Method for assessing the state of health of a lithium-ion or sodium-ion electric battery
Patent Information
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- VGA
- Filing Date
- 2024-08-22
- Publication Date
- 2026-07-01
AI Technical Summary
Existing battery management systems in electric vehicles struggle to accurately predict the state of health of lithium-ion or sodium-ion batteries due to limited computational power and the need for high computational effort and large data sets for reliable predictions.
A method using discrete wavelet transform decomposition of battery voltage signals from initial and subsequent charging/discharging cycles to calculate the state of health, requiring no high computational power or additional sensor technology, by leveraging existing battery management system data.
Enables simple and accurate calculation of battery state of health, allowing for timely replacement and improving safety and reliability of electric vehicle batteries without the need for advanced computational resources.
Smart Images
Figure IB2024058165_27022025_PF_FP_ABST
Abstract
Description
[0001] “METHOD FOR ASSESSING THE STATE OF HEALTH OF A LITHIUM-ION OR SODIUM-ION ELECTRIC BATTERY”
[0002] DESCRIPTION
[0003] Technical field of the invention
[0004] Object of the invention is a method for assessing the health of an electric battery of both the lithium-ion and sodium-ion type. In particular, such method is applicable in the automotive field or in the field of electricity storage obtained, for example, from renewable sources.
[0005] Known prior art
[0006] It is well known that recent climate change directives aim to accelerate the clean energy transition by taking action in the most polluting sectors, such as transportation. To reduce the greenhouse gas emissions and pollutants, especially in urban areas, massive electrification of transportation is expected. In this context, lithium-ion batteries, or also sodium-ion batteries, are used as an on-board energy carrier to power light electric vehicles thanks to their high efficiency, fast response, high power and energy density and low self-discharge. Such vehicles are referred to as battery electric vehicles.
[0007] However, the main drawbacks related to the so-called "range anxiety" and lack of fast charging infrastructure have yet to be addressed. Furthermore, the lithium or sodium batteries are subject to degradation. Mechanical, electrical and thermal factors, such as operating temperature, manufacturing defects, and the charging and discharging rates, result in more or less rapid cell degradation, which is reflected in a decrease in capacity and an increase in internal resistance. Every battery electric vehicle includes a battery management system that is able to provide various information, including the measured voltage and current, pack and cell temperature, and estimated battery capacity. However, the battery management system generally has low computing power and estimates the state of health of the battery by simple methods, such as measuring the charge or discharge current and integrating it over time to determine its capacity (also referred to as “coulombic counting”). Furthermore, since in the battery electric vehicles the depth of discharge of lithium or sodium batteries is usually limited for safety reasons, the battery management system calculates the state of health of the battery based on partial charge and discharge cycles. This negatively affects the accuracy of the coulombic counting method. In general, lithium or sodium batteries in electric vehicles have to be replaced when their capacity is less than 80% of their initial value.
[0008] Therefore, accurate real-time prediction of the state of health is essential to ensure the safety and reliability of a lithium-ion or sodium-ion battery. In general, two main categories of estimating the state of health of a battery can be distinguished: i) methods based on mathematical models and ii) methods based on data. Therefore, in view of the expected deployment of the electric vehicles, various methodologies for estimating the health of the lithium or sodium batteries and predicting their remaining useful life have been extensively studied in the literature. In general, such methods aim to predict in depth the processes involved in lithium-ion or sodium-ion battery degradation due to the age (calendar aging) and number of cycles made (cycle aging).
[0009] For example, Carkhuff et al. developed a management system that implements multifrequency impedance measurements made in real-time to efficiently identify cell coupling errors and emerging faults. Liu et al. submitted regression models of the Gaussian process to predict both calendar aging and cycle aging of lithium-ion batteries. Goud et al. proposed an on-line technique for estimating the state of health of a lithium-ion battery based on a modified coulombic counting method for solar photovoltaic systems. Jia et al. focused on an integrated framework of aging mechanisms and data-driven methods for the diagnosis of accelerated aging of lithium-ion batteries that proved to be very accurate. Su et al. submitted various machine learning models based on data to predict the cycle life of lithium-ion batteries. However, machine learning methods require high computational effort and a large data set for accurate and reliable prediction, which can not be easily implemented in on-board management and diagnostic systems. As already mentioned, since the management system of an electric vehicle has limited computational power, computationally heavy methods such as Kalman filters, neural networks or fuzzy logic to calculate degradation parameters of the lithium-ion battery are difficult to implement.
[0010] CN110850322 A in the name of UNIV XI AN JIAOTONG describes a method of estimating the relative state of health of the battery based on wavelet signal decomposition.
[0011] Document US2014 / 278169 Al in the name of Kim Jong-Hoon also describes an apparatus to predict the state of health (SOH) of a battery pack by using a discrete wavelet transform.
[0012] CN112379274 in the name of UNIV HENAN SCIENCE & TECH relates to a method to predict the remaining useful life of a power battery and belongs to the technical field of degradation prediction of the power battery performance and management of the state of health.
[0013] CN111707956 A in the name of UNIV NORTH CHINA describes a method for predicting the state of health and the remaining life of a management system of multi-type lithium-ion battery packs.
[0014] Finally, CN108845264 in the name of UNIV XI AN JIAOTONG describes a method of estimating the state of health of the battery based on wavelet.
[0015] Therefore, purpose of the present invention is to implement a method by which the state of health of an electrochemical battery can be calculated with good approximation and in an extremely simple manner.
[0016] Further purpose of the present invention is to make a program that implements such a method and can be used to calculate the state of health of an electrochemical battery.
[0017] Summary of the invention
[0018] The aforementioned purposes are achieved thanks to a method for assessing the state of health of an electrochemical battery, preferably of the lithium-ion or sodium-ion type, according to claim 1. In particular, such method comprises the steps of: a) detecting in the first charging / discharging cycle of said battery, for a certain period of time and at a certain sampling frequency, the voltage output of said battery as a result of the current absorption to which said battery is subjected when operating; b) performing the discrete wavelet transform decomposition of said voltage signal determined in the first charging / discharging cycle during said step a), to obtain an approximate low- frequency signal of said voltage signal and a high-frequency detail signal of said voltage signal in order to determine the coefficient of the approximate signal and the coefficients of the detail signal; c) detecting, in at least one further charging / discharging cycle of said battery following said first charging / discharging cycle, for a certain period of time and at a certain sampling frequency, the voltage output of said battery as a result of the current absorption to which said battery is subjected when operating; d) performing the discrete wavelet transform decomposition of said voltage signal detected in said step c) to obtain an approximate low-frequency signal of said voltage signal and a high- frequency detail signal of said voltage signal to determine the coefficient of the approximate signal and the coefficients of the detail signal; e) counting the number of charging / discharging cycles performed by said battery at least until said further charging / discharging cycle; f) calculating the percentage residual capacity of said battery, compared to the maximum rated capacity, by means of a function of calculating the residual capacity which depends at least on the number of cycles performed by said battery and calculated during said step e), on the ratio of the coefficient of the approximate signal in said first charging / discharging cycle to the coefficient of the approximate signal in said further charging / discharging cycle, and on the ratio of the summation of the detail coefficients in said further charging / discharging cycle to the summation of the detail coefficients in said first charging / discharging cycle.
[0019] The solution enables to calculate, in an extremely simple way and with excellent approximation, the state of health of the battery. As a matter of fact, the use of discrete wavelet transforms on both the voltage signal of the battery in the first charge / discharge cycle of the battery and the voltage signal of the battery in the charge / discharge cycle at which we’d like to know the state of health, allows to use a management system of an electric vehicle that requires neither high computational power nor additional sensor technology because it exploits data already made available by conventional management systems of the battery. The Applicant identified a function which has never been used in any of the Patent documents cited above and allows to identify the residual capacity of the battery simply depending on the number of cycles performed by said battery and calculated during said step e), on the ratio of the coefficient of the approximate signal in said first charging / discharging cycle to the coefficient of the approximate signal in said further charging / discharging cycle, and on the ratio of the summation of the detail coefficients in said further charging / discharging cycle to the summation of the detail coefficients in said first charging / discharging cycle.
[0020] In particular, in said function of calculating the residual capacity, the ratio of the summation of the detail coefficients in said further charging / discharging cycle to the summation of the detail coefficients in said first charging / discharging cycle is used as negative exponent of the Euler number.
[0021] Furthermore, said negative exponent can be multiplied by the ratio of said number of cycles performed until said further cycle to the coefficient of the approximate signal in said further charge / discharge cycle.
[0022] According to a preferred but not limiting aspect of the invention, said number of cycles is raised to an exponent c between 0.8 e 1.2, preferably 1, if said at least one battery is a lithium- ion battery, or else is raised to an exponent between -0.5 e -0.4, preferably -0.425, if said at least one battery is a sodium-ion battery.
[0023] Again, said negative exponent may further be multiplied by a first coefficient x whose value is between 0.05 and 0.15, preferably 0.1, if said at least one battery is a lithium-ion battery, or else the value of which is between 15 and 25, preferably 20, if said battery is a sodium-ion battery.
[0024] According to a particular aspect, said ratio of the coefficient of the approximate signal in said first charging / discharging cycle to the coefficient of the approximate signal in said further charging / discharging cycle is multiplied by said Euler number.
[0025] Finally, said Euler number may be multiplied by a second coefficient y whose value is between 0.08 and 1.2, preferably 1.
[0026] In practice, the percent residual capacity is calculated according to the following formula: wherein:
[0027] Ai is the approximation coefficient at said further i-th charge / discharge cycle;
[0028] Aois the approximation coefficient at said first charge / discharge cycle;
[0029] Ni is the number of cycles performed until said further i-th cycle;
[0030] Dn iis the detail coefficient at the n level of decomposition at said further i-th charge / discharge cycle;
[0031] Dn 0is the detail coefficient at the n level of decomposition at said first charge / discharge cycle.
[0032] It should be noted that the exponent c, in the case of the lithium-ion battery, is absent because it takes a value equal to one, so the formula would be as follows:
[0033] In a particular embodiment of the invention, said discrete wavelet transform of the electric voltage output in the first charge / discharge cycle of said battery, and said discrete wavelet transform of the electric voltage output in at least one further charge / discharge cycle of said battery, are based on a Daubechies-type wavelet.
[0034] In particular, said discrete wavelet transform of the electric voltage output in the first charge / discharge cycle of said battery, and said discrete wavelet transform of the electric voltage output in at least one additional charge / discharge cycle of said battery, are decomposed to the fourth level.
[0035] Finally, the method, both in the case of the first embodiment and in the case of the second embodiment (which will be described further below), may comprise the step h) of replacing said battery in case the residual capacity value calculated during said step f) is less than a selected threshold value, preferably less than 80% of the maximum capacity value of said battery at its first life cycle io.
[0036] Furthermore, the purposes are also achieved by means of a computer program to assess the state of health of an electrochemical battery, preferably of the lithium-ion or sodium-ion type, wherein the program comprises instructions for implementing the steps of a method according to one or more of claims 1 to 14 when the program is executed by a central processing unit, wherein said central processing unit is used in a car or in a system storing the energy contained in one or more electric batteries.
[0037] Finally, the purposes are also achieved by means of a vehicle comprising at least one electrochemical battery, preferably of the lithium-ion or sodium-ion type, and at least one central processing unit adapted to execute a program according to claim 15, which implements a method according to one or more of claims 1 to 14.
[0038] Brief description of the figures
[0039] Reference will be made to the figures in the attached drawings, in which:
[0040] Figure 1 shows a simplified schematic of a first embodiment of the method according to the invention applied to a lithium-ion battery;
[0041] Figures 2A and 2B show, respectively, the variation of the vehicle speed and intensity of current absorbed by the battery as time changes during the absorption simulation of the battery according to the urban test drive SC03;
[0042] Figure 3 shows in graphical form the comparison between the values obtained by means of the calculation function performed in the course of the evaluation method according to the invention and the values actually measured;
[0043] Figure 4 shows a simplified schematic of a second embodiment of the method applied to a lithium-ion battery;
[0044] Figure 5 shows a simplified schematic for determining the first normalisation function and the second normalisation function applied in the second embodiment of the method.
[0045] Detailed description of preferred embodiments
[0046] Herein below is described an embodiment related to the method of assessing the state of health of an electrochemical battery 1, preferably of the lithium-ion type.
[0047] A similar solution can also be used for batteries of the sodium-ion type.
[0048] Such method, with reference to Figure 1, comprises the steps of: a) detecting in the first charging / discharging cycle io of the battery 1, for a certain period of time and at a certain sampling frequency, the voltage output xo(t) of the battery 1 as a result of the current absorption to which the battery 1 is subjected when operating (block 201); b) performing the discrete wavelet transform decomposition of the voltage signal xo(t) determined in the first charging / discharging cycle during said step a), to obtain an approximate low-frequency signal of the voltage signal uoAo and a high-frequency detail signal woDi,o, woD2,o, woD3,o, woD4,o,... woDn,o of the voltage signal xo(t) in order to determine the coefficient Ao of the approximate signal and the coefficients Di,o, Di,o, Da,o, D4,o,...Dn,o of the detail signal (block 202); c) detecting, in at least one further charging / discharging cycle i of the battery 1 following the first charging / discharging cycle io, for a certain period of time and at a certain sampling frequency, the voltage output xi(t) of said battery 1 as a result of the current absorption to which the battery 1 is subjected when operating (block 201); d) performing the discrete wavelet transform decomposition of the voltage signal detected Xi(t) in the step c) to obtain an approximate low-frequency signal of the voltage signal UiAi and a high-frequency detail signal WiDij,, WiD 24, WiD3j, WiD4j,... WiDnj of the voltage signal xi(t) to determine the coefficient Ai of the approximate signal and the coefficients Dij, D2J, D3J,D4J, . . .Dn,i of the detail signal (block 202); e) counting the number of charging / discharging cycles Ni performed by said battery at least until said further charging / discharging cycle i (block 203); f) calculating the percentage residual capacity Cf of the battery 1, compared to the maximum rated capacity Cmax, by means of a function of calculating the residual capacity C(Ai, Di.,, D2J, D3J, D4J, ...D nj, Ni,i) which depends at least on the number of cycles Ni performed by the battery and calculated during said step e), on the ratio of the coefficient Ao of the approximate signal in the first charging / discharging cycle io to the coefficient Ai of the approximate signal in the further charging / discharging cycle io, and on the ratio of the summation of the detail coefficients Dij, D2J, D3J, D4J, ...Dnj in the further charging / discharging cycle i to the summation of the detail coefficients Di,o, D2,o, D3;o, D4,O, .. .Dn,o in the first charging / discharging cycle io (block 204).
[0049] It should be emphasized that, as it happens and is described in the known art, the method described here is also performed by a management system of the electrochemical battery 1 that is able to provide various information, including the measured voltage and current, pack and cell temperature, and estimated battery capacity.
[0050] In particular, in such calculation function of the residual capacity C(Ai, Dij, D2J, D3j, D4J, ...D nj, Ni,i) the ratio of the summation of the detail coefficients Dij, D2J D3J, D4J ...Dnj in said further charging / discharging cycle i to the summation of the detail coefficients Di,o, D2;o, D3.O, D4>O, . . . Dnji in said first charging / discharging cycle io is used as negative exponent of the Euler number e.
[0051] Furthermore, such negative exponent is multiplied by the ratio of the number of cycles Ni performed until the further cycle to the coefficient Ai of the approximate signal in the further charge / discharge cycle i.
[0052] In particular, in the case of the lithium battery, the number of cycles Ni is raised to an exponent c between 0.8 and 1.2, preferably 1 (as in the case of the example below). In the case of a sodium-ion battery, such exponent c is between -0.5 and -0.4, preferably - 0.425.
[0053] Again, the negative exponent, in the case described here of using lithium-ion batteries, is also multiplied by a first coefficient x the value of which is between 0.05 and 0.15, preferably 0.1. In the case of sodium-ion battery, such coefficient is between 15 and 25, preferably 20.
[0054] In particular, according to the embodiment described here, the discrete wavelet transform used in the steps b) and d) is based on a Daubechies-type wavelet and is decomposed to the fourth level.
[0055] Furthermore, in the calculation function of the residual capacity C(Ai, Dy, D2,i, Da,i, Dy, ...Dn,i, Ni,i), the ratio of the coefficient Ao of the approximate signal in the first charge / discharge cycle io to the coefficient Ai approximate signal in the further charge / discharge cycle i is multiplied by the Euler number e.
[0056] Again, the Euler number e is multiplied by a second coefficient y between 0.08 and 1.2, preferably 1.
[0057] In practice, in the case of the lithium-ion battery, the function of calculating the residual capacity C(Ai, Dy, D2,i, Da,i, Dy, ...Dn,i, Ni,i) can be expressed mathematically in the following way: wherein:
[0058] Ai is the approximation coefficient at said further i-th charge / discharge cycle;
[0059] Aois the approximation coefficient at said first charge / discharge cycle;
[0060] Ni is the number of cycles performed until said further i-th cycle;
[0061] Dn iis the detail coefficient at the n level of decomposition at said further i-th charge / discharge cycle;
[0062] Dn 0is the detail coefficient at the n level of decomposition at said first charge / discharge cycle.
[0063] According to the embodiment described here, the detail coefficient is decomposed to the fourth level.
[0064] In general terms, the calculation function of the residual capacity C(Ai, Dy, D2,i, Da,i, Dy, . . .Dn,i, Ni,i) can be expressed mathematically in the following way: 100 [%]
[0065] In which, compared with the previous formula, the exponent c is added to the number of cycles Ni because such exponent c takes a value different from the unit value, when using the formula with sodium-ion batteries.
[0066] In the embodiment described here, the Applicant performed a series of charge and discharge cycles on a lithium battery 1. In particular, the charge and discharge cycles are performed by running the SC03 urban test drive, which was introduced by the “Supplemental Federal Test Procedure” (SFTP) to represent the engine load associated with air conditioning use in vehicles certified in the FTP75 test cycle (such as, for example, taught in the publication “US: Light-duty SC03 Test.” [Online], Available: https: / / www.transportpolicy.net / standard / us- light-duty-scO3-test / . The cycle simulates a vehicle running a mileage of 12.8 km at a maximum speed of 88.2 km / h and for a duration of 596 seconds. The two graphs of Figure 2A,2B depict, respectively, the variation of the vehicle speed and intensity of current absorbed by the battery 1 as time changes during the absorption simulation of the battery 1 according to the urban test drive SC03.
[0067] Subsequently, the above-described method was used to detect, in the first charging / discharging cycle io of the battery 1, thus during the step a), for a certain period of time and at a certain sampling frequency, which in this case correspond to 596 seconds and 10 Hz, the voltage output xo(t) of the battery 1 as a result of the current absorption to which the battery 1 is subjected when operating. Again, thanks to the method, it was detected during the phase c), in a plurality of further charging / discharging cycles i of the battery 1, following the first charging / discharging cycle io, for a certain period of time (i.e. 596 seconds) and at a certain sampling frequency (i.e. 10Hz), the voltage output Xi(t) of said battery 1 as a result of the current absorption to which the battery 1 is subjected when operating. In particular, the subsequent further cycles correspond to cycle 30, 60, 90, 120, 150, 180, 210 and 240.
[0068] Then, in the course of the steps b) and d), the wavelet transform decompositions of the xo(t) e X3o(t), X6o(t), X9o(t), Xi2o(t), xi5o(t), xi8o(t), X2io(t) e X24o(t) signals were performed.
[0069] The results of such decompositions made it possible to identify the respective coefficients Ai of the approximate signal and the coefficients of the detailed signal, which are depicted below in a table: illustrano, rispettivamente, la variazione della velocità del veicolo e dellintensità di corrente assorbita dalla batteria 1 al variare del tempo nel corso della simulazione di assorbimento della batteria 1 secondo il test drive urbano SC03. In seguito, è stato impiegato il metodo sopra descritto per rilevare nel primo ciclo i0di carica / scarica della batteria 1, dunque durante la fase a), per un determinato periodo di tempo e ad una determinata frequenza di campionamento, che nel caso in ispecie corrispondono a 596 secondi e 10 Hz, l’uscita in tensione x0(t) della batteria 1 a seguito dell’assorbimento di corrente a cui la batteria 1 è soggetta nel proprio funzionamento. Sempre grazie al metodo è stato rilevato, nel corso della fase c), in una pluralità di ulteriori cicli di carica / scarica i della batteria 1, successivo al primo ciclo di carica / scarica i0, per un determinato periodo di tempo (ovvero 596 secondi) e ad una determinata frequenza di campionamento (ovvero 10Hz), l’uscita in tensione xi(t) della batteria 1 a seguito dell’assorbimento di corrente a cui la batteria 1 è soggetta nel proprio funzionamento. In particolare, i successivi ulteriori cicli corrispondono al ciclo 30, 60, 90, 120, 150, 180, 210 e 240. Nel cor posizioni in trasformata wavelet del seg 0(t) e x240(t). I risultati di tali decomposizioni hanno permesso di individuare i rispettivi coefficienti del segnale approssimato Aied i coefficienti del segnale di dettaglio che sono qui di seguito rappresentati in tabella: Capacità Riduzione Cicli misurata di capacità T (°C) D1D2D3D4A 0 0.012 0.008 0.004 213.39 30 3116 99.1% 20 0.018 0.013 0.009 0.004 211.94 60 3037 96.6% 20 0.024 0.018 0.012 0.006 209.08 90 3027 963% 20 0033 0025 0017 0.008 206.47 both during the step a) (To), i.e., during the initial charge and discharge cycle io, and during the step c) (block 205) (T30, Teo T90, T120 T150, T180 T210, T240), i.e., during the further charge and discharge cycles ii after the initial cycle io. The detail coefficients Dy, Dij, D3J, D4,i,...Dn,i identified during the step d) and used in the function C(Ai, Dy, D2,i, D3J, D4,i, . . .Dn,i, Ni,i)) during the step f) and the detail coefficients DEO, D^.O, D30, D4,o,...Dn,o identified during said step b) and used in said function C(Ai, Dy, D2,i, D3J, D4,i, . . .Dn,i, Ni,i)) during the step f) are multiplied by a first normalisation function (N1(T)) (block 206).
[0070] Additionally, the coefficient Ai of the approximate signal identified during the step d) and used in the calculation function of the residual capacity C(Ai, Dy, D2,i, D3J, D4,i, . . .Dn,i, Ni,i)) during the step f) and the coefficient Ao of the approximate signal identified during the step b) and used in the function C(Ai, Dy, D2,i, D3J, D4,i, ...Dn,i, Ni,i)) during the step f) are multiplied by a second normalisation function (N2(T)) (block 206). Such a first normalisation function (N1(T)) and such a second normalisation function (N2(T)) are able to transform, respectively, the detail coefficients and the approximation coefficient obtained at the temperature measured during the step g), into the detail coefficients DTrefpo, DTrefy), DTrefy, DTrefy,.. .DTrefiy; DTrefy, DTrefy, DTrefy, DTrefy,... DTrefy and into the approximation coefficient ATrefo; ATrefi; obtainable at a reference temperature Tref at the first cycle and in further charge and discharge cycles. This reference temperature Tref is preferably 20°C.
[0071] The first normalisation function N1(T) depends on the percentage variation of the detail coefficients obtained at the reference temperature, compared to the detail coefficients obtained at the temperatures measured during said step g).
[0072] The second normalisation function N2(T) depends on the percentage variation of the approximation coefficient ATrefo and ATrefi which can be obtained at a reference temperature Tref, compared to the approximation coefficient ATrefo and ATrefi obtained at the temperature measured during said step g).
[0073] The Applicant surprisingly found that both the first normalisation function N1(T) and the second normalisation function N2(T) are linear functions, or however, linearizable with high accuracy.
[0074] In particular, the first normalisation function N1 (T) and the second normalisation function N2(T) are derived during a step i) preceding step a), in which a plurality of test batteries 10, 20, 30 identical to electrochemical battery 1 are subjected, in their first charge / discharge cycle, to a predetermined current absorption cycle (see Figure 5). Each battery' 10, 20, 30 of the plurality of test batteries are in an environment with distinct controlled temperature, such as, for example, 0°C, 20°C and 30°C. Among these distinct test temperatures, 20°C is selected as the Tref reference temperature. Such step i) comprises, for each test battery' 10, 20, 30, the step il) of detecting, in the first charging / discharging cycle iopof each test battery 10, 20, 30, for a certain period of time and at a certain sampling frequency, the voltage output XToP(t) as a result of the current absorption to which the test battery is subjected according to a pre-set law (block 210); the step i2) of performing the discrete wavelet transform decomposition of the voltage signal XT0p(t) for each test battery 10, 20, 30 to obtain an approximate low-frequency signal of said voltage signal UTOPATOPand a high-frequency detail signal WTOPDTOIP, WTOPDTO2P, WTODTO3P, WTODTO4P, ... WTODTOHP of the voltage signal XToP(t) in order to determine the coefficient ATOPof the approximate signal and the coefficients DTOIP, DTO?.P, DTO3P, DTO4P, ...DTOBP of the detail signal (block 211); the step i3) of identifying the first linear function N1(T) as function expressing, as temperature varies, the percentage variation of the detail coefficients Direfoip, DTref02p, DTref03p, DTref04P,...DTref0np obtained at the reference temperature Tref, compared to the detail coefficients DTOIP, DTOIP, DTO3P, DTO4P, . . .DTOHPobtained at the general test temperature, i.e. at 0°C and 30°C, and also of identifying the second linear function N2(T) as function expressing, as the temperature varies, the percentage variation of the approximate coefficient AirefOp obtained at the reference temperature Tref, compared to the approximate coefficient ATOPobtained at the general test temperature, i.e. at 0°C and 30°C (block 212).
[0075] It should be noted that the number of temperatures at which the test can be carried out can be more than three.
[0076] In particular, as with steps a) and c), the charge and discharge cycles are performed by running the SC03 urban test drive, which was introduced by the "Supplemental Federal Test Procedure" (SFTP) to represent the engine load associated with air conditioning use in vehicles certified in the FTP75 test cycle (such as, for example, taught in the publication “US: Light-duty SC03 Test.” [Online], Available: https: / / www.transportpolicy.net / standard / us- light-duty-scO3-test / . The cycle simulates a vehicle running a mileage of 12.8 km at a maximum speed of 88.2 km / h and for a duration of 596 seconds. The two graphs of Figure la, lb depict, respectively, the variation of the vehicle speed and intensity of current absorbed by the battery' 1 as time changes during the absorption simulation of the battery 1 according to the urban test drive SC03 (see Figures 1 A and IB).
[0077] Here below is the summary table of the results obtained by using the method following the steps il) to i3) in the case of lithium-ion battery' (identical procedure would be performed for a sodium-ion battery with different numerical results):
[0078] The following table shows the percentage variations identified by using the following formula, for each temperature: wherein Von and VAn correspond to the percentage variations of the detail and approximation coefficients for each distinct temperature.
[0079] As mentioned above, said discrete wavelet transform of the electric voltage output in the first charge / discharge cycle of said battery, and said discrete wavelet transform of the electric voltage output in at least one additional charge / discharge cycle of said battery, are decomposed to the fourth level, so we have four detail coefficients.
[0080] Thus, the functions N1(T) and N2(T) are of the type:
[0081] N2(T)ri = 1 + (A-rrefop—^TOpV ^-rop
[0082] In the embodiment described here, also taking into account the tables identified above, the two functions N1(T) and N2(T) for lithium batteries assume the following formulation in mathematical terms
[0083] A1(T) = 1 + (0,0318 * T — 0,6294)
[0084] A2(T) = 1 + (- 0.0016 * T + 0.0366) However, these functions N1(T) and N2(T), although not calculated and shown here, are similar even in the case of sodium-ion batteries with different numerical values, however.
[0085] It should be emphasized that the normalisation functions N1(T) and N2(T) play a key role in determining the state of health of a battery and, therefore, in calculating the percentage of residual capacity (Cf) of said battery (1) compared to the maximum rated capacity (Cmax), since they allow for the temperature present in the containment region of the battery to be taken into account and, therefore, allow greater calculation accuracy than can be obtained by a method of the known art. Such aspect was neither described nor mentioned in any of the documents of the known art.
[0086] Furthermore, a computer program can be arranged to assess the state of health of an electrochemical battery 1, preferably of the lithium-ion or sodium -ion type. The program, preferably executed by means of the aforementioned management system of the electrochemical battery 1, comprises instructions for implementing the steps of the method described above or, otherwise, according to one or more of claims 1 to 14 when the program is executed by a central processing unit. Such a central processing unit is used in a car or in a system for storing the energy contained in one or more batteries.
[0087] Such central processing unit is therefore comprised in the aforementioned management system of the electrochemical battery 1.
[0088] Finally, the electrochemical battery 1 is comprised in a vehicle which in turn is comprising a central processing unit adapted for executing a program of the type described above capable of implementing a method for assessing the state of health of an electrochemical battery 1 as described above, or otherwise according to one or more of claims 1 to 14.
[0089] Finally, the method comprises the step h) of replacing said battery 1 in case the residual capacity value calculated during said step f) is less than a selected threshold value, preferably less than 80% of the maximum capacity value of said battery 1 at its first life cycle io.
Claims
CLAIMS1) Method for assessing the state of health of an electrochemical battery (1), preferably of the lithium-ion or sodium -ion type, by a management system of said electrochemical battery (1), comprising the steps of: a) detecting in the first charging / discharging cycle (io) of said battery (1), for a certain period of time and at a certain sampling frequency, the voltage output (xo(t)) of said battery (1) as a result of the current absorption to which said battery (1) is subjected when operating; b) performing the discrete wavelet transform decomposition of said voltage signal (xo(t)) determined in the first charging / discharging cycle during said step a), to obtain an approximate low-frequency signal of said voltage signal (uoAo) and a high-frequency detail signal (woDi,o, woD2,o, woD3,o, woD4,o,... woDn,o) of said voltage signal (xo(t)) in order to determine the coefficient (Ao) of the approximate signal and the coefficients (Di,o, Di,o, Da,o, D4,O, . . .Dn,o) of the detail signal; c) detecting, in at least one further charging / discharging cycle (i) of said battery (1) following said first charging / discharging cycle (io), for a certain period of time and at a certain sampling frequency, the voltage output (xi(t)) of said battery (1) as a result of the current absorption to which said battery (1) is subjected when operating; d) performing the discrete wavelet transform decomposition of said voltage signal detected (xi(t)) in said step c) to obtain an approximate low-frequency signal of said voltage signal (uiAi) and a high-frequency detail signal (wiDy, WiD 24, W1D3J, WiD4,i,... WiDn,i) of said voltage signal (xi(t)) to determine the coefficient (A0 of the approximate signal and the coefficients (Dy, D24 D3J, D44 . . .Dn,i) of the detail signal; e) counting the number of charging / discharging cycles (Ni) performed by said battery at least until said further charging / discharging cycle (i); f) calculating the percentage residual capacity (Cf) of said battery (1), compared to the maximum rated capacity (Cmax), by means of a function of calculating the residual capacity (C(Ai, Dy, D2,i, D3,i, D4,i, ...D nj, Ni,i)) which depends at least on the number of cycles (Ni) performed by said battery and calculated during said step e), on the ratio of the coefficient (Ao) of the approximate signal in said first charging / discharging cycle (io) to the coefficient (Ai) of the approximate signal in said further charging / discharging cycle (i), and on the ratio of the summation of the detail coefficients (Dy, D24 D3J, D44 ...Dn,i) in said further charging / discharging cycle (i) and the summation of the detail coefficients (Di,o, D2,o, D3,o, D4,O, . • -Dn,o) in said first charging / discharging cycle (io).2) Method according to claim 1, wherein in said function of calculating the residual capacity,said ratio of the summation of the detail coefficients (Dij, D2,i, D34, D4,i, . . .Dn,i) in said further charging / discharging cycle (i) to the summation of the detail coefficients (Di,o, D2,o, Da,o, D4,o,...Dn,o) in said first charging / discharging cycle (io) is used as negative exponent of the Euler number (e).3) Method according to claim 2, wherein said negative exponent is multiplied by the ratio of said number of cycles (Ni) performed until said further cycle to the coefficient (Ai) of the approximate signal in said further charging / discharging cycle (i), preferably said number of cycles (Ni) is raised to an exponent (c) between 0.8 and 1.2, preferably 1, if said at least one battery is a lithium-ion battery, or else is raised to an exponent between -0.5 e -0.4, preferably -0.425, if said at least one battery is a sodium-ion battery.4) Method according to claim 3, wherein said negative exponent is further multiplied by a first coefficient (x) whose value is between 0.05 and 0.15, preferably 0.1, if said at least one battery is a lithium-ion battery, or else the value of which is between 15 and 25, preferably 20, if said battery is a sodium-ion battery.5) Method according to one or more of claims 2 to 4, wherein in said function of calculating the residual capacity, the ratio of the coefficient (Ao) of the approximate signal in said first charging / discharging cycle (io) to the coefficient (Ai) of the approximate signal in said further charging / discharging cycle (i) is multiplied by said Euler number (e).6) Method according to one or more of claims 2 to 5, wherein said Euler number (e) is multiplied by a second coefficient (y) between 0.08 and 1.2, preferably 1.7) Method according to one or more of claims 1 to 6, wherein said discrete wavelet transform is based on a Daubechies-type wavelet.8) Method according to claim 7, wherein said discrete wavelet transform is decomposed to the fourth level.9) Method according to one or more of claims 1 to 8, wherein said function of calculating the residual capacity (C(Ai, Dy, D2,i, D34, D4.
1. ...Dn,i, Ni,i)) is expressed by the following mathematical formula: 100 [%]10) Method according to one or more of claims 1 to 9, comprising the step g) of measuring the temperature of the containment region of said at least one battery both during said step a) and during said step c), wherein said detail coefficients (Dy, D24, D34, D44, ...Dn,i) identified during said step d) and used in said function C(Ai, Dy, D24, D34, D44, . . .Dn,i, Ni,i)) during said step f) and said detail coefficients (Di,o, D2,o, D3,o, D4,o,...Dn,o) identified during said step b)and used in said function C(Ai, Dy, D2,i, Dy, Dy ...Dn,i, Ni,i)) during said step f) are multiplied by a first normalisation function (N1(T)), and wherein said coefficient (Ai) of the approximated signal identified during said step d) and used in said function C(Ai, Dy, D2,i, Dy, Dy ...D y, Ni,i)) during said step f) and said coefficient (Ao) of the approximate signal identified during said step b) and used in said function C(Ai, Dy, D2,i, D3J, Dy, ...Dn,i, Ni,i)) during said step f) are multiplied by a second normalisation function (N2(T)), said first normalisation function (N1(T)) and said second normalisation function (N2(T)), transforming, respectively, said detail coefficients and said approximation coefficient obtained at the temperature measured during said step g), in the detail coefficients (DTrefi,o, DTref’2,0, DTrefy, DTrefy,. . .DTrefy, DTrefy, DTrefy, DTrefy, DTrefy. . .DTref y) and in the approximation coefficient (ATrefo;ATrefi;) which can be obtained at a reference temperature (Tref), said reference temperature being preferably 20°C.11) Method according to claim 10, wherein the first normalisation function (N1(T)) depends at least on the percentage variation of said detail coefficients obtained at said reference temperature, compared to said detail coefficients obtained at the temperatures measured during said step g).12) Method according to claim 10 or 11, wherein the second normalisation function (N2(T)) depends at least on the percentage variation of said approximation coefficient (ATrefo and ATrefi) which can be obtained at a reference temperature (Tref), compared to said approximation coefficient (ATrefo and ATrefi) obtained at the temperature measured during said step g).13) Method according to one or more of claims 10 to 12, wherein said first normalisation function and said second normalisation function are linear or, in any case, functions linearisable with high accuracy,14) Method according to one or more of claims 10 to 13, wherein said first normalisation function (N1(T)) and second normalisation function (N2(T)) are obtained during a step i) prior to said step a), wherein a plurality of test batteries identical to said first battery are subjected, in their first charging / discharging cycle, to a pre-set current absorption cycle, each test battery of said plurality of test batteries being in an environment with distinct controlled temperature, wherein a temperature between said distinct temperatures is selected as the reference temperature Tref, said step i) comprising, for each test battery, the step il) of detecting, in the first charging / discharging cycle (iop) of each test battery for a certain period of time and at a certain sampling frequency, the voltage output (xToP(t)) as a result of the current absorption to which said test battery is subjected according to a pre-set law; the stepi2) of performing the discrete wavelet transform decomposition of said voltage signal (xToP(t)) for each test battery to obtain an approximate low-frequency signal of said voltage signal (UTOPATOP) and a high-frequency detail signal (WTOPDTIOP, WTOPDT2OP, WTODT3OP, WTODT4OP, . . . WTODTIIOP) of said voltage signal (xiop(t)) in order to determine the coefficient (ATOP) of the approximate signal and the coefficients (DTIOP, DT2OP, DT3OP, DT4OP, . .. D-mop) of the detail signal; the step i3) of identifying said first linear function (N1(T)) as function expressing, as temperature varies, the percentage variation of said detail coefficients (Direfiop, DTrei2oP, DTref3oP, DTref4oP, ... DirefnOp) obtained at the reference temperature (Tref), compared to said detail coefficients (DTIOP, DT2OP, DT3OP, DT4OP, ... D-mop) obtained at the general test temperature, and also of identifying said second linear function (N2(T)) as function expressing, as the temperature varies, the percentage variation of said coefficient approximate (Airefop) obtained at the reference temperature (Tref), compared to said approximate coefficient (ATOP) obtained at the general test temperature.15) Computer program for assessing the state of health of an electrochemical battery (1), preferably of the lithium-ion or sodium-ion type, executed by a management system of said electrochemical battery (1), the program comprising instructions for implementing the steps of a method according to one or more of claims 1 to 14 when the program is executed by a central processing unit, said central processing unit being used in a car or in a system storing the energy contained in one or more of said electrochemical batteries.16) Vehicle comprising at least one electrochemical battery and at least one central processing unit adapted to execute a program according to claim 15, which implements a method according to one or more of claims 1 to 14.