A lithium battery state of charge estimation method based on an adaptive grey system model
By using an adaptive grey system model and an extended Kalman filter algorithm, combined with lithium battery discharge data and an equivalent circuit model, the problem of low SOC estimation accuracy for lithium batteries is solved, achieving high-precision and robust SOC estimation and supporting reasonable charging schedules.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-03-12
- Publication Date
- 2026-05-29
AI Technical Summary
Existing methods for estimating the state of charge (SOC) of lithium batteries are not very accurate under real-world conditions. They are particularly sensitive to current measurement errors and rely on a large amount of measurement work, making it difficult to achieve accurate estimation during the operation of electric vehicles.
An adaptive grey system model is adopted, combined with an equivalent circuit model and an extended Kalman filter algorithm. By collecting lithium battery discharge data, a nonlinear mapping relationship between SOC and open circuit voltage (OCV) is constructed. The simulated annealing intelligent algorithm is used to optimize the model parameters and realize online SOC estimation.
It provides high-precision and robust SOC estimation, helping users accurately understand battery usage, formulate reasonable charging strategies, and reduce reliance on current measurement errors.
Smart Images
Figure CN121805875B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of electric vehicle battery management system technology, and in particular relates to a method for estimating the state of charge of lithium batteries based on an adaptive grey system model. Background Technology
[0002] Lithium-ion batteries, due to their high energy density and convenience, are widely used in indispensable fields of modern life, such as new energy vehicles, aerospace systems, and consumer electronics. Key indicators such as state of charge (SOC), state of health (SOH), and state of power (SOP) are crucial for evaluating battery performance during operation and predicting lifespan. Among these, SOC is the most intuitive indicator, defined as the ratio of remaining usable capacity to full capacity, and is a fundamental parameter for battery system research and application. However, SOC cannot be directly measured and must be estimated through quantitative calculation methods. Due to the inherent nonlinear behavior of lithium-ion batteries and their sensitivity to constantly changing operating conditions, achieving accurate SOC estimation remains a significant challenge.
[0003] State of Charge (SOC) estimation has long been considered a core technology in the design and application of Battery Management Systems (BMS). To this end, researchers have developed various estimation algorithms. According to a literature review, these methods can be broadly categorized into two types: direct estimation methods and indirect estimation techniques.
[0004] The concept of direct SOC estimation methods is to establish a direct mapping between SOC and measurable signals such as current, voltage, and other observable parameters. One class of direct methods is based on the basic definition of SOC. For example, the discharge experiment method is an offline method involving discharging the battery with a constant current until the cutoff voltage is reached. The product of the discharge time and the current yields the discharge capacity, and due to its simplicity, it can estimate the SOC relatively accurately. Another widely used technique is the ampere-hour integration method, also known as the coulomb counting method. This method is based on a known initial SOC and calculates the remaining battery capacity by integrating the input / output current over time. While conceptually simple and commonly used, the coulomb counting method has several limitations. It cannot directly determine the initial SOC, and its accuracy is highly sensitive to current measurement errors. In practice, current fluctuations and discrete sampling intervals can lead to integration errors that accumulate over time, especially when the sampled values deviate from the actual average current. Another class of direct estimation methods focuses on identifying empirical mappings between other measurable parameters and SOC. For example, the open-circuit voltage (OCV) method estimates SOC based on the voltage measured after the battery has been left to rest. By curve fitting based on experimental measurements at different SOC levels, a data-driven function or lookup table mapping SOC to OCV is constructed. In recent years, direct estimation methods based on machine learning have attracted attention. These models learn the nonlinear relationship between dynamic operating data (such as voltage, current, and temperature) and SOC through training on historical data. For example, a temperature-sensing SOC estimation model has been developed, which uses an optimized long short-term memory network combined with a weighted decaying EKF to achieve robust performance over a wide temperature range.
[0005] Indirect estimation methods are based on the ampere-hour integral method, indirectly obtaining the State of Charge (SOC) through other battery models, machine learning, and filters. The first category combines battery models, such as electrochemical models and equivalent circuit models (ECMs). From a physics-based perspective, these models describe the degradation mechanism. The second category combines machine learning methods, applying convolutional neural networks and long short-term memory recurrent neural networks to SOC estimation. The third category combines filtering algorithms based on the ampere-hour integral method. Kalman filtering (KF) is widely used for real-time data processing of nonlinear systems and shows good performance in predicting the state of charge (SOC) of electric vehicles during operation. All algorithms within the machine learning framework are built upon extensive data collection; by comparing actual data with calculated data, the algorithms are continuously optimized, becoming increasingly sophisticated.
[0006] However, the practical application of the aforementioned SOC estimation methods has several limitations. For direct estimation techniques, discharge experiments are mainly used for model parameter identification and verification in laboratory environments. Under real-world conditions, such as during non-constant current discharge in electric vehicle operation, this method becomes ineffective. Similarly, the ampere-hour integration method must be combined with supplementary estimation techniques to address issues related to unknown initial SOC and integration errors accumulating over time. While the OCV method is theoretically simple, its accuracy is significantly affected by different operating conditions. Furthermore, it requires extensive measurement work, thus limiting its applicability in real-world scenarios. For indirect methods, especially machine learning-based methods, the accuracy of SOC estimation is highly dependent on the quality and consistency of the input features. Even small deviations in the input, such as current, voltage, or other relevant parameters, can lead to significant estimation errors. Summary of the Invention
[0007] To address the shortcomings of the aforementioned background technologies, this invention proposes a lithium battery state of charge estimation method based on an adaptive grey system model. By leveraging the concise modeling structure and uncertainty handling capabilities of grey system modeling, the nonlinear information relationship between SOC and OCV can be extracted using only limited experimental data. This aims to obtain accurate lithium battery state of charge estimation results, enabling battery manufacturers and users to accurately understand the remaining battery capacity and thus make reasonable charging plans.
[0008] To achieve the above-mentioned technical objectives, the present invention proposes the following technical solution:
[0009] A method for estimating the state of charge of a lithium battery based on an adaptive grey system model, which specifically includes the following steps:
[0010] S1. Collect data on the discharge process of lithium battery, calculate the state of charge (SOC) of lithium battery and analyze the SOC characteristics, and then obtain the open circuit voltage (OCV) of lithium battery under different states of charge.
[0011] S2. Construct an adaptive real-domain grey system model ARGM, establish a nonlinear mapping relationship between SOC and OCV, wherein the adaptive real-domain grey system model contains an optimizable real-domain nonlinear order; derive the discrete recursive formula of the ARGM model, and obtain the predicted open-circuit voltage value;
[0012] S3. Based on the reference and predicted values of the open-circuit voltage, the simulated annealing intelligent algorithm is used to optimize the nonlinear order in the real domain. After optimization, the optimal adaptive real-domain gray system model is obtained.
[0013] S4. Combine the optimal adaptive real-domain grey system model with the equivalent circuit model of the lithium battery to construct the state equation of the lithium battery; based on the state equation, online estimation of the state of charge (SOC) is achieved through the extended Kalman filter algorithm.
[0014] Furthermore, step S1 specifically includes:
[0015] After the lithium battery completes initialization and reaches full charge, it is discharged completely with a constant current until the lithium battery cutoff voltage is reached. Data on the lithium battery discharge process, including timestamps, terminal voltage, current value, battery surface temperature, and cumulative discharge capacity, are collected.
[0016] Based on lithium battery discharge process data, the state of charge (SOC) is calculated using the ampere-hour integration method. The continuous integration is transformed into a discrete accumulation form to obtain the SOC of the lithium battery at each sampling time. At the same time, the rate of change of SOC and its coupling characteristics with the terminal voltage are analyzed.
[0017] Voltage response was observed through hybrid pulse power characteristic (HPPC) experiments, and the internal resistance, polarization characteristics, and open-circuit voltage (OCV) under equilibrium conditions of the lithium battery were extracted.
[0018] Furthermore, step S2 specifically includes:
[0019] Instead of using traditional polynomial data fitting, an adaptive real-domain grey system model is constructed, denoted as ARGM(1,1,m,R), with the SOC accumulation operator as the independent variable and the OCV accumulation operator as the dependent variable. Its formula is expressed as:
[0020] ;
[0021] in, The term index of the independent variable term. Indicates the total number of items. For the first The nonlinear order of each independent variable term is used to describe the nonlinear relationship between SOC and OCV, and ≠0; The coefficient of the dependent variable. For constant terms, For the first The coefficients of the independent variable terms; The OCV accumulation operator at sampling time t, The SOC accumulation operator at sampling time t is expressed by the following formula:
[0022] , ;
[0023] in, For the first Each sampling time;
[0024] By obtaining reference values of SOC and OCV of the lithium battery at each sampling time through lithium battery discharge process data, and discretizing the adaptive real-domain grey system model, the parameters are estimated using the least squares method. , Then, the adaptive real-domain grey system model is recursively iterated to obtain the discrete recursive formula of ARGM(1,1,m,R), which is expressed as:
[0025] ;
[0026] in, Indicates the first Each sampling time;
[0027] Based on the discrete recursive formula, the predicted open-circuit voltage value is obtained. .
[0028] Furthermore, step S3 specifically includes:
[0029] Design an objective function based on reference and predicted values of open-circuit voltage. ,in This is the set of nonlinear orders for the ARGM model;
[0030] Perform initialization settings: Given an initial set of nonlinear orders in the real field. Initial temperature of simulated annealing intelligent algorithm Cooling rate Minimum temperature and maximum number of iterations ;Will Substituting into the objective function, we obtain the initial objective function. ;
[0031] Iterative optimization is performed using a two-layer loop structure: the outer loop controls the temperature change, and when the current temperature... Greater than the preset minimum temperature The algorithm continues to execute at each temperature; the inner loop executes at each temperature. In each iteration of the search, the algorithm starts from the current solution. Generate a new candidate solution from the neighborhood. And calculate its corresponding objective function value. ;
[0032] The Metropolis criterion is used to determine whether to accept the newly generated solution; if the new solution is better than the current solution, it is accepted directly, and the current solution is updated. for If the new solution is poor, the algorithm will not reject it directly, but will calculate the probability of acceptance. and with probability Accept the solution;
[0033] When the temperature is less than or equal to the minimum temperature When the time comes, the algorithm terminates and returns the optimal solution. and its corresponding objective function value At this time That is, the optimal set of nonlinear orders for the ARGM model.
[0034] Furthermore, step S4 specifically includes:
[0035] Based on the collected data of the lithium battery discharge process, a second-order RC equivalent circuit model of the lithium battery is constructed, expressed by the following formula:
[0036] ;
[0037] in, It is the internal resistance in ohms, that is, the contact resistance inside the lithium battery. , Polarization resistor, , Polarizing capacitor; , The voltage across the two RC circuits;
[0038] Based on the ampere-hour integral method and Kirchhoff's laws, the discretized state of charge of the lithium battery is... With the polarization voltage of lithium batteries Applying the state variables to the extended Kalman filter, the state equation of the lithium battery is obtained, expressed as follows:
[0039] ;
[0040] in, , For circuit current, The sampling time interval, This refers to the battery's rated capacity.
[0041] Discrete values of open-circuit voltage obtained based on the optimal ARGM model Substituting the above state equations, the online estimation of the lithium battery's SOC is achieved using the extended Kalman filter algorithm.
[0042] This invention also discloses a power battery state of charge estimation system based on an adaptive grey system model, which includes a data acquisition and analysis module, an ARGM model construction module, a model parameter optimization module, and an online SOC estimation module, wherein:
[0043] The data acquisition and analysis module is used to collect data on the lithium battery discharge process, calculate the state of charge (SOC) of the lithium battery and analyze its characteristics, and at the same time obtain the open circuit voltage (OCV) of the lithium battery under different SOCs.
[0044] The ARGM model building module is used to construct an adaptive real-domain grey system model ARGM that includes an optimizable real-domain nonlinear order, establish a nonlinear mapping relationship between SOC and OCV, derive the discrete recursive formula of the model, and obtain the OCV prediction value.
[0045] The model parameter optimization module is used to optimize the real-domain nonlinear order of the ARGM model based on the OCV reference value and the predicted value, using the simulated annealing intelligent algorithm to obtain the optimal adaptive real-domain gray system model.
[0046] The online SOC estimation module combines the optimal adaptive real-domain grey system model with the lithium battery equivalent circuit model to construct the lithium battery state equation, and then uses the extended Kalman filter algorithm to estimate the lithium battery SOC online based on this state equation.
[0047] An electronic device is also disclosed, comprising a memory and a processor, wherein:
[0048] Memory is used to store computer programs that can run on a processor;
[0049] The processor is configured to execute, while running the computer program, a lithium battery state-of-charge estimation method based on an adaptive grey system model as described above.
[0050] A computer-readable storage medium is also disclosed, which stores computer instructions for causing a processor to execute a lithium battery state-of-charge estimation method based on an adaptive grey system model as described above.
[0051] Based on the above technical solution, the present invention has at least the following beneficial effects:
[0052] 1. To address the nonlinear relationship between SOC and OCV of lithium batteries, a novel adaptive grey system model is constructed. Combining an equivalent circuit model and an extended Kalman filter algorithm, a more accurate SOC estimate can be obtained. This adaptive grey system model replaces the traditional high-order polynomial model, using model parameters to more accurately describe the nonlinear relationship, and adaptively describes SOC changes under different discharge test experiments.
[0053] 2. The SOC estimation technology based on the adaptive grey system model can provide high-precision and robust power assessment. This accurate and reliable SOC data is crucial for users, as it not only helps them understand battery usage more accurately and confidently, but also provides reliable decision-making basis for users or systems, enabling the formulation of more reasonable and scientific charging strategies and schedules. Attached Figure Description
[0054] Figure 1 This is a flowchart illustrating the method proposed in this invention;
[0055] Figure 2 This is a diagram showing the actual SOC-OCV relationship at different temperatures in the embodiments of this application;
[0056] Figure 3 This is the SOC-OCV relationship diagram estimated by the ARGM model in the embodiments of this application;
[0057] Figure 4 The figure shows the SOC estimation results of the method proposed in this invention under standard test cycles;
[0058] Figure 5 The figure shows the SOC estimation results of the method proposed in this invention under a mixed test cycle. Detailed Implementation
[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0060] Although the steps in this invention are arranged by reference numerals, this is not intended to limit the order of the steps. Unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" as used herein refers to and covers any and all possible combinations of one or more of the associated listed items.
[0061] Please refer to Figures 1 to 5 A specific implementation method of this embodiment is given:
[0062] like Figure 1 As shown, this invention presents a method for estimating the state of charge of a power battery based on an adaptive grey system model, which specifically includes the following steps:
[0063] S1. Collect data on the discharge process of lithium battery, calculate the state of charge (SOC) of lithium battery and analyze the SOC characteristics, and then obtain the open circuit voltage (OCV) of lithium battery under different states of charge.
[0064] In a preferred embodiment, step S1 specifically includes:
[0065] After the lithium battery completes initialization and reaches full charge, it is fully discharged at a constant current. Discharge testing is the fundamental step in obtaining battery characteristic data. Discharge to the lithium battery's cutoff voltage and collect data on the lithium battery discharge process, including timestamps, terminal voltage, current values, battery surface temperature, and cumulative discharge capacity. Through this complete discharge process, the actual discharge capacity of the battery can be obtained, providing benchmark data for subsequent SOC calculations.
[0066] Based on lithium battery discharge process data, the state of charge (SOC) is calculated using the ampere-hour integration method, and the continuous integration is transformed into a discrete accumulation form to obtain the SOC of the lithium battery at each sampling time; the formula is expressed as:
[0067] ;
[0068] in, This represents the initial state of charge (100% when fully charged). At the initial moment, The rated capacity of the battery. This represents the instantaneous discharge current; in practical calculations, the continuous integral is transformed into a discrete accumulation form. Setting the initial SOC to 100%, for each sampling time, the discretized SOC is obtained as follows: ;in The current value at that moment. This represents the sampling time interval.
[0069] Voltage response was observed using the hybrid pulse power characteristic (HPPC) experiment to extract the internal resistance, polarization characteristics, and open-circuit voltage at equilibrium of the lithium battery. The HPPC experiment is crucial for obtaining the battery's open-circuit voltage and dynamic characteristics, bringing the battery to electrochemical equilibrium. The voltage measured at this equilibrium is the true open-circuit voltage (i.e., the open-circuit voltage reference value). In this embodiment, the HPPC experiment was conducted at multiple SOC points to obtain a complete OCV-SOC characteristic curve. The test points included 11 SOC values: 100%, 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, 10%, and 0%.
[0070] S2. Construct an adaptive real-domain grey system model ARGM, establish a nonlinear mapping relationship between SOC and OCV, wherein the adaptive real-domain grey system model contains an optimizable real-domain nonlinear order; derive the discrete recursive formula of the ARGM model, and obtain the predicted open-circuit voltage value;
[0071] Step S1 yields the true values of SOC and OCV. Based on these, this method constructs a nonlinear mapping relationship between SOC and OCV to estimate SOC. Therefore, the accuracy and robustness of SOC estimation largely depend on the accuracy of handling the nonlinear relationship between SOC and OCV. Although the relationship between SOC and OCV is relatively stable compared to changes in other components of the circuit model, it is still affected by some important factors. For the same battery with the same battery material, the SOC-OCV curve performance differs in discharge tests at different temperatures. This application first uses the ARGM model to describe the relationship between SOC and OCV.
[0072] In a preferred embodiment, step S2 specifically includes:
[0073] Instead of using traditional polynomial data fitting, an adaptive real-domain grey system model is constructed, denoted as ARGM(1,1,m,R), with the SOC accumulation operator as the independent variable and the OCV accumulation operator as the dependent variable. Its formula is expressed as:
[0074] ;
[0075] in, The term index of the independent variable term. Indicates the total number of items. For the first The nonlinear order of each independent variable term is used to describe (in a broader sense) the nonlinear relationship between SOC and OCV (the change in OCV depends on the cumulative discharge capacity, and conversely, OCV can be used to predict SOC online), and ; Its range extends from the traditional continuous sequence of natural numbers to the entire real number domain, thus avoiding a large nonlinear order dimension; The coefficient of the dependent variable. For constant terms, For the first The coefficients of the independent variable terms; The OCV accumulation operator at sampling time t, Let SOC be the accumulation operator at sampling time t, and let represent the accumulated discharge capacity. The formula is as follows:
[0076] , ;
[0077] in, For the first Each sampling time;
[0078] In this embodiment, unlike traditional methods for data fitting, the form is as follows:
[0079] ;
[0080] The ARGM proposed in this method takes into account The cumulative effect of voltage decreases in the sequence. Importantly, the ARGM model considers... The rate of change of OCV in the term also includes its relationship with SOC. Traditional methods, which use high-order polynomial functions to fit and plot smooth SOC-OCV curves, can lead to overfitting and are highly sensitive to small changes in the data; voltage measurement errors can cause significant changes in the polynomial function coefficients. Furthermore, the nonlinear order in the ARGM model... The sequence of natural numbers is not continuous, which simplifies the parameter dimension and avoids overfitting in high-order polynomial fitting. Furthermore, traditional polynomial fitting does not use cumulative sequence modeling, thus failing to fully exploit the hidden information of the sequence to some extent.
[0081] By obtaining reference values of SOC and OCV of the lithium battery at each sampling time through lithium battery discharge process data, and discretizing the adaptive real-domain grey system model, the parameters are estimated using the least squares method. , , ;
[0082] The ARGM model can be transformed into:
[0083] ;
[0084] Least squares method for parameter estimation , , The process is as follows:
[0085] Minimize the sum of squared errors The estimated parameters are obtained in matrix form. (include , , (estimates) ;
[0086] in, ;
[0087] ;
[0088] Then, the adaptive real-domain grey system model is recursively iterated to obtain the discrete recursive formula ARGM(1,1,m,R), which is expressed as:
[0089] ;
[0090] in, Indicates the first Each sampling time;
[0091] Based on the discrete recursive formula, the predicted open-circuit voltage value is obtained. .
[0092] S3. Based on the reference and predicted values of the open-circuit voltage, the simulated annealing intelligent algorithm is used to optimize the nonlinear order in the real domain. After optimization, the optimal adaptive real-domain gray system model is obtained.
[0093] The nonlinear order determined by the simulated annealing intelligent algorithm can not only maximize the exploration of the relationship between OCV and SOC, but also reduce the computational burden. In fact, designing the nonlinear order can omit some irrelevant orders in the Taylor expansion.
[0094] In a preferred embodiment, step S3 specifically includes:
[0095] Design an objective function based on reference and predicted values of open-circuit voltage. ,in This is the set of nonlinear orders for the ARGM model;
[0096] Perform initialization settings: Given an initial set of nonlinear orders in the real field. Initial temperature of simulated annealing intelligent algorithm Cooling rate Minimum temperature and maximum number of iterations ;Will Substituting into the objective function, we obtain the initial objective function. ;
[0097] Iterative optimization is performed using a two-layer loop structure: the outer loop controls the temperature change, and when the current temperature... Greater than the preset minimum temperature The algorithm continues to execute at each temperature; the inner loop executes at each temperature. The algorithm performs a multi-iteration search, with each iteration starting from the current solution (i.e., the set of nonlinear orders for the current iteration). A new candidate solution (a set of candidate nonlinear orders) is generated in the neighborhood. And calculate its corresponding objective function value. ;
[0098] The Metropolis criterion is used to determine whether a new solution is acceptable. If the new solution is better than the current solution, then... If so, then directly accept the new solution and update. for If the new solution is poor, the algorithm will not reject it directly, but will calculate the probability of acceptance. , and with probability Accept the solution; this mechanism allows the algorithm to escape local optima during the search process, enhancing its global search capability. The acceptance probability is related to the difference between temperature and the objective function value; the higher the temperature, the greater the probability of accepting a worse solution.
[0099] After receiving a new solution, the algorithm checks whether the current solution is better than the previously recorded best solution. If Then update the optimal solution. For the current solution And update the optimal objective function value. for This ensures that the algorithm always retains the optimal solution found during the search process;
[0100] Complete at a fixed temperature After the next iteration, the outer loop performs a cooling operation according to the cooling rate. Update temperature, i.e. As the temperature decreases, the algorithm gradually shifts from global search to local fine-grained search, the probability of accepting a poor solution gradually decreases, and it eventually converges to the global optimum or a near-optimal solution;
[0101] When the temperature is less than or equal to the minimum temperature The algorithm terminates and returns the optimal solution when the following conditions are met. and its corresponding objective function value At this time That is, the optimal set of nonlinear orders for the ARGM model.
[0102] By using the simulated annealing algorithm, this invention can effectively search for the optimal nonlinear order of the ARGM model in the real number domain, avoiding getting trapped in local optima, thereby improving the accuracy of SOC-OCV relationship modeling.
[0103] S4. Combine the optimal adaptive real-domain grey system model with the equivalent circuit model of the lithium battery to construct the state equation of the lithium battery; based on the state equation, online estimation of the state of charge (SOC) is achieved through the extended Kalman filter algorithm.
[0104] In a preferred embodiment, step S4 specifically includes:
[0105] Based on existing lithium battery charge-discharge experimental data, a second-order RC equivalent circuit model of a lithium battery is constructed, expressed by the following formula:
[0106] ;
[0107] in, It is the internal resistance in ohms, that is, the contact resistance inside the lithium battery. , Polarization resistor, , Polarizing capacitor; , The voltages across the two RC circuits are given. To estimate the State of Charge (SOC) using an equivalent circuit model, the relevant parameters in the equivalent circuit model must first be estimated. Since the parameters of the equivalent circuit model vary with SOC, temperature, C-rate, and battery degradation, their values are relatively unstable. Therefore, this application uses the nonlinear relationship obtained in S3. This serves as a reference for the relationship between OCV and SOC.
[0108] Based on the ampere-hour integral method and Kirchhoff's laws, the discretized state of charge (SOC) of the lithium battery is correlated with the polarization voltage of the lithium battery. Applying the state variables to the extended Kalman filter, the state equation of the lithium battery is obtained, expressed as follows:
[0109] ;
[0110] in, , For circuit current, The sampling time interval, This refers to the battery's rated capacity.
[0111] The result based on the optimal ARGM model Substituting the above state equations, the online estimation of the lithium battery's SOC is achieved using the extended Kalman filter algorithm.
[0112] In this embodiment, the mean absolute percentage error (MAPE), standard deviation (STD), and root mean square percentage error (RMSPE) are used as evaluation criteria to evaluate the accuracy of the SOC estimate obtained in step S4. The specific evaluation formula is as follows:
[0113] ;
[0114] ;
[0115] .
[0116] Furthermore, this embodiment also discloses a power battery state of charge estimation system based on an adaptive grey system model, which includes a data acquisition and analysis module, an ARGM model construction module, a model parameter optimization module, and an online SOC estimation module, wherein:
[0117] The data acquisition and analysis module is used to collect data on the lithium battery discharge process, calculate the state of charge (SOC) of the lithium battery and analyze its characteristics, and at the same time obtain the open circuit voltage (OCV) of the lithium battery under different SOCs.
[0118] The ARGM model building module is used to construct an adaptive real-domain grey system model ARGM that includes an optimizable real-domain nonlinear order, establish a nonlinear mapping relationship between SOC and OCV, derive the discrete recursive formula of the model, and obtain the OCV prediction value.
[0119] The model parameter optimization module is used to optimize the real-domain nonlinear order of the ARGM model based on the OCV reference value and the predicted value, using the simulated annealing intelligent algorithm to obtain the optimal adaptive real-domain gray system model.
[0120] The online SOC estimation module combines the optimal adaptive real-domain grey system model with the lithium battery equivalent circuit model to construct the lithium battery state equation, and then uses the extended Kalman filter algorithm to estimate the lithium battery SOC online based on this state equation.
[0121] An electronic device is also disclosed, comprising a memory and a processor, wherein:
[0122] Memory is used to store computer programs that can run on a processor;
[0123] The processor is configured to execute, while running the computer program, a lithium battery state-of-charge estimation method based on an adaptive grey system model as described above.
[0124] A computer-readable storage medium is also disclosed, which stores computer instructions for causing a processor to execute a lithium battery state-of-charge estimation method based on an adaptive grey system model as described above.
[0125] In this embodiment, the following experimental example is also conducted: The effectiveness of the proposed method is verified by testing lithium batteries for electric vehicles. In the actual experiment, LA92, US06, and three hybrid driving cycle tests were selected for battery SOC estimation. To reflect the effectiveness of ARGM in mining the SOC-OCV relationship, m=2 is set here. The nonlinear order determined by the optimization algorithm is shown in Table 1 below:
[0126] Table 1. Numerical values of ARGM nonlinear order at different temperatures
[0127]
[0128] Figure 2 The true SOC-OCV relationship at different temperatures is shown. Figure 3The results show the SOC-OCV relationship estimated by ARGM. The results demonstrate that ARGM can accurately estimate the relationship between SOC and OCV even with only 10 data points. The shape of the SOC-OCV curve varies significantly at different temperatures, and ARGM effectively reflects the details of OCV changes. Compared to traditional polynomial fitting, ARGM provides a more accurate depiction of the SOC-OCV relationship while avoiding overfitting caused by the choice of polynomial order and higher-order polynomials.
[0129] To facilitate the expression of discharge duration, the unit has been converted from seconds to hours. Figure 4 and Figure 5 The SOC estimation results are shown for standard cycle test and mixed cycle test at 25°C. Figure 5 In the table, mix1, mix2, and mix3 represent three different hybrid driving cycles. Table 2 lists the specific SOC estimation accuracy evaluation results. As can be seen from the figure, the method proposed in this invention yields relatively accurate results. The estimation error is small in the error variation graph.
[0130] Table 2. Evaluation of SOC estimation accuracy
[0131]
[0132] In summary, this invention proposes an SOC estimation method that uses an adaptive grey system model within an indirect method framework to mine the nonlinear relationship between SOC and OCV. Within the grey system model framework, the cumulative effect of discharge capacity during discharge is considered, and a mining approach that does not use high-order polynomial fitting is introduced. Based on limited data collected from HPPC tests, a novel adaptive grey system model is developed, extending the traditional grey model to the entire real number domain and reducing the dimensionality of nonlinear parameters. This allows SOC-OCV curves with different characteristics to be mapped using fewer parameters in the ARGM. High-precision SOC estimation in five different driving cycle tests fully demonstrates the effectiveness of the proposed method.
[0133] In this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to at least one embodiment or example described in connection with a specific feature, structure, material, or characteristic. These specific features, structures, materials, or characteristics may be combined in a suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples and their features described in this specification.
[0134] The logic and / or steps shown in the flowchart or otherwise described can be viewed as a sequence of executable instructions for implementing logical functions. These instructions may be implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device. Such systems, apparatus, or devices include processor systems or other systems capable of receiving and executing instructions.
[0135] The above embodiments detail the principles and implementation methods of the present invention, and illustrate its working principle using specific examples. These examples are only used to help understand the method and core ideas of the present invention. Furthermore, based on the ideas of the present invention, actual implementation methods and application scope may vary. Therefore, the content of this specification should not be construed as limiting the present invention.
Claims
1. A method for estimating the state of charge of a lithium battery based on an adaptive grey system model, characterized in that, Specifically, the following steps are included: S1. Collect data on the discharge process of lithium battery, calculate the state of charge (SOC) of lithium battery and analyze the SOC characteristics, and then obtain the open circuit voltage (OCV) of lithium battery under different states of charge. S2. Construct an adaptive real-domain grey system model ARGM, establish a nonlinear mapping relationship between SOC and OCV, wherein the adaptive real-domain grey system model contains an optimizable real-domain nonlinear order; derive the discrete recursive formula of the ARGM model, and obtain the predicted open-circuit voltage value; Step S2 specifically includes: Instead of using traditional polynomial data fitting, an adaptive real-domain grey system model is constructed, denoted as ARGM(1,1,m,R), with the SOC accumulation operator as the independent variable and the OCV accumulation operator as the dependent variable. Its formula is expressed as: ； in, The term index of the independent variable term. Indicates the total number of items. For the first The nonlinear order of each independent variable term is used to describe the nonlinear relationship between SOC and OCV, and ; The coefficient of the dependent variable. For constant terms, For the first The coefficients of the independent variable terms; The OCV accumulation operator at sampling time t, The SOC accumulation operator at sampling time t is expressed by the following formula: ， ； in, For the first Each sampling time; By obtaining reference values of SOC and OCV of the lithium battery at each sampling time through lithium battery discharge process data, and discretizing the adaptive real-domain grey system model, the parameters are estimated using the least squares method. , , Then, the adaptive real-domain grey system model is recursively iterated to obtain the discrete recursive formula of ARGM(1,1,m,R), which is expressed as: ； in, Indicates the first Each sampling time; Based on the discrete recursive formula, the predicted open-circuit voltage value is obtained. ; S3. Based on the reference and predicted values of the open-circuit voltage, the simulated annealing intelligent algorithm is used to optimize the nonlinear order in the real domain. After optimization, the optimal adaptive real-domain gray system model is obtained. S4. Combine the optimal adaptive real-domain grey system model with the equivalent circuit model of the lithium battery to construct the state equation of the lithium battery; based on the state equation, online estimation of the state of charge (SOC) is achieved through the extended Kalman filter algorithm.
2. The method for estimating the state of charge of a lithium battery based on an adaptive grey system model according to claim 1, characterized in that, Step S1 is as follows: After the lithium battery completes initialization and reaches full charge, it is discharged completely with a constant current until the lithium battery cutoff voltage is reached. Data on the lithium battery discharge process, including timestamps, terminal voltage, current value, battery surface temperature, and cumulative discharge capacity, are collected. Based on lithium battery discharge process data, the state of charge (SOC) is calculated using the ampere-hour integration method. The continuous integration is transformed into a discrete accumulation form to obtain the SOC of the lithium battery at each sampling time. At the same time, the rate of change of SOC and its coupling characteristics with the terminal voltage are analyzed. Voltage response was observed through hybrid pulse power characteristic (HPPC) experiments, and the internal resistance, polarization characteristics, and open-circuit voltage (OCV) under equilibrium conditions of the lithium battery were extracted.
3. The method for estimating the state of charge of a lithium battery based on an adaptive grey system model according to claim 2, characterized in that, Step S3 is as follows: Design an objective function based on reference and predicted values of open-circuit voltage. ,in This is the set of nonlinear orders for the ARGM model; Perform initialization settings: Given an initial set of nonlinear orders in the real field. Initial temperature of simulated annealing intelligent algorithm Cooling rate Minimum temperature and maximum number of iterations ;Will Substituting into the objective function, we obtain the initial objective function. ; Iterative optimization is performed using a two-layer loop structure: the outer loop controls the temperature change, and when the current temperature... Greater than the preset minimum temperature The algorithm continues to execute at each temperature; the inner loop executes at each temperature. In each iteration of the search, the algorithm starts from the current solution. Generate a new candidate solution from the neighborhood. And calculate its corresponding objective function value. ; The Metropolis criterion is used to determine whether to accept the newly generated solution; if the new solution is better than the current solution, it is accepted directly, and the current solution is updated. for If the new solution is poor, the algorithm will not reject it directly, but will calculate the probability of acceptance. and with probability Accept the solution; When the temperature is less than or equal to the minimum temperature When the time comes, the algorithm terminates and returns the optimal solution. and its corresponding objective function value At this time That is, the optimal set of nonlinear orders for the ARGM model.
4. The method for estimating the state of charge of a lithium battery based on an adaptive grey system model according to claim 3, characterized in that, Step S4 is as follows: Based on the collected data of the lithium battery discharge process, a second-order RC equivalent circuit model of the lithium battery is constructed, expressed by the following formula: ； in, It is the internal resistance in ohms, that is, the contact resistance inside the lithium battery. , Polarization resistor, , Polarizing capacitor; , The voltage across the two RC circuits; Based on the ampere-hour integral method and Kirchhoff's laws, the discretized state of charge of the lithium battery is... With the polarization voltage of lithium batteries Applying the state variables to the extended Kalman filter, the state equation of the lithium battery is obtained, expressed as follows: ； in, , For circuit current, The sampling time interval, This refers to the battery's rated capacity. Discrete values of open-circuit voltage obtained based on the optimal ARGM model Substituting the above state equations, the online estimation of the lithium battery's SOC is achieved using the extended Kalman filter algorithm.
5. A system applied to the lithium battery state-of-charge estimation method based on an adaptive grey system model according to any one of claims 1-4, characterized in that, It includes a data acquisition and analysis module, an ARGM model building module, a model parameter optimization module, and an online SOC estimation module, among which: The data acquisition and analysis module is used to collect data on the lithium battery discharge process, calculate the state of charge (SOC) of the lithium battery and analyze its characteristics, and at the same time obtain the open circuit voltage (OCV) of the lithium battery under different SOCs. The ARGM model building module is used to construct an adaptive real-domain grey system model ARGM that includes an optimizable real-domain nonlinear order, establish a nonlinear mapping relationship between SOC and OCV, derive the discrete recursive formula of the model, and obtain the OCV prediction value. The model parameter optimization module is used to optimize the real-domain nonlinear order of the ARGM model based on the OCV reference value and the predicted value, using the simulated annealing intelligent algorithm to obtain the optimal adaptive real-domain gray system model. The online SOC estimation module combines the optimal adaptive real-domain grey system model with the lithium battery equivalent circuit model to construct the lithium battery state equation, and then uses the extended Kalman filter algorithm to estimate the lithium battery SOC online based on this state equation.
6. An electronic device, characterized in that, The electronic device includes a memory and a processor, wherein: Memory is used to store computer programs that can run on a processor; A processor is configured to, while running the computer program, execute a lithium battery state-of-charge estimation method based on an adaptive grey system model as described in any one of claims 1-4.
7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute a lithium battery state-of-charge estimation method based on an adaptive grey system model as described in any one of claims 1-4.