A dynamic identification method and system of a battery calendar and cycle aging nonlinear coupling coefficient

Abstract

The application provides a battery calendar and cycle aging nonlinear coupling coefficient dynamic identification method and system, which is suitable for energy storage battery system life prediction with 20-year calendar life requirement. The method establishes a nonlinear mapping relationship between the calendar aging acceleration coefficient and the cycle aging intensity index and the cycle history cumulative effect, introduces a damage memory kernel function to quantify the hysteresis effect of cycle history on calendar aging, constructs a double-channel coupled differential equation set containing cross terms, and uses a recursive least squares algorithm with physical constraint projection to identify the coupling sensitive coefficient and memory time constant online, realizes real-time dynamic identification and adaptive correction of the coupling coefficient. The method breaks through the limitation of independent or weak coupling of cycle and calendar aging in traditional technology, reduces the maximum error of 20-year life prediction from 18.7% to 4.2%, and has clear physical meaning of model parameters and easy engineering implementation of system architecture, which meets the actuarial needs of 20-year warranty of energy storage power station.

Description

Technical Field

[0001] This invention relates to the field of battery management technology, and more specifically, to a method and system for dynamically identifying the nonlinear coupling coefficient between battery calendar and cyclic aging. Background Technology

[0002] As a core component of energy storage systems, the accuracy of lithium-ion battery life prediction directly affects the total life cycle cost and warranty service quality of energy storage power stations. In particular, the high requirement of 20-year calendar life for energy storage battery systems places stringent standards on the accuracy and adaptability of battery aging models. In existing battery aging prediction technologies, calendar aging and cycle aging are generally regarded as independent processes, and the total aging loss is calculated by linear superposition. At the same time, a fixed coupling coefficient is used to characterize the interaction between the two.

[0003] However, existing battery aging prediction technologies have the following problems:

[0004] (1) The nonlinear coupling relationship between cyclic aging and calendar aging is ignored. Under high cyclic intensity conditions, the calendar aging prediction error exceeds 20%.

[0005] (2) The coupling coefficient cannot be adaptively adjusted according to the dynamically changing operating conditions, making it difficult to match the coupling characteristics of the battery under different aging stages and different operating conditions.

[0006] (3) The inability to correct the parameter drift of the aging model in real time leads to low confidence in the prediction of the long-term battery life.

[0007] (4) The inability to quantify the lag effect of cycle history on subsequent calendar aging, and the omission of the "memory effect" of battery damage, further reduces the accuracy of aging prediction.

[0008] This invention can quantify the nonlinear coupling relationship between cycle and calendar aging in real time and realize dynamic correction of the coupling coefficient, breaking through the limitation of the two being independent or weakly coupled, and meeting the life prediction requirements of 20-year warranty for energy storage batteries. Summary of the Invention

[0009] The present invention aims to solve the technical problems mentioned in the background art and provide a dynamic identification method and system for the nonlinear coupling coefficient of battery calendar and cyclic aging.

[0010] To achieve the above objectives, the present invention provides the following technical solution: a method for dynamically identifying the nonlinear coupling coefficient between battery calendar and cyclic aging, comprising the following steps:

[0011] S1. Establish a nonlinear mapping relationship: Define the calendar aging acceleration coefficient. For time-varying functions, establish With instantaneous cyclic aging intensity index Circular history cumulative effect function The nonlinear mapping relationship is as follows: ,in Based on the baseline calendar aging rate, , The coupling sensitivity coefficient to be identified;

[0012] S2. Calculating the cumulative effect of cyclical history: Introducing the damage memory kernel function. The hysteresis effect of cyclic history on subsequent calendar aging is described, and the cumulative effect function of cyclic history is calculated. The damage memory kernel function is an exponentially decaying kernel, expressed as follows: , For memory time constant;

[0013] S3. Construct a dual-channel coupled differential equation system: Construct a system that includes a calendar aging channel, a cyclic aging channel, and nonlinear coupled cross terms. The dual-channel coupled differential equations characterize the total battery capacity decay law, and the total capacity decay formula is as follows: , For nonlinear coupled cross terms, For correction factor, This is the initial capacity of the battery. Due to calendar aging capacity loss, Capacity loss due to cyclic aging;

[0014] S4. Online parameter identification: A recursive least squares algorithm with a forgetting factor is used, combined with the physical constraint projection on the coupling sensitivity coefficient. , Nonlinear cross term coefficients and memory time constant Perform online identification, with the following physical constraints: , , ;

[0015] S5. Convergence Test and Result Output: Set a prediction error threshold. When the absolute value of the prediction error is less than the threshold and remains stable for a continuous period, the parameters are considered to have converged, and the time-varying calendar aging acceleration coefficient is output. Dynamic acceleration coefficient and corrected confidence interval for 20-year battery life prediction.

[0016] A further preferred option: the instantaneous cyclic aging intensity index mentioned in step S1 The calculation formula is: ,in, Instantaneous cyclic aging rate, This refers to the battery's nominal capacity. This is a stress correction function that converts the actual working condition into the equivalent strength under the reference working condition.

[0017] A further preferred embodiment: the stress correction function The expression is: ,in, This is a multiplier correction term. This refers to the actual charge / discharge rate. For reference ratio, This is the rate sensitivity index; This is the temperature correction term, constructed based on the Arrhenius formula. For activation energy, The gas constant is This represents the actual battery temperature. For reference temperature; This is a depth of discharge correction term. This represents the actual depth of discharge. For reference discharge depth, This is the DOD sensitivity index.

[0018] A further preferred solution: The parameter update process of the recursive least squares algorithm with forgetting factor described in step S4 is as follows:

[0019] Define prediction error ,in This is the measured value of the battery capacity. For parameter-based The capacity forecast, ;

[0020] Calculate the gain matrix ,in The covariance matrix is ​​the value at the previous time step. For the regression vector, Forgetting factor, It is the identity matrix;

[0021] Update parameters ;

[0022] Update covariance matrix Among them, the forgetting factor .

[0023] A further preferred option: Step S1 includes a parameter initialization step: calibrating the baseline calendar aging rate based on an equivalent accelerated test at 45℃. Calendar aging rate coefficient Calendar aging power Calibrate the cyclic aging rate coefficient based on standard cyclic testing. Cyclic aging power Ratio Sensitivity Index DOD Sensitivity Index Initialize the coupling sensitivity coefficient , Nonlinear cross term coefficients Memory time constant .

[0024] A dynamic identification system for the nonlinear coupling coefficient of battery calendar and cyclic aging, used to implement the method described in any of the above, includes a cyclic intensity index calculation module, a history effect accumulation module, a dual-channel coupled solver, an online parameter identification engine, and a convergence monitoring module.

[0025] A further preferred embodiment: The cycle strength index calculation module calculates the instantaneous cycle aging strength index based on real-time operating condition data. The historical effect accumulation module calculates based on the exponential decay kernel function. The dual-channel coupled solver integrates cross terms. The system of ordinary differential equations; the online parameter identification engine executes a recursive least squares algorithm with a forgetting factor and physical constraint projection; the convergence monitoring module adaptively adjusts the forgetting factor and outputs the identification confidence.

[0026] Beneficial effects:

[0027] 1. By introducing memory effect and cross-coupling term, the nonlinear acceleration phenomenon in the later stage of aging is accurately captured, and the maximum prediction error in the 20-year life cycle is reduced from 18.7% of the traditional model to 4.2%, which meets the actuarial requirements of the 20-year warranty of energy storage power station.

[0028] 2. Through the model's various parameters (such as sensitivity) Both τmemory (memory time) and τmemory (memory duration) have clear physical meanings, providing quantitative tools for analyzing battery failure mechanisms. For example, The day indicates that the damage caused by the cycle will continue to affect calendar aging for the next month and a half;

[0029] 3. By adopting the recursive least squares method with forgetting factor, it can dynamically adapt to the changes in coupling characteristics of the battery under different aging stages and different operating conditions. Furthermore, through physical constraint projection, the rationality of the identification results and the stability of the model are guaranteed.

[0030] 4. The clear division and logical structure between modules facilitates embedded deployment and engineering implementation in BMS or cloud-based EMS. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the system architecture of the present invention.

[0032] Figure 2 This is a schematic diagram of the multi-stress coupling cyclic aging strength calculation process of the present invention.

[0033] Figure 3 The exponential decay kernel function curve of this invention is different. Comparison diagram.

[0034] Figure 4 This is a schematic diagram illustrating the calculation of the cyclic history cumulative effect of the present invention.

[0035] Figure 5 This is a schematic diagram illustrating the relationship between the memory time constant and battery temperature in this invention.

[0036] Figure 6 The instantaneous cyclic intensity sensitivity coefficient of this invention Schematic diagram.

[0037] Figure 7 The historical cumulative effect coefficient of this invention Schematic diagram.

[0038] Figure 8 The nonlinear cross term coefficients of this invention Schematic diagram.

[0039] Figure 9 The damage memory time constant of the present invention Schematic diagram.

[0040] Figure 10 The results of the three-stage coupling test of the present invention Schematic diagram of the change curve.

[0041] Figure 11 This is a schematic diagram comparing the measured capacity decay value with the model prediction value of the present invention.

[0042] Figure 12 This is a schematic diagram comparing the cumulative distribution of prediction errors in this invention. Detailed Implementation

[0043] The following will refer to the appendices in the embodiments of the present invention. Figures 1-12 The technical solutions in the embodiments of the present invention will be clearly and completely described.

[0044] Please see Figure 1-12 In this embodiment of the invention, a method for dynamically identifying the nonlinear coupling coefficient between a battery calendar and cyclic aging includes the following steps:

[0045] S1. Establish a nonlinear mapping relationship: Define the calendar aging acceleration coefficient. For time-varying functions, establish With instantaneous cyclic aging intensity index Circular history cumulative effect function The nonlinear mapping relationship is as follows: ,in Based on the baseline calendar aging rate, , The coupling sensitivity coefficient to be identified;

[0046] S2. Calculating the cumulative effect of cyclical history: Introducing the damage memory kernel function. The hysteresis effect of cyclic history on subsequent calendar aging is described, and the cumulative effect function of cyclic history is calculated. The damage memory kernel function is an exponentially decaying kernel, expressed as follows: , For memory time constant;

[0047] S3. Construct a dual-channel coupled differential equation system: Construct a system that includes a calendar aging channel, a cyclic aging channel, and nonlinear coupled cross terms. The dual-channel coupled differential equations characterize the total battery capacity decay law, and the total capacity decay formula is as follows: , For nonlinear coupled cross terms, For correction factor, This is the initial capacity of the battery. Due to calendar aging capacity loss, Capacity loss due to cyclic aging;

[0048] S4. Online parameter identification: A recursive least squares algorithm with a forgetting factor is used, combined with the physical constraint projection on the coupling sensitivity coefficient. , Nonlinear cross term coefficients and memory time constant Perform online identification, with the following physical constraints: , , ;

[0049] S5. Convergence Test and Result Output: Set a prediction error threshold. When the absolute value of the prediction error is less than the threshold and remains stable for a continuous period, the parameters are considered to have converged, and the time-varying calendar aging acceleration coefficient is output. Dynamic acceleration coefficient and corrected confidence interval for 20-year battery life prediction.

[0050] Instantaneous Cyclic Aging Intensity Index in Step S1 The calculation formula is: ,in, Instantaneous cyclic aging rate, This refers to the battery's nominal capacity. This is a stress correction function that converts the actual working condition into the equivalent strength under the reference working condition.

[0051] Stress correction function The expression is: ,in, This is a multiplier correction term. This refers to the actual charge / discharge rate. For reference ratio, This is the rate sensitivity index; This is the temperature correction term, constructed based on the Arrhenius formula. For activation energy, The gas constant is This represents the actual battery temperature. For reference temperature; This is a depth of discharge correction term. This represents the actual depth of discharge. For reference discharge depth, This is the DOD sensitivity index.

[0052] The parameter update process of the recursive least squares algorithm with forgetting factor in step S4 is as follows:

[0053] Define prediction error ,in This is the measured value of the battery capacity. For parameter-based The capacity forecast, ;

[0054] Calculate the gain matrix ,in The covariance matrix is ​​the value at the previous time step. For the regression vector, Forgetting factor, It is the identity matrix;

[0055] Update parameters ;

[0056] Update covariance matrix Among them, the forgetting factor .

[0057] Step S1 includes a parameter initialization step: calibrating the calendar aging rate based on a 45℃ equivalent accelerated test. Calendar aging rate coefficient Calendar aging power Calibrate the cyclic aging rate coefficient based on standard cyclic testing. Cyclic aging power Ratio Sensitivity Index DOD Sensitivity Index Initialize the coupling sensitivity coefficient , Nonlinear cross term coefficients Memory time constant .

[0058] A dynamic identification system for the nonlinear coupling coefficient between battery calendar and cyclic aging, used to implement any of the above methods, includes: a cyclic intensity index calculation module, a historical effect accumulation module, a dual-channel coupled solver, an online parameter identification engine, and a convergence monitoring module. The cyclic intensity index calculation module calculates the instantaneous cyclic aging intensity index based on real-time operating condition data. The historical effect accumulation module is calculated based on the exponential decay kernel function. Dual-channel coupled solver with integrated cross terms The system of ordinary differential equations; the online parameter identification engine executes the recursive least squares algorithm with forgetting factor and physical constraint projection; the convergence monitoring module adaptively adjusts the forgetting factor and outputs the identification confidence;

[0059] To verify the effectiveness of this invention, a dynamic identification experiment was conducted using a 280Ah lithium iron phosphate (LFP) prismatic cell (3.2V) as the experimental subject. The specific implementation steps are as follows:

[0060] With a sample size of ≥3 cells, a SOC of 50% and a T of 45°C, a 180-day pure calendar aging test was conducted, and the results were fitted. , ; Set to 1C charge / discharge, DOD=80%, 25℃, and perform 1000 cycle tests on the battery cell, then obtain the fitted result. Then, a three-stage variable cycle strength experiment was designed to simulate different actual operating conditions of the energy storage battery:

[0061] Phase A (1-30 days): 2C charge / discharge, 100% DOD, simulating frequency modulation conditions;

[0062] Phase B (31-60 days): 0.2C supplementary power supply, 10% DOD shallow circulation, simulating peak shaving and valley filling conditions;

[0063] Phase C (61-90 days): Pure static setting, observe the decay of hysteresis effect;

[0064] Based on the characteristics of lithium iron phosphate batteries, initial values ​​for the parameters to be identified are set as follows: , , , The experimental data are input into the method and system of this invention. After running for 6 months, the identified parameters converge to a stable value.

[0065] 1. Instantaneous cycle intensity sensitivity coefficient The value converged to 0.73 after 60 days.

[0066] 2. Historical cumulative effect coefficient The value converged to 0.18 after 90 days.

[0067] 3. Nonlinear cross-term coefficients It converged to 0.12 in 120 days;

[0068] 4. Impaired memory time constant It converged to 45 in 150 days;

[0069] The prediction results of the method of the present invention were compared with those of the traditional independent stacking model. The results showed that the prediction error of the traditional model for 20-year lifespan was 18.7%, while the method of the present invention reduced the maximum prediction error of 20-year lifespan to 4.2%, which greatly improved the prediction accuracy.

[0070] The method and system of this invention are not only applicable to 280Ah lithium iron phosphate energy storage batteries, but can also be extended to different types of lithium-ion batteries such as ternary lithium-ion batteries and lithium manganese oxide batteries, as well as battery systems with different capacities and application scenarios (such as power batteries and portable energy storage batteries). Accurate dynamic identification of the coupling coefficient can be achieved simply by completing the benchmark parameter calibration and initial parameter setting according to the battery type and application conditions. For different types of batteries, only the sensitivity index in the stress correction function needs to be adjusted. , , Given the baseline parameters and the initial values ​​of the parameters to be identified, the core algorithm and system architecture of this invention do not require substantial modification, possessing good versatility and scalability. Furthermore, the dynamic identification method and system of this invention can be directly embedded and deployed in a battery management system (BMS) or a cloud-based energy management system (EMS), enabling online and accurate prediction of the lifespan of energy storage battery systems. This provides quantitative basis for the full life cycle management of energy storage power stations, battery warranty services, and cascade utilization planning, demonstrating significant industrial application value and market prospects. It is applicable to the lifespan management of various energy storage battery systems and is ready for large-scale industrial application.

[0071] The above embodiments only illustrate preferred embodiments of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can freely combine the above technical features without departing from the concept of the present invention, and can also make several modifications and improvements, all of which fall within the protection scope of the present invention. Therefore, all equivalent transformations and modifications made with respect to the scope of the claims of the present invention should fall within the scope of the claims of the present invention.

Claims

1. A method for dynamically identifying the nonlinear coupling coefficient between battery calendar and cyclic aging, characterized in that: Includes the following steps: S1. Establish a nonlinear mapping relationship: Define the calendar aging acceleration coefficient. For time-varying functions, establish With instantaneous cyclic aging intensity index Circular history cumulative effect function The nonlinear mapping relationship is as follows: ,in Based on the baseline calendar aging rate, , The coupling sensitivity coefficient to be identified; S2. Calculating the cumulative effect of cyclical history: Introducing the damage memory kernel function. The hysteresis effect of cyclic history on subsequent calendar aging is described, and the cumulative effect function of cyclic history is calculated. The damage memory kernel function is an exponentially decaying kernel, expressed as follows: , For memory time constant; S3. Construct a dual-channel coupled differential equation system: Construct a system that includes a calendar aging channel, a cyclic aging channel, and nonlinear coupled cross terms. The dual-channel coupled differential equations characterize the total battery capacity decay law, and the total capacity decay formula is as follows: , For nonlinear coupled cross terms, For correction factor, This is the initial capacity of the battery. Due to calendar aging capacity loss, Capacity loss due to cyclic aging; S4. Online parameter identification: A recursive least squares algorithm with a forgetting factor is used, combined with the physical constraint projection on the coupling sensitivity coefficient. , Nonlinear cross term coefficients and memory time constant Perform online identification, with the following physical constraints: , , ; S5. Convergence Test and Result Output: Set a prediction error threshold. When the absolute value of the prediction error is less than the threshold and remains stable for a continuous period, the parameters are considered to have converged, and the time-varying calendar aging acceleration coefficient is output. Dynamic acceleration coefficient and corrected confidence interval for 20-year battery life prediction.

2. The method for dynamic identification of the nonlinear coupling coefficient between battery calendar and cyclic aging according to claim 1, characterized in that: The instantaneous cyclic aging intensity index mentioned in step S1 The calculation formula is: ,in, Instantaneous cyclic aging rate, This refers to the battery's nominal capacity. This is a stress correction function that converts the actual working condition into the equivalent strength under the reference working condition.

3. The method for dynamically identifying the nonlinear coupling coefficient between battery calendar and cyclic aging according to claim 2, characterized in that: The stress correction function The expression is: ,in, This is a multiplier correction term. This refers to the actual charge / discharge rate. For reference ratio, This is the rate sensitivity index; This is the temperature correction term, constructed based on the Arrhenius formula. For activation energy, The gas constant is... This represents the actual battery temperature. For reference temperature; This is a depth of discharge correction term. This represents the actual depth of discharge. For reference discharge depth, This is the DOD sensitivity index.

4. The method for dynamically identifying the nonlinear coupling coefficient between battery calendar and cyclic aging according to claim 1, characterized in that: The parameter update process of the recursive least squares algorithm with forgetting factor described in step S4 is as follows: Define prediction error ,in This is the measured value of the battery capacity. For parameter-based The capacity forecast, ; Calculate the gain matrix ,in The covariance matrix is ​​the value at the previous time step. For the regression vector, Forgetting factor, It is the identity matrix; Update parameters ; Update covariance matrix Among them, the forgetting factor .

5. The method for dynamic identification of the nonlinear coupling coefficient between battery calendar and cyclic aging according to claim 1, characterized in that: Step S1 includes a parameter initialization step: calibrating the calendar aging rate based on a 45℃ equivalent accelerated test. Calendar aging rate coefficient Calendar aging power Calibrate the cyclic aging rate coefficient based on standard cyclic testing. Cyclic aging power Ratio Sensitivity Index DOD Sensitivity Index Initialize the coupling sensitivity coefficient , Nonlinear cross term coefficients Memory time constant .

6. A dynamic identification system for the nonlinear coupling coefficient of battery calendar and cyclic aging, used to implement the method of any one of claims 1-5, characterized in that: It includes a cyclic intensity index calculation module, a historical effect accumulation module, a dual-channel coupled solver, an online parameter identification engine, and a convergence monitoring module.

7. The dynamic identification system for the nonlinear coupling coefficient of battery calendar and cyclic aging according to claim 6, characterized in that: The cycle intensity index calculation module calculates the instantaneous cycle aging intensity index based on real-time operating condition data. The historical effect accumulation module calculates based on the exponential decay kernel function. The dual-channel coupled solver integrates cross terms. The system of ordinary differential equations; the online parameter identification engine executes a recursive least squares algorithm with a forgetting factor and physical constraint projection; the convergence monitoring module adaptively adjusts the forgetting factor and outputs the identification confidence.

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