Energy storage system capacity attenuation modeling method based on multi-stress coupling

Abstract

The invention provides an energy storage capacity attenuation modeling method based on multi-stress coupling, and the method specifically comprises the steps: single stress model modeling: firstly, decomposing a multi-source working condition into three single channels, namely temperature stress, state-of-charge stress and discharge depth, and respectively depicting the marginal influence on capacity degradation; an identifiable parameter set is formed under a unified statistical caliber and is used as the input of subsequent coupling and aggregation; semi-empirical model modeling: adopting a parallel aggregation framework of calendar aging-cyclic aging-total degradation to construct a computable life attenuation model with a unified metering caliber; the nonlinear degradation dynamics and partition expression comprises the following steps of: firstly, normalizing capacity loss according to rated capacity, and recording a life state as L belonging to [0, 1]; according to the method, multi-stress coupling and stages are accurately described, model parameters can be identified, and single-cycle decomposition is easy to embed in engineering, so that the re-calibration cost is reduced; model output supports rolling evaluation and strategy comparison and selection.

Description

Technical Field

[0001] This invention relates to the field of energy storage and dispatch technology. Background Technology

[0002] Against the backdrop of a high proportion of renewable energy grid connection and the continuous growth in demand for grid flexibility, electrochemical energy storage has become a key infrastructure in scenarios such as peak shaving, frequency regulation and backup. Its availability directly depends on the ability to maintain energy storage capacity and the rate of decay.

[0003] Existing engineering methods often collect experimental data on capacity changes with cycle number or duration under single stress conditions, and use empirical formulas such as exponential, power functions, or piecewise linear functions for fitting. Alternatively, they may establish capacity decay models based solely on single factors such as cycle number, time, and average temperature. These methods typically estimate capacity based on single-dimensional indicators such as cycle number, depth, and time aging, making it difficult to reflect the parallel and mutually amplifying effects of multi-source stresses during actual operation. This is especially true when facing complex trajectories involving high temperatures, wide power fluctuations, local high power ratios, and long periods of static storage, where capacity decay exhibits significant nonlinearity and stages. Traditional approaches often approximate complex power sequences with equivalent cycles, neglecting the cumulative impact of ramp rates and frequent small fluctuations on side reactions and impedance evolution, leading to biased lifetime assessments and strategy mismatches.

[0004] While mechanistic models offer interpretability, their numerous parameters and high identification costs make real-time iteration difficult in large-scale power grid simulations. Simultaneously, planning and scheduling urgently require embeddable lifetime constraints and cost functions to achieve a balance between economy and reliability; however, the non-convexity and non-differentiability of existing models limit their depth of application in optimization. Furthermore, the lack of a consistent framework for lifetime cost definitions and marginalization across different projects makes it difficult to uniformly measure current capacity, remaining lifetime, and operational benefits, potentially leading to capacity allocation deviations and fluctuations in operation and maintenance strategies.

[0005] Therefore, there is an urgent need for a multi-stress coupled capacity decay modeling method for engineering applications, which can characterize the combined effect of cyclic and calendar stresses with fewer parameters, perform equivalent stress analysis and damage aggregation on the real power trajectory, and output in an optimized and user-friendly form, providing consistent, updatable and implementable lifetime assessment and cost quantification capabilities for planning, scheduling and operation and maintenance in source-grid-load-storage coordination. Summary of the Invention

[0006] To overcome the problems of bias and strategy mismatch in traditional model lifetime assessment, as well as the lack of a unified framework for measurement, this invention provides a capacity decay modeling method for energy storage systems based on multi-stress coupling.

[0007] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0008] The present invention provides a method for modeling the capacity decay of an energy storage system considering multi-stress coupling, comprising the following steps:

[0009] Single stress modeling,

[0010] To establish a basic framework for capacity degradation, the multi-source operating condition is first decomposed into three single channels: temperature stress, state of charge (SOC) stress, and depth of discharge (DoD). Each channel is used to characterize its marginal impact on capacity degradation, and an identifiable set of parameters is formed under a unified statistical framework, which serves as the input for subsequent coupling and aggregation.

[0011] Semi-empirical modeling,

[0012] This step, under the premise that a single stress channel has been defined, adopts a parallel aggregation framework of "calendar aging - cyclic aging - total degradation" to construct a calculable lifetime decay model with a unified measurement caliber.

[0013] Nonlinear degradation dynamics and partitioning representation

[0014] The above-mentioned lifetime degradation model is used to characterize the nonlinearity and stages of capacity degradation. First, the capacity loss is normalized according to the rated capacity, and the lifetime state is denoted as L∈[0,1]. When L=0, it represents a new battery. In engineering, the lifetime termination point is the state where only 80% of the rated maximum capacity can be provided, and L=0.2 is taken.

[0015] The specific steps for semi-empirical model building are as follows:

[0016] Temperature stress directly modulates the kinetic rates of side reactions and film growth, thereby altering the effective damage dose per unit time or per cycle; this is expressed using Arrhenius dependence, as shown in equation (1):

[0017] ;

[0018] In the formula, The degree of capacity decay of lithium-ion batteries, This represents the actual temperature (°C). The coefficient of thermal stress. The reference temperature (°C) is 293K (25°C), which is the reference temperature for most battery aging tests. This expression treats temperature as an independent variable, reflects the chemical kinetics response to temperature changes with exponential sensitivity, and establishes a comparison baseline across scenarios using the reference temperature.

[0019] To represent the independent marginal effect of state of charge on capacity decay, it is defined as a function of the intensity of side reactions induced by electrode chemical potential and phase region occupancy under a given temperature reference condition; when the cell resides in a high or low SOC range for a long time, the probability and rate of electrolyte oxidation / reduction, side reaction consumption of lithium source and interface film thickening processes change significantly, thus forming an observable "residence-decay" mapping on the time scale; the SOC dependence of calendar aging is not simple and monotonic, and it often shows a decay rate step or inflection point in the medium and high SOC range, and the slope and inflection position of this dependence are different at different temperatures. Therefore, the relevant functional relationship is established as shown in equation (2):

[0020] ;

[0021] In the formula, The capacity decay rate (%) is given under a certain SOC condition. For SOC model parameters, For reference SOC, a value of around 0.4-0.5 is usually chosen; the SOC model parameters are a set of identifiable parameters formed under a unified statistical caliber; the expression uses the SOC interval as the core indicator to generate a marginal damage intensity that matches the working window, which is used to represent the direct effect of the residence location on capacity evolution.

[0022] To provide an identifiable and extrapolable engineering expression from a single stress perspective, an exponential single-channel model with DoD as the sole independent variable is adopted, mapping DoD∈[0,1] to the capacity decay intensity per unit cycle, as shown in equation (3):

[0023] ;

[0024] In the formula, For amplitude parameters, Let exp(·) be the exponential sensitivity parameter, and let exp(·) be the natural exponential function; this form satisfies , ,and Monotonicity and convexity constraints; when ξ→0, The linear response is given for shallow loops, while in the semi-loop / deep loop region, the response is given by... The dominant curvature causes the unit cycle damage to increase exponentially with DoD; the aforementioned exponential density sensitivity parameters form an identifiable set of parameters under a unified statistical caliber.

[0025] The specific steps for semi-empirical model building are as follows:

[0026] Calendar aging, with time, average state of charge, and average temperature as independent variables, describes the natural degradation of a battery under static conditions caused by processes such as interface / electrolyte. Its expression is shown in equation (4):

[0027] ;

[0028] In the formula, For the duration of the observation interval, This represents the average state of charge (SOC) for that interval. This represents the average core / cycle temperature within this range; The output, in the selected metering caliber, is expressed as capacity loss or loss rate, representing the calendar decay at that metering caliber.

[0029] Cyclic aging takes the mapping from the features of the i-th cycle to the unit cycle damage as the basic unit, and then sums them according to the occurrence frequency or weight. Its expression is shown in Equation (5):

[0030] ;

[0031] In the formula, Let SOC be the average SOC of the i-th cycle. The depth of the loop (DoD). This is the equivalent temperature corresponding to this cycle. This represents the number of times (or equivalent weight) this type of loop appears within the statistical window. To be The function mapped to unit cyclic damage; the resulting cyclic decay has the same caliber as equation (4), which facilitates subsequent aggregation;

[0032] Under a unified definition, the total degradation is obtained by superimposing the calendar term and the cycle term in parallel, resulting in equation (6):

[0033] ;

[0034] In the formula, the left end The expression represents the overall degradation function over a given time window and a set of cycles; the first term on the right-hand side of equation (6) is the calendar decay within the window, and the second term is the cyclic decay accumulated according to the cyclic characteristics and frequency. The horizontal line “ˉ” above the parameter in equation (6) represents the mean within the statistical window.

[0035] When the operation is periodic and all cycles are approximately identical, the cycle aging can be linearized within a short time window into the product of the number of cycles and the degradation of a single cycle, as shown in equation (7).

[0036] ;

[0037] In the formula, N is the number of loops within the window. This represents the degradation of a representative single cycle. This linearization operation is enabled under the assumptions of "consistent cycle shape, stable operating conditions, and sufficiently short window" for rapid estimation and optimization modeling.

[0038] To connect with a single stress channel, the degradation of a representative single cycle can be further decomposed into the product of three single-variable functions: DoD, SOC, and temperature, as shown in equation (8):

[0039] ;

[0040] In the formula, ξ∈[0,1] is the normalized depth of discharge (DoD). The average SOC of a representative cycle, The equivalent temperature of a representative cycle; , , These are single-stress mapping functions, and the output is the marginal damage factor under a single-cycle aperture.

[0041] Equation (8) makes the contribution of the three types of stress to single-cycle degradation explicit in a separable form, which is convenient for calibration based on the test stratification of DoD, SOC and temperature during parameter identification; after entering Equation (7) and Equation (6), it can achieve consistent aggregation from single cycle to multi-cycle and then to full window.

[0042] The specific steps for nonlinear degradation dynamics and partitioning representation are as follows:

[0043] The fundamental reason for the nonlinear decay rate is that the capacity loss rate per unit cycle is proportional to the number of remaining active lithium ions in the battery, that is, proportional to (1−L).

[0044] The above mechanism can be expressed in differential form as shown in equation (9):

[0045] ;

[0046] Where N is the cycle count. To represent the degree of degradation of a single cycle,

[0047] Based on the above lifetime decay model, the overall analytical expression obtained by integrating N with equation (9) is shown in equation (10):

[0048] ;

[0049] In the formula To study within the research window The cumulative amount, Equations (9) and (10) give the basic law that the larger the remaining battery capacity, the easier it is to cause damage per cycle, and the marginal damage per cycle decreases as the lifespan progresses. The result corresponds to a typical exponential decay trajectory.

[0050] However, in reality, equations (9) and (10) are difficult to reflect the sudden drop characteristics in the early stage of film formation;

[0051] To address this, a partitioned representation is introduced, and a smoothing weight is used to continuously transition between early and mid-to-late-stage degradation mechanisms; let the lifetime increment in the nth computational step be... Then we can obtain equations (11)-(14):

[0052] ,

[0053] ,

[0054] ,

[0055] ;

[0056] In the formula, This is a dose stretching function used to scale the dose in stages for the degree of degradation per unit cycle. As an early weighting factor for SEI, The shape index is used to adjust the curvature. To smoothly switch weights; It is the central location of the early-to-middle transition. For the transition width; logically, when hour, The updates are mainly driven by early branch paths. The instantaneous degradation density was magnified, representing the sudden capacity drop caused by rapid SEI film formation; when hour, The model automatically switches to the mid-to-late stage branch, and the decay enters a relatively flat phase. This indicates the construction of a calculable lifetime decay model using a unified measurement standard. This enables a continuous description of stage transitions without introducing discrete segmentation.

[0057] The beneficial effects of this invention are as follows: it accurately characterizes multi-stress coupling and stages; the method simultaneously describes the calendar channel of temperature-SOC and the cyclic channel of cycle depth-mean SOC-equivalent temperature under the same metrological caliber; moreover, the exponential lifetime kinetics and smooth weights achieve a continuous transition from rapid decay in the early stage to gradual change in the middle and late stages; dose stretching r(N) is used for staged gain modulation; the curve shape and time scale can be self-adjusted according to the environment without additional modifications. Moreover, the model parameters are identifiable and easily embedded in engineering; single-cycle decomposition allows for partitioned calibration and independent updating of the effects of DoD, SOC, and temperature; stage differences are absorbed by dimensionless gain, reducing recalibration costs; the model output is a standardized sequence of "capacity-time / cycle-operating condition", which can be directly connected to EMS / BMS and source-grid-load-storage optimization scheduling, supporting rolling evaluation and strategy comparison. Attached Figure Description

[0058] Figure 1 This is a flowchart of the model construction process according to an embodiment of the present invention.

[0059] Figure 2 This is a diagram showing the effect of a discharge depth of 10% in an embodiment of the present invention;

[0060] Figure 3 This is a diagram showing the effect of a discharge depth of 20% in an embodiment of the present invention;

[0061] Figure 4 This is a diagram showing the effect of a discharge depth of 50% in an embodiment of the present invention;

[0062] Figure 5 This is a diagram showing the effect when the discharge depth is 80% in an embodiment of the present invention. Detailed Implementation

[0063] The present invention will be further explained and described below with reference to the accompanying drawings and embodiments.

[0064] The following explains the terminology used in this invention:

[0065] Energy storage: refers to energy storage units or systems with electrochemical devices as the main body, including subsystems such as cells / battery clusters, BMS, PCS, thermal management and monitoring / protection, and can be extended to station-level application scenarios.

[0066] Capacity decay: The phenomenon and quantification of capacity decrease over time and cycle count, which can be represented by decreased capacity retention rate, capacity loss, or health status; the end-of-life point is set according to the application threshold.

[0067] Stress: A general term for external / internal operating conditions that affect the rate or mechanism of capacity decay, including but not limited to temperature, state of charge, depth of discharge, etc.

[0068] Multi-stress coupling: Within a unified model framework, stress interactions and gains are explicitly introduced, causing the time scales and curve shapes corresponding to temperature, SOC, DoD, etc., to change in tandem, and can be characterized by structures such as amplification factor, weight, or stage function.

[0069] Decay modeling: The process of establishing a parameterized mathematical model for the evolution of capacity over time / cycles. Mechanistic, semi-empirical, or empirical frameworks can be used to output interpretable, identifiable, and verifiable predictive relationships.

[0070] The present invention provides a method for modeling the capacity decay of an energy storage system considering multi-stress coupling, comprising the following steps:

[0071] Step S1: Single stress model modeling

[0072] To establish a basic framework for capacity degradation, the multi-source operating condition is first decomposed into three single channels: temperature stress, state of charge (SOC) stress, and depth of discharge (DoD), which represent their marginal impact on capacity degradation. Under a unified statistical framework, an identifiable set of parameters is formed as the input for subsequent coupling and aggregation.

[0073] S11, temperature stress directly modulates the kinetic rates of side reactions and film growth, thereby changing the effective damage dose per unit time or per cycle; therefore, it is expressed using Arrhenius dependence, as shown in equation (1):

[0074] ;

[0075] In the formula, The degree of capacity decay of lithium-ion batteries, This represents the actual temperature (°C). The coefficient of thermal stress. The reference temperature is in °C, with a reasonable value of 293K (25°C), which is the reference temperature for most battery aging tests. This expression treats temperature as an independent variable, reflects the chemical kinetics response to temperature changes with exponential sensitivity, and establishes a comparison baseline across scenarios using the reference temperature.

[0076] S12, representing the independent marginal effect of state of charge on capacity decay, is defined as a function of the intensity of side reactions induced by electrode chemical potential and phase region occupancy under a given temperature reference condition. When the cell resides in a high or low SOC range for a long time, the probability and rate of electrolyte oxidation / reduction, side reactions consuming lithium source, and interface film thickening will change significantly, thus forming an observable "residence-decay" mapping on a time scale.

[0077] In fact, the SOC dependence of calendar aging is not simple and monotonic. It often shows a decay rate step or inflection point in the medium to high SOC range, and the slope and inflection point of this dependence are different at different temperatures. Therefore, the relevant function relationship is established as shown in equation (2):

[0078] ;

[0079] In the formula, The capacity decay rate (%) is given under a certain SOC condition. For SOC model parameters, For reference SOC, a value of around 0.4-0.5 is typically chosen. This expression uses the SOC range as the core indicator to generate a marginal damage intensity that matches the working window, representing the direct effect of residence location on capacity evolution;

[0080] To provide an identifiable and extrapolable engineering expression from a single stress perspective, an exponential single-channel model with DoD as the sole independent variable is adopted, mapping DoD∈[0,1] to the capacity decay intensity per unit cycle, as shown in equation (3):

[0081] ;

[0082] In the formula, For amplitude parameters, Let exp(·) be the exponential sensitivity parameter, and let exp(·) be the natural exponential function; this form satisfies , ,and Monotonicity and convexity constraints; when ξ→0, The linear response is given for shallow loops, while in the semi-loop / deep loop region, the response is given by... The dominant curvature causes unit cycle damage to increase exponentially with DoD.

[0083] Step S2: Semi-empirical model building

[0084] This step, under the premise that a single stress channel has been defined, adopts a parallel aggregation framework of "calendar aging - cyclic aging - total degradation" to construct a calculable lifetime decay model with a unified measurement caliber.

[0085] S21, calendar aging, with time, average state of charge and average temperature as independent variables, describes the natural degradation of the battery under static conditions caused by processes such as interface / electrolyte, and its expression is shown in equation (4):

[0086] ;

[0087] In the formula, For the duration of the observation interval, This represents the average state of charge (SOC) for that interval. This represents the average core / cycle temperature within this range; The output, in the selected metering caliber, is expressed as capacity loss or loss rate, representing the calendar decay at that metering caliber.

[0088] S22, Cyclic aging takes the mapping from the characteristics of the i-th cycle to the unit cycle damage as the basic unit, and then sums them according to the occurrence frequency or weight. Its expression is shown in Equation (5):

[0089] ;

[0090] In the formula, Let SOC be the average SOC of the i-th cycle. The depth of the loop (DoD). This is the equivalent temperature corresponding to this cycle. This represents the number of times (or equivalent weight) this type of loop appears within the statistical window. To be The function mapped to unit cyclic damage; the resulting cyclic decay has the same caliber as equation (4), which facilitates subsequent aggregation;

[0091] S23, under a unified standard, the total degradation is obtained by superimposing the calendar term and the cycle term in parallel to obtain equation (6):

[0092] ;

[0093] In the formula, the left end represents the overall degradation function over a given time window and cyclic set; the first term on the right is the calendar decay within the window, and the second term is the cyclic decay accumulated according to the cyclic characteristics and frequency. The horizontal line “ˉ” above the parameter in equation (6) represents the mean within the statistical window.

[0094] S24, when the operation is periodic and all cycles are approximately consistent, the cycle aging can be linearized in a short window into the product of the number of cycles and the degradation of a single cycle, as shown in equation (7);

[0095] ;

[0096] In the formula, N is the number of loops within the window. This represents the degradation of a representative single cycle. This linearized form is enabled under the assumptions of "consistent cycle shape, stable operating conditions, and sufficiently short window" for rapid estimation and optimization modeling.

[0097] To connect with a single stress channel, the degradation of a representative single cycle can be further decomposed into the product of three single-variable functions: DoD, SOC, and temperature, as shown in equation (8):

[0098] ;

[0099] In the formula, ξ∈[0,1] is the normalized depth of discharge (DoD). The average SOC of a representative cycle, The equivalent temperature of a representative cycle; , , These are single-stress mapping functions, and the output is the marginal damage factor under a single-cycle aperture.

[0100] Equation (8) makes the contribution of the three types of stress to single-cycle degradation explicit in a separable form, which is convenient for calibration based on the test stratification of DoD, SOC and temperature when identifying parameters; after entering Equation (7) and Equation (6), consistent aggregation from single cycle to multi-cycle and then to full window can be achieved.

[0101] Step S3: Nonlinear Degradation Dynamics and Partition Representation

[0102] To characterize the nonlinearity and stages of capacity decay, the capacity loss is first normalized to the rated capacity, and the lifetime state is denoted as L∈[0,1]. When L=0, it represents a new battery. In engineering, the lifetime termination point is defined as the state where only 80% of the rated maximum capacity can be provided, and L=0.2 is taken.

[0103] S31, the fundamental reason for the nonlinear decay rate is that the capacity loss rate per unit cycle is proportional to the number of remaining active lithium ions in the battery, that is, proportional to (1−L); the above mechanism is expressed in differential form, as shown in equation (9):

[0104] ;

[0105] Where N is the cycle count. The degree of degradation of a representative single cycle is obtained from step S2. The overall analytical expression is obtained by integrating equation (9) with respect to N, as shown in equation (10):

[0106] ;

[0107] In the formula To study within the research window The cumulative amount.

[0108] Equations (9) and (10) give the basic law that the larger the remaining battery capacity, the easier it is to cause damage per cycle, and the marginal damage per cycle decreases as the lifespan progresses. The result corresponds to a typical exponential decay trajectory. However, equations (9) and (10) are difficult to reflect the sudden drop characteristics in the early stage of film formation.

[0109] S32, thus introducing a partitioned representation and using smooth weights to continuously transition between early and mid-to-late stage degradation mechanisms; let the lifetime increment in the nth computational step be... Then we can obtain equations (11)-(14):

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] In the formula, This is a dose stretching function used to scale the dose in stages for the degree of degradation per unit cycle. As an early weighting factor for SEI, The shape index is used to adjust the curvature. To smoothly switch weights; It is the central location of the early-to-middle transition. For the transition width; logically, when hour, The updates are mainly driven by early branch paths. The instantaneous degradation density was magnified, indicating the sudden capacity drop caused by rapid SEI film formation; when hour, The model automatically switches to the mid-to-late stage branches, where the decay becomes relatively gradual. This achieves a continuous description of stage transitions without introducing discrete segmentation.

[0115] In a specific embodiment, lithium iron phosphate (LFP) cells / clusters are selected as the object, and the capacity loss-cycle count (or time) trajectory is used as the measurement caliber. Calendar and cycle aging are characterized according to equations (4)-(6) and aggregated under a unified measurement caliber. The representative single-cycle degradation is decomposed into a depth of discharge function according to equation (8). SOC function With temperature function The nonlinear evolution of the lifetime state with the cycle is calculated according to equations (9)-(10), and the continuous transition from the early to the middle and late stages is achieved through the dose stretching function and smoothing weight.

[0116] The specific implementation process follows the principle of "single-point calibration - stress extrapolation". Using a base condition of 60℃ temperature, 50% median SOC, and 20% DoD, a one-time mechanistic parameter identification is performed to obtain a fixed parameter set: SEI early amplification factor. Stage switching center and width , Dose stretching and weight-related shape / offset parameters , , , Temperature and SOC amplification factor in a single-cycle separable mapping , The DoD function adopts an exponentially dominant form, and its amplitude and sensitivity parameters are respectively... , The above parameters remain unchanged in all subsequent stress combinations and do not need to be recalibrated.

[0117] Stress extrapolation is performed as follows:

[0118] Firstly, in terms of discharge depth, based on the observation that the equivalent rate increases monotonically with depth and the curvature is smooth, the rate benchmark at 20% is extended to other depths using a unified family of functions, so that the marginal damage and curve curvature under deep cycling are enhanced simultaneously.

[0119] Secondly, in terms of SOC dimension, log-linear regression was performed on the equivalent rates of different SOC medians under 60℃ conditions to obtain... This enables time-scale scaling from baseline SOC to target SOC without altering the curve shape.

[0120] Thirdly, in the temperature dimension, the generalized Arrhenius independent variable is used to fit the change of rate with temperature, resulting in... Using 60℃ as a reference, robust extrapolation is performed to other temperature ranges, ensuring that the rate constant is self-consistently matched with the ambient temperature.

[0121] Then, the three types of amplification factors are substituted into equation (8) to obtain the single-cycle degradation intensity, and then the nonlinear evolution of the lifetime state LLL is advanced by equations (9)-(10); where, Intensity modulation for early branches, , Determine the center and width of the transition phase. , , , The combined effects of dose stretching and the shape and offset of the weighted surface ensure a continuous and differentiable kinetic transition between rapid early decay and gradual mid-to-late-stage decay.

[0122] The parameter set remains constant throughout the entire process to avoid evaluation deviations caused by repeated parameter adjustments under different stress conditions.

[0123] like Figures 2-5 As shown, to verify the model's usability, interval evaluations were performed on the capacity-loop trajectory at typical depths of 10%, 20%, 50%, and 80%, yielding RMSE values ​​of 0.008126, 0.009931, 0.010559, and 0.005495, respectively, and MAPE values ​​of 3.8904, 4.6045, 5.8877, and 2.5869, respectively. The error remained low with increasing temperature, SOC, and DoD linkage, and the residual distribution was balanced with no significant bias. The actual model performance is shown in Table 1. This demonstrates that the parameter set of the "single-point calibration-multi-scenario extrapolation" method possesses both stability and generalization ability, and can be directly used as a unified input for scheduling optimization and lifetime cost assessment.

[0124] Therefore, this embodiment provides a landing process including actual fitting parameters without changing the structure of equations (4)-(10): unified calibrated modeling, one-time calibration and solidification, cross-stress extrapolation reconstruction and quantitative verification, to ensure that the model has interpretable, transferable and easy-to-embed engineering practicality under multi-stress disturbance.

[0125] Table 1

[0126]

[0127] By constructing and identifying parameters of a multi-stress capacity decay model, several post-processing results can be obtained. These include predicted trajectories of capacity changes with cycle count and duration under different combinations of temperature, state of charge, and depth of discharge, which can be used to intuitively compare the lifespan differences under various operating conditions. At the same time, based on preset lifespan termination thresholds, evaluation indicators such as usable lifespan, equivalent cycle count, and annual degradation rate are extracted and further organized into indicator tables and parameter libraries that are easy to use for planning and operation and maintenance.

[0128] This invention has been described through embodiments. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A method for modeling the capacity decay of energy storage systems based on multi-stress coupling, characterized in that, include: Single stress modeling, First, the multi-source operating condition is decomposed into three single channels: temperature stress, state of charge stress, and depth of discharge. The marginal impact of each channel on capacity degradation is characterized, and an identifiable set of parameters is formed under a unified statistical caliber, which serves as the input for subsequent coupling and aggregation. Semi-empirical modeling, Given that a single stress channel has been defined, a parallel aggregation framework of "calendar aging - cyclic aging - total degradation" is adopted to construct a calculable lifetime decay model with a unified measurement standard. Nonlinear degradation dynamics and partitioning representation The above lifetime decay model is used to characterize the nonlinearity and stage of capacity decay. First, the capacity loss is normalized according to the rated capacity, and the lifetime state is denoted as L∈[0,1]. When L=0, it indicates a new battery. In engineering, the end of its lifespan is defined as when it can only provide 80% of its rated maximum capacity.

2. The energy storage system capacity decay modeling method according to claim 1, characterized in that, The specific steps for modeling a single stress model are as follows: Temperature stress directly modulates the kinetic rates of side reactions and film growth, thereby altering the effective damage dose per unit time or per cycle; this is expressed using Arrhenius dependence, as shown in equation (1): ； In the formula, The degree of capacity decay of lithium-ion batteries, This is the actual temperature, in °C. The coefficient of thermal stress. This is a reference temperature in °C. The reasonable value is 293K, which is equivalent to 25°C. This is the reference temperature for most battery aging tests. When a battery cell resides in a high or low SOC range for an extended period, the probability and rate of electrolyte oxidation / reduction, lithium source consumption by side reactions, and interface film thickening processes change significantly, thus forming an observable "residence-degradation" mapping on a time scale. The SOC dependence of calendar aging often shows a degradation rate step or inflection point in the medium-high SOC range, and the slope and inflection point of this dependence differ at different temperatures. Therefore, a relevant functional relationship is established, as shown in equation (2): ； In the formula, The capacity decay rate (%) is given under a certain SOC condition. For SOC model parameters, For reference SOC, a value of around 0.4-0.5 is selected; the SOC model parameters are a set of identifiable parameters formed under a unified statistical caliber. This expression uses the SOC interval as the core indicator to generate a marginal damage intensity that matches the working window. To provide an identifiable and extrapolable engineering expression from a single stress perspective, an exponential single-channel model with DoD as the sole independent variable is adopted, mapping DoD∈[0,1] to the capacity decay intensity per unit cycle, as shown in equation (3): ； In the formula, For amplitude parameters, Let exp(·) be the exponential sensitivity parameter, and let exp(·) be the natural exponential function; this form satisfies , ,and Monotonicity and convexity constraints; the above-mentioned exponential density sensitivity parameters form an identifiable set of parameters under a unified statistical caliber.

3. The energy storage system capacity decay modeling method according to claim 1, characterized in that, The specific steps for semi-empirical model building are as follows: Calendar aging, with time, average state of charge, and average temperature as independent variables, describes the natural degradation of a battery under static conditions caused by interface / electrolyte processes. Its expression is shown in equation (4): ； In the formula, For the duration of the observation interval, This represents the average state of charge for that interval. This represents the average core / cycle temperature within this range; The output, in the selected metering caliber, is expressed as capacity loss or loss rate, representing the calendar decay at that metering caliber. Cyclic aging takes the mapping from the features of the i-th cycle to the unit cycle damage as the basic unit, and then sums them according to the occurrence frequency or weight. Its expression is shown in Equation (5): ； In the formula, Let SOC be the average SOC of the i-th cycle. The depth of the loop (DoD). This is the equivalent temperature corresponding to this cycle. This represents the number of times this type of loop appears within the statistical window, or its equivalent weight. To be The function mapped to unit cyclic damage; the resulting cyclic decay has the same caliber as equation (4); Under a unified definition, the total degradation is obtained by superimposing the calendar term and the cycle term in parallel, resulting in equation (6): ； In the formula, the left end denoted as the overall degradation function over a given time window and cyclic set; the first term on the right is the calendar decay within the window, and the second term is the cyclic decay accumulated according to the cyclic characteristics and frequency. The horizontal line "ˉ" above the parameter in equation (6) represents the mean within the statistical window. When the operation is periodic and all cycles are approximately consistent, the cycle aging is linearized within a short window into the product of the number of cycles and the degradation of a single cycle, as shown in equation (7). ； In the formula, N is the number of loops within the window. The amount of degradation in a representative single cycle; To connect with a single stress channel, the degradation of a representative single cycle can be further decomposed into the product of three single-variable functions: DoD, SOC, and temperature, as shown in equation (8): ； In the formula, ξ∈[0,1] is the normalized depth of discharge (DoD). The average SOC of a representative cycle, The equivalent temperature of a representative cycle; , , These are the marginal damage factors output by the single stress mapping function under a single cyclic aperture; Equation (8) makes the contribution of the three types of stress to single-cycle degradation explicit in a separable form, which is convenient for calibration based on the test stratification of DoD, SOC and temperature during parameter identification.

4. The energy storage system capacity decay modeling method according to claim 1, characterized in that, The specific steps for nonlinear degradation dynamics and partitioning representation are as follows: The nonlinear mechanism of the decay rate, expressed in differential form, is shown in equation (9): ； Where N is the cycle count. To represent the degree of degradation of a single cycle, Based on the above lifetime decay model, the overall analytical expression obtained by integrating N with equation (9) is shown in equation (10): ； In the formula, To study within the research window The cumulative amount; Equations (9) and (10) give the basic law that the larger the remaining capacity of the battery, the easier it is to cause damage per cycle, and the marginal damage per cycle decreases as the lifespan progresses. The result corresponds to a typical exponential decay trajectory. However, equations (9) and (10) are difficult to reflect the sudden drop characteristics in the early stage of film formation. To address this, a partitioned representation is introduced, and a smoothing weight is used to continuously transition between early and mid-to-late-stage degradation mechanisms; let the lifetime increment in the nth computational step be... Then we can obtain equations (11)-(14): ， ， ， ； In the formula, This is a dose stretching function used to scale the dose in stages for the degree of degradation per unit cycle. As an early weighting factor for SEI, The shape index is used to adjust the curvature. To smoothly switch weights; It is the central location of the early-to-middle transition. For the transition width; logically, when hour, The updates are mainly driven by early branch paths. The instantaneous degradation density was magnified, representing the sudden capacity drop caused by rapid SEI film formation; when hour, The model automatically switches to the mid-to-late stage branch, and the decay enters a relatively flat phase. This indicates the construction of a calculable lifetime decay model using a unified measurement standard.

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