Method for managing maximum power of an electric battery

Abstract

One aspect of the invention relates to a method (100) for managing a maximum power Pmax of an electric battery comprising in particular steps of: determining (160) an equivalent time teq as a function of an equivalent direct current resistance DCReqt, of a simple resistance R0t of the battery for the present instant t, determining (170) a direct current resistance DCR teq+Δt of the battery for a future equivalent instant teq+Δt, estimating (180) a voltage Ut+Δt of the battery, for a future instant t+Δt, and determining (190) the maximum power Pmax of the battery as a function of: the estimated voltage Ut+Δt of the battery for the future instant t+Δt, and the maximum predetermined current Imax of the battery or an estimated maximum current Imax estimated of the battery. Figure to be published with the abstract: Figure 3

Description

Title of the invention: Method for managing the maximum power of an electric battery TECHNICAL FIELD OF THE INVENTION

[0001] The technical field is that of the management of electric batteries, in particular electric batteries on board a vehicle, notably in an aircraft.

[0002] The present invention relates to a method for managing a maximum power of an electric battery and an associated system. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] Climate change is a major concern for many legislative and regulatory bodies around the world. Indeed, various restrictions on carbon emissions have been, are being, or will be adopted by various States. In particular, an ambitious standard applies both to new types of aircraft and those currently in circulation, requiring the implementation of technological solutions in order to make them compliant with current regulations. Civil aviation has been mobilizing for several years now to make a contribution to the fight against climate change.

[0004] Technological research efforts have already made it possible to significantly improve the environmental performance of aircraft. The Applicant takes into consideration the factors impacting all phases of design and development, to obtain less energy-intensive, more environmentally friendly aeronautical components and products whose integration and use in civil aviation have moderate environmental impacts with the aim of improving the energy efficiency of aircraft. The Applicant is constantly working to reduce its climate impact by using methods and operating virtuous development and manufacturing processes and minimizing greenhouse gas emissions to the minimum possible to reduce the environmental footprint of its activity.

[0005] This sustained research and development work covers new generations of aircraft engines, the lightening of aircraft, particularly through the materials used and lighter on-board equipment, the development of the use of electrical technologies to provide propulsion, and finally aeronautical biofuels.

[0006] In this context, the use and management of electric batteries within aircraft must be optimized. It is particularly essential to be able to manage the maximum power of an electric battery. The maximum power, also called peak maximum power, and noted here Pmax, is the maximum power that the battery can provide continuously for a given period.

[0007] It is known that the maximum power Pmax varies depending on different parameters of the battery. The maximum power Pmax varies in particular depending on the state of charge of the battery, the temperature of the battery, the current applied to the battery during charging or discharging as well as the state of health of the battery. For example, a so-called "balanced" battery, i.e. with zero current and stable voltage, has a greater maximum power Pmax than when a non-zero current is applied to the battery, during a charging or discharging period. Furthermore, the higher the charge level of a battery, the higher the maximum power Pmax of the battery is during charging of the battery but is lower during discharging of the battery. In addition, a battery having a low temperature has a low maximum power Pmax. Finally, the more the state of health of a battery deteriorates, the more the maximum power Pmax of the battery decreases.

[0008] Thus, it is necessary to take into account at least a part of these different parameters of the battery in order to determine, in a reliable and precise manner, the maximum power Pmax of a battery. The determination of the maximum power Pmax of the battery can be carried out at a present time t, for a future time t+At with a variable application duration At, for example between 1 and 60 seconds. In addition, this determination must be carried out instantaneously according to the dynamic state of the battery, in particular to allow sufficient precision of the management of the battery in critical transient phases such as the takeoff or landing of an aircraft. It is possible to note that the application duration At, for which the maximum power Pmax of a battery is determined, also influences the determination of the maximum power Pmax.Indeed, when the application duration At increases, the maximum power Pmax of a battery decreases during a discharge period and during a charge period. The application duration At is defined according to the needs of each application. For the same application, it is possible to determine the maximum power Pmax for several application durations At, and therefore for example to determine the maximum power PmaxiOs for an application duration At= 10 seconds, the maximum power Pmax30s for an application duration At= 30 seconds. It is therefore possible to determine at a present time t, the maximum power at the future time t+At with the following equation: . [°009] ftWW PTnax(ti + M)=~-------= U(ti + At) xI(ti + M)

[0010] With: • U, the battery voltage, and • I, the current applied to the battery.

[0011] The maximum power Pmax can be defined by reaching predefined limit voltages and predefined limit currents. These predefined limit voltages and predefined limit currents are the maximum limit current Imax for charging the battery during the charging phase, the maximum limit current 1max for discharging the battery during the discharging phase, the maximum limit voltage Umax during the charging phase and the minimum limit voltage during the discharging phase. These limit voltages and limit currents can for example be defined by the battery supplier or by the constraints of the application in which the battery is used. Thus, four cases can be identified: • during a battery charging phase, the maximum power Pmax corresponds to: • Pmax — IX Umax with I < Imax, load, * Pmax— Jmax X with U Umax • During a battery discharge phase, the maximum power Pmax corresponds to • Pmax = I x < Imax^discharge, or * Pmax — ^max XU with UU min

[0012] Several methods therefore make it possible to determine, for a future instant t+At distant from the present instant t by the duration of application At, the maximum power Pmax of a battery.

[0013] A first group of methods uses machine learning to determine the maximum power Pmax of a battery. However, these methods require a large amount of data for training the neural network. This training data is, however, difficult or sometimes impossible to obtain.

[0014] A second group of methods uses an electrical representation, such as the equivalent electrical circuit illustrated in [Fig.l], in order to model the behavior of a battery. These methods determine the maximum power Pmax of a battery as a function of a previously determined internal resistance of the battery. [Fig.l] illustrates an example of an equivalent model 1 of an electric battery that can be used by a method of this second group. Model 1 of [Fig.l] allows a good compromise between simplicity and accuracy in determining the maximum power Pmax of a battery. A current denoted Iceu is applied to model 1 and model 1 includes: • an instantaneous open circuit source OCV, representing the battery voltage when it is at rest, • a resistance Ro, representing the resistances of connections and those of rapid transient phenomena, • preferably, a parallel RC circuit, representing the diffusion phenomenon and comprising a resistor Rdiff and a capacitor Cdiff.

[0015] Some of the methods in this second group of methods are based on Kalman filters and least squares optimization. The equations of the electrical model are then used iteratively in order to converge over time towards the maximum power Pmax of the battery. These methods therefore involve a very significant computational load in order to determine the maximum power Pmax of the battery. These methods are therefore more difficult to use for an on-board application, for example in an aircraft.

[0016] Other methods of this second group of methods based on an electrical representation, perform a direct calculation of the maximum power Pmax of the battery in a manner similar to a simulation of an online electrical model. However, this calculation is simplified in order to be adapted to an embedded application. In order to simplify the calculation, it is for example possible not to take into account appropriately the state of the battery at the time of the estimation, or to ignore the voltage drop caused by the application of the maximum authorized current, or even to ignore the variation of the characteristics of the battery such as the parameters of the internal resistance of the equivalent electrical model of the battery during a current slot, in particular as a function of the state of charge of the battery.These methods are therefore imprecise, in particular because they do not take into account the state of the battery in an appropriate manner in order to determine a maximum power Pmax of an electric battery. The state of a battery at a given moment can be evaluated from different parameters such as the battery voltage, the current applied to the battery during charging or discharging, the state of charge of the battery, the temperature of the battery or even the state of health of the battery.

[0017] There is therefore a need for a method for managing the maximum power of an electric battery which limits, at least in part, the problems linked to the use of the aforementioned methods of the prior art. Summary of the invention

[0018] The invention provides a solution to the problems mentioned above, by making it possible to manage a maximum power Pmax of an electric battery in a reliable, precise and economical manner in terms of computing resources. Indeed, the maximum power Pmax of the battery is determined by carrying out a simplified simulation of an equivalent model of a battery. The invention preferably comprises updating the parameters of the equivalent model of a battery as illustrated in [Fig.l]. The updating Updating the parameters can, for example, be carried out using previously implemented battery characterization tests and studies. These battery characterization tests and studies make it possible to obtain maps, or equations, of these parameters at different battery health states. Finally, determining the battery health state makes it possible to identify the value to be used for at least some of the parameters of the equivalent battery model.

[0019] The simulation of the equivalent model makes it possible to make a projection in time, for a future instant t+At distant from the present instant t by a duration of time At, of the maximum power Pmax of the battery, avoiding making iterations requiring significant computing resources. The present instant t is the instant at which the method according to the invention is implemented. The method according to the invention thus defines the characteristics of an overvoltage present A Ut at the present instant t in order to be able to carry out said projection. The method according to the invention makes it possible to overcome the history of use of the battery, i.e. the current profile which has been applied to the battery and / or is being applied at the present instant t. Indeed, in the method according to the invention, a correspondence is found between the history of use and an equivalent direct current resistance DCReq generated under a fixed current Io.The equivalent direct current resistance DCReq preferably corresponds to the real part of the impedance of an equivalent model as illustrated in Figure 1. Thus, at the present time t, the cell voltage Vt can be obtained by the following equation: .

[0020] Ut = OCVt+àUt

[0021] With A Ub the overvoltage at the present time t can be obtained by the following equation: A Ut — l*DCRCqt

[0022] With DCReqt, the equivalent direct current resistance DCReq t at the present time t generated by a fixed current It during an equivalent time of current application, also called in the present application equivalent time and noted teq. The equivalent time corresponds to the time necessary to reach the voltage Ut of the electric battery by applying the current It in a constant manner to the electric battery. In other words, the equivalent time is the time of application of the current current It making it possible to obtain the current voltage Ut of the battery; the current lt being applied with a constant value and the battery being initially new.

[0023] The method according to the invention therefore comprises a determination of the equivalent direct current resistance DCReq t for the present instant t and the equivalent time teq in order to carry out the projection in time of the battery voltage up to the future equivalent instant teq+At, and in order to obtain the battery voltage Ut+^ for this future instant t+At. [Fig.2] shows a diagram 10 illustrating the principle of the equivalent direct current resistance DCReq t for the instant t and the equivalent time teq. The axis vertical 11 represents the battery voltage, expressed in volts, and the horizontal axis 12 represents the time, expressed in seconds. The double arrow 13 represents the equivalent time teq for the present instant t and the double arrow 14 represents the result of the product between the current It applied to the battery at the present instant t and the equivalent direct current resistance DCReq t. Curve 15 represents the battery voltage and curve 16 the open circuit voltage OCV of the battery, expressed in volts. Rectangle 17 represents the estimate of the maximum power Pmax of the battery for a future duration of time At.

[0024] One aspect of the invention thus relates to a method for managing a maximum power Pmax of an electric battery comprising computer-implemented steps of: • obtaining, for a present instant t, an open circuit voltage OCVt of the battery, a battery voltage Utet and a current It applied to the battery, • determination, for the present moment t, of an equivalent direct current resistance DCReqt as a function of the open circuit voltage OCVt, the battery voltage Ut and the current It applied to the battery obtained, • determination of an equivalent time teq as a function of the determined equivalent direct current resistance DCReqt, of a simple resistance R^ of the battery for the present instant t, the equivalent time corresponding to the time necessary to reach the voltage Ut of the electric battery by applying the current It constantly to the electric battery, • determination of a direct current resistance DCR teq+At for a future equivalent instant teq+At, distant from the equivalent time teq by a duration of time At, the determination of the direct current resistance DCRteq+At being carried out as a function of the simple resistance value ROt+At of the battery for the future instant t+At, • estimation of a voltage Ut+At of the battery, for a future instant t+At distant from the present instant t by the same duration of time At, as a function of a future open circuit voltage OCVt+At for the future instant t+At, of the direct current resistance DCR teq+At for the future instant t+At and of a maximum predetermined current Imax of the battery, • determination of the maximum power Pmax as a function. • the estimated voltage Ut+At of the battery for the future instant t+At and the maximum predetermined current Imax of the battery, when the voltage Ut+At for the future instant t+At is included in a predetermined interval of limit voltages of the battery, • or the estimated battery voltage Ut+At for the future time t+At and an estimated maximum current Imaxestimated for the battery, when the battery voltage Ut+At for the future time t+At is not included in the predetermined range of limit voltages of the battery, the estimated maximum current Imaxestimated for the battery being determined from a terminal of the predetermined range of limit voltages of the battery, the future open circuit voltage OCVt+At of the battery for the future time t+At and the direct current resistance DCRteq+At for the future equivalent time teq+At.

[0025] Thanks to the invention, it is possible to manage a maximum power Pmax of an electric battery in a reliable and precise manner since the method according to the invention takes into account the state of the battery at the current time. In addition, the method can be used in an embedded system with limited space and computing resources, since the computing power necessary for implementing the method is limited. Applications, in particular aeronautical, but also maritime and automotive, of the method according to the invention are therefore possible. Finally, the invention makes it possible to do without a large quantity of training data for a machine learning algorithm, data which can be difficult to obtain.

[0026] In addition to the characteristics which have just been mentioned in the preceding paragraph, the method according to one aspect of the invention may have one or more complementary characteristics among the following, considered individually or according to all technically possible combinations: • the step of determining an equivalent time teq further comprises determining a diffusion resistance Rdifft of the battery for the present time t and a diffusion time constant Tdifff for the present time t, and wherein determining the direct current resistance DCR teq +At for the future equivalent time teq+At is further performed as a function of the diffusion resistance value Rdifft+At of the battery for the future time t+At and the diffusion time constant of the battery for the future time t+At. • the future open circuit voltage OCV t+At for the future time t+At is determined using preliminary steps including: • Determination, for the future instant t+At, of a future state of charge SOCt+At of the battery as a function of a state of charge SOCt for the present instant t, the future state of charge SOCt+At for the future instant t+At being determined for the maximum predetermined current Imax applied to the battery during the time duration At, and • Determination, for the future instant t+At, of the future open circuit voltage OCVt+At of the battery as a function of the future state of charge SOCt+At of the battery. • the method further comprises an initial step of obtaining a temperature Tt of the battery and a first mapping of an open circuit voltage OCV as a function of a state of charge SOC of the battery and the temperature Tt of the battery and in which the determination of the equivalent direct current resistance DCReqt at the present time t is carried out using the first mapping obtained, • the initial step of obtaining the first mapping also includes: • Obtaining a second mapping of the simple resistance Ro of the battery as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery, and in which: • the simple resistance R^ of the battery at the present time t is determined from the second map with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature Tt of the battery at the present time t, • the initial step of obtaining the first mapping also includes: • Obtaining a third map of the diffusion resistance Rdiffen as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery, and in which: • the diffusion resistance Rdifft of the battery at the present time t is determined from the third map with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature Tt of the battery Tt at the present time t, • the initial step of obtaining the first mapping also includes: • Obtaining a fourth mapping of the diffusion time constant as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery and in which: • the diffusion time constant at the present time t is determined from the fourth map with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature Tt of the battery at the present time t, • the first mapping of the open circuit voltage OCV is furthermore based on a SOH state of health of the battery, and / or • the second mapping of the simple resistance Ro is furthermore based on the SOH state of health of the battery, and / or • the third mapping of the diffusion resistance Rdiffest further depends on the SOH state of health of the battery, and / or • the fourth mapping the diffusion time constant is furthermore a function of the SOH state of health of the battery, and in which the state of health SOH of the battery is taken into account to determine the maximum power Pmax of the battery, • the method further comprises a final step of modifying the conditions of use of the battery as a function of the maximum power Pmax determined.

[0027] A second aspect of the invention relates to a system for managing an electric battery comprising an electronic processing and control system configured to execute the steps of the method according to the invention.

[0028] A third aspect of the invention relates to an aircraft comprising an electric battery and a battery management system according to the invention.

[0029] A fourth aspect of the invention relates to a computer program comprising instructions which, when the program is executed by a computer, cause the latter to implement a method according to the invention.

[0030] A fifth aspect of the invention relates to a non-transitory computer-readable data carrier on which the computer program according to the invention is recorded.

[0031] The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0032] The figures are presented for information purposes only and in no way limit the invention. • [Fig. 1] shows an example of an equivalent model of an electric battery, • [Fig.2] shows a diagram illustrating the principle of modeling the equivalent direct current resistance DCReq and the equivalent time teq, • [Fig.3] shows a block diagram illustrating the steps of the method 100 according to an exemplary embodiment of the invention. DETAILED DESCRIPTION

[0033] Unless otherwise specified, the same element appearing in different figures has a single reference.

[0034] [Fig. 3] is a block diagram illustrating the steps of an example of the method according to the invention. The mandatory steps of the example of the method 100 are indicated by a solid line rectangle and the optional steps are indicated by a dotted line rectangle.

[0035] The method 100 is a method for managing a maximum power Pmax of one or more electric batteries. It allows more reliable management of the maximum power Pmax of one or more electric batteries by reliably and accurately determining this maximum power Pmax. The method 100 can be applied during a period of charging or discharging the battery. For the sake of simplicity, the examples below are provided for a period of discharging the battery but the method applies in a similar manner for a period of charging the battery.

[0036] The electric battery to which the method 100 is applied is, for example, a battery on board an aircraft. The battery is for example used to store and / or deliver electrical energy to equipment of an aircraft turbomachine. The battery is for example used for electric propulsion functions within the turbomachine. Alternatively, the electric battery is a battery of an on-board automotive, railway, maritime, etc. system.

[0037] A first optional step 110 of the method 100 comprises obtaining a first map of an open circuit voltage OCV as a function of a state of charge SOC of the battery and a temperature of the battery. The term “obtain” may mean in the present application “measure” and / or “receive” and / or “calculate”. A map makes it possible to determine the evolution of a first variable, an open circuit voltage OCV for the first map, as a function of one or more other variables, a state of charge SOC of the battery and a temperature of the battery for the first map. In one example, the first optional step 110 of the method 100 also comprises obtaining three other maps. The second map is a map of the simple resistance R0 as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature of the battery.The third map is a map of the diffusion resistance Rdiff as a function of the battery state of charge SOC, the current I applied to the battery and the battery temperature. The fourth map is a map of the diffusion time constant as a function of the battery state of charge SOC, the current I applied to the battery and the battery temperature.

[0038] In one example, compatible with the previous example, the first optional step 110 of the method 100 also comprises obtaining a temperature Tt of the battery. The temperature Ttest expressed in degrees Celsius. Alternatively, obtaining the battery temperature Tt can also be done in step 120.

[0039] In an example, compatible with the previous example, a map or certain maps or each of the four maps obtained in step 110 is furthermore based on a state of health SOH of the battery. Thus, for said maps, the influence of the state of health SOH of the battery is taken into account. The first map is therefore a map of the open circuit voltage OCV as a function of the state of charge SOC of the battery, the temperature Tt of the battery and the state of health SOH of the battery. The second map is a map of the simple resistance Ro as a function of the state of charge SOC of the battery, the current I applied to the battery, the temperature Tt of the battery and the state of health SOH of the battery.The third mapping is a mapping of the diffusion resistance Rdiff as a function of the state of charge SOC of the battery, the current I applied to the battery, the temperature Tt of the battery and the state of health SOH of the battery. The fourth mapping is a mapping of the diffusion time constant Tdiff as a function of the state of charge SOC of the battery, the current I applied to the battery, the temperature Tt of the battery and the state of health SOH of the battery. When the four maps obtained in step 110 include the state of health SOH of the battery, the method 100 can determine the maximum power Pmax of the battery by taking into account the state of health SOH of the battery. In this example, the method 100 is therefore even more reliable and precise in managing the maximum power Pmax of the battery.

[0040] A second step 120 of the method 100 comprises obtaining, for the present moment t, an open circuit voltage OCVt of the battery, a battery voltage Ut, a current It applied to the battery and a temperature Tt of the battery. The voltages OCVt and Ut are expressed in volts. The current It is expressed in amperes. In one example, compatible with the previous examples, this data can be measured.

[0041] A third optional step 130 of the method 100 comprises determining, for the future instant t+At, a future state of charge SOCt+At of the battery as a function of a state of charge SOCt of the battery at the present instant t. A state of charge is often expressed as a percentage of the total capacity of the battery. The future state of charge SOCt+At is determined for a maximum current Imax applied to the battery during the duration of time At. In an example, compatible with the previous examples, the future state of charge SOCt+At of the battery can be obtained for a discharge phase at maximum current Imax with the following equation:

[0042] SOCM,= SOC,+ 100x / ,„„ x;^

[0043] With: • Capacity, the battery capacity expressed in amperes per second, and • imax, the maximum current applied to the battery.

[0044] The maximum current Imax, also called limit current, can be a value predetermined. This maximum current Imax can for example be provided by the battery manufacturer and obtained during step 110. The maximum current Imax can be different depending on whether the charging or discharging of the battery is considered.

[0045] A fourth optional step 140 of the method 100 comprises determining, for the future instant t+At, the future open circuit voltage OCVt+At of the battery as a function of the future state of charge SOCt+At of the battery. The determination of the future open circuit voltage OCVt+At can be carried out using the following equation: [00461 ocv,+i, = ocv( soc,J

[0047] In one example, consistent with the previous examples, the determination of the future open circuit voltage OCVt+At can be performed by taking into account the temperature Tt at the present time t using the following equation:

[0048] OCVt Af = OCV( SOC, T^ans 'c last example, it is also possible to use the future temperature Tz+A / , instead of the temperature Tt at the present time t, to determine the future open circuit voltage OCVt+At The future temperature Tz+Az can for example be estimated using a thermal model of the electric battery.

[0049] A fifth step 150 of the method 100 comprises determining an equivalent direct current resistance DCReq t at the present time t. The equivalent direct current resistance DCReq t being determined as a function of the open circuit voltage OCVt, the battery voltage Ut at the present time t, the current It applied to the battery at the present time t obtained in step 120. For example, the equivalent direct current resistance DCReq t at the present time t can be obtained with the following equation:

[0051] In one example, compatible with the previous examples, the determination 150 of the equivalent direct current resistance DCReqt at the present time t is carried out using the first mapping obtained in step 110.

[0052] A sixth step 160 of the method 100 comprises the determination of an equivalent time teq at the present time t as a function of the equivalent direct current resistance DCReq t determined in step 150, of a simple resistance R^ of the battery for the present time t, and optionally as a function of a diffusion resistance Rdifft of the battery for the present time t and of a time constant of diffusion TWft for the present time t. The equivalent time teq corresponds to the time of application of the fixed current It at the present time in order to obtain the equivalent direct current resistance DCReq t for the present time t. The equivalent direct current resistance DCReq t for the present time t is considered equivalent to the battery usage history. Thus, regardless of the battery usage history, the equivalent time teq corresponds to the time of application of the fixed current It which would allow to arrive at the same voltage as that measured at the present time t if the internal resistance of the battery were the equivalent direct current resistance DCReqt for the present time. The equivalent time teq can for example be determined using the following equation:

[0053] . teq= - ----J

[0054] With the diffusion time constant of the battery at the present time t being obtainable by:

[0055] Tdifft~ Rdifft ^-^difft

[0056] With: • Cdifft, the diffusion capacity of the battery at the present time t, expressed in Farads.

[0057] In one example, compatible with the previous examples, the simple resistance ROt of the battery at the present time t is determined from the second map obtained in step 110 using the state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature of the battery at the present time t,

[0058] In one example, consistent with the previous examples, the diffusion resistance Rdifft of the battery at the present time t is determined from the third map using the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature of the battery at the present time t, and

[0059] In one example, compatible with the previous examples, the diffusion time constant at the present time t is determined from the fourth mapping with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature of the battery at the present time t. Alternatively, it is also possible to use a mapping of the diffusion capacity of the battery C^-y ft.

[0060] A seventh step 170 of the method 100 comprises the determination of a direct current resistance DCRteq+At for a future equivalent instant teq+At, distant from the present equivalent time teq by the duration of time At. The determination of the resistance in direct current DCRteq+At is performed as a function of the simple resistance value ROt +At of the battery for the future time t+At, the diffusion resistance value Rdifft+At of the battery for the future time t+At and the diffusion time constant Tdifft+At of the battery for the future time t+At. The direct current resistance DCRteq+At for the future equivalent time teq+At can for example be determined using the following equation:

[0061] TW"'» _ » । ny [ 1 teq+At \ 1 ^teq+At - ^0 t+At+ ^dif f t+At

[0062] The calculations of the simple resistance value Rot+At of the battery for the future time t+At, of the diffusion resistance value Rdifft+At of the battery for the future time t+At and of the diffusion time constant of the battery for the future time t+At can be carried out as a function of the maximum predetermined current Imax of the battery. In addition, these calculations can be carried out as a function of the temperature Tt at the present time or as a function of the future temperature Tï+A / ​​at the future time T,+A / . The calculation of the simple resistance value ROt+At of the battery for the future time t+At can for example be carried out using the following equation: 100631 koi+a,= «(1(socw4z, T,)

[0064] An eighth step 180 of the method 100 comprises determining a voltage Ut+At of the battery for the future instant t+At. The determination of the voltage Ut+At of the battery is carried out as a function of the open circuit voltage OCVt+At for the future instant t+At, the direct current resistance DCR teq+At for the future equivalent instant teq+At and the predetermined maximum current Imax of the battery. In one example, compatible with the previous examples, this predetermined maximum current Imax was obtained in step 110.

[0065] A ninth step 190 of the method 100 comprises determining the maximum power Pmax of the battery. When the voltage Ut+At of the battery for the future equivalent instant t+At is within a predetermined range of limit voltages of the battery during a discharge of the battery, the determination is made as a function of the voltage Ut+At of the battery for the future instant t+At and the predetermined maximum current Imax of the battery. When the voltage Ut+At of the battery for the future instant t+At is not within the predetermined range of limit voltages of the battery, the determination is made as a function of the voltage Ut+At of the battery for the future instant t+At as a function of an estimated maximum current Imax estimated of the battery.The estimated maximum current Imax of the battery is determined from a terminal of the predetermined range of limit voltages of the battery, the future open circuit voltage OCVt+At for the future instant t+At of the battery and the direct current resistance DCRteq+At for the future equivalent instant teq+At. . The predetermined range of limit voltages of the battery may be provided by the battery manufacturer. The predetermined range of limit voltages may be obtained during step 110 of the method 100. The predetermined range of limit voltages includes a minimum voltage Umin and a maximum voltage Umax. When the voltage Ut+At of the battery for the future time t+At is within the predetermined range of limit voltages of the battery, the maximum power Pmax l+Aldc of the battery for the future time t+At may be determined with the following equation:

[0066] P max t + At ~ Ut+ â / ^max

[0067] When the battery voltage Ut+At for the future time t+At is not included in the predetermined range of battery limit voltages, the maximum power Pmax t+At of the battery for the future time t+At can be determined with the following equation:

[0068] p A / ]— TT *T 1 max\l~ min imax estimated

[0069] With estimate that can be obtained by the following equation:

[0070] j _UmùrOCVr.A, ^estimated mux DCR^^

[0071] For a battery discharge phase, the battery voltage Ut+At for the future time t+At is not included in the predetermined range of battery limit voltages when the battery voltage Ut+At for the future time t+At is lower than the minimum voltage Umin. For a battery charge phase, the battery voltage Ut+At for the future time t+At is not included in the predetermined range of battery limit voltages when the battery voltage Ut+At for the future time t+At is higher than the maximum voltage Umax. Thus, in this case, in order to determine the estimated I>nax, the following equation is used:

[0072] T & A / +az *estimated max ~ DCRteq^t

[0073] An optional tenth step 200 of the method 100 comprises a modification of the conditions of use of the battery as a function of the maximum power Pmax determined in step 190. This modification of the conditions of use of the battery may be automatic, semi-automatic or manual, i.e. requiring human intervention. In examples, this modification of the conditions of use of the battery may comprise at least one action among:

[0074] display of maximum power Pmax,

[0075] generation of an alert message when the maximum power Pmax of the battery is lower than a predetermined threshold power,

[0076] decision-making, by a user, concerning an aircraft maneuver, such as a landing, and implementation of the action resulting from the decision-making,

[0077] charging a battery whose power setpoint is determined as a function of the maximum power Pmax determined by the method 100,

[0078] prediction of a minimum remaining charge duration of the battery as a function of the maximum power Pmax determined by the method 100,

[0079] changing a first battery powering a system, such as a system contained in an aircraft or of an aircraft, and whose maximum power Pmax has been determined by the method 100, by a battery whose maximum power Pmax is greater than the maximum power Pmax, and

[0080] implementation of a maintenance operation of a system, such as a system contained in an aircraft or of an aircraft, powered by the battery whose maximum power Pmax is determined.

[0081] The present invention also relates to a system for managing an electric battery comprising means for implementing the method 100. For example, the management system according to the invention may comprise an electronic processing and control system, otherwise called a “computer”, comprising at least one processor and one memory, the electronic processing and control system being configured to execute the steps of the method 100. In addition, optionally, the system for managing an electric battery may comprise a means for displaying the maximum power Pmax determined by the method 100, at least one means for measuring the temperature of the battery, at least one means for measuring the voltage at the terminals of the battery, and at least one means for measuring the current flowing between the terminals of said battery.

Claims

1. Claims Method (100) for managing a maximum power Pmax of an electric battery, the method comprising computer-implemented steps of: - obtaining (120), for a present instant t, an open circuit voltage OCVt of the battery, a battery voltage Ut and a current It applied to the battery, - determination (150), for the present instant t, of an equivalent direct current resistance DCReq t as a function of the open circuit voltage OCVt, the battery voltage Ut and the current It applied to the battery obtained (120), - determination (160) of an equivalent time teq as a function of the equivalent direct current resistance DCReq t determined (150), of a simple resistance R^ of the battery for the present instant t, the equivalent time corresponding to the time necessary to reach the voltage Ut of the battery by applying the current It constantly to the battery, - determination (170) of a direct current resistance DCR teq+At for a future equivalent instant teq+At, distant from the equivalent time teq by a duration of time At, the determination of the direct current resistance DCRteq+At being carried out as a function of the simple resistance value Ro t+At of the battery for the future instant t+At, - estimation (180) of a voltage Ut+At of the battery, for a future instant t+At distant from the present instant t by the same duration of time At, as a function of a future open circuit voltage OCVt+At for the future instant t+At, of the direct current resistance DCR teq+At for the future instant t+At and of a maximum predetermined current Imax of the battery, - determination (190) of the maximum power Pmax as a function of: • the estimated voltage Ut+At of the battery for the future instant t+At and the predetermined current maximum Imax of the battery, when the voltage Ut + At for the future instant t + At is included in a predetermined range of limit voltages of the battery, • or of the estimated voltage Ut + At of the battery for the future instant t + At and of an estimated maximum current Imaxestimated of the battery, when the voltage Ut + At of the battery for the future instant t + At is not included in the predetermined range of limit voltages of the battery, the estimated maximum current Imaxestimated of the battery being determined from a terminal of the predetermined range of limit voltages of the battery, the future open circuit voltage OCVt + At of the battery for the future instant t + At and the direct current resistance DCRteq + At for the future equivalent instant teq

2. +At* The method (100) of claim 1 wherein the step of determining (160) an equivalent time t^ further comprises determining a diffusion resistance Rdifft of the battery for the present time t and a diffusion time constant for the present time t, and wherein determining (170) the direct current resistance DCR teq+At for the future equivalent time teq+At is further performed as a function of the diffusion resistance value Rdifft+At of the battery for the future time t+At and the diffusion time constant of the battery for the future time t+At.

3. Method (100) according to claim 2 in which the future open circuit voltage OCV t+At for the future instant t+At is determined using prior steps comprising: - Determining (130), for the future instant t+At, a future state of charge SOCt+At of the battery as a function of a state of charge SOCt for the present instant t, the future state of charge SOCt+At for the future instant t+At being determined for the maximum predetermined current Imax applied to the battery during the time duration At, and - Determination (140), for the future instant t+At, of the future open circuit voltage OCVt+At of the battery as a function of the future state of charge SOCt+At of the battery.

4. Method (100) according to claim 2 or 3 further comprising an initial step (110) of obtaining a temperature Tt of the battery and a first mapping of an open circuit voltage OCV of the battery as a function of a state of charge SOC of the battery and the temperature Tt of the battery, and wherein the determination (150) of the equivalent direct current resistance DCReq t at the present time t is carried out using the first mapping obtained.

5. Method according to claim 4, in which the initial step (110) of obtaining the first mapping further comprises: - Obtaining a second mapping of the simple resistance Ro of the battery as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery, and in which: - the simple resistance R^ of the battery at the present time t is determined from the second mapping with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature Tt of the battery at the present time t.

6. Method according to claim 4 or 5, wherein the initial step (110) of obtaining the first mapping further comprises: - Obtaining a third mapping of the diffusion resistance Rdiffen as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery, and wherein: - the diffusion resistance Rdifft of the battery at the present time t is determined from the third mapping with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature Tt of the battery at the present time t.

7. Method according to claim 4, 5 or 6, wherein the initial step (110) of obtaining the first mapping further comprises: - Obtaining a fourth mapping of the diffusion time constant Tdiff as a function of the state of charge SOC of the battery, the current I applied to the battery and the temperature Tt of the battery and wherein: - the diffusion time constant 'at the present time t is determined from the fourth mapping with the current state of charge SOCt at the present time t, the current It applied to the battery at the present time t and the temperature of the battery Tt at the present time t.

8. Method (100) according to any one of claims 4 to 7, wherein: - the first mapping of the open circuit voltage OCV is furthermore a function of a state of health SOH of the battery, and / or - the second mapping of the simple resistance Ro is furthermore a function of the state of health SOH of the battery, and / or - the third mapping of the diffusion resistance Rdiff is furthermore a function of the state of health SOH of the battery, and / or - the fourth mapping of the diffusion time constant Td'ff is furthermore a function of the state of health SOH of the battery, and wherein the state of health SOH of the battery is taken into account to determine (190) the maximum power Pmax of the battery.

9. Aircraft comprising an electric battery and an electric battery management system comprising an electronic processing and control system configured to execute the steps of the method (100) according to one of the preceding claims.

10. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to implement a method according to any one of claims 1 to 8.

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