A lithium battery multi-time scale model parameter identification method based on time domain separation

Abstract

The present application relates to a kind of lithium battery multi-time scale model parameter identification method based on time domain separation in new energy automobile battery management system technical field, based on the analysis voltage recovery curve, the corresponding relationship between macroscopic voltage response characteristic and microcosmic multi-time scale electrochemical mechanism is established, the separation basis of fast dynamic and slow dynamic is proposed;With bipolarization equivalent circuit model as object, introduce fast dynamic and slow dynamic separation point information, construct its prior relationship with state of charge, and introduce it into parameter identification process;Under the prior constraint condition, establish time domain separation recursive least square model parameter identification framework, realize the low-dimensional, weakly coupled separation estimation of fast dynamic and slow dynamic parameters, to improve model precision.The present application fully considers the significant multi-time scale effect inside battery, has the advantages of high model precision, good stability and fast online calculation speed, provides reliable model basis for high-precision estimation and optimization management control of battery state.

Description

Technical Field

[0001] This invention relates to the field of power battery modeling technology in new energy vehicle battery management systems, and provides a method for identifying parameters of lithium battery multi-timescale models based on time-domain separation, which is mainly applicable to power battery modeling and state estimation in new energy vehicle battery management systems. Background Technology

[0002] Lithium-ion batteries are rechargeable secondary batteries that use lithium metal or lithium alloys as positive / negative electrode materials and a non-aqueous electrolyte solution. Due to their advantages such as long lifespan, high energy density, and low self-discharge rate, they have been widely used in the field of new energy vehicles. To fully utilize the performance of lithium-ion batteries, a Battery Management System (BMS) is typically used to monitor and control the battery's operating state. Accurate estimation of the State of Charge (SoC) and State of Health (SOH) is a core function of the BMS. Achieving highly reliable state estimation of power batteries mainly relies on high-precision battery models. Therefore, research on battery models is of great significance for improving the overall performance of battery management systems in new energy vehicles.

[0003] Existing battery modeling methods mainly include electrochemical models, equivalent circuit models, and data-driven models. Among them, electrochemical models have clear mechanisms but high computational complexity, making them difficult to meet the needs of real-time applications; data-driven models are highly dependent on training data and have limited generalization ability; in contrast, equivalent circuit models achieve a better balance between model accuracy and computational complexity, and therefore have become the most widely used model form in lithium battery state estimation.

[0004] Due to the significant nonlinear electrochemical characteristics of lithium batteries, their equivalent model parameters exhibit obvious time-varying features and are easily affected by various factors such as temperature, charge / discharge rate, and aging state. To improve model accuracy and enhance its ability to characterize the time-varying characteristics of parameters, online real-time identification of the equivalent circuit model parameters is usually required. Online parameter identification is considered an effective technical means to address the dynamic changes in battery parameters caused by various internal and external uncertainties.

[0005] Currently, various methods have been proposed for parameter identification of equivalent circuit models of lithium batteries. Among them, recursive least squares (RLS) and adaptive filtering methods are widely used due to their advantages such as simple principle, convenient implementation, and strong engineering applicability. In particular, the RLS algorithm has become a commonly used method for real-time parameter identification of power batteries. However, in practical applications, the RLS algorithm still faces challenges brought about by the multi-timescale characteristics. During the charging and discharging process of lithium batteries, there are mainly two types of internal dynamic processes: charge transfer and ion diffusion. These are usually described in the equivalent circuit model through two different RC branches, where charge transfer corresponds to the fast dynamic process and ion diffusion corresponds to the slow dynamic process. Traditional recursive least squares does not distinguish the above-mentioned multi-timescale characteristics during parameter identification, but estimates all parameters simultaneously. This makes it susceptible to the cross-coupling between different time constants, resulting in a decrease in parameter identification accuracy and even problems with unclear physical meaning of parameters.

[0006] To address the aforementioned issues, existing research often employs a method of designing two separate identification algorithms for different time scales to independently estimate fast and slow dynamic parameters. However, this approach increases computational complexity and system load, hindering online real-time applications. Furthermore, improper coupling between the fast and slow dynamic modules can still negatively impact parameter identification accuracy.

[0007] Therefore, there is an urgent need to propose an equivalent circuit model parameter identification method that fully considers the multi-timescale effects of lithium batteries, so as to improve the accuracy and stability of parameter identification while reducing computational complexity, thereby better meeting the needs of high-precision modeling and online application of power batteries for new energy vehicles. Summary of the Invention

[0008] To address the above issues and overcome the shortcomings and deficiencies of traditional modeling methods and existing multi-timescale modeling methods in the prior art, this invention discloses a method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation.

[0009] To achieve the above objectives, this invention provides a method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation, comprising the following steps: S1. First, based on the analysis of the voltage recovery curve, the relationship between the macroscopic voltage response change trend and the microscopic multi-scale electrochemical mechanism is established, and a separation basis for fast dynamics (FD) and slow dynamics (SD) is proposed to support the multi-scale separation and identification of model parameters. S2. Secondly, based on the dual polarization (DP) equivalent circuit model, the separation point information of FD and SD is introduced to establish the prior relationship between it and SoC, and this prior relationship is introduced as a constraint into the model parameter identification process. S3. Finally, under the above prior constraints, a parameter identification framework for the time-domain separated RLS of the DP equivalent circuit model is established to achieve low-dimensional, weakly coupled separation estimation of FD and SD parameters, thereby improving the model accuracy.

[0010] Furthermore, in step S1 above, based on the voltage recovery curve after the battery discharge ends, the correspondence between the macroscopic voltage response change trend and the microscopic multi-timescale electrochemical evolution mechanism is analyzed. Then, it is proposed that the first zero-crossing point of the second derivative of the recovery voltage be used as the separation point of the FD and SD processes, so as to provide a basis for the multi-scale separation and identification of model parameters.

[0011] Furthermore, in step S2 above, based on the DP equivalent circuit model structure, the FD and SD separation point information obtained in step S1 is determined as the fast time constant. t 1, and construct t The prior mapping relationship between 1 and SoC is used to further calculate the slow time constant. t 2; the aforementioned t 1 and t The prior information of 2 is introduced as a constraint condition into the model parameter identification process to achieve rapid acquisition of fast and slow time constants under different SoC conditions, thereby avoiding blind search of time constants in the real-time identification process and improving the efficiency and reliability of parameter identification.

[0012] Furthermore, step S3 above includes: under the prior constraints established in step S2, pre-solving the model coefficients in the recursive least squares difference equation that are only related to the time constant, so that in the online parameter identification process, it is not necessary to estimate all parameters at the same time, but only to update the unknown parameters related to RC coupling, thereby reducing the parameter identification dimension, simplifying the algorithm implementation complexity, weakening the coupling interference between parameters, and improving the modeling accuracy and system identification stability.

[0013] Furthermore, step S1 specifically involves the following: After the battery completes discharge and enters a resting state, the battery terminal voltage undergoes a dynamic evolution process of gradual recovery from a non-equilibrium state to a quasi-equilibrium state. This voltage recovery process comprehensively reflects the coupling effect of various electrochemical dynamic behaviors within the battery at the macroscopic voltage level. The voltage recovery process is mainly influenced by both charge transfer and ion diffusion processes, where charge transfer corresponds to fast dynamic behavior over a shorter timescale, and ion diffusion corresponds to slow dynamic behavior over a longer timescale.

[0014] Voltage recovery curves were collected after discharge, and their first and second derivatives were calculated to characterize the voltage recovery rate and the rate of change of the voltage recovery rate, respectively. The voltage recovery curve reflects the overall evolution trend of the terminal voltage; the first derivative characterizes the rate of voltage change per unit time, reflecting the intensity of potential changes within the battery; and the second derivative reflects the speed of change of the voltage recovery rate, revealing the switching characteristics of the dominant time periods for different electrochemical mechanisms.

[0015] The characteristics of the first derivative show that its absolute value is relatively large in the early stages of voltage recovery and decays rapidly, indicating that charge transfer is dominant in this phase. As time progresses, the first derivative gradually decreases and approaches zero, indicating that ion diffusion gradually becomes the dominant mechanism. Furthermore, the characteristics of the second derivative show that it changes rapidly in the initial stage and crosses zero for the first time before oscillating slightly around zero. This first zero-crossing point corresponds to the critical moment when the voltage recovery mechanism shifts from charge transfer dominance to ion diffusion dominance, and has clear physical significance.

[0016] Based on the above analysis, the first zero-crossing point of the second derivative of the voltage recovery curve is extracted as the time separation point of the FD and SD processes. Based on this separation point, the quantitative division of the electrochemical dynamic process at multiple time scales is realized, thus providing physical constraints and reliable time scale division basis for the separation modeling and online identification of fast and slow time constant parameters in the subsequent equivalent circuit model.

[0017] Furthermore, step S2 specifically involves: the DP model achieving a good balance between model accuracy and computational complexity, and modeling and describing the dynamic response characteristics of the power battery based on the DP model.

[0018] Electrochemical impedance spectroscopy (EIS) is an effective analytical tool for revealing the characteristics of internal electrochemical processes in lithium-ion batteries. It also serves as a bridge between the battery's internal mechanisms and equivalent circuit models. The characteristic parameters in the EIS spectrum can be correlated with the circuit elements in the dynamics model (DP). Under actual vehicle operating conditions, power batteries are typically not subjected to high-frequency current excitation; therefore, in typical equivalent circuit models, the inductive effect reflected in the high-frequency band can be ignored.

[0019] Resistor in equivalent circuit model RThe pure ohmic internal resistance of the battery is represented by the impedance. When a current excitation is instantaneously applied to the battery, it causes a sudden change in the terminal voltage, which corresponds to the pure real part impedance in the low-frequency range of the impedance spectrum. Both charge transfer and ion diffusion processes exhibit low-pass filtering characteristics in the battery terminal voltage response, but their corresponding frequency ranges differ significantly: the charge transfer process mainly affects the impedance characteristics in the frequency range of 0.2 Hz to several hundred Hz, while the ion diffusion process mainly dominates the low-frequency impedance characteristics below 0.2 Hz. This difference indicates that the two RC networks composed of R1C1 and R2C2 in the DP model have significantly different time constants, corresponding to FD and SD in the battery dynamic response, respectively, thus reflecting the inherent multi-timescale characteristics of the internal electrochemical processes of lithium batteries.

[0020] In the DP model, the RC branch consisting of R1 and C1 is used to simulate the rapid voltage change characteristics caused by the charge transfer process, while the RC branch consisting of R2 and C2 is used to describe the slow voltage change characteristics caused by the ion diffusion process. Based on the above mechanism analysis, this invention innovatively uses the first zero-crossing point of the second derivative of the voltage recovery curve as the time-domain separation point of the lithium battery model parameters to distinguish between the FD and SD processes.

[0021] Under the same temperature and SoH conditions, different discharge rates have little impact on the open-circuit voltage and SoC relationship curve. Therefore, an intermittent discharge test was conducted on the lithium battery at a current of 0.2C to obtain the voltage recovery curve after discharge. The entire SoC range was divided into 10 sub-ranges, with a sampling point set at every 10% of the SoC. The second derivative of the voltage recovery curve after discharge in each sub-range was calculated, and the first zero-crossing point was determined by analyzing the second derivative curve. The time corresponding to this zero-crossing point was then defined as the fast time constant. t 1. Establish based on experimental data t The offline function relationship between 1 and SoC is expressed through piecewise linearization of the function. f (·) can be approximated as shown in equation (1): (1) During the period from the zero-crossing point to the end of the resting phase, the internal process of the battery is mainly dominated by ion diffusion, corresponding to the SD characteristic in the DP model. Therefore, the slow time constant... t 2 can be approximately expressed as the total battery resting time. t r With fast time constant t The difference of 1 is shown in equation (2): (2) Considering that excessively long resting times can lead to a decrease in effective information increment and introduce factors such as temperature drift and voltage hysteresis, affecting the reliability of parameter identification, a reasonable resting time is selected while ensuring sufficient decay of the main SD response. Typically, a 1-hour resting time is sufficient to approximately eliminate polarization effects in lithium batteries. Considering both experimental accuracy and time cost, this invention optimizes the battery resting time... t r Set to 1 hour, that is t r =3600s.

[0022] Furthermore, step S3 specifically involves: In order to fully reflect the multi-timescale characteristics of lithium batteries, this invention improves the DP model parameter identification process based on the separation point of fast and slow timescales, on the basis of the traditional RLS algorithm derivation.

[0023] First, the fast time constant established according to formula (1) t The functional relationship between 1 and SoC was further calculated to obtain the corresponding slow time constant. t 2. Secondly, in the above t 1 and t Under the prior information constraint of 2, the model coefficients in the RLS difference equation that are only related to the time constant are pre-solved. Based on this, during the parameter identification process, it is not necessary to simultaneously estimate all parameters in the DP model, but only to recursively update the unknown parameters related to RC coupling. This effectively reduces the dimensionality of parameter identification, simplifies the algorithm implementation complexity, and significantly weakens the coupling interference between fast and slow dynamic parameters, achieving effective decoupling estimation of FD and SD processes.

[0024] Within the above framework, a time-domain separation RLS online parameter identification algorithm was constructed and applied to the real-time identification of parameters in the DP equivalent circuit model. The implementation process of the time-domain separation RLS online parameter identification algorithm is as follows: The output equation of the DP model in the complex frequency domain is: (3) The difference between the open-circuit voltage and the terminal voltage is defined as... E ( s )= U oc ( s ) U ( s Therefore, the system transfer function is: (4) The system is mapped from the s-plane to the z-plane using a bilinear transformation, as shown in equation (5): (5) In the formula, T This is the system sampling time interval. Based on... z The discrete transfer function of the plane is: (6) in, a 1. a 2. a 3. a 4. a 5 represents the corresponding coefficient for each item.

[0025] (7) Transforming equation (6) into a difference equation yields: (8) Due to time constant t 1. t 2. Given that the sampling time interval is... T Since it has been pre-defined, the coefficient correspondence in the bilinear transformation can be used to transform the system's difference equations. a 1. a 2. These are obtained through direct calculation and are therefore considered as known constant terms. Based on this, the parameter identification process can focus on... a 3. a 4. a 5. The estimation of the three unknown coefficients does not require further calculation. a 1. a 2. Online identification.

[0026] Therefore, intermediate variables can be defined. y ( k As shown in equation (9): (9) make For the system's data matrix, The parameter matrix to be identified by the system: (10) (11) Based on equations (8)–(11), they can be simplified as follows: (12) The parameters of equation (12) are identified using the common RLS recursive formulas with forgetting factor shown in equations (13)–(16), and then the parameters are estimated. i The optimal estimate.

[0027] (13) (14) (15) (16) In the formula, K ( k +1) represents the gain of the algorithm; I It is the identity matrix; P ( k +1) is the error covariance matrix of the state estimate; It is an estimate of the parameter vector; e ( k +1) represents the estimation error; l The forgetting factor is introduced in RLS parameter identification. In RLS parameter identification, the accumulation of large amounts of historical data can easily lead to data saturation, making it difficult for the algorithm to reflect the characteristics of new data in a timely manner. Therefore, the forgetting factor is introduced. l (0< l <1) By attenuating the weight of old data, the ability of RLS to track time-varying parameters is improved. l Generally, 0.95 is taken. l <1, In this invention, the following are taken l =0.98.

[0028] Substituting the bilinear inverse transform factor shown in equation (17) into equation (6) yields equation (18): (17) (18) Equation (19) can be obtained by matching the coefficients of equations (4) and (18): (19) The coefficients in equation (19) a 3. a 4. a 5. Can be identified online via RLS. (In time constant) t 1. t 2 and constant terms a 1. a Given the given information, the unknown resistance parameters in the model can be solved by combining the parameter analytical relationship established by equation (19). R、R 1 、R 2. Furthermore, based on the functional relationship between the time constant and the resistance and capacitance, the capacitance can be derived. C 1. C 2.

[0029] The present invention also includes other components that enable its normal use, all of which are conventional means in the art. In addition, any devices or components not limited in the present invention adopt the prior art in the art.

[0030] The beneficial effects of this invention are as follows: 1. This invention addresses the limitation of TRLS in simultaneously accommodating fast and slow dynamic characteristics. By introducing multi-timescale separation and an improved recursive identification strategy, it effectively overcomes the problem of mutual interference between FD and SD parameters at the same time scale, significantly improving the model's identification accuracy and dynamic tracking performance under complex conditions.

[0031] 2. This invention is based on the multi-timescale electrochemical mechanism of lithium batteries. It utilizes timescale separation points with clear physical meaning to effectively distinguish between FD and SD, avoiding the problem of filter cutoff frequency dependence on empirical selection in traditional frequency response-based methods, and improving the theoretical completeness and engineering applicability of multi-timescale separation.

[0032] 3. This invention transforms the traditional high-dimensional, strongly coupled parameter identification problem into a low-dimensional, weakly coupled recursive estimation problem, thereby achieving separate identification and decoupled estimation of FD and SD parameters. This significantly reduces the computational complexity of the online identification process and improves the real-time performance and engineering feasibility of the algorithm.

[0033] 4. This invention effectively reduces the mutual interference between FD and SD parameters, avoids the error coupling problem caused by the parallel operation of multiple identification algorithms, and thus significantly improves the accuracy, stability and robustness of the identification of the equivalent model parameters of the power battery.

[0034] 5. This invention maintains good parameter tracking capability and model consistency under different operating conditions, which is beneficial to improving the reliability of battery models in state estimation and battery management systems, and has good engineering promotion value and practicality. Attached Figure Description

[0035] Figure 1 This is a structural diagram of the DP model in this invention; Figure 2 This is a voltage recovery curve of the present invention at SoC of 0.9; Figure 3 The first and second derivative curves of the voltage of this invention are shown in the figure when the SoC is 0.9. Figure 4 This is a flowchart illustrating the design of the lithium battery multi-timescale model parameter identification method based on time-domain separation in Example 2. Figure 5 This is a schematic diagram of the battery testing system in Example 3; Figure 6 This is a diagram of the DST operating condition in Example 3; Figure 7 This is a diagram of the WLTC operating conditions in Example 3; Figure 8 This is a schematic diagram showing the comparison of terminal voltage prediction results between the DST condition and the TRLS method in Example 3. Figure 9 This is a schematic diagram showing the comparison of the absolute error of the terminal voltage under the DST condition and the TRLS method in Example 3; Figure 10 This is a schematic diagram showing the comparison of terminal voltage prediction results between the WLTC and TRLS methods under the WLTC operating condition in Example 3. Figure 11 This is a schematic diagram showing the results of comparing the absolute error of the terminal voltage under the WLTC condition with that of the TRLS method in Example 3. Detailed Implementation

[0036] The present invention will now be clearly described in conjunction with the accompanying drawings and specific embodiments. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art based on the embodiments of the present invention without inventive effort to obtain all other embodiments should be included within the scope of protection of the present invention.

[0037] Example 1 This invention provides a method for identifying parameters of a multi-timescale model of lithium batteries based on time-domain separation. Its working principle is as follows: First, based on the analysis of voltage recovery curves, a connection is established between the macroscopic voltage response change trend and the microscopic multi-scale electrochemical mechanism. A separation criterion for the fast dynamic process (FD) and the slow dynamic process (SD) is proposed to support the multi-scale separation and identification of model parameters. Second, based on the dual-polarization DP equivalent circuit model, the separation point information of FD and SD is introduced to establish a priori relationship between FD and SD and the system-on-a-chip (SoC). This priori relationship is then used as a constraint in the model parameter identification process. Finally, under the above prior constraints, a time-domain separation RLS framework for parameter identification of the DP model is established, achieving low-dimensional, weakly coupled separation estimation of FD and SD parameters, thereby improving model accuracy.

[0038] like Figure 1-3 As shown, the method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation includes the following steps: S1. Based on the analysis of voltage recovery curves, the connection between macroscopic voltage response and microscopic multi-scale electrochemical mechanism is established, and a separation basis for FD and SD is proposed to support the multi-scale separation and identification of model parameters. S2. Based on the DP equivalent circuit model, introduce the FD and SD separation point information, establish the prior relationship between it and SoC, and introduce this relationship as a constraint into the model parameter identification process. S3. Under the above prior constraints, establish a parameter identification framework for the time-domain separated RLS of the DP equivalent circuit model, realize low-dimensional and weakly coupled separation estimation of FD and SD parameters, and improve model accuracy.

[0039] In step S1, based on the voltage recovery curve after the battery discharge ends, the correspondence between the macroscopic voltage response change trend and the microscopic multi-timescale electrochemical evolution mechanism is analyzed. Then, it is proposed that the first zero-crossing point of the second derivative of the recovery voltage be used as the separation point of the FD and SD processes, so as to provide a basis for the multi-scale separation and identification of model parameters.

[0040] In step S2, based on the DP equivalent circuit model structure, the FD and SD separation point information obtained in step S1 is determined as the fast time constant. t 1, and construct t The prior mapping relationship between 1 and SoC is used to further calculate the slow time constant. t 2; the aforementioned t 1 and t The prior information of 2 is introduced as a constraint condition into the model parameter identification process to achieve rapid acquisition of fast and slow time constants under different SoC conditions, thereby avoiding blind search of time constants in the real-time identification process and improving the efficiency and reliability of parameter identification.

[0041] Step S3 includes: under the prior constraints established in step S2, pre-solving the model coefficients in the recursive least squares difference equation that are only related to the time constant, so that in the online parameter identification process, it is not necessary to estimate all parameters at the same time, but only to update the unknown parameters related to RC coupling, thereby reducing the parameter identification dimension, simplifying the algorithm implementation complexity, weakening the coupling interference between parameters, and improving the modeling accuracy and system identification stability.

[0042] Example 2 Based on Example 1, this example provides a method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation. The specific steps are as follows: S1. Based on the analysis of voltage recovery curves, the connection between macroscopic voltage response and microscopic multi-scale electrochemical mechanism is established, and a basis for separating FD and SD is proposed. After the battery completes discharge and enters a resting state, the battery terminal voltage undergoes a dynamic evolution process, gradually recovering from a non-equilibrium state to a quasi-equilibrium state. This voltage recovery process comprehensively reflects the coupling effect of various electrochemical dynamic behaviors within the battery at the macroscopic voltage level. This voltage recovery process is mainly influenced by both charge transfer and ion diffusion processes, with charge transfer corresponding to fast dynamic behavior over a shorter timescale and ion diffusion corresponding to slow dynamic behavior over a longer timescale.

[0043] Voltage recovery curves were collected after discharge, and their first and second derivatives were calculated to characterize the voltage recovery rate and the rate of change of the voltage recovery rate, respectively. The voltage recovery curve reflects the overall evolution trend of the terminal voltage; the first derivative characterizes the rate of voltage change per unit time, reflecting the intensity of potential changes within the battery; and the second derivative reflects the speed of change of the voltage recovery rate, revealing the switching characteristics of the dominant time periods for different electrochemical mechanisms.

[0044] The characteristics of the first derivative show that its absolute value is relatively large in the early stages of voltage recovery and decays rapidly, indicating that charge transfer is dominant in this phase. As time progresses, the first derivative gradually decreases and approaches zero, indicating that ion diffusion gradually becomes the dominant mechanism. Furthermore, the characteristics of the second derivative show that it changes rapidly in the initial stage and crosses zero for the first time before oscillating slightly around zero. This first zero-crossing point corresponds to the critical moment when the voltage recovery mechanism shifts from charge transfer dominance to ion diffusion dominance, and has clear physical significance.

[0045] Based on the above analysis, the first zero-crossing point of the second derivative of the voltage recovery curve is extracted as the time separation point of the FD and SD processes. Based on this separation point, the quantitative division of the electrochemical dynamic process at multiple time scales is realized, thus providing physical constraints and reliable time scale division basis for the separation modeling and online identification of fast and slow time constant parameters in the subsequent equivalent circuit model.

[0046] S2. Based on the DP equivalent circuit model, introduce the FD and SD separation point information, establish the prior relationship between it and SoC, and introduce this relationship as a constraint into the model parameter identification process. Dynamic processing (DP) models strike a good balance between model accuracy and computational complexity, and have become one of the mainstream methods for modeling power batteries. This invention models and describes the dynamic response characteristics of power batteries based on DP models.

[0047] Electrochemical impedance spectroscopy (EIS) is an effective analytical tool for revealing the characteristics of internal electrochemical processes in lithium-ion batteries. It also serves as a bridge between the battery's internal mechanisms and equivalent circuit models. The characteristic parameters in the EIS spectrum can be correlated with the circuit elements in the dynamics model (DP). Under actual vehicle operating conditions, power batteries are typically not subjected to high-frequency current excitation; therefore, in typical equivalent circuit models, the inductive effect reflected in the high-frequency band can be ignored.

[0048] Resistor in equivalent circuit model RThis represents the pure ohmic internal resistance of the battery. When a current excitation is instantaneously applied to the battery, it causes a sudden change in the terminal voltage, which corresponds to the pure real impedance in the low-frequency range of the impedance spectrum. Previous studies have shown that both charge transfer and ion diffusion processes exhibit low-pass filtering characteristics in the battery terminal voltage response, but their corresponding frequency ranges differ significantly: charge transfer mainly affects the impedance characteristics in the frequency range of 0.2 Hz to several hundred Hz, while ion diffusion mainly dominates the low-frequency impedance characteristics below 0.2 Hz. This difference indicates that the two RC networks formed by R1C1 and R2C2 in the DP model have significantly different time constants, corresponding to FD and SD in the battery dynamic response, respectively, thus reflecting the inherent multi-timescale characteristics of the internal electrochemical processes of lithium batteries.

[0049] In the DP model, the RC branch consisting of R1 and C1 is used to simulate the rapid voltage change characteristics caused by the charge transfer process, while the RC branch consisting of R2 and C2 is used to describe the slow voltage change characteristics caused by the ion diffusion process. Based on the above mechanism analysis, this invention innovatively uses the first zero-crossing point of the second derivative of the voltage recovery curve as the time-domain separation point of the lithium battery model parameters to distinguish between the FD and SD processes.

[0050] Under the same temperature and SoH conditions, different discharge rates have little impact on the open-circuit voltage and SoC relationship curve. Therefore, an intermittent discharge test was conducted on the lithium battery at a current of 0.2C to obtain the voltage recovery curve after discharge. The entire SoC range was divided into 10 sub-ranges, with a sampling point set at every 10% of the SoC. The second derivative of the voltage recovery curve after discharge in each sub-range was calculated, and the first zero-crossing point was determined by analyzing the second derivative curve. The time corresponding to this zero-crossing point was then defined as the fast time constant. t 1. Establish based on experimental data t The offline function relationship between 1 and SoC is expressed through piecewise linearization of the function. f (·) can be approximated as shown in equation (1): (1) During the period from the zero-crossing point to the end of the resting phase, the internal process of the battery is mainly dominated by ion diffusion, corresponding to the SD characteristic in the DP model. Therefore, the slow time constant... t 2 can be approximately expressed as the total battery resting time. t r With fast time constant t The difference of 1 is shown in equation (2): (2) Considering that excessively long resting times can lead to a decrease in effective information increment and introduce factors such as temperature drift and voltage hysteresis, affecting the reliability of parameter identification, a reasonable resting time is selected while ensuring sufficient decay of the main SD response. Typically, a 1-hour resting time is sufficient to approximately eliminate polarization effects in lithium batteries. Considering both experimental accuracy and time cost, this invention optimizes the battery resting time... t r Set to 1 hour, that is t r =3600s.

[0051] S3. Under the above prior constraints, establish a parameter identification framework for the time-domain separated RLS of the DP equivalent circuit model, realize low-dimensional and weakly coupled separation estimation of FD and SD parameters, and improve model accuracy. To fully reflect the multi-timescale characteristics of lithium batteries, the parameter identification process of the DP model is improved based on the derivation of the traditional RLS (Traditional RLS, TRLS) algorithm and the separation point of the fast and slow timescales. First, the fast time constant is established according to formula (1). t The functional relationship between 1 and SoC was further calculated to obtain the corresponding slow time constant. t 2. Secondly, in the above t 1 and t Under the prior information constraint of 2, the model coefficients in the RLS difference equation that are only related to the time constant are pre-solved. Based on this, during the parameter identification process, it is not necessary to simultaneously estimate all parameters in the DP model, but only to recursively update the unknown parameters related to RC coupling. This effectively reduces the dimensionality of parameter identification, simplifies the algorithm implementation complexity, and significantly weakens the coupling interference between fast and slow dynamic parameters, achieving effective decoupling estimation of FD and SD processes.

[0052] Within the above framework, a time-domain separation RLS online parameter identification algorithm was constructed and applied to the real-time identification of parameters in the DP equivalent circuit model. The implementation process of the time-domain separation RLS online parameter identification algorithm is as follows.

[0053] The output equation of the DP model in the complex frequency domain is: (3) The difference between the open-circuit voltage and the terminal voltage is defined as... E ( s )= U oc ( s ) U ( s Therefore, the system transfer function is: (4) The system is mapped from the s-plane to the z-plane using a bilinear transformation, as shown in equation (5): (5) In the formula, T This is the system sampling time interval. Based on... z The discrete transfer function of the plane is: (6) in, a 1. a 2. a 3. a 4. a 5 represents the corresponding coefficient for each item.

[0054] (7) Transforming equation (6) into a difference equation yields: (8) Due to time constant t 1. t 2. Given that the sampling time interval is... T Since it has been pre-defined, the coefficient correspondence in the bilinear transformation can be used to transform the system's difference equations. a 1. a 2. These are obtained through direct calculation and are therefore considered as known constant terms. Based on this, the parameter identification process can focus on... a 3. a 4. a 5. The estimation of the three unknown coefficients does not require further calculation. a 1. a 2. Online identification.

[0055] Therefore, intermediate variables can be defined. y ( k As shown in equation (9): (9) make For the system's data matrix, The parameter matrix to be identified by the system: (10) (11) Based on equations (8)–(11), they can be simplified as follows: (12) The parameters of equation (12) are identified using the common RLS recursive formulas with forgetting factor shown in equations (13)–(16), and then the parameters are estimated. i The optimal estimate.

[0056] (13) (14) (15) (16) In the formula, K ( k +1) represents the gain of the algorithm; I It is the identity matrix; P ( k +1) is the error covariance matrix of the state estimate; It is an estimate of the parameter vector; e ( k +1) represents the estimation error; l The forgetting factor is introduced in RLS parameter identification. In RLS parameter identification, the accumulation of large amounts of historical data can easily lead to data saturation, making it difficult for the algorithm to reflect the characteristics of new data in a timely manner. Therefore, the forgetting factor is introduced. l (0< l <1) By attenuating the weight of old data, the ability of RLS to track time-varying parameters is improved. l Generally, 0.95 is taken. l <1, In this invention, the following are taken l =0.98.

[0057] Substituting the bilinear inverse transform factor shown in equation (17) into equation (6) yields equation (18): (17) (18) Equation (19) can be obtained by matching the coefficients of equations (4) and (18): (19) The coefficients in equation (19) a 3. a 4. a 5. Can be identified online via RLS. (In time constant) t 1. t 2 and constant terms a 1. a Given the given information, the unknown resistance parameters in the model can be solved by combining the parameter analytical relationship established by equation (19). R、R 1 、R 2. Furthermore, based on the functional relationship between the time constant and the resistance and capacitance, the capacitance can be derived. C 1. C 2. Based on the above derivation, the time-domain separated RLS parameter identification process proposed in this invention is shown in Table 1.

[0058] The design flowchart of the lithium battery multi-timescale model parameter identification method based on time-domain separation of this invention is as follows: Figure 4 As shown in the figure, this processing strategy, based on fully considering the multi-timescale characteristics of lithium batteries, utilizes the timescale separation points with well-defined electrochemical mechanisms to transform the traditional high-dimensional, strongly coupled parameter identification problem into a low-dimensional, weakly coupled recursive estimation problem, thereby effectively improving the modeling accuracy and the stability of system identification.

[0059] Table 1. Time-Domain Separation RLS Parameter Identification Process

[0060] Example 3 Based on the above embodiments, this embodiment uses a self-built experimental testing platform to collect operating data such as voltage and current of lithium batteries under actual operating conditions to simulate the real working state of the battery and provide experimental data support for verifying the advancement of the proposed time-domain separation RLS parameter identification method.

[0061] This embodiment uses the Panasonic NCR18650GA ternary lithium battery as the test object, and its main performance parameters are shown in Table 2. The battery testing system mainly consists of the lithium battery under test, a host computer, a mid-level computer, a programmable electronic load, and a BPH-060A temperature-controlled test chamber. Its overall structure is shown in the diagram below. Figure 5 As shown.

[0062] The programmable electronic load, model CT-4008T-5V6A-S1, features multiple operating modes, including constant current charge / discharge and constant voltage charge / discharge, meeting battery testing requirements under various conditions. This electronic load has eight independent test channels, each independently controllable, with current and voltage measurement errors both less than 1%. Its maximum current rise time is 1ms, effectively ensuring rapid response to the applied current. During the experiment, the system sampling frequency was set to 2Hz to achieve real-time and accurate recording of key operating parameters such as battery terminal voltage and current.

[0063] The host computer is equipped with Neware BTS8.0 software for controlling the programmable electronic load. The intermediate computer acts as a communication bridge, connecting the host computer and the programmable electronic load to achieve bidirectional data and command transmission and real-time interaction. In the experiment, the lithium battery is fixed and connected to the programmable electronic load using a dedicated fixture. The host computer control software enables precise simulation and control of various operating conditions. The temperature control environment is provided by a BPH-060A temperature-controlled experimental chamber, with a temperature adjustment range of [range missing]. With a temperature control accuracy of ±0.5℃, the system can conduct battery tests in a stable and controllable thermal environment, effectively reducing the impact of external environmental factors on experimental results and thus improving data reliability.

[0064] Table 2 Main parameters of lithium batteries

[0065] like Figure 6 and Figure 7 The diagram shows two typical test conditions used in verifying the method's advancement in this invention. These two conditions are based on the Dynamic Stress Test (DST) and the World Light Vehicle Test Cycle (WLTC), respectively, and are referred to as the DST condition and the WLTC condition in this paper. In these conditions, a current greater than zero indicates that the lithium battery is in a discharging state, a current less than zero indicates that the lithium battery is in a charging state, and a current equal to zero indicates that the lithium battery is in a static state. This condition setting is used to simulate the dynamic charging and discharging characteristics of the power battery during actual operation.

[0066] First, the time-domain separation RLS parameter identification method proposed in this invention is compared and analyzed with the TRLS parameter identification method to evaluate the improvement effect of the proposed method in terms of model accuracy. The TRLS method does not consider the mutual coupling relationship between DP model parameters and requires synchronous online identification of the five-dimensional parameter vector, including the ohmic internal resistance and the parameters of the two polarization branches, to achieve real-time updating of model parameters.

[0067] like Figure 8 to Figure 11 As shown, the terminal voltage prediction results and error comparisons obtained by the time-domain separation RLS parameter identification method and the TRLS parameter identification method under different operating conditions are presented. The comparison results show that, compared with the TRLS method, the time-domain separation RLS method proposed in this invention has higher parameter estimation accuracy in the later stages of identification, a smaller peak value of the absolute error of the terminal voltage, better tracking performance, and the model output results are more consistent with the actual operating conditions. The main reason for this is that the method of this invention fully considers the multi-timescale dynamic characteristics inside the lithium battery, effectively weakening the mutual coupling and interference between model parameters, thereby significantly improving the stability and accuracy of the parameter identification results. Furthermore, simulation verification shows that when the slow time constant is set to 3600 or 3600... t At time 1, the simulation results show relatively small differences. To more reasonably characterize the weak coupling characteristics between FD and SD, this invention selects... t 2 = 3600 t 1 is used as an approximate value for the slow time constant, for subsequent parameter identification calculations.

[0068] Table 3 shows the statistical results of the mean absolute error (MAE) and root mean square error (RMSE) of the terminal voltage identification results under different operating conditions. As can be seen from the data in Table 3, under DST operating conditions, compared with the TRLS parameter identification method, the method of this invention improves the terminal voltage MAE by approximately 50.02% and the RMSE by approximately 43.92%. Under WLTC operating conditions, the method of this invention also shows significant advantages, with the MAE improving by approximately 48.47% and the RMSE by approximately 39.79%.

[0069] Table 3 MAE and RMSE under different operating conditions

[0070] The above comparison results further demonstrate that the parameter identification method proposed in this invention can significantly improve the estimation accuracy of the power battery terminal voltage under different dynamic operating conditions, and has good adaptability to operating conditions and engineering application value.

[0071] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation, characterized in that, Includes the following steps: S1. Based on the analysis of voltage recovery curves, establish the correspondence between macroscopic voltage response characteristics and microscopic multi-timescale electrochemical mechanisms, and derive the basis for separating the fast dynamic process FD and the slow dynamic process SD. S2. Taking the dual-polarization equivalent circuit model DP as the object, the separation point information of the fast dynamic process and the slow dynamic process is introduced to establish the prior relationship between the separation point and the state of charge SoC, and this relationship is introduced as a constraint into the model parameter identification process. S3. Under the constraints of prior relations, establish a model parameter identification framework for time-domain separated recursive least squares (RLS) to achieve low-dimensional, weakly coupled separation estimation of fast dynamic process parameters and slow dynamic process parameters, thereby improving model accuracy.

2. The method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation according to claim 1, characterized in that, In step S1, the voltage recovery curve is collected after the battery discharge ends and enters a resting state. By analyzing the correspondence between the macroscopic voltage response characteristics and the microscopic multi-timescale electrochemical mechanism, and taking the first zero crossing point of the second derivative of voltage recovery as the separation point between the fast dynamic process and the slow dynamic process, a basis is provided for the multi-timescale separation and identification of model parameters.

3. The method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation according to claim 1, characterized in that, Step S2 specifically involves: based on the dual-polarization equivalent circuit model structure, determining the separation point information between the fast and slow dynamic processes obtained in step S1 as the fast time constant. τ 1. And construct a fast time constant. τ The prior relationship between 1 and the state-of-charge SoC is further used to calculate the slow time constant. τ 2; then change the fast time constant. τ 1 and slow time constant τ The prior information of 2 is introduced as a constraint condition into the model parameter identification process to achieve rapid acquisition of fast and slow time constants under different states of charge, avoiding blind search of time constants during real-time identification.

4. The method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation according to claim 1, characterized in that, Step S3 includes: under the prior relation constraints established in step S2, pre-solving the model coefficients in the recursive least squares difference equation that are only related to the time constant, so that in the online parameter identification process, it is not necessary to estimate all model parameters at the same time, but only to recursively update the unknown parameters related to RC coupling, thereby reducing the parameter identification dimension, simplifying the algorithm implementation complexity, weakening the coupling interference between model parameters, and improving the modeling accuracy and system identification stability.

5. The method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation according to claim 2, characterized in that: The voltage recovery process is influenced by both charge transfer and ion diffusion processes. Charge transfer corresponds to a fast dynamic process on a shorter timescale, while ion diffusion corresponds to a slow dynamic process on a longer timescale. The voltage recovery curve can reflect the overall evolution trend of the lithium battery voltage recovery process. The first and second derivatives of the voltage recovery curve are calculated. The first derivative is used to characterize the rate of voltage change per unit time, which can reflect the intensity of the potential change inside the battery. The second derivative is used to reflect the rate of change of the voltage recovery rate, which can reveal the switching characteristics of the dominant time period of different electrochemical mechanisms.

6. The method for identifying parameters of a multi-timescale model of a lithium battery based on time-domain separation according to claim 3, characterized in that: Fast time constant τ The prior relationship between 1 and the state of charge (SoC) is expressed by a piecewise linearized function as follows: τ 1= f ( SoC ) Slow time constant τ 2. Total battery resting time t r With fast time constant τ The difference of 1 is used to represent: In the formula, the polarization effect of a lithium battery can be approximately eliminated by leaving it to stand for 1 hour. t r =3600s.

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