising switchable battery cells is denoted as C. k It consists of multiple (N) battery cells, namely C1, C2, C3, up to C N .

[0044] Battery cell C k (k varies from 1 to N) They are usually arranged in series.

[0045] Each battery cell C k It is switchable in the sense that it can be used in series with other battery cells when activated. Conversely, each battery cell C k It can be isolated and bypassed when it is not in use and needs to be removed from the circuit.

[0046] For each battery cell, a representation T is provided. k An electrical switch that allows the activation or deactivation of the battery cell. For example, denoted as T... k Each electrical switch provides two contacts, that is, in Figure 1 The first contact of the bypass battery cell is shown vertically in the middle, and in Figure 1 The middle horizontal line shows another contact that connects the main branch to the positive terminal of the battery cell.

[0047] Another solution is to have two independent electrical switches driven by coupled logic. Only one switch (or only one contact) is closed at a time, and one of the switches (or contacts) is always closed at a given time.

[0048] Power transistors with low RDSon resistance can be used. The use of electromechanical relays is also not excluded.

[0049] By activating switch T k The binary selection performed corresponds to the representation u for cell k. k Logical commands.

[0050] Represented as (u1 to u) N ) or even simply for u The control vector corresponds to the electrical switch T for each battery cell. k The state, and as time progresses, that is, from time t... o As time tf evolves, this time interval (called the range) is represented as 'hor' in this presentation.

[0051] The output is the voltage at the battery terminals, denoted as Vout. It can be written as: Only activated battery cells contribute to establishing the output voltage.

[0052] The number of battery cells put into use at a given time is mc = .

[0053] In a specific example, the number of battery cells, N, is 36. Generally, N can be considered greater than 20, which makes the number of possible combinations particularly large and difficult to identify the optimal solution.

[0054] Each battery cell C k Its characteristic lies in its nominal capacity QQ k The nominal capacity is a static characteristic.

[0055] In addition, as is generally known, each battery cell k Its characteristic lies in its current voltage v k and its state-of-charge SoC k .

[0056] Non-static characteristics also primarily include capacity loss (referred to as Qloss). k (Therefore, the actual observed capacity is QQ) k -Qloss k ), and secondly includes r. k The internal resistance represents the health status (SoH) and / or the actual aging of the battery cells.

[0057] In non-static characteristics, the temperature of the individual battery cells can also be used.

[0058] Within the meaning of this disclosure, a battery cell can be a module consisting of multiple battery cells arranged in parallel and / or series.

[0059] In the examples shown, these are battery cells based on lithium-ion electrochemistry, but this method can be applied to the electrochemistry of any type of battery cell.

[0060] Figure 2 It demonstrates similarity in its structure and problems. Figure 1 However, unlike the configuration of modular batteries, according to the first example, each selectable component is a valve controlled in an incomplete-or-nothing mode, which allows fluid flow FL connected to the main fluid circuit. k In this main fluid loop, fluid flow is added to other fluid flows from other valves to provide a total outflow FL. tot Represented as u k The logical command represents the open or closed state of a valve in sequence k. Generally, the evolution of the command over time is represented as u. k (t), where t is from 0 to T (time range 'hor').

[0061] According to another configuration, it is still based on Figure 2Each optional component is an electronic switch. When the switch is in the ON state, the current flowing is allowed to be added to the current from other electronic switches (FL1, FL2, FL3, etc.), because the connection here is made in parallel with the current.

[0062] In all cases, there are optional components that contribute cumulatively to the supply output, which can generally be voltage or another property.

[0063] Generally, it should be noted that each selectable component is assigned static and non-static characteristics.

[0064] The setpoint variable Vreq and the output variable Vout correspond to the following constraint form: and in, and , It is the result of the mandatory discretization implied by the binary command, which allows for deviation. It can be parameterized and / or calibrated.

[0065] Optimization Standards .

[0066] To optimize the overall use of individual battery cells, the goal is to minimize the reduction in state of charge during the power consumption phase and maximize the increase in state of charge during the charging phase, both for individual battery cells and for the entire battery system.

[0067] Let us write in, It refers to the state of charge of battery cell k. It is the time derivative of the charged state. = The current flowing in the main branch of the battery (the same for all battery cells in use). = Nominal capacity of battery cells in order k It is a binary command as defined above. It is a specific function of the load dynamic characteristics of a single battery cell. An example of function f1 is given at the end of the specification.

[0068] They also sought to minimize the sum of the internal resistances of all the battery cells in use.

[0069] This is written using the following formula.

[0070] Where, r k It is the internal resistance of the battery cell k. R It is the total resistance seen at the battery terminals.

[0071] You can also try to use the battery cells with the highest nominal capacity to the maximum extent.

[0072] We also seek to minimize the aging effects of each individual battery cell. This is expressed by the following formula.

[0073] It is a specific function of the aging dynamic characteristics of a single battery cell.

[0074] As defined above.

[0075] An example of function f2 is given at the end of the manual.

[0076] Given the above, the Hamiltonian H to be minimized will be a term that minimizes the sum of the resistances of the activated battery cells, a term that minimizes the state of charge degradation of each battery cell and / or the entire battery, and a term that minimizes the aging rate of each battery cell and / or the entire battery.

[0077] The above three criteria are weighted using Lagrange multipliers.

[0078] The Hamiltonian H can be written as follows: Advantageously, it should be noted that the Hamiltonian expression for u k It is linear, and therefore u k It can be factored.

[0079] Then, a generalized cost function denoted by Φ is defined, representing one or more cost functions to be minimized. The generalized cost function Φ is represented as a vector ( ) Therefore, the Hamiltonian H is written in vector form. H = ,in, It is the transpose of vector Φ, and u This represents the control vector.

[0080] Logic used to determine optimal control Advantageously, according to the invention, the costate (λ) is determined using Pontryagin's maximum principle (PMP) logic over the time range [0,T], utilizing the Hamiltonian H defined above. k μ k And the minimum value of the Hamiltonian is determined using the Mixed Integer Linear Parser Module (MILP).

[0081] It should be noted that the Pontryagin principle, in its title, involves the search for a maximum value, but if the mathematical formula is adapted to the situation under discussion, it is certainly valid for the search for a minimum value. Here, we seek the minimum value of the Hamiltonian.

[0082] One class of optimization problems involves determining the extrema of a function, that is, a function of a function. Here, the goal is to identify the extrema of the control function u on the range [0,T]. k The extreme values ​​of (t). k This is the system input, also known as a command. A key characteristic to note here is that the command uses a binary value.

[0083] The generalized state variables are: , , , ,in, = = The state of charge of a single battery cell. Typically, the state variable is represented by x.

[0084] The Pontryagin extremum condition corresponds to the condition of the partial differential equation, as is known in this art and therefore will not be described in detail here.

[0085] Readers may refer to Michael Ross’s “A Primer on Pontryagin’s Principle in Optimal Control”, ISBN 978-0984357116.

[0086] Pontryagin's proposed solution uses comorphism.

[0087] In this formula, the costates discussed are vectors λ and μ, also written as λ k and μ k , where k varies from 1 to N.

[0088] exist Figure 3 The costate in question is initialized in step 12 of the flowchart. After each new computational loop, the costate is updated, as follows: Figure 3As shown in box 19.

[0089] exist Figure 3 In step 11 of the flowchart, the control unit acquires the voltage setpoint Vreq over the entire prediction range to allow for costate initialization.

[0090] exist Figure 3 In step 13 of the flowchart, the control unit acquires the voltage setpoint and current setpoint at each sampling time t. The control unit also acquires the voltage v across its terminals and its state of charge q for each battery cell.

[0091] exist Figure 3 In step 14 of the flowchart, the control unit acquires the internal resistance r and capacity loss Qloss for each battery cell at each sampling time t.

[0092] exist Figure 3 In step 15 of the flowchart, control unit 1 calculates the generalized cost function Φ.

[0093] exist Figure 3 In step 16 of the flowchart, the control unit calculates the lower and upper limits of the target range of the output voltage Vout.

[0094] exist Figure 3 In step 17 of the flowchart, the control unit calculates a set of constraints in the form of a matrix equation of type Ax < b.

[0095] exist Figure 3 In step 18 of the flowchart, the control unit runs the mixed integer linear parser module.

[0096] For the mixed-integer linear parser module, you can choose the one in Matlab™. intlinprog The ()™ function. Alternatively, open-source solutions called “Branch&Bond”™ or “Simplex”™ can be chosen, without excluding other equivalent solutions.

[0097] It should be noted that sensors can be used to acquire the state of the system; that is, physical measurements can be performed on the battery or system in question. According to an alternative approach, certain states of the system can be acquired by reading the output of a behavioral model that mathematically reproduces the system's behavior based on other state information and / or using the system's behavioral equations.

[0098] Move to Figure 4 The figure shows Figure 3 The principle described herein is a generalization, and the setpoint quantity Vreq obtained in step 11 can be voltage, flow rate, or current, without any restrictions on its properties.

[0099] about Figure 3 All comments made can be applied after making the necessary modifications. Figure 4 A generalized state is represented by the letter x. The function f represents the time derivative of each state.

[0100] The state of the system is measured or obtained from the behavioral model. It should be noted that the costate λ can be an entity with multiple dimensions, specifically a vector with n dimensions, the number of which equals the number of state variables to be considered.

[0101] The function g represents the cost function to be minimized. The command u is a vector of binary values, which forms a noteworthy feature of the method presented here.

[0102] exist Figure 5 In this system, control unit 1 receives voltage setpoint Vreg and current setpoint Ireg at its input terminal.

[0103] Control unit 1 calculates the optimal command u k And then transfer it to battery 10.

[0104] command u k The switch T applied to the battery cell of battery 10 k In the example shown, battery 10 delivers output voltage Vout and current Iout to motor 2 via an inverter, where appropriate.

[0105] Control unit 1 receives the battery status v k q k r k .

[0106] Control unit 1 includes a parameter library or calibration table. This specifically contains the nominal capacity (QQ) of each battery cell. k And the definitions of the behavioral modeling functions f1 and f2.

[0107] The calibration table may also include the parameters discussed above. .

[0108] The feedback of the costate is represented by λ. k and μ k These are updated in each iteration.

[0109] In the timing diagram of Figure 6, the upper part (labeled 6A) shows the evolution of the setpoint voltage along with the output voltage Vout over time, as well as the evolution of the current Iout delivered by the battery over time.

[0110] The portion directly below (marked 6B) represents the evolution of the battery's total apparent resistance R.

[0111] The section below (marked as 6C) indicates the evolution of the state of charge and the number of battery cells in use, mc.

[0112] The bottom part of Figure 6 (labeled 6D) shows the evolution of the activation state of each of the N = 36 battery cells over time.

[0113] The dotted line at the midpoint of the current curve (partial 6A) represents zero current (i = 0). Positive current corresponds to the current leaving the battery, and negative current corresponds to the regeneration phase with current entering the battery. At time t1, the current moves from the positive domain to the negative domain, and it should be noted that the SoC curve reaches its minimum at this time. Later, at time t2, the current moves from the negative domain back to the positive domain, and it should be noted that the SoC curve reaches its peak at this time.

[0114] According to a non-limiting example, the voltage across the terminals of each battery cell can be between 5 volts and 25 volts, preferably between 10 volts and 16 volts.

[0115] Benefits and Applications Advantageously, the proposed method leads to the equilibrium of the state of charge over time, even from the state of charge Soc k This is also true when starting with a large difference between individual battery cells. According to this method, this balancing is natural and does not require invoking any specific permutation or prioritization logic.

[0116] This principle applies regardless of the quantity N, as the number of data points increases. The computational difficulty is related to the quantity N. 2 This increases proportionally, which is far lower than according to 2. N The general number of possible combinations that can be increased.

[0117] Therefore, applications with N greater than 50 (e.g., N equals 100) or even larger can be foreseen.

[0118] The input quantity can be the electrical power to be delivered, not just the voltage. In this case, the optimization mechanism will also determine pairs of u and i corresponding to the setpoint power to be delivered.

[0119] Example of function f1 For F1, you can choose: Example of function f2 For f2, you can choose: Typically between [0.001 and 0.05]. .

Claims

1. A control method for controlling a system comprising at least a plurality of components, wherein the components can be selected and invoked in a binary manner to contribute cumulatively to the output of the system, the system thereby achieving optimal matching of the output with a setpoint. Each selectable component (C) k ) via binary command u k The method, which is put into use, includes a step of defining a time range, and is characterized in that it includes repeating the following steps in a first cycle: a) Obtain the set point quantity (v) req ) is used as the setpoint for the output quantity (v). b) Obtain at least one state (q) for each selectable component. k SOC k ), c) Determine a set of constraints to be followed (AX < b), which in particular includes constraints that conform to the setpoint quantity for the output. d) Use the Pontryagin maximum principle (PMP) algorithm on this time range to determine the costate (λ) by constructing the Hamiltonian H. k μ k ), in, Represented as a vector ( The function Φ is a generalized cost function, which represents one or more cost functions to be minimized while adhering to this set of constraints. e) Use a Mixed Integer Linear Parser (MILP) module to determine the minimum of the Hamiltonian while adhering to the set of constraints, in order to obtain the optimal control vector u. (u) 1 to u N ), f) Apply the optimal control vector u , g) Calculate the gradient of the costate of the Pontryagin maximum principle algorithm for use in subsequent iterations.

2. The method as described in claim 1, characterized in that, These optional components are electrochemical cell units of a battery that include switchable cell units, and the output is the voltage across the terminals of the cell, with the selected electrochemical cell units arranged in series in the cell, which is designed to supply a setpoint voltage that varies over time.

3. The method according to any one of claims 1 and 2, characterized in that, Each selectable component is assigned static and non-static properties.

4. The method of claim 3 when subordinate to claim 2, wherein, These static characteristics include the nominal capacity (Q) of the battery cell. k ), and these non-static characteristics include voltage (v) k ), State of charge (SoC) k ), capacity loss (Qloss) k ) and internal resistance (r) k ).

5. The method of claim 4, wherein, Regarding the Hamiltonian H, the generalized cost function Φ includes terms aimed at minimizing the sum of the resistances of the activated battery cells, terms aimed at minimizing the decrease in the state of charge of each battery cell and / or the entire battery, and terms aimed at minimizing the aging rate of each battery cell and / or the entire battery.

6. The method of claim 5, wherein, The Hamiltonian H is written as follows: in, It is the resistance of the battery cell with the order k. : is the costate associated with the state of charge of the battery cell, represented as q or SoC. : is the time derivative of the state of charge of the battery cell k. : is the costate associated with the capacity loss of the battery cell of order k. : is the time derivative of the capacity loss of the battery cell k. QQ k The nominal capacity of the battery in order k is... so .

7. The method according to any one of claims 1 to 6, wherein, The setpoint value Vreq and the output value Vout correspond to the constraint form written as follows: and in, V min and V max It is the acceptable limit, that is to say, and , It is a parameterizable tolerance.

8. The method according to any one of claims 1 to 7, wherein, The first cycle is between 0.5 Hz and 4 Hz.

9. A control system comprising: At least one battery, the at least one battery comprising a switchable battery cell; and an electronic control unit (1) in which the method as described in any one of claims 1 to 8 is implemented.

10. A vehicle comprising: At least one battery, the at least one battery comprising a switchable battery cell; and an electronic control unit (1) in which the method as described in any one of claims 1 to 8 is implemented.

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