System and method for measuring the entropic heat coefficient of a battery

Abstract

The present invention concerns a method (200) and system (110) for automatically estimating an entropic heat coefficient (hereafter "EHC") of a battery (120), the method comprising: a) receiving or acquiring (210) a current, voltage, and temperature of the battery in function of the time, wherein said current, voltage and temperature have been measured simultaneously during a constant charge and discharge cycle; b) receiving or acquiring (220) an open-circuit voltage, hereafter "OCV", of the battery as a function of its state-of- charge, hereafter "SoC"; c) feeding (230) said current, voltage and temperature in function of the time and said OCV in function of the SoC in an identification algorithm based on a battery thermal model, said identification algorithm being configured for determining said EHC as a function of the SoC, wherein, for said determination, the EHC is defined as a function of N+1 real parameters a0,...,aN, wherein the identification algorithm is configured for determining the value of each real parameter a0,...,aN, by minimizing a difference between an estimated battery temperature and said measured temperature, wherein the estimated battery temperature is obtained by modeling, with said battery thermal model, a heat generated by the battery during said charge and discharge cycle; d) outputting (250), by said identification algorithm, the determined EHC as function of the SoC.

Description

[0001]System and method for measuring the entropic heat coefficient of a battery The invention relates to a system and a method for measuring the entropic heat coefficient, called hereafter EHC of a bat- tery. Said EHC is defined as a rate of change of a battery open-circuit voltage (hereafter OCV or Uoc) with respect to its temperature Tcell, usually written as EHC = dUOC / dTcell[mV / K], wherein said rate is a function of the state-of-charge (here- after SoC) of the battery. It is an important parameter when calculating or managing the thermal exchanges of a battery with its surrounding environment, which became of high inter- est with the increasing electrification of vehicles and the attempts to extend the lifetime of batteries as well as to maintain maximum efficiency. More precisely, the total heat generation Hgenfor a battery in operation is the sum of an irreversible heat Qirrev(ohmic loss, diffusion loss, etc.) lost by the battery during operation and a reversible heat Qrevresulting from the entropic effect: ^gen = Qirrev + Qrev (Eq. 1) wherein Qirrev= I·(Uoc– Ubatt) (Eq. 2) Qrev= I·dUoc / dTcell·Tcell(Eq. 3) with I being the battery current, Ubattits voltage in opera- tion, Tcellthe battery temperature, and Uocits open-circuit voltage, and wherein the EHC of the battery, i.e. dUoc / dTcellis, as previously explained, a function of the SoC. Up to now, different methods have been proposed for determining the EHC of a battery. Said methods are for instance: - the potentiometric method (see for instance X.-F. Zhang et al., “Potentiometric measurement of entropy change for lithium batteries,” Phys. Chem. Chem. Phys., vol. 19, no. 15, pp. 9833– 9842, Apr. 2017, doi: 10.1039 / C6CP08505A); - the calorimetric method (see for instance N. Damay, C. Forgez, M.-P. Bichat, and G. Friedrich, “Thermal modeling of large prismatic LiFePO4 / graphite battery. Coupled thermal and heat generation models for characterization and simulation,” Journal of Power Sources, vol. 283, pp. 37–45, Jun. 2015, doi: 10.1016 / j.jpowsour.2015.02.091); - the frequency analysis method (see for instance Z. Geng, J. Groot, and T. Thiringer, “A Time- and Cost-Effective Method for Entropic Coefficient Determination of a Large Commercial Battery Cell,” IEEE Transactions on Transportation Electrifi- cation, vol. 6, no. 1, pp. 257–266, Mar. 2020, doi: 10.1109 / TTE.2020.2971454). While the potentiometric method provides very accurate re- sults, it however requires a lot of time for determining the EHC of a battery (typically several days up to weeks), needs highly accurate voltage measurement equipment, and only pro- vides discontinuous EHC results (i.e. for some specific SoC values and not for continuous values of SoC). The calorimetric method is already faster than the potentiom- etric method (typically 40 hours of tests against 190 hours for the potentiometric method) and still accurate, and addi- tionally enables to get continuous values of the EHC in func- tion of SoC. However, its disadvantages are the need of a specific housing for thermally controlling the surrounding en- vironment of a tested battery, and specific equipment for car- rying out the test (e.g. calorimeter, electrochemical imped- ance spectrometer, etc.). Finally, the frequency analysis method, which is the fastest method among the three (typically 32h of tests), has the ad- vantage of enabling in-situ measurements, but provides only discontinuous EHC results and presents higher errors results in the obtained EHC values. There is therefore still a need for a system and method capable of quickly determining or measuring the EHC of a battery while providing accurate results, wherein said method and system are simpler in terms of required experimental efforts compared to the existing techniques, and wherein said system and method might be implemented in situ, free of a system or structure configured for enclosing the battery and controlling thermally its surrounding environment. An objective of the present invention is therefore to propose a method and a system that enable a faster, simpler, and ac- curate determination of the EHC of a battery. This objective is achieved according to the present invention by a method and a system for determining the EHC of a battery according to the object of the independent claims. Dependent claims present further advantages of the invention. The present invention proposes thus a method, preferentially a computer implemented method, for automatically determining the EHC of a battery, the method comprising: a) receiving or acquiring, notably via a first interface and for said battery, a current, voltage, and temperature of the battery in function of the time, wherein said current, voltage and temperature have been measured simultaneously during a constant charge and discharge cycle, preferen- tially performed at constant ambient temperature. In par- ticular, if the ambient temperature is not constant, then the ambient temperature, current, voltage, and battery tem- perature, are received or acquired data that have been simultaneously measured in function of the time during said constant charge and discharge cycle; b) receiving or acquiring, notably via a second interface, an OCV of the battery as a function of its SoC; c) feeding said current, voltage and battery temperature in function of the time, optionally said ambient temperature, notably the ambient temperature in function of the time if said ambient temperature is not constant, and said OCV in function of the SoC in an identification algorithm based on a battery thermal model, said identification algorithm being configured for determining said EHC as a function of the SoC, wherein, for said determination, the EHC is defined as a function of N+1 real parameters a0,…,aN(i.e. a0,…,aNtaking real values), in other words EHC = dU / dT = f(a0,…,aN), said function being for instance a polynomial function of order N, i.e. dU / dT = a0+a1·SoC + a2·SoC2+ … + aN·SoCN, with a0,…,aNbeing real parameters of the Nthorder polynomial function. The identification algorithm is configured for determining the value of each real parameter a0,…,aN, by minimizing a difference between an estimated battery tem- perature and said measured temperature, wherein the esti- mated battery temperature is obtained by modeling, with said battery thermal model, a heat generated by the battery during said charge and discharge cycle; d) outputting, by said identification algorithm and notably via a third interface, the determined EHC as function of the SoC. The objective of the present invention is also solved by a system configured for automatically determining the EHC of a battery, said system comprising: - a first interface configured for receiving or acquir- ing, for said battery, a current, voltage, and tempera- ture of the battery in function of the time, wherein said current, voltage and temperature have been measured simultaneously during a constant charge and discharge cycle, notably performed at ambient temperature, prefer- entially constant ambient temperature; - a second interface configured for receiving or acquir- ing (102) an OCV of the battery as a function of its SoC; - a memory for storing the OCV, current, voltage, and temperature acquired via the first and second inter- faces, and optionally said ambient temperature, notably if not constant; - a processing unit comprising at least one processor and one or more processor-executable instructions stored on at least one computer-readable storage medium of the system, which might be said memory, wherein said proces- sor-executable instructions comprise instructions that, when executed by said processor: - feed said current, voltage and temperature in function of the time, optionally said ambient tem- perature in function of the time, and said OCV in function of the SoC in an identification algorithm based on a battery thermal model; - execute said identification algorithm, the latter being configured for determining said EHC as a function of the SoC, wherein, for said determina- tion, the EHC is defined as a function of N+1 pa- rameters a0,…,aNtaking real values, wherein the identification algorithm is configured for deter- mining the value of each real parameter a0,…,aN, by minimizing a difference between an estimated bat- tery temperature and said measured temperature, wherein the estimated battery temperature is ob- tained by modeling, with said battery thermal model, a heat generated by the battery during said charge and discharge cycle; - output, via a third interface, the EHC as function of the SoC as determined by the identification al- gorithm; - said third interface notably configured for displaying the determined EHC. Preferentially, the first, second, and third interface are one and the same interface. Preferentially, in order to optimize the precision of the EHC outputted by the identification algorithm, the present inven- tion further proposes to add a sinus-like curve of the EHC in function of the SoC to said outputted EHC as function of the SoC in order to create a new EHC in function of the SoC, wherein said sinus-like curve is defined by a set of fitting real parameters, and wherein said new EHC is used as a new input to the identification algorithm which is further config- ured for optimizing the values of said fitting real parameters of said set by minimizing said difference between the estimated battery temperature and said measured temperature, wherein the EHC in function of the SoC that is finally outputted by the identification algorithm is then said new EHC obtained with the optimized values of the fitting real parameters. Finally, the present invention concerns also a non-transitory machine-readable medium storing instructions executable by a processing unit to cause a computing system to perform the steps of the claimed method. Preferred but not exclusive embodiments of the invention will now be described with reference to the accompanying drawings, wherein like numbers designate like objects, and which depict in: Figure 1 Illustration of the variation of an EHC of a battery in function of its SoCs; Figure 2 Illustration of a preferred embodiment of the method according to the invention; Figure 3 Examples of variations of (A) current, (B) voltage, and (C) temperature of a battery during constant charge and discharge cycles; Figure 4 Examples of an OCV curve in function of SoC obtained for the battery of Fig. 3 in charge and in discharge; Figure 5 Preferred embodiment of a thermal model of a battery; Figure 6 Illustration of a modeling of an EHC profile in func- tion of SoCs; Figure 7 Illustration of a preferred embodiment of a first method for determining the EHC for a battery accord- ing to the invention; Figure 8 Example of sinus-like curve used for optimizing the EHC estimated profile; Figure 9 Illustration of a preferred embodiment of an opti- mization of said first method for determining the EHC for a battery according to the invention; Figure 10 Illustration of a preferred embodiment of a system for estimating the EHC according to the invention. FIGURES 1 through 10, discussed below, and the various embod- iments used to describe the principles of the present disclo- sure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged device. The numerous innovative teach- ings of the present application will be described with refer- ence to exemplary non-limiting embodiments. The present invention falls in the field of electric battery testing and proposes a fast and simple method to extract the EHC of an electric battery from easily measurable experimental parameters that are typically accessible via sensors and / or directly provided in currently available datasheets character- izing such electric batteries. Compared to existing techniques for extracting the EHC, the proposed technique is notably sim- pler in terms of experimental instrumentation and faster with respect to the time needed for determining said EHC. Figure 1 shows a curve representing the variation of the EHC (dU / dT [mV / K]) in function of different SoCs (given in [%] of charge) for a typical lithium-ion battery. As it can be seen from said curve, the EHC increases with SoCs. The present invention proposes to determine such a curve for characteriz- ing a battery by using an identification algorithm that re- quires simple inputs while outputting an accurately estimated EHC for the battery. Figure 2 is a flowchart of a preferred embodiment of the method according to the invention. Said method might be implemented by the system 110 schematically illustrated in Fig. 10. Said system 110 is configured for automatically estimating the EHC of a battery 120. Said system 110 comprises notably a first interface 111, a second interface 112, and a third interface 113. At step 210, the system is configured for receiving or acquir- ing, notably via its first interface 111, a current, a voltage, and a temperature of the battery in function of the time. Typically, said system 110 comprises connection means, like electric cables, configured for connecting the electrical poles of the battery 120 to one or several measuring devices of the system 110, said measuring devices comprising typically a voltage sensor, a current sensor, and a temperature sensor, in order to enable a measurement of the battery current, volt- age, and temperature in function of the time. For instance, a first pair of cables might be configured for connecting the positive (anode) and negative (cathode) poles of the battery 120 to the voltage sensor of a first measuring device 114 as well to a current sensor of said first measuring device 114, current and voltage measurements being thus realized by said first measuring device 114 of the system 110. Preferentially, the system 110 may further comprise a second measuring device comprising a temperature sensor 115 configured for measuring the temperature of said battery 120. Typically, the tempera- ture sensor 115 provides, via another cable or pair of cables, measured temperature values to the system 110 via said inter- face 111. According to the present invention, the current, voltage and temperature that are acquired or measured by the system 110 have notably been simultaneously measured during a constant charge and discharge cycle that is preferentially performed at constant ambient temperature. If the ambient tem- perature is not constant, then another temperature sensor of the system 110 might be configured for measuring the ambient temperature in function of the time. Said constant charge and discharge cycle might be performed by the system 110, which, in such case, may comprise a charging device configured for controlling the charging and discharging of the battery 120 in function of the time, said charging device being for instance connected to the first interface 110. Preferentially, said charging device might also measure said current, voltage, and temperature of the battery in function of the time. Alterna- tively, said charging and discharging might be performed by another charging device not comprised within the system 110 according to the invention. Whatever the method or device used for performing constant charge and discharge cycles, the con- stant charge and discharge cycle according to the invention comprises preferentially a discharge phase during which the fully charged battery is discharged at constant current until its cut-off voltage, and / or a charge phase during which the battery is charged at a constant current until its maximal voltage is reached. In particular, the charge phase comprises, after reaching said battery maximal voltage, a charge at con- stant voltage until the battery current decreases to a prede- fined level (e.g., a small current value of C / 20, wherein C is the nominal capacity of the battery). In other words, the measured current, voltage and temperature are experimental data that characterize the battery for which the EHC has to be determined by the system 110. Part or all said experimental data might be directly determined (i.e. ex- perimentally measured) by the system 110 according to the in- vention, or data representing the current, and / or voltage, and / or the temperature measured in function of the time for said battery might be acquired by the system 110. An example of constant charge and discharge cycle is shown in Figure 3. Preferentially, the system 110 according to the in- vention might be implemented as a battery test bench that may cooperate with a climate chamber for controlling the ambient temperature surrounding the battery. In particular, said am- bient temperature might be controlled by the system according to the invention, and / or measured in function of the time simultaneously to the measurement of current, voltage and tem- perature of the battery. During the acquisition of said cur- rent, voltage and temperature, the battery 120 is placed in the climate chamber, preferentially at constant ambient tem- perature, the system 110 delivering a current to the battery and measuring its current, voltage, and temperature, notably surface temperature during a period of time which is usually less than 5 hours. Graphics A, B, and C of Figure 3 show respectively the measured values for the current, voltage, and temperature for a time period ~18·103[s]. At step 220, the system 110 is configured for receiving or acquiring, notably via its second interface 112, an OCV of the battery as a function of its SoCs. The OCV is an important parameter of the identification algorithm according to the invention. Preferentially, said OCV is obtained by averaging OCV values obtained by charging the battery and OCV values obtained during discharge of the battery. The OCV in function of the SoC might be directly determined (i.e. experimentally measured) by the system according to the invention, or data representing the OCV of the battery in function of its SoCs might be acquired by the system 110. In order to experimentally determine the OCV for the battery, the system 110 according to the invention may implement different methods. For instance, in order to obtain the OCV in discharge, the system 110 might be configured for discharging the battery successively and discontinuously at different SoCs from 100% to 0%, wherein a relaxation phase is followed after each SoC change. At each SoC, the relaxed voltage at the end of the relaxation phase is considered to be the OCV. Applying the same procedure in charge allows the system to measure the OCV in charge. Figure 4 presents an example of the OCV in charge and in discharge obtained with successive discharges and charges at different SoCs. Preferentially, the system accord- ing to invention uses the averaged values between the values of the OCV in discharge and the values of the OCV in charge as input into the identification algorithm according to the in- vention. According to another method, the system 110 might be configured for extracting the OCV from a charge and discharge cycle at a small constant current (e.g., at a current of C / 20). Again, the average profile of the discharge voltage and the charge voltage is then preferentially used as input to the identifi- cation algorithm. Alternatively, the system 110 might be configured for extract- ing the OCV by averaging the discharge voltage and charge voltage in a constant discharge and charge cycle as performed in step 210 wherein the charge and discharge internal re- sistances are considered as equal by the system. Preferentially, the OCV, current, voltage and temperature (called together “acquired data” hereafter) acquired via the first and second interfaces might be stored in a memory 116 of the system 110. The latter further typically comprises a pro- cessing unit 117 for processing the acquired data. Said pro- cessing unit 117 may comprise one or several processors and one or more processor-executable instructions stored on at least one computer-readable storage medium of the system, e.g. the memory 116. The execution of said instructions by said one or several processors is configured for implementing the pro- cessing of the acquired data according to the invention in order to estimate the EHC in function of the SoC of the bat- tery. More precisely, the processing unit 117 comprises therefore instructions, which, when executed by the processor, are con- figured, at step 230, for feeding said current, voltage and temperature in function of the time and said OCV in function of the SoC in an identification algorithm based on a battery thermal model. The identification algorithm enables to iden- tify or determine different thermal parameters of the battery, namely the EHC profile (i.e. the EHC in function of the SoC), the battery specific heat Cp, and the convective heat exchange coefficient hconvof the battery. The battery thermal model is illustrated in Fig. 5. It is a battery equivalent circuit model comprising a heat source Hgenrepresenting the heat generated by the battery during said charge and discharge cycle, a thermal capacitor Cth connected in parallel with the heat source Hgenand representing a battery heat capacity, a source of thermal energy Tambconnected in parallel with the heat source Hgenand the thermal capacitor Cthand representing the ambient temperature (“Tamb” will be used therefore to simply refer to the ambient temperature) of the environment surrounding the battery, and a thermal re- sistance Rthconnecting the thermal capacitor Cthto the source of thermal energy Tamband representing convective heat exchange between the battery and its surrounding environment. Finally, Tcellis the temperature of the battery. The total heat generated Hgenby the battery comprises the irreversible heat Qirrevrelated to the battery impedance and the reversible heat Qrevdue to the entropic effect as expressed in Eq. 1. For the battery thermal model, the total heat gen- erated is expressed by: The irreversible heat is obtained via – Ubatt), where I and Ubattare respectively the current and voltage of the battery measured in operation (in function of the time), and Uocis its open circuit voltage (also in function of the time). The thermal capacitor Cthand the thermal resistance Rthare respectively given by the following equations: ^^^^ℎ= ^^ ∙ ^^^^Eq. 5 where m is the battery mass, and Sconvis the battery convective heat exchange surface. From equations (2) to (6), equation (1) can be rewritten as: The OCV Uoc, the current I, the battery voltage Ubatt, the bat- tery temperature Tcellare the so-called “acquired data” that are thus measured input data, the mass m, the battery convec- tive heat exchange surface Sconv, and, if constant, the ambient temperature Tambare also known fixed parameters. Optionally, the ambient temperature might be data measured in function of the time, and thus part of the “acquired data” used as input data in Eq. 7. Therefore, the only unknown parameters in Eq. 7 are the battery specific heat Cp, the convective heat ex- change coefficient hconv, and the EHC, i.e. the rate of change dUoc / dTcell, wherein the latter is typically a profile over SoC as represented in Fig. 1. The present invention proposes to represent the EHC as a func- tion f of N+1 parameters a0,…,aNtaking real values: For determining said EHC as a function of the SoC, the iden- tification algorithm is configured for determining the value of each real parameter a0,…,aN, by minimizing a difference between an estimated battery temperature (hereafter ^^^^^^^^^^^^^^^^) and said measured temperature (hereafter ^^^^^^^^^^^^^^^^) that is part of the acquired data, wherein ^^^^^^^^^^^^^^^^ is obtained by modeling, with said battery thermal model, the heat generated by the battery during the charge and discharge cycle. In other words, minimizing the difference between the experimentally measured temperature of the battery, i.e. and the estimated temperature mod- elled by Eq. 7 wherein the EHC has been replaced by the ex- pression given by Eq. 8, i.e. f(a0,…,aN), all unknown might be automatically determined by the identification algorithm. Preferentially, the function f is a polynomial function of the SoC of order N, i.e. dUoc / dTcell= a0+a1·SoC + a2·SoC2+ … + aN·SoCN, with a0,…,aN being real parameters of the Nthorder polynomial function. According to another embodiment illus- trated by Fig. 6, the function f might define, for each state of charge SoCiof a set S of discrete values of SoCs, S = {SoC0,…SoCN}, a corresponding value aiof the entropic coeffi- cient. In other words, f is configured for associating to each SoCiof said set S, a corresponding entropic coefficient ai, with i=0,…,N (with N=10 in the example provided by Fig. 6). Each of the SoCimight be a pre-fixed value, e.g. SoC0= 0%, SoC1= 10%, S0CN= 100%. Given the expression of Eq. 8, the unknown parameters of Eq. 7 are thus the battery specific heat Cp, the convective heat exchange coefficient hconv, and the series a0,…,aN. These un- known parameters are all real value parameters. Preferen- tially, the identification algorithm is configured for using a first optimization method or algorithm, such as a least square fitting algorithm, for identifying or determining said unknown parameters by minimizing the error (ε) (i.e. the dif- ference) between the estimated battery temperature pro- vided through Eq. 7 and the measured battery temperature ^^^^^^^^^^^^^^^^received as input within said acquired data. The identifica- tion algorithm according to the invention is schematically represented in Figure 7, wherein the identification algorithm uses the OCV (i.e. Uoc), the current I, the battery voltage Ubatt, the ambient temperature Tamb, the mass m and the battery convective heat exchange surface Sconvas input to Eq. 7 in order to estimate the battery temperature ^^^^^^^^^^^^^^^^ while minimizing the difference ( ^) with measured battery temperature ^^^^^^^^^^^^^^^^via a first optimization algorithm that is configured for automat- ically adjusting the values of Cp, hconv, and a0,…,aNso that the difference be minimal. At step 250, notably at the end of said optimization, the identification algorithm outputs, notably via the third inter- face 113, at least the values of a0,…,aN, and optionally, also the values of Cpand hconv, for which the difference between ^^^^^^^^^^^^^^^^ and ^^^^^^^^^^^^^^^^was minimal. In other words, the processing unit 117 is configured for outputting, via its identification algo- rithm, the EHC as function of the SoCs of the battery according to Eq. 8: EHC = f(a0,…,aN). Preferentially, said EHC might be displayed via said third interface 113. In particular, the obtained EHC, and preferably Cpand hconv, might be stored in the memory 116 of the system 110. Prefer- entially, the system 110 according to the invention further comprises, or is configured for cooperating with, a thermal management system of the battery. The latter is configured for controlling, in function of the obtained EHC, a charge and / or a discharge of the battery, notably in function of the battery temperature. For instance, at step 250, the EHC as function of the SoC is used as input in said battery thermal management system of the battery. Using said EHC as function of the SoC, the thermal management system is configured for controlling the current and / or voltage applied to the battery during charg- ing and / or discharging phases. Preferentially, the processing unit might be configured for automatically sending the obtained EHC to said battery thermal management system, enabling there- fore to optimize the charging and / or discharging of the battery by said thermal management system. Preferentially, the method according to the invention com- prises an additional step, namely step 240, that follows step 230 and enables to further optimize the values of a0,…,aN, Cp, and hconvthat minimize the difference between More precisely, the processing unit 117 comprises preferen- tially additional instructions, which, when executed by the processor, are configured, at step 240, for adding a sinus- like curve, that represents a variation of EHC values in func- tion of the SoC, to the EHC as function of the SoC obtained at the end of step 230. Preferentially, the sinus-like curve is defined by a set S1 of fitting parameters having real values. Adding said sinus-like curve to the EHC obtained at the end of step 230 enables to create a new EHC in function of the SoC that can be then used as new input to said identification algorithm. The latter is then configured for using a second optimization method or algorithm, such as a least square fit- ting algorithm, for identifying or determining said fitting parameters of the sinus-like curve by minimizing the error (ε) (i.e. the difference) between the estimated battery tempera- ture ^^^^^^^^^^^^^^^^ and the measured battery temperature The second optimization algorithm may use the same optimization technique as the first optimization algorithm, like said least square fitting, and is thus configured for optimizing the values of the fitting real parameters of said set S1 by minimizing said difference between the estimated battery temperature ^^^^^^^^^^^^^^^^ and said measured temperature ^^^^^^^^^^^^^^^^. At the end of said additional optimization, step 250 takes place again, wherein the identi- fication algorithm is configured for outputting, notably via said third interface 113, said EHC in function of the SoC as being the new EHC obtained with the optimized values of the fitting parameters of the sinus-like curve. A schematic illustration of the step 240 is presented in Figure 8, wherein a new EHC 803 is obtained by adding a sinus-like curve 802 to the previously obtained EHC 801. This enables to capture an oscillation (for instance a presence of an inter- mediate minimum value and of an intermediate maximum value of the EHC between the minimum value at SoC = 0% and the maximum value at SoC = 100%) of the entropic coefficient that takes place with respect to an interval of values of the SoC, e.g. for 30% < SoC < 60%. The sinus-like curve can thus be used for performing a second fit with the identified entropic coeffi- cient values obtained at the end of step 230. Preferentially, said sinus-like curve is a cubic spline de- fined by 5 real parameters, namely SoC0, DSoC, y1, y2, y3(see graphic 804 in Figure 8), wherein said cubic spline takes value from an interval [SoC0; SoC0+ ^SoC] and maps them to real numbers representing EHC values, and comprises two maxima among said EHC values, namely y1and y3, and one EHC minimum value, namely y2. Said cubic spline passes for instance through the set of points {(SoC0,0),(x1,y1),(x2,y2),(x3,y3), (SoC0+ ^SoC,0)}, with SoC0< x1< x2< x3< SoC0+ ^SoC, and wherein the distance along the X-axis between any two adjacent points of said set is preferentially a constant. Said second optimization of the identification algorithm enables to identify or determine said 5 real fitting parameters SoC0, ^SoC, y1, y2, y3that minimize the difference between ^^^^^^^^^^^^^^^^ and Figure 9 better illustrates the method according to the inven- tion when comprising the steps 230 and 240. At the end of step 230, the identification algorithm preferentially outputs the determined EHC in function of SoC, i.e. f(a0,…,aN) and the values obtained for Cpand hconvfor which the difference between ^^^^^^^^^^^^^^^^ and ^^^^^^^^^^^^^^^^was minimal. Then, in particular instead of out- putting them via the third interface notably for displaying them, the identification algorithm might be configured for further running said step 240 in which the previously outputted data (i.e. f(a0,…,aN), Cp, and hconv) are used as new inputs 901 for a second fitting procedure implemented by said identifi- cation algorithm. In said second fitting procedure, the EHC = dUoc / dTcell= f(a0,…,aN) received as new input is modified by adding said sinus-like curve g(SoC) in order to create a new EHC in function of SoC (e.g. EHCnew(SoC) = f(a0,…,aN,SoC)+ g(SoC)), which, together with Cpand hconv, is used in Eq. 7 configured for estimating the battery temperature, wherein the unknown parameters 902 that need to be adjusted are this time the fitting parameters of the sinus-like curve, i.e. SoC0, ^SoC, y1, y2, y3. The second optimization algorithm determines the value of each of said fitting parameters that minimizes the difference (or error ^) between and at the end, outputs the values of SoC0, ^SoC, y1, y2, y3for which said difference was minimal. In fact, the second optimization al- gorithm is configured for finding the best interval [SoC0; SoC0+ ^SoC] for inserting or adding said sinus-like curve into the previously obtained EHC so that said difference or error be minimized. At the end, the identification algorithm outputs, for instance via said third interface 113, the new EHC, i.e. EHCnew, as defined by the parameters a0,…,aN, Cp, hconv, SoC0, ^SoC, y1, y2, y3 that minimized said difference between ^^^^^^^^^^^^^^^^ and ^^^^^^^^^^^^^^^^at the end of step 240. Said new EHC might be then used by the thermal management system of the battery for controlling, in function of said new EHC, a charge or discharge of the battery. Preferentially, the system according to the invention may use a battery electrical model for estimating said battery voltage Ubattin function of the time that is then used as input in said identification algorithm in step 230. In this case, the battery voltage measuring is not necessary, notably when using an ac- curate battery electric model to estimate the battery voltage. In order to further improve the precision of the new EHC es- timated by the identification algorithm, the latter may repeat step 240 several times, using each time a previously obtained “new EHC” that has been outputted at the end of step 240 as an inputted EHC when newly repeating said step 240 (i.e., when starting again step 240). This allows to add several sinus- like curves to the EHC obtained at the end of step 230. In such a case, the results of a previous iteration (i.e. a0,…,aN, Cp, hconv, SoC0, ^SoC, y1, y2, y3as obtained at the end of step 240) are used as input for a directly next iteration, adding therefore to the EHC curve defined by a0,…,aN, SoC0, ^SoC, y1, y2, y3a new sinus-like curve, and performing then again step 240. In conclusion, the present invention advantageously provides a new system and method for estimating the EHC of a battery. Compared to existing methods, the present invention provides several advantages: - the determination of the EHC is faster than other existing methods. It typically takes approx. 5 hours for determining the EHC with the proposed method when a 1C rate charge and discharge current is used, against ~190 hours for the po- tentiometric method, ~20 hours for a continuous curve of the calorimetric method, and ~16 hours for the frequency analysis method; - it requires less experimental effort (e.g., no need of spe- cific equipment such as calorimeter and electrochemical im- pedance spectroscopy (EIS), no need of additional thermal isolation of the battery under test, etc.; - it gives accurate results compared to the literature; - it is suitable for “in-situ” applications. For example, the system might be used for estimating the EHC of a battery pack in a vehicle, since the voltage, current and tempera- ture are measurable for each battery cell inside the pack. Additionally, the proposed method can be used by a battery management system (BMS) to identify the entropic coefficient of the battery cells during the charging phase of the bat- tery pack. Since the entropic coefficient profile changes when a battery cell ages, the estimated entropic coefficient of each cell can be used to monitor the state of health of the battery pack. Additionally, the system according to the invention may automatically detect a potential defective or less efficient cell of a pack by comparing the entropic coefficients obtained for each cell and identifying a dif- ference (e.g. EHC value at a given SoC, or a shift of an EHC curve with respect to another one) between one of said entropic coefficients and the other entropic coefficient(s).

Claims

Claims 1. Method (200) for automatically determining an entropic heat coefficient, hereafter “EHC”, of a battery (120), the method comprising: a) receiving or acquiring (210), for said battery (120), a current, voltage, and temperature of the battery (120) in function of the time, wherein said current, voltage and temperature have been measured simultaneously during a con- stant charge and discharge cycle; b) receiving or acquiring (220) an open-circuit voltage, here- after “OCV”, of the battery as a function of its state-of- charge, hereafter “SoC”; c) feeding (230) said current, voltage and temperature in function of the time and said OCV in function of the SoC in an identification algorithm based on a battery thermal model, said identification algorithm being configured for determining said EHC as a function of the SoC, wherein, for said determination, the EHC is defined as a function of N+1 real parameters a0,…,aN, wherein the identification algo- rithm is configured for determining the value of each real parameter a0,…,aN, by minimizing a difference between an estimated battery temperature and said measured tempera- ture, wherein the estimated battery temperature is obtained by modeling, with said battery thermal model, a heat gen- erated by the battery during said charge and discharge cycle; d) outputting (250), by said identification algorithm, the determined EHC as function of the SoC.

2. The method (200) according to claim 1, wherein said constant charge and discharge cycle comprises: - a discharge phase during which the fully charged battery isdischarged at constant current until its cut-off voltage.

3. The method (200) according to claim 1 or 2, wherein said constant charge and discharge cycle comprises: - a charge phase during which the battery (120) is charged at a constant current until its maximal voltage is reached.

4. The method (200) according to claim 3, wherein the charge phase comprises, after reaching said battery maximal voltage, a charge at constant voltage until the battery current de- creases to a predefined level.

5. The method (200) according to one of the claims 1 to 4, wherein the battery thermal model is a battery equivalent cir- cuit model comprising a heat source Hgenrepresenting the heat generated by the battery (120) during said charge and discharge cycle, a thermal capacitor Cthconnected in parallel with the heat source Hgenand representing a battery heat capacity, a source of thermal energy Tambconnected in parallel with the heat source Hgenand the thermal capacitor Cthand representing the ambient temperature of the environment surrounding the battery, and a thermal resistance Rthconnecting the thermal capacitor Cthto the source of thermal energy Tamband repre- senting convective heat exchange between the battery (120) and its surrounding environment.

6. The method (200) according to one of the claims 1 to 5, wherein a sinus-like curve (802) of the EHC in function of the SoC is added (240) to the determined EHC (801) as function of the SoC in order to create a new EHC (803) in function of the SoC, wherein said sinus-like curve (801) is defined by a set of fitting real parameters, wherein said new EHC (803) is used as a new input to the identification algorithm which is furtherconfigured for optimizing the values of the fitting real pa- rameters of said set by minimizing said difference between the estimated battery temperature and said measured temperature, the identification algorithm being then configured for output- ting said EHC in function of the SoC as being the new EHC as obtained with the optimized values of the fitting real param- eters.

7. The method (200) according to claim 6, wherein said sinus- like curve (802) is a cubic spline defined by 5 real parame- ters, namely SoC0, ^SoC, y1, y2, y3, wherein said cubic spline takes value from an interval [SoC0; SoC0+ ^SoC] and maps them to real numbers, and comprises two maxima, namely y1and y3, and one minimum, namely y2.

8. The method (200) according to one of the claims 1 to 7, wherein the EHC as function of the SoC is used as input in a thermal management system of the battery (120) configured for controlling, in function of said EHC, a charge or discharge of the battery (120) in function of the battery temperature.

9. A system (110) configured for automatically determining an entropic heat coefficient, hereafter “EHC”, of a battery (120), said system (110) comprising: - a first interface (111) configured for receiving or ac- quiring (210), for said battery (120), a current, volt- age, and temperature of the battery (120) in function of the time, wherein said current, voltage and temperature have been measured simultaneously during a constant charge and discharge cycle; - a second interface (112) configured for receiving or acquiring (220) an open-circuit voltage, hereafter“OCV”, of the battery as a function of its state-of- charge, hereafter “SoC” - a memory (116) for storing the OCV, current, voltage, and temperature acquired via the first and second inter- faces; - a processing unit (117) comprising at least one proces- sor and one or more processor-executable instructions stored on at least one computer-readable storage medium of the system (110), wherein said processor-executable instructions comprise instructions that, when executed by said processor: - feed (230) said current, voltage and temperature in function of the time and said OCV in function of the SoC in an identification algorithm based on a battery thermal model; - execute said identification algorithm, the latter being configured for determining said EHC as a function of the SoC, wherein, for said determina- tion, the EHC is defined as a function of N+1 pa- rameters a0,…,aNtaking real values, wherein the identification algorithm is configured for deter- mining the value of each real parameter a0,…,aN, by minimizing a difference between an estimated bat- tery temperature and said measured temperature, wherein the estimated battery temperature is ob- tained by modeling, with said battery thermal model, a heat generated by the battery during said charge and discharge cycle; - output (250), via a third interface (113), the EHC as function of the SoC as determined by the iden- tification algorithm; - said third interface (113) notably configured for dis- playing the determined EHC.

10. System (110) according to claim 9, comprising a charging device connected to the first interface (111), configured for implementing said constant charge and discharge cycle per- formed at ambient temperature and for acquiring said current, voltage, and temperature of the battery (120) in function of the time.

11. System (110) according to claim 9 or 10, wherein said processor-executable instructions comprise further instruc- tions that, when executed by said processor: - add (240) a sinus-like curve (802) of EHC in function of the SoC to the previously determined EHC (801) as function of the SoC in order to create a new EHC (803) in function of the SoC, wherein said sinus- like curve (802) is defined by a set of fitting real parameters; - feed the identification algorithm with said new EHC (803), wherein said identification algorithm is fur- ther configured for optimizing the values of the fitting real parameters of said set by minimizing said difference between the estimated battery tem- perature and said measured temperature; - run or execute said identification algorithm, which, upon execution, is configured for outputting said new EHC (803) as obtained with the optimized values of the fitting real parameters; wherein the EHC outputted by said third interface is said new EHC obtained with the optimized values of the fitting real parameters.

12. System (110) according to one of the claims 9 to 11, comprising a thermal management system of the battery (120),connected to said third interface (113) for acquiring said EHC in function of the SoC, and configured for controlling, in function of said EHC, a charge or discharge of the battery (120) in function of its temperature.

13. A non-transitory machine-readable medium storing instruc- tions executable by a processing unit (117) to cause a compu- ting system to: a) receive or acquire (210) a current, voltage, and temperature of a battery (120) in function of the time, wherein said current, voltage and temperature have been measured simul- taneously during a constant charge and discharge cycle; b) receive or acquire (220) an open-circuit voltage, hereafter “OCV”, of the battery as a function of its state-of-charge, hereafter “SoC”; c) feed (230) said current, voltage and temperature in function of the time and said OCV in function of the SoC in an identification algorithm based on a battery thermal model; d) execute said identification algorithm, the latter being configured for determining said EHC as a function of the SoC, wherein, for said determination, the EHC is defined as a function of N+1 real parameters a0,…,aN, wherein the identification algorithm is configured for determining the value of each real parameter a0,…,aN, by minimizing a dif- ference between an estimated battery temperature and said measured temperature, wherein the estimated battery tem- perature is obtained by modeling, with said battery thermal model, a heat generated by the battery (120) during said charge and discharge cycle; e) output (240) the EHC as function of the SoC as determined by the identification algorithm.

14. Non-transitory machine-readable medium according to claim13, further storing instructions executable by said processing unit (117) to cause the computing system to: - add (240) a sinus-like curve of EHC in function of the SoC to the previously determined EHC as function of the SoC in order to create a new EHC in function of the SoC, wherein said sinus-like curve is defined by a set of fitting real parameters, - feed the identification algorithm with said new EHC, wherein said identification algorithm is further configured for optimizing the values of the fitting real parameters of said set by minimizing said dif- ference between the estimated battery temperature and said measured temperature; - run or execute said identification algorithm, which, upon execution, is configured for outputting said new EHC with the optimized values of the fitting real parameters; wherein the outputted EHC in function of the SoC is said new EHC as obtained with the optimized values of the fitting real parameters.

15. Non-transitory machine-readable medium according to claim 13 or 14, further storing instructions executable by said pro- cessing unit (117) to cause the computing system to: - implement a thermal management of the battery in function of the determined EHC in function of the SoC, wherein said thermal management of the battery is con- figured for controlling, in function of said EHC, a charge or discharge of the battery in function of its temperature.

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