Method for controlling a plurality of binary-selectable members that additively contribute to an output quantity, in particular a voltage in a modular electric battery

Abstract

The invention relates to a control method for controlling a system comprising a plurality of N binary-selectable members, solicited in order to contribute together additively to an output quantity, which the system must make coincide as closely as possible with a setpoint quantity, wherein each selectable member (Ck) is activated by a binary control command uk, the method comprising repetition of the steps of: - acquiring a setpoint quantity; - acquiring at least one state (SOCk) of each selectable member; - determining a set of constraints to be complied with; - using a Pontryagin maximum principle algorithm to determine adjoint states with a Hamiltonian quantity to be minimised; - using a mixed-integer linear programming solver module to determine a minimum of the Hamiltonian quantity while complying with the set of constraints, in order to deduce therefrom an optimal control vector u* to be applied.

Description

[0001] DESCRIPTION

[0002] Method for controlling a plurality of selectable components in a binary manner and contributing additively to an output quantity, in particular a voltage in a modulating electric battery

[0003]

[0001] The present invention relates to a control method for controlling a plurality of selectable organs in a binary manner and contributing additively to an output quantity, in particular for example a voltage in a modulating electric battery.

[0004]

[0002] The output quantity must follow an evolving setpoint over time.

[0005] More specifically, the present invention relates to a control method for controlling a plurality of electrochemical cells of an electric battery, selected in a binary manner and contributing additively (series arrangement) to an output voltage of such a modulating electric battery.

[0006] We are particularly interested here in electric batteries with switchable cells, sometimes referred to in the industry by the acronym SWIBA (for Switched Battery).

[0007]

[0005] It is important to note here that binary selection is not a continuous control. Indeed, in the possible control solutions, over time there will be jumps between 0 and 1 with a discontinuous effect. It generally follows that optimal computational solutions based on analytical calculations involving continuous or differentiable functions will not be directly usable in the present context.

[0008]

[0006] When the number of selectively mobilizable organs (respectively, battery cells / modules) becomes large, the selection combinatorics quickly become very broad, and the selection decision is no longer trivial. In practice, if the number of organs is N, the combinatorics evolve as 2 NIf N > 20, the number of possible combinations already exceeds one million, and if N equals 32, the number of possible combinations exceeds one billion. At these scales, it is no longer reasonable to perform calculations without involving at least one powerful computing unit, especially for real-time decision-making.

[0007] A SWIBA switchable battery, i.e., modular or configurable, is a battery that can vary its output voltage depending on whether certain cells from the set of cells available in the SWIBA battery are activated, the cells being arranged in a series configuration.In known implementations, when a modular battery has a number of cells that can each be activated or not, with a number of cells of 30 or more, it is usual to use decision rules based on permutations based on the previous usage time of each of the cells or on the measured voltages or respective states of charge of these cells.

[0009]

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

[0010]

[0010] Furthermore, attempts have also been made to apply optimal analytical control methods, but these methods use real numbers and do not give good results if one tries to round the results of the real numbers to integers as is necessary for the on / off control of cell activation.

[0011]

[0011] The inventors sought to propose a computational solution that could be implemented on a microcontroller of an embedded computer in a time of a few milliseconds or a few tens of milliseconds, in order to be able to run in real time the decision logic for selecting the battery cells.

[0012] To this end, a control method is proposed for controlling a system comprising at least a plurality of binary selectable components, each activated to contribute additively to an output quantity, which the system must make coincide as closely as possible with a setpoint quantity, each selectable component being activated (i.e.activated) by a binary command Uk, the process comprising a step of defining a time horizon, and the process being characterized in that it comprises, according to a first periodicity, a repetition of the steps: a) acquire a setpoint quantity as a setpoint for the output quantity, b) acquire at least one state of each selectable organ, c) determine a set of constraints to be respected, including in particular a constraint of respecting the setpoint quantity for the output quantity, d) use an algorithm of the Pontryagin Maximum Principle type on the time horizon to determine adjoint states with a formulation of a Hamiltonian quantity H,. where the function <t>, expressed as a vector ((p1, (p2, .., (p k , .., (p N ) is a generalized cost function representing one or more cost function(s) to be minimized and compliance with the set of constraints, e) use a linear integer mixed solver module to determine a minimum of the Hamiltonian quantity while respecting the set of constraints, to deduce an optimal control vector, f) apply the optimal control vector, g) calculate gradients of the adjoint states of the Pontryagin Maximum Principle type algorithm for the next iteration.

[0013]

[0013] For the record, 'Pontryagin' is the name of a Russian scientist also written in technical literature as Pontryagin or noHTpsirMH.

[0014] Thanks to these provisions, the software embodying said process can be implemented on an embedded computer microcontroller and can perform an iteration of steps a) to g) in a reasonable time for real-time execution, namely typically less than 50 ms, preferably less than 10 ms.

[0015]

[0015] It should be noted that the time horizon in question here is much greater than the first periodicity. The time horizon extends from a moment t o (or '0') at a time tf (or T). The time horizon is noted by the interval between brackets [0,T]. For a vehicle, this can be a driving cycle that lasts several tens of minutes or even a few hundred minutes, for example the driving cycle with the acronym WLTC, which lasts 30 minutes.

[0016]

[0016] We will also see that the set of constraints to be respected can be written, in line with the literature relating to optimal control, by a matrix relation (AX < b), A being a matrix, X and b being vectors, X representing the generalized state variables.

[0017] We observe that each selectable component can be in an operational state (i.e., 'activated' or 'sought') or, conversely, in an 'unactivated' or 'non-activated' state. There is no possible intermediate state between the activated and non-activated states. In other words, we have Uk=0 or Uk=1, and intermediate values ​​are not possible.

[0017] The Pontryagin Maximum Principle type algorithm is known by the acronym PMP used later in this document, and in technical field reference documents.

[0018]

[0019] The mixed-integer linear resolver module is known by the acronym MILP (from the English Mixed-Integer Linear Programming) used later in this document and in technical field reference documents.

[0019]

[0020] It should be noted that the number N of selected organs can be at least equal to 10, or at least equal to 20, or even at least equal to 30, and even greater than 30. We will see later that the interest in using the present process increases with the number N.

[0020]

[0021] The phrase "contributing together in an additive manner" should be understood broadly, as it also covers "contributing together in a subtractive manner".

[0021] According to one aspect, the selected elements are electrochemical cells of a switchable-cell battery, and the output quantity is a voltage across the battery. The selected electrochemical cells are arranged in series in the battery, which is designed to provide a time-varying setpoint voltage. Each cell is switchable in the sense that it is activated, in series with the others, when activated, and it is isolated and bypassed when it is not activated or deactivated. This binary selection corresponds to a command denoted Uk for cell k, where k ranges from 1 to N.

[0022] A double electrical switch, or two logically coupled electrical switches, is planned to switch from the activated state to the inactivated state and vice versa.

[0023]

[0025] Applying the optimal control vector u* (u* to U*N) means that for each cell, the control Uk is applied to the corresponding electrical switch Tk. In one aspect, each selectable element is affected by static and non-static, or even dynamic, characteristics. Some characteristics can be known in advance and do not need to be measured or estimated in real time. In contrast, the non-static characteristics must be continuously re-evaluated, i.e., measured by sensors on the actual system or alternatively extracted from the output of a dynamic behavioral model.

[0024] According to one aspect, static characteristics include the nominal cell capacity (QQk) and non-static characteristics include the voltage (v k ), the state of charge (SoCk), the capacitance loss (Qlossk), the internal resistance (r k ). According to one aspect, concerning the Hamiltonian quantity H, the generalized cost function <t>includes a term that aims to minimize a sum of the resistances of the activated cells, a term that aims to minimize a drop in the state of charge of each cell and / or the complete battery, a term that aims to minimize an aging rate of each cell and / or the complete battery.

[0025] The weighting of the three criteria mentioned above can be done using Lagrange multipliers, as is known in the technical field of optimal control calculations. It should be noted that it is possible to use other criteria to be minimized, both for the case of a battery and for the general case of a system with multiple selectable components.

[0026] According to one aspect, the Hamiltonian quantity H can be written as follows: with r k : electrical resistance of the k-rank cell,

[0027] HAS k : adjoint state associated with the cell's charge state, denoted q or SoC, q k : time derivative of the cell's charge state k =

[0028] H k : adjoint state associated with the loss of capacity of the cell of rank k

[0029] Qloss k : time derivative of the cell capacity loss k = f2(i, Qloss) k ). u k SO QQk is the nominal capacity of the k-rank battery.

[0030]

[0033] It should be understood that the functions fi and f2 can be arbitrary; the example given in the description is in no way limiting.

[0031] According to one aspect, the setpoint quantity Vreq and the output quantity Vout conform to a constraint formalism written as follows:

[0032] V out > V min and V out < V max with V out = î 1 u k . v k

[0033]

[0035] Vmin and Vmax being acceptable limits, i.e.

[0034] AV accU racy being a configurable tolerated deviation.

[0035]

[0036] This expression of the constraint on the output quantity allows us to take into account the discretization involved by the binary control and the on / off mode activation of the selected cells.

[0036]

[0037] AV settings accuracy allows you to adjust the desired precision and therefore the computation time that will be used (the more tolerant you are, the faster the algorithm can be executed). Vreq "h AV accuraC y

[0037]

[0039] According to one aspect, the first periodicity is between 0.5 Hz and 4 Hz. According to another example, the first periodicity may be close to 1 Hz. For example, the first periodicity may correspond to a recurrence of steps a) to g) every second.

[0038]

[0040] Thus, the decision is repeated every second, to determine which cells should be involved in supplying the output voltage.

[0039]

[0041] The calculation time is on the order of a few milliseconds or a few tens of milliseconds; on a standard embedded serial computer, used in automotive applications, it is generally less than 50 ms.

[0040] The present invention also relates to a control system comprising at least one switchable-cell electric battery and an electronic control unit in which the method as described above is implemented.

[0043] The present invention also relates to a vehicle comprising at least one switchable-cell electric battery and an electronic control unit in which the method as described above is implemented.

[0041] The invention will be further detailed by describing non-limiting embodiments, and based on the accompanying figures illustrating variants of the invention, in which:

[0042] - [Fig. 1] schematically illustrates an example of the structure of a series-switchable cell battery, for which the method according to the present invention can be advantageously applied;

[0043] - [Fig. 2] schematically illustrates an example of a generalized system with a plurality of organs selected in a binary manner, for which the method according to the present invention can be applied;

[0044] - [Fig. 3] illustrates an example of a schematic logic diagram in the context of the application of the proposed process to a switchable cell battery;

[0045] - [Fig. 4] illustrates an example of a schematic logic diagram in the context of applying the proposed process to a generalized system with a plurality of selected organs;

[0046] - [Fig. 5] illustrates an example of a functional block diagram of the promoted process;

[0047] - [Fig. 6] shows an example of chronograms illustrating a result obtained with the proposed method.

[0048]

[0045] In the various figures, the same reference numerals designate identical or similar elements. For the sake of clarity, some elements are not necessarily shown to scale.

[0049] As seen in Figure 1, a switchable cell battery, labeled 10, has been represented. The switchable cell battery is composed of a plurality of N cells denoted Ck, namely Ci, C2, C3, up to CN.

[0050]

[0047] The Ck cells, k varying from 1 to N, are generally arranged in series mode.

[0051] Each cell Ck is switchable in the sense that it can be activated, in series with the others, when it is enabled. Conversely, each cell Ck can be isolated and bypassed when it should not be activated and must be excluded from the circuit.

[0052] Each cell is equipped with an electrical switch, labeled Tk, which activates or deactivates the cell. Each electrical switch, labeled Tk, has a double contact: a first contact that bypasses the cell (shown vertically in Figure 1) and another contact (shown horizontally in Figure 1) that connects the main branch to the positive terminal of the cell.

[0053]

[0050] Another solution is to have two independent electrical switches controlled according to coupled logic. Only one switch (or one contact) is closed at a time, and there is always one of the switches (or contacts) that is closed at any given time.

[0054] Low-resistance power transistors (RDSon) can be used. The use of electromechanical relays is also a possibility.

[0055]

[0052] Binary selection by activation of switch Tk corresponds to a logical command denoted Uk for cell k.

[0056] The control vector noted Ü (ui to UN) OR even simply u corresponds to the state of the electrical switch Tk corresponding to each cell, it evolves over time, from the instant t0 to the instant tf, a time interval which is called the horizon noted 'hor' in this presentation.

[0057] The output quantity is a voltage across the terminals of the electric battery, denoted Vout. We can write: V out = ,i U k . v k

[0058] Only activated cells contribute to establishing the output voltage.

[0059] The number of cells involved at any given time is me u k .

[0060] In one particular example, the number of cells N is 36. In general, we can consider that N is greater than 20, which makes the combinatorial possibilities particularly wide and the optimal solution difficult to identify.

[0061]

[0058] Each cell Ck is characterized by its nominal capacity QQk, which is a static characteristic.

[0062] Furthermore, as is generally known, each cell Ck is characterized by its current voltage Vk and by its state of charge SoCk.

[0063] Among the non-static characteristics, we will also find on the one hand the loss of capacity noted Qlossk, (the actual capacity observed is therefore QQk - Qlossk) and on the other hand the internal resistance noted Ck, representative of the state of health SoH and / or in practice of the aging of the cell.

[0064] Among the non-static characteristics, the cell temperature can also be used.

[0062] For the purposes of this disclosure, a cell can be a module of several unit cells arranged in parallel and / or in series.

[0065] In the illustrated example, the cells are based on lithium-ion electrochemistry, but the process can be applied to any type of battery cell electrochemistry. Figure 2 illustrates a configuration similar in structure and problem to Figure 1, but which differs from a modular battery. According to a first example, each selectable component is an on / off controlled valve that can allow a fluid flow FLk to flow into a main fluid circuit where it combines with the other fluid flows from the other valves to give the total outgoing flow FLtot. The logical control denoted Uk represents the open or closed state of the kth valve. Generally, the evolution of the control over time is denoted Uk(t) for t from 0 to T (time horizon 'hor').

[0066]

[0065] According to another configuration, still based on Figure 2, each selectable element is an electronic switch. The current that the switch allows to pass when it is conducting is added to the currents (FL1 FL2 FL3 etc.) that come from the other electrical switches, because the connection is made in parallel with regard to the current.

[0067] In all cases, we have selectable organs which contribute additively to providing an output quantity which can be an electrical voltage or of another nature in the generalized case.

[0068] In general, it is observed that each selectable organ is affected by static and non-static characteristics.

[0069] The setpoint quantity Vreq and the output quantity Vout conform to a constraint formalism written as follows:

[0070] Worth — V m t n and V O ut — nax V accuracy is a tolerated deviation, a consequence of the mandatory discretization implied by the binary command. V accuracy is configurable and / or calibrable.

[0071]

[0070] Optimization criteria.

[0072]

[0071] To optimize the overall use of the cells, we seek to minimize the decrease in the state of charge during consumption phases, or to maximize the increase in the state of charge during the charging phase, cell by cell and also globally for the complete battery.

[0073] We ask with q k : state of charge of cell k, q k : time derivative of the state of charge i = current flowing in the main branch of the battery, (the same for all cells involved),

[0074] QQ k = nominal capacity of the cell of rank ku k binary command as defined previously

[0075] = specific function of the cell's load dynamics

[0076] An example of the fi function is given at the end of the description.

[0077]

[0073] Furthermore, we seek to minimize the sum of the internal resistances of all the cells involved.

[0078] This is written using the following formulas.

[0079] R = ' ï r k . u k )

[0080]

[0076] with Tk being the internal resistance of the cell k

[0081]

[0077] R is the total resistance seen across the battery terminals.

[0082] It is also possible to try to maximize the use of cells with the highest nominal capacities. to minimize the aging effects on each cell. This can be expressed using the following formulas. cell aging process. k as defined previously.

[0083] An example of the function f2 is given at the end of the description.

[0084] In light of the above, the Hamiltonian quantity H that we seek to minimize therefore involves a term that aims to minimize the sum of the resistances of the activated cells, a term that aims to minimize the decrease in the state of charge of each cell and / or the complete battery, and a term that aims to minimize the aging rate of each cell and / or the complete battery.

[0087] The three criteria above are weighted using Lagrange multipliers.

[0085] The Hamiltonian quantity H can be written as follows:

[0086]

[0090] Advantageously, we note that the expression of the Hamiltonian is linear in Uk and therefore we can factor Uk.

[0087] We then define a generalized cost function denoted <t>which is representative of one or more cost functions to be minimized. The generalized cost function <t>is expressed as a vector ( 1( (p2, (p k , .., (p N )

[0088] The Hamiltonian quantity H can therefore be written in vector form being the transpose of the vector <t>and u denoting the control vector.

[0089] Logic for determining the optimal order

[0090] Advantageously according to the present invention, a Pontryagin Maximum Principle (PMP) logic is used on the time horizon [0,T] to determine adjoint states (Àk.pk) with a Hamiltonian quantity H defined above and a mixed integer linear resolver module (MILP) to determine the minimum of the Hamiltonian quantity.

[0091]

[0097] Note that Pontryagin's principle, as its title states, concerns the search for a maximum, but it is of course also valid for finding a minimum, provided that the mathematical formulas have been adapted to the specific case. Here, we are looking for a minimum of the Hamiltonian quantity.

[0092] One class of optimization problems concerns determining the extrema of functionals, that is, functions of functions. Here, we seek to identify the extrema with respect to the control function Uk(t) on the horizon [0, T]. Uk is the system input, also called the control. The peculiarity here is that the control takes binary values.

[0093] The generalized state variables are: q k , q k Qloss k , Ql ss k , with q k = SoC = state of charge of the cell. Genericly, state variables are denoted x.

[0100] Pontryagin's extrema conditions correspond to conditions on partial differential equations as is known in the technical field, therefore not described in detail here.

[0094] The reader may consult Michael Ross's reference work "A Primer on Pontryagin's Principle in Optimal Control" ISBN 978-0984357116.

[0095] The solution proposed by Pontryagin uses adjunct states called "co-states" in the literature.

[0096]

[0103] In the present formulas, the adjoint states in question are the vectors A and p, also written Ak and pk with k varying from 1 to N.

[0097] The adjoint states in question are initialized in step 12 of the logic diagram in Figure 3. After each new computation cycle, the adjoint states are updated as symbolized by frame 19 in Figure 3.

[0098]

[0105] At step 11 of the logic diagram in Figure 3, the control unit acquires the voltage setpoint Vreq over the entire prediction horizon to allow the initialization of co-states (adjoint states).

[0099]

[0106] In step 13 of the logic diagram in Figure 3, the control unit acquires the voltage and current setpoints at each sampling instant t. The control unit also acquires for each cell its terminal voltage v and its state of charge q.

[0100]

[0107] At step 14 of the logic diagram in Figure 3, the control unit acquires, at each sampling instant t, for each cell the internal resistance r and the capacitance loss Qloss.

[0101] In step 15 of the flowchart in Figure 3, control unit 1 performs the calculation of the generalized cost function. <t>.

[0102]

[0109] At step 16 of the logic diagram in Figure 3, the control unit calculates the lower and upper bounds of the target range for the output voltage Vout.

[0103] At step 17 of the logic diagram in Figure 3, the control unit calculates all the constraints in the form of a matrix equation, of the type Ax < b.

[0104] At step 18 of the logic diagram in Figure 3, the control unit runs the linear integer mixed resolver module.

[0105] Regarding the mixed integer linear resolver module, the intlinprog() function in Matlab can be chosen. Alternatively, open-source solutions such as "Branch&Bond" or "Simplex" can also be used, without excluding other equivalent solutions.

[0106] It is noted that system state acquisition can be performed using sensors, i.e., by taking physical measurements on the battery or the system under consideration. Alternatively, certain system states can be acquired by reading the outputs of a behavioral model that mathematically reproduces the system's behavior based on other state information, and / or using behavioral equations for the system.

[0107] Looking at figure 4, we find a generalization of the principle shown in figure 3, the setpoint quantity Vreq acquired in step 11, can be a voltage, a flux, a current without limit of nature.

[0108] All comments made about Figure 3 can be applied, mutatis mutandis, to Figure 4. The generalized states are identified by the letter x. The function f characterizes the time derivatives of each state.

[0109] The system states are measured or retrieved from behavioral models. Note that the adjoint state A can be a multidimensional entity, in particular a vector of dimension n, equal to the number of state variables to be considered.

[0110] The function g represents a cost function to be minimized. The command u is a vector of binary values, which is what makes the method presented here unique.

[0111] In figure 5, the control unit 1 receives as input the voltage and current setpoints respectively Vreg and Ireg.

[0112] The control unit 1 calculates the optimal command u and transmits it to the battery 10.

[0113]

[0120] The u commands are applied to the Tk switches of the battery cells 10. As an illustrated example, the battery 10 delivers an output voltage Vout and a current lout to an electrical machine 2, optionally via an inverter.

[0114] Control unit 1 receives the battery states Vk, qk, rk.

[0115] The control unit 1 includes a parameter database or calibration tables. This includes, in particular, the nominal capacity of each cell QQk, and the definition of the behavioral modeling functions f1 and f2.

[0116]

[0123] Calibration tables may also include the parameter Al^ ccuracy discussed above.

[0117] Note the looping concerning the adjoint states Àk and juk-, which are updated at each iteration.

[0118]

[0125] On the timing diagrams in Figure 6, the upper portion marked 6A shows the evolution over time of the setpoint voltage as well as the output voltage Vout and the evolution over time of the current lout delivered by the battery.

[0119]

[0126] The portion located just below, marked 6B, represents the evolution of the total apparent resistance R of the battery.

[0120]

[0127] The portion located below, marked 6C, represents the evolution of the state of charge as well as the number of cells involved.

[0121] The lower portion of Figure 6, labeled 6D, illustrates the evolution over time of the activation state for each of the N=36 cells.

[0122]

[0129] The dashed line at mid-height of the current graph (portion 6A) represents zero current (i=0). A positive current corresponds to a current leaving the battery, and a negative current corresponds to a regenerative phase with a current entering the battery. At time t1, the current switches from the positive to the negative domain, and the state of charge curve SoC shows that it passes through a minimum at this time. A little later, at time t2, the current switches back from the negative to the positive domain, and the state of charge curve SoC shows that it passes through a peak.

[0123]

[0130] According to a non-limiting example, the voltage across each cell can be between 5 volts and 25 volts, for example preferably between 10 volts and 16 volts.

[0124] Benefits and applications

[0125]

[0132] Advantageously, the proposed method leads to an equalization of the charge states over time, even if starting from an initial situation where the Sock charge states are very different between the different cells. This equalization is inherent in the method, and there is no need to resort to any particular permutation or prioritization logic.

[0133] The principle is applicable regardless of the number N, when considering increasingly larger numbers. The computational difficulty increases proportionally to the number N. 2 , which is far below the general combinatorics which progresses like 2 N .

[0126] We can thus foresee applications where N is greater than 50, for example N equal to 100, or even more.

[0127]

[0135] The input quantity can be an electrical power to be delivered and not just an electrical voltage, in which case the optimization mechanism will also determine the pair u and i corresponding to the setpoint power to be delivered.

[0128]

[0136] Example of Function fi

[0129]

[0137] We can choose for fi: rant expressed in [Amp] e of cell k expressed in [A. h]

[0130] SoC k expressed between [0 ... 1] without units, giving in [sec -1 ]

[0131] Example of Function f2 2: . abs(i) 1 7

[0132]

[0146] with i = current expressed in [Amp]

[0133] Jtab = ta ble function of the SoC, typically between [0.001 and 0.05]

[0134] K q , HAS q and m q = constants, equal for example: K q = 4. e 26 , HAS q = 200, and m q = 4

[0135]

[0149] Qloss k : cell capacity loss k expressed in [A. sec]

[0136] SoH k expressed between [0 ... 1] without units giving f2en [Asec / sec]< / t> < / t> < / t> < / t> < / t> < / t>

Claims

DEMANDS 1. A control method for controlling a system comprising at least a plurality of binary selectable components that are activated to contribute additively to an output quantity, which the system must make coincide as closely as possible with a setpoint quantity, each selectable component (Ck) being activated by a binary control Uk, the method comprising a step of defining a time horizon, and the method being characterized in that it comprises, according to a first periodicity, a repetition of the steps: a) acquiring a setpoint quantity (v req) as a setpoint for the output quantity (v), b) acquire at least one state (qk, SOCk) of each selectable component, c) determine a set of constraints to be respected (AX < b), including in particular a constraint of respecting the setpoint quantity for the output quantity, d) use a Pontryagin Maximum Principle (PMP) type algorithm over the time horizon to determine adjoint states (Àk,pk) with a Hamiltonian quantity formulation H, where the function <t>, expressed as a vector ( 1( (p2,.., (p k ,..,(p N ) is a generalized cost function representing one or more cost function(s) to be minimized and compliance with the set of constraints, e) use a linear integer mixed solver module (LIMS) to determine a minimum of the Hamiltonian quantity while respecting the set of constraints, to deduce an optimal control vector u* (u* to U*N), f) apply the optimal control vector u*, g) calculate gradients of the adjoint states of the Pontryagin Maximum Principle type algorithm for the next iteration.

2. A method according to claim 1, characterized in that the selected elements are electrochemical cells of a switchable-cell electric battery, and the output quantity is a voltage across the terminals of the electric battery, the selected electrochemical cells being arranged in series in the electric battery, the electric battery being intended to provide a time-varying setpoint voltage.

3. A method according to any one of claims 1 to 2, characterized in that each selectable element is affected by static and non-static characteristics.

4. A method according to claim 3 when it depends on claim 2, wherein the static characteristics include the nominal cell capacity (Qk) and the non-static characteristics include the voltage (Vk), the state of charge (SOCk), the capacitance loss (Qlossk), the internal resistance (rk).

5. A method according to claim 4, wherein, with respect to the Hamiltonian quantity H, the generalized cost function <t>includes a term that aims to minimize a sum of the resistances of the activated cells, a term that aims to minimize a drop in the state of charge of each cell and / or the complete battery, and a term that aims to minimize an aging rate of each cell and / or the complete battery.

6. A method according to claim 5, wherein the Hamiltonian quantity H is written as follows: with r k : electrical resistance of the k-rank cell : Adjunct state associated with the cell's charge state, denoted q or SoC q k : time derivative of the cell's charge state k = i k : adjoint state associated with the loss of capacity of the cell of rank k Ql ss k : time derivative of the cell capacity loss k = f2i, Qloss k ). u k QQk being the nominal capacity of the k-rank battery, therefore 7. A method according to any one of claims 1 to 6, wherein the setpoint quantity Vreq and the output quantity Vout conform to a constraint formalism written as follows: with V out = i U k . v k Vmin and Vmax being acceptable limits, i.e. V accuracy being a configurable tolerated deviation.

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

9. Control system comprising at least one switchable cell electric battery and an electronic control unit (1) in which the method according to any one of claims 1 to 8 is implemented.

10. Vehicle comprising at least one switchable cell electric battery and an electronic control unit (1) in which the method according to any one of claims 1 to 8 is implemented.< / t> < / t>

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