A method of state of charge estimation for an energy storage battery system

Abstract

This invention relates to a method for estimating the state of charge (SOC) of an energy storage battery system, specifically a method comprising the following steps: setting an initial state estimate of the energy storage battery system under test and its corresponding initial covariance matrix; updating the SOC using a variable structure filter and dynamically adjusting the parameters of the variable structure filter according to the operating conditions of the energy storage battery system; introducing an adaptive mechanism into the variable structure filter based on changes in noise characteristics during system operation; introducing a strong tracking factor into the variable structure filter to enhance the tracking capability for rapidly changing states and ensure accurate SOC estimation under complex environments; and using the variable structure filter with the introduced strong tracking factor to estimate the SOC of the energy storage battery. This invention reduces estimation errors and improves the accuracy of SOC estimation through variable structure filtering and iterative smoothing techniques.

Description

Technical Field

[0001] This invention relates to the field of state of charge estimation technology for energy storage battery systems, and specifically to a method for estimating the state of charge of energy storage battery systems. Background Technology

[0002] With the rapid development of new energy technologies and the widespread application of clean energy, energy storage battery systems are playing an increasingly important role in electric vehicles, smart grids, and renewable energy grid integration. Accurately estimating the State of Charge (SOC) of energy storage batteries is crucial for improving battery efficiency, extending battery life, and ensuring safe system operation. However, due to the inherent nonlinear characteristics of energy storage battery systems, complex external environmental factors, and various uncertainties, accurate SOC estimation still faces many challenges.

[0003] Traditional SOC estimation methods, such as the ampere-hour integration method and the open-circuit voltage method, are often limited by accumulated errors and measurement accuracy in practical applications. In recent years, SOC estimation methods based on various filtering algorithms have been extensively studied, with Kalman filtering and its variants favored due to their superior noise suppression and real-time performance. However, these methods still suffer from insufficient estimation accuracy and poor robustness when faced with variations in battery model parameters, complex and changing external conditions, and measurement noise interference. Especially under dynamic conditions, the internal state of the battery and the external environment may change rapidly, making it difficult for traditional filtering algorithms to adjust their parameters in a timely manner, leading to significant deviations in the estimation results. Simultaneously, model uncertainties and non-Gaussian noise in the battery system also pose challenges to existing algorithms. Furthermore, in practical applications, due to sensor accuracy limitations and measurement errors, the acquired data often contains complex noise components, further increasing the difficulty of SOC estimation.

[0004] Energy storage batteries face complex dynamic operating conditions such as frequent charging and discharging and load fluctuations in practical applications. Most existing SOC estimation algorithms are based on fixed model parameters, making it difficult to adapt to the dynamic characteristics of batteries under different operating conditions. For example, the Extended Kalman Filter (EKF) is prone to filter divergence when the state changes rapidly, and while the Unscented Kalman Filter (UKF) improves nonlinearity handling capabilities, its high computational complexity makes it difficult to meet real-time estimation requirements. The insufficient adaptability of these algorithms under dynamic operating conditions limits their application effectiveness in practical systems.

[0005] Energy storage battery systems contain various noise sources, such as measurement noise and process noise, which severely affect the accuracy of SOC estimation. Traditional Kalman filtering algorithms assume that the system noise is Gaussian white noise and that the covariance matrix is ​​known, which is difficult to satisfy in practical applications. Although adaptive Kalman filtering (AKF) improves filtering performance by adjusting the noise covariance matrix online, it still suffers from estimation bias and slow convergence speed under strong noise interference.

[0006] Furthermore, existing algorithms have limited ability to suppress abrupt noise, easily leading to significant fluctuations in filtering results. Battery model parameters change with usage time, ambient temperature, and other factors, resulting in model uncertainty. Most existing SOC estimation methods rely on accurate battery models and are sensitive to changes in model parameters. For example, model-based observer methods produce significant estimation errors when model parameters have large deviations. Although some researchers have proposed adaptive observer-based methods, their adaptability to changes in model structure is limited, making it difficult to cope with model structure changes caused by battery aging, etc.

[0007] Existing SOC estimation methods are mostly based on single information sources, such as voltage and current, neglecting the potential advantages of multi-source information fusion. Although some studies have attempted to combine multiple measurement methods such as electrochemical impedance spectroscopy (EIS), the lack of an effective information fusion mechanism makes it difficult to fully utilize the complementarity of different information sources, thus limiting further improvements in estimation accuracy.

[0008] Finally, high-precision SOC estimation algorithms typically require complex mathematical models and iterative calculations, resulting in a heavy computational burden that makes it difficult to meet the real-time requirements of battery management systems (BMS). While methods such as model simplification and order-reduction filtering can improve computational efficiency, they often come at the cost of estimation accuracy. In existing research, a high-precision and high-efficiency SOC estimation method remains an unsolved problem. Summary of the Invention

[0009] This invention aims to develop a state-of-charge (SOC) estimation method for energy storage battery systems based on iterative smooth variable structure filtering and adaptive Kalman algorithm, in order to solve the problems of large SOC estimation errors and poor robustness in the prior art due to battery model uncertainty, complexity of external operating conditions and noise interference.

[0010] This invention discloses a method for estimating the state of charge (SOC) of an energy storage battery system, comprising the following steps: Step 1, Initialization: Set the initial state estimate of the energy storage battery system under test and its corresponding initial covariance matrix to provide a basis for subsequent state of charge estimation; The initial covariance matrix is ​​used to characterize the uncertainty of the initial state estimation and the initial noise level, serving as the starting point for the subsequent filtering process. Step 2, State of Charge Update: The state of charge is updated through a variable structure filter, and the parameters of the variable structure filter are dynamically adjusted according to the operating conditions of the energy storage battery system to adapt to changes in the state of the energy storage battery. Step 3, Noise Adaptive Estimation: Based on the changes in noise characteristics during system operation, an adaptive mechanism is introduced into the variable structure filter to adjust the process noise covariance matrix and the observation noise covariance matrix in real time. Among them, the process noise covariance matrix is ​​dynamically optimized based on the statistical characteristics of the historical state estimation error to adapt to the uncertainty generated by the evolution of the system state over time. The observation noise covariance matrix is ​​updated in real time based on the variance characteristics of the sensor measurement data to reflect the changes in observation error under different measurement conditions; Through the adaptive adjustment mechanism of the covariance matrix, the filter gain of the variable structure filter can be updated in real time according to the system operating conditions, realizing accurate response to the system state under complex dynamic environment; significantly improving the filter's adaptability to changes in operating conditions and estimation robustness, thereby effectively improving the accuracy and stability of state of charge estimation. Step 4, Strong Tracking Filter: Based on Step 3, a strong tracking factor is introduced into the variable structure filter to enhance the tracking ability of rapidly changing states and ensure accurate state of charge estimation in complex environments. Step 5, Iterative smoothing and outputting the estimated state of charge of the energy storage battery: Based on step 4, the state of charge of the energy storage battery is estimated using a variable structure filter with a strong tracking factor. By adjusting the dynamic parameters of the filter in real time, the tracking ability of the rapidly changing state is enhanced, ensuring the accuracy and robustness of the estimated value. If the estimation error exceeds the set threshold, return to step four and readjust the filter parameters until the error converges to an acceptable range, thus completing the current stage of state of charge estimation. By using measurement information from future moments to correct the current estimate in each iteration, the estimated value is gradually optimized. Specifically, after the initial estimate is output through a variable structure filter, it enters an iterative smoothing process. In each iteration, the smoothing gain is dynamically updated and the current estimate is corrected based on the error between the measurement data from future moments and the current estimate. When all iteration steps are completed or the error meets the set convergence condition, the final estimated value of the energy storage battery state of charge is output.

[0011] Preferably, the state of the energy storage battery system is represented as follows: (19); in, Indicates the system status. Indicates control input, Indicates process noise; The measurement equation is then: (20); in, Indicates the measured value. Indicates measurement noise; This refers to the system status; Therefore, in step three, the formula for calculating the filter gain of the variable structure filter is: (twenty one); in, Indicates time The prediction error covariance matrix, Represents the measurement matrix. Let T represent the observation noise covariance matrix, and T represent the transpose of the matrix. Formula (21) is the formula for calculating the filter gain of the variable structure filter. Its derivation is based on the system measurement model and state prediction information described by formula (20), and is used to dynamically adjust the filter parameters to improve the estimation accuracy and system robustness.

[0012] Specifically, formula (19) defines the state transition model of the energy storage battery system, which describes the system state x. k The evolution law at time k+1 reflects the dynamic characteristics of the energy storage battery system. Formula (20) defines the measurement model of the system. The relationship between the measured value yk and the system state xk describes the characteristics of the measurement process. Combining formulas (19) and (20), the prediction error covariance matrix and the measurement noise covariance matrix of the system can be calculated. Furthermore, the filter gain K in formula (21) can be used to calculate the system's prediction error covariance matrix and the measurement noise covariance matrix. k Dynamic adjustments are made; the core function of formula (21) is to optimize the state estimation process by utilizing the difference between system state prediction and measurement update, thereby improving the accuracy and robustness of charge state estimation.

[0013] Preferably, the iterative smoothing process in step five is represented as follows: (twenty two); in, Indicates the smooth time interval Inside, for time The obtained smoothed estimate; Indicates time The filtered estimate; Indicates time The smoothed estimate; For time The filtered estimate; It is important to note that the filtered estimate It is the preliminary estimate obtained based on measurement information at the current moment, while the smoothed estimate is... The result is obtained by combining the estimated value with measurement information from future times and further optimizing it using a fixed-interval smoothing method. The logical relationship between the two is that the filtered estimate is the basis for the smoothed estimate, and the smoothed estimate further improves the accuracy and robustness of the estimation through multiple iterations.

[0014] The smoothing gain matrix is ​​represented by the following formula: (twenty three); in, This represents the state transition matrix, used to describe the dynamic evolution model of the energy storage battery system within a small range. The filter error covariance matrix at time k is defined as the covariance of the state estimation error during the state of charge estimation process of the energy storage battery, and is used to measure the uncertainty of the current estimation result. Indicates time The prediction error covariance matrix is ​​given by T, where T represents the transpose of the matrix.

[0015] Preferably, in step four, the variable structure filter update formula introducing a strong tracking factor is: (twenty four); in, The filtered state estimate is used to represent the system state estimate updated based on the observed and predicted states at the current time k. The predicted state estimate represents the estimated state of the system at time $k-1$ based on the state transition equation, and is used as the initial input for the filter update. Let k be the observation value at time k. For the observation matrix, To introduce the Kalman gain after introducing a strong tracking factor, this formula adjusts the filter gain by introducing the strong tracking concept, enabling the filter to respond quickly to changes in system state and improve the accuracy and robustness of charge state estimation under complex dynamic conditions.

[0016] Preferably, the dynamic adjustment of the noise covariance matrix in step three specifically includes the process noise covariance matrix and the observation noise covariance matrix, whose update formulas are as follows: (25); (26); in, and Let these represent the updated process noise covariance matrix and the observation noise covariance matrix, respectively. and It is an adaptive factor, and its value range is within ; Here is the state transition matrix. The observation matrix; , These are the filtered state estimates for the current time and the previous time, respectively. The current observation value is represented by T, which represents the transpose of the matrix. This dynamic adjustment mechanism corrects the covariance matrix online by statistically analyzing historical estimation errors and observation residuals, thereby enhancing the filter's adaptability to different operating conditions and noise variations.

[0017] Preferably, the update formula used in step five to estimate the state of charge of the energy storage battery and obtain the initial estimate is: (2); Among them, Kalman gain By introducing a strong tracking factor for dynamic adjustment, its calculation formula is as follows: (3); Among them, the prediction error covariance matrix The calculation expression is: (4); in, The state prediction estimate at time k; These are measured values; The observation matrix; This is the state transition matrix; and These are the process noise covariance matrix and the observation noise covariance matrix, respectively. Their values ​​can be dynamically adjusted by introducing an adaptive factor, and T represents the transpose of the matrix.

[0018] Preferably, the iterative smoothing process in step five, by iteratively correcting the previous filtering results, makes the final estimation result more accurate, and its mathematical expression is: (5); in, This represents the smoothed state estimate. For measured values, This is the estimated state before smoothing.

[0019] Formula (22) is used to obtain the initial state estimate as the input for iterative smoothing; while the smoothing step in Formula (5) uses the initial estimate and the observation information at future times to perform iterative correction, further optimize the state estimate result, and output the final estimate.

[0020] By combining variable structure filtering with iterative smoothing methods, this scheme significantly improves the accuracy of state of charge estimation, making it particularly suitable for energy storage battery management systems under complex operating conditions and dynamic changing scenarios.

[0021] This invention reduces estimation error and improves the accuracy of SOC estimation by using variable structure filtering and iterative smoothing techniques.

[0022] This invention utilizes an adaptive Kalman algorithm to dynamically adjust the noise covariance, thereby improving the system's resistance to model uncertainties and external disturbances.

[0023] This invention introduces the concept of strong tracking filtering to improve the algorithm's tracking ability and convergence speed under rapidly changing operating conditions.

[0024] This invention utilizes variable structure filtering technology to enable the algorithm to adaptively adjust parameters according to different working conditions, thus adapting to various complex working situations.

[0025] This invention provides a more accurate basis for decision-making in battery management systems by estimating SOC with high precision and high reliability, thereby improving the overall performance of the system.

[0026] This invention is of great significance for the safe operation, performance optimization, and lifespan extension of energy storage battery systems. Accurate SOC estimation can prevent overcharging and over-discharging, optimize charging and discharging strategies, and improve energy utilization efficiency. Furthermore, the method of this invention is expected to promote technological advancements in electric vehicles, smart grids, and other energy storage fields, providing strong support for the widespread application of new energy technologies.

[0027] This invention achieves high-precision and stable estimation of the State of Charge (SOC) of energy storage batteries through the synergistic effect of iterative smoothing variable structure filtering and adaptive Kalman algorithm. This invention is not only theoretically advanced but also demonstrates superior performance in practical applications, significantly improving the overall performance of battery management systems, extending battery life, and increasing energy utilization efficiency, thus providing solid technical support for the widespread application of electric vehicles and renewable energy systems.

[0028] This invention introduces variable structure filtering technology, enabling the filter to flexibly adjust its structure according to changes in operating conditions to adapt to different working environments. Simultaneously, by combining it with an adaptive Kalman filter algorithm, the filter can update its parameters in real time during operation, further improving estimation accuracy. Furthermore, this invention introduces iterative smoothing technology, optimizing the filtering results through multiple iterations, further enhancing the adaptability and stability of the filtering algorithm under complex operating conditions. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the process of the present invention.

[0030] Figure 2 This is a comparison chart of the SOC estimation accuracy under different operating conditions in the examples.

[0031] Figure 3 The figure shows a comparison of the convergence speed of SOC estimation using adaptive Kalman filtering (AKF), particle filtering (PF), and the method proposed in this invention in the embodiments.

[0032] Figure 4 This is a comparison of the SOC estimation accuracy of different algorithms under dynamic noise conditions in the examples.

[0033] Figure 5 This is a comparative analysis diagram of the robustness of SOC estimation using Kalman filtering (KF), extended Kalman filtering (EKF), and the present invention in the embodiments.

[0034] Figure 6 The figure shows the improvement in the accuracy of lithium-ion battery state of charge (SOC) estimation by multi-sensor fusion in the embodiment. Detailed Implementation

[0035] This invention discloses a method for estimating the state of charge (SOC) of an energy storage battery system, comprising the following steps: Step 1, Initialization: Set the initial state estimate of the energy storage battery system under test and its corresponding initial covariance matrix to provide a basis for subsequent state of charge estimation. The initial covariance matrix is ​​used to characterize the uncertainty of the initial state estimation and the initial noise level, serving as the starting point for the subsequent filtering process. Step 2, State of Charge Update: The state of charge is updated through a variable structure filter, and the parameters of the variable structure filter are dynamically adjusted according to the operating conditions of the energy storage battery system to adapt to changes in the state of the energy storage battery. Step 3, Noise Adaptive Estimation: Based on the changes in noise characteristics during system operation, an adaptive mechanism is introduced into the variable structure filter to adjust the process noise covariance matrix and the observation noise covariance matrix in real time. Among them, the process noise covariance matrix is ​​dynamically optimized based on the statistical characteristics of historical state estimation errors to adapt to the uncertainty generated by the evolution of system state over time; the observation noise covariance matrix is ​​updated in real time based on the variance characteristics of sensor measurement data to reflect the changes in observation error under different measurement conditions. Through the adaptive adjustment mechanism of the covariance matrix, the filter gain of the variable structure filter can be updated in real time according to the system operating conditions, realizing an accurate response to the system state under complex dynamic environments. This method significantly improves the filter's adaptability to changes in operating conditions and its estimation robustness, thereby effectively improving the accuracy and stability of state of charge estimation. Step 4, Strong Tracking Filter: Based on Step 3, a strong tracking factor is introduced into the variable structure filter to enhance the tracking ability of rapidly changing states and ensure accurate state of charge estimation in complex environments. Step 5, Iterative smoothing and outputting the estimated state of charge of the energy storage battery: Based on step 4, the state of charge of the energy storage battery is estimated using a variable structure filter with a strong tracking factor. By adjusting the dynamic parameters of the filter in real time, the tracking ability of the rapidly changing state is enhanced, ensuring the accuracy and robustness of the estimated value. If the estimation error exceeds the set threshold, return to step four and readjust the filter parameters until the error converges to an acceptable range, thus completing the current stage of state of charge estimation. By using measurement information from future moments to correct the current estimate in each iteration, the estimated value is gradually optimized. Specifically, after the initial estimate is output through a variable structure filter, it enters an iterative smoothing process. In each iteration, the smoothing gain is dynamically updated and the current estimate is corrected based on the error between the measurement data from future moments and the current estimate. When all iteration steps are completed or the error meets the set convergence condition, the final estimated value of the energy storage battery state of charge is output.

[0036] The status of an energy storage battery system is represented as follows: (19); in, Indicates the system status. Indicates control input, Indicates process noise; The measurement equation is then: in, Indicates the measured value. Indicates measurement noise; This refers to the system status; Therefore, in step three, the formula for calculating the filter gain of the variable structure filter is: (twenty one); in, Indicates time The prediction error covariance matrix, Represents the measurement matrix. Let T denote the observation noise covariance matrix, and let T denote the transpose of the matrix.

[0037] In one embodiment, the iterative smoothing process in step five is represented as follows: (twenty two); in, Indicates the smooth time interval Inside, for time The obtained smoothed estimate; Indicates time The filtered estimate; Indicates time The smoothed estimate; For time The filtered estimate; The smoothing gain matrix is ​​calculated using the following formula: (twenty three); in, This represents the state transition matrix, used to describe the dynamic evolution model of the energy storage battery system within a small range. The filter error covariance matrix at time k is defined as the covariance of the state estimation error during the state of charge estimation process of the energy storage battery, and is used to measure the uncertainty of the current estimation result. Indicates time The prediction error covariance matrix. T denotes the transpose of the matrix.

[0038] In one embodiment, the formula for the variable structure filter that introduces a strong tracking factor in step four is: (twenty four); in, The filtered state estimate is used to represent the system state estimate updated based on the observed and predicted states at the current time k. The predicted state estimate represents the estimated state of the system at time $k-1$ based on the state transition equation, and is used as the initial input for the filter update. Let k be the observation value at time k. For the observation matrix, To introduce the strong tracking factor, the Kalman gain is adjusted so that the filter can respond quickly to changes in the system state.

[0039] Preferably, the dynamic adjustment of the noise covariance matrix in step three specifically includes the process noise covariance matrix and the observation noise covariance matrix, and their update formulas are as follows: The formulas for the process noise covariance matrix and the observation noise covariance matrix are: (25); (26); in, and Let these represent the updated process noise covariance matrix and the observation noise covariance matrix, respectively. and It is an adaptive factor, and its value range is within ; Here is the state transition matrix. The observation matrix; , These are the filtered state estimates for the current time and the previous time, respectively. Let T represent the current observation value, and let T denote the transpose of the matrix.

[0040] In one embodiment, the update formula used in step five to estimate the state of charge of the energy storage battery and obtain the initial estimate is: (2); Among them, Kalman gain By introducing a strong tracking factor for dynamic adjustment, its calculation formula is as follows: (3); Among them, the prediction error covariance matrix The calculation expression is: (4); in, The state prediction estimate at time k; These are measured values; The observation matrix; This is the state transition matrix; and These are the process noise covariance matrix and the observation noise covariance matrix, respectively, whose values ​​can be dynamically adjusted by introducing an adaptive factor. T represents the transpose of the matrix.

[0041] In one embodiment, the iterative smoothing process in step five, by iteratively correcting the previous filtering results, makes the final estimation result more accurate. Its mathematical expression is: (5); in, This represents the smoothed state estimate. For measured values, This is the estimated state before smoothing.

[0042] Example II. Description and Analysis of the Characteristics of the Application Objects 2.1 Analysis of the characteristics of the research object 2.1.1 Electrochemical characteristics of energy storage battery systems The electrochemical characteristics of energy storage batteries are primarily determined by their internal chemical reactions. The basic working principle of a battery can be summarized as follows: during charging and discharging, the positive and negative electrode materials inside the battery undergo redox reactions through the electrolyte, thereby achieving energy storage and release. Specifically, there is a non-linear relationship between the battery's open-circuit voltage (OCV) and state of charge (SOC), which can usually be obtained by fitting experimental data. Assuming the battery's open-circuit voltage is... SOC is The relationship between the two can be expressed as: ; in, It is a nonlinear function, and its specific form can be obtained by experimental fitting based on different types of batteries.

[0043] In addition, the battery's internal resistance Internal resistance is also a crucial factor affecting battery performance. It is typically categorized into ohmic internal resistance, polarization internal resistance, and diffusion internal resistance, all of which collectively influence the battery's terminal voltage. When the battery is working, the terminal voltage can be expressed as: ; in, Let be the battery's discharge current. Since changes in internal resistance affect the battery's terminal voltage, thus influencing the estimation of SOC, the dynamic changes in internal resistance need to be considered in the model.

[0044] To improve the accuracy of SOC estimation, this invention employs variable structure filtering technology and an adaptive Kalman filter. Variable structure filtering technology can automatically adjust the filter structure when the system model changes, thereby maintaining the stability and accuracy of the estimation.

[0045] The adaptive Kalman filter enhances the tracking capability of nonlinear systems by adjusting the filter gain in real time.

[0046] Specifically, the state-space model of the Kalman filter can be represented as: ; ; in, For state vectors, To control the input, and These are process noise and measurement noise, respectively. , and The system matrix is ​​used to adaptively adjust the parameters of these matrices, which can improve the performance of the filter.

[0047] Iterative smoothing techniques further optimize the SOC estimation results. This technique improves the accuracy of the estimation by using measurement information from future time steps in each iteration to correct the current time step estimate.

[0048] The basic principle of iterative smoothing can be expressed as: ; in, For the smoothed state estimation, To smooth the gain, and These are the state estimates for the current time and the next time, respectively.

[0049] 2.1.2 Dynamic Change Pattern of SOC State of Charge (SOC) is a key parameter for measuring the remaining capacity of a battery. The dynamic change of SOC is a complex process, influenced by various factors, including but not limited to the battery's charging and discharging process, temperature changes, discharge rate, and battery cycle history. To accurately describe the dynamic change of SOC; This invention employs a combination of electrochemical models and filtering algorithms to improve the accuracy of SOC estimation.

[0050] First, the charging and discharging process of a battery has the most direct impact on its State of Charge (SOC). During charging, the chemical reactions inside the battery cause charge to gradually accumulate, leading to a gradual increase in SOC. During discharging, charge is released, causing SOC to gradually decrease. This process can be described by the following electrochemical equation: ; in, Indicates time State of charge at time t, Indicates the battery's rated capacity. Indicates time Current at any given moment; Secondly, temperature changes also have a significant impact on SOC. The chemical reaction rate and electrolyte conductivity of the battery change with temperature, thus affecting the actual capacity and SOC of the battery. The temperature effect can be described by the Arrhenius equation: ; in, Indicates temperature The reaction rate constant at the given time, It is a frequency factor. It is activation energy. It is the gas constant.

[0051] Discharge rate is also a significant factor affecting State of Charge (SOC). A high discharge rate leads to internal polarization within the battery, increasing internal resistance and thus reducing its effective capacity. This phenomenon can be described by the Peukert equation: ; in, Indicates effective capacity. Indicates the nominal capacity. It is the reference current. This is the actual discharge current. It is the Peukert index.

[0052] The battery's cycle history also affects the dynamic change pattern of its State of Charge (SOC). After multiple charge-discharge cycles, the battery's capacity gradually decreases. This phenomenon can be described by the following empirical formula: ; in, Indicates the first Capacity after the next iteration It is the capacity decay coefficient.

[0053] 2.2 Theoretical Model of the Research Object 2.2.1 Electrochemical Model of Energy Storage Battery First, understanding the basic electrochemical reactions of a battery is fundamental to understanding its performance and behavior. For lithium-ion batteries, the charging and discharging process can be simplified to the following electrochemical reactions: ; During charging, lithium ions migrate from the positive electrode (LiCoO2) to the negative electrode (C6), while during discharging, lithium ions migrate from the negative electrode back to the positive electrode. This process is accompanied by the transfer of electrons, forming an electric current.

[0054] Secondly, ion transport is a crucial step in the electrochemical reaction of a battery. According to the Nernst-Planck equation, the migration rate of ions under the influence of an electric field and a concentration gradient can be expressed as: ; in, It is ion flux. It is the ion diffusion coefficient. It refers to ion concentration. It is the ionic charge number. It is ion mobility. It is Faraday's constant. It is the gas constant. It's temperature. It is electric potential.

[0055] Current density is one of the important parameters describing the operating state of a battery. According to Faraday's law, the relationship between current density and lithium-ion migration rate can be expressed as: ; in, It is the current density. It is the number of electrons transferred in an electrochemical reaction. It is Faraday's constant. It is ion flux.

[0056] The open-circuit voltage (OCV) of a battery is an important basis for estimating SOC. According to the Nernst equation, OCV can be expressed as: ; in, It is the battery's open voltage. It is the standard electrode potential. and These represent the activities of the oxidized and reduced states, respectively.

[0057] To establish a dynamic model to describe the state of charge (SOC) changes of a battery under different operating conditions, this invention comprehensively considers factors such as electrolyte concentration, temperature, and the conductivity of battery materials. Electrolyte concentration affects ion migration rate and battery internal resistance, temperature affects reaction rate and conductivity, while the conductivity of battery materials directly affects current conduction efficiency.

[0058] The change in SOC can be described by the charging and discharging process of the battery. Assuming the initial SOC of the battery is... In time The SOC after that can be expressed as: ; in, It is the battery's rated capacity. It is time The current at that time.

[0059] 2.2.2 Electrodynamic Model of Energy Storage Battery The electrodynamic model of an energy storage battery is the core component describing the battery's behavior under dynamic operating conditions. Based on electrochemical principles and circuit theory, it effectively reflects the battery's performance changes under different operating conditions. To achieve high-precision SOC estimation, it is necessary to comprehensively consider the battery's equivalent circuit model, dynamic SOC updates, the differential equation of the battery voltage response, and the influence of temperature on the electrochemical reaction rate.

[0060] First, the equivalent circuit model of a battery typically consists of a voltage source, internal resistance, and several RC networks. The voltage source represents the open-circuit voltage (OCV), and the internal resistance (RC network) represents the open-circuit voltage (OCV). The RC network reflects the ohmic impedance of the battery, while the polarization effect and dynamic response of the battery are simulated. The voltage response of the equivalent circuit model can be expressed as: ; in, It is the battery terminal voltage. It is electric current. It is the first Voltage drop of an RC network.

[0061] Similarly, the dynamic update of SOC is based on the battery's coulomb counting method and current integration method. The change in SOC can be expressed as: ; in, It is the battery's nominal capacity. It is the initial time.

[0062] The differential equation for the battery voltage response is determined by both circuit theory and electrochemical kinetic equations. For each RC network, its voltage drop can be described by the following differential equation: ; in, and They are the first The capacitance and resistance of an RC network.

[0063] Furthermore, the effect of battery temperature changes on the electrochemical reaction rate is also significant. Temperature changes affect the battery's open-circuit voltage and internal resistance, and also alter the battery's reaction rate constant. The effect of temperature on the reaction rate can be described by the Arrhenius equation: ; in, It is temperature The reaction rate constant at the given time, It is a pre-index factor. It is activation energy. It is the gas constant.

[0064] III. Innovative Content 3.1 Purpose of the Invention 3.1.1 Improve the accuracy and stability of SOC estimation With the rapid development of electric vehicles and renewable energy systems, the performance of energy storage batteries directly affects the reliability and efficiency of the entire system. Therefore, accurate estimation of the battery's State of Charge (SOC), a key indicator of its remaining energy, is crucial. However, due to the nonlinear characteristics of batteries, environmental variations, and the diversity of usage conditions, traditional SOC estimation methods suffer from significant shortcomings in accuracy and stability.

[0065] This invention proposes a State of Charge (SOC) estimation method for energy storage battery systems based on iterative smoothing variable structure filtering and an adaptive Kalman algorithm. The aim is to significantly improve the accuracy and stability of SOC estimation by introducing advanced filtering and estimation techniques. Iterative smoothing variable structure filtering effectively handles the nonlinearity and uncertainty of the system under complex operating conditions, while the adaptive Kalman algorithm improves the ability to track the system state by adjusting the filtering parameters in real time. The combination of these two methods not only provides high-precision SOC estimation under dynamic operating conditions but also effectively suppresses noise and interference, enhancing the robustness of the system.

[0066] The core innovation of this invention lies in achieving high-precision and stable estimation of the State of Charge (SOC) of energy storage batteries through the synergistic effect of iterative smoothing variable structure filtering and adaptive Kalman algorithm. This method is not only theoretically advanced but also demonstrates excellent performance in practical applications, significantly improving the overall performance of battery management systems, extending battery life, and increasing energy utilization efficiency, thus providing solid technical support for the widespread application of electric vehicles and renewable energy systems.

[0067] In summary, the purpose of this invention is to address the shortcomings of existing SOC estimation methods in terms of accuracy and stability under complex operating conditions by introducing iterative smoothing variable structure filtering and adaptive Kalman algorithm, and to provide an efficient and accurate SOC estimation method to significantly improve the performance and reliability of energy storage battery systems.

[0068] 3.1.2 Improved Adaptability of Filtering Algorithms under Dynamic Operating Conditions Traditional filtering algorithms often struggle to adjust filtering parameters in real time under dynamic operating conditions, leading to decreased estimation accuracy and consequently affecting the performance and lifespan of energy storage batteries. To address this, this invention proposes an innovative algorithm combining variable structure filtering and adaptive Kalman filtering. By adjusting filtering parameters in real time, it significantly improves the adaptability of the filtering algorithm under dynamic conditions, thereby ensuring high-precision estimation of the energy storage battery's state of charge.

[0069] Specifically, this invention introduces variable structure filtering technology, enabling the filter to flexibly adjust its structure according to changes in operating conditions to adapt to different working environments. Simultaneously, by combining it with an adaptive Kalman filter algorithm, the filter can update its parameters in real time during operation, further improving estimation accuracy. Furthermore, this invention also introduces iterative smoothing technology, optimizing the filtering results through multiple iterations, further enhancing the adaptability and stability of the filtering algorithm under complex operating conditions.

[0070] In summary, this invention innovatively combines variable structure filtering, adaptive Kalman filtering, and iterative smoothing techniques to form a highly efficient and intelligent adaptive filtering algorithm enhancement scheme under dynamic operating conditions. This scheme not only significantly improves the accuracy and reliability of energy storage battery state-of-charge estimation but also has strong practical application value and can be widely applied in various complex and variable real-world environments.

[0071] 3.2 Basic Scheme 3.2.1 Cooperative Design of Variable Structure Filtering and Iterative Smoothing

[0072] Variable structure filtering is a technique that adaptively adjusts filter parameters based on changes in system state and measurement noise. In this invention, the variable structure filter is designed based on Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) to adapt to nonlinearity and non-Gaussian characteristics under different operating conditions. Specifically, the system state equation can be expressed as: ; in, Indicates the system status. Indicates control input, This represents process noise. The measurement equation is then: ; in, Indicates the measured value. This indicates measurement noise.

[0073] In a variable structure filter, the filter gain is dynamically adjusted by calculating the covariance matrix of the state estimation error and the observation error in real time, enabling the filter to adaptively respond to state changes under different operating conditions. The formula for calculating the filter gain is: ; in, This represents the filter gain matrix at time k; This represents the state prediction error covariance matrix; Represents the observation matrix; This represents the observation noise covariance matrix.

[0074] The dynamic adjustment mechanism of the filter gain combines system prediction and measurement errors, and can adaptively optimize the filtering performance under different measurement noise levels and system dynamic characteristics, thereby further improving the accuracy and robustness of state estimation.

[0075] Iterative smoothing utilizes historical data and further improves estimation accuracy through iterative optimization.

[0076] In this invention, iterative smoothing is based on Fixed Interval Smoother (FIS) and Fixed Point Smoother (FPS) techniques. The basic idea is to optimize local estimations using global information through the synergistic effect of forward filtering and backward smoothing. The specific smoothing process can be expressed as follows: ; in, Indicates the smooth time interval Inside, for time The obtained smoothed estimate; Indicates time The filtered estimate; Indicates time The smoothed estimate; For time The filtered estimate; The smoothing gain matrix is ​​calculated using the following formula: ; in, This represents the state transition matrix, used to describe the dynamic evolution model of the energy storage battery system within a small range. The filter error covariance matrix at time k is defined as the covariance of the state estimation error during the state of charge estimation process of the energy storage battery, and is used to measure the uncertainty of the current estimation result. Indicates time The prediction error covariance matrix is ​​given by T, where T represents the transpose of the matrix.

[0077] By employing a synergistic design of variable structure filtering and iterative smoothing, this invention enables adaptive filtering under dynamic operating conditions and significantly improves the stability of SOC estimation through the utilization of historical data. This method not only enhances the accuracy of the estimation but also strengthens the system's robustness to noise and changes in operating conditions, providing reliable technical support for energy storage battery management systems.

[0078] 3.2.2 Fusion Algorithm of Strong Tracking Filter and Adaptive Kalman Filter Strong tracking filtering is a filtering method that can achieve high-precision state estimation in nonlinear and non-Gaussian environments. Its core idea is to introduce a strong tracking factor, enabling the filter to respond quickly to sudden changes in system state, thereby improving the filter's dynamic performance. Specifically, the state update formula for strong tracking filtering is: ; in, The filtered state estimate is used to represent the system state estimate updated based on the observed and predicted states at the current time k. The predicted state estimate represents the estimated state of the system at time $k-1$ based on the state transition equation, and is used as the initial input for the filter update. Let k be the observation value at time k. For the observation matrix, To introduce the strong tracking factor, the Kalman gain is adjusted so that the filter can respond quickly to changes in the system state.

[0079] Adaptive Kalman filtering improves the robustness of the filter by adjusting the process noise covariance matrix and the observation noise covariance matrix in real time to adapt to changes in system and observation noise. Its core idea is to dynamically adjust the noise covariance matrix based on the statistical characteristics of the estimation error. Specifically, the update formulas for the process noise covariance matrix and the observation noise covariance matrix of adaptive Kalman filtering are: ; ; in, and These are the process noise covariance matrix and the observation noise covariance matrix, respectively. and As an adaptive factor, Let be the state transition matrix.

[0080] The fusion algorithm of this invention combines strong tracking filtering with adaptive Kalman filtering. By introducing strong tracking factors and adaptive factors, the filter not only has the ability to quickly respond to changes in system state, but also can adjust the noise covariance matrix in real time to adapt to complex environments and random noise. Specifically, the state update formula of the fusion algorithm of this invention is as follows: ; Among them, Kalman gain Adjustments were made by introducing a strong tracking factor: ; ; Process noise covariance matrix and observation noise covariance matrix Adjusted using an adaptive factor.

[0081] In summary, the SOC estimation algorithm designed in this paper has the following flow: Figure 1 As shown, The main steps include: initialization, state update, noise adaptive estimation, strong tracking filtering, iterative smoothing, and outputting the SOC estimate.

[0082] First, in the initialization phase, the initial state estimate and covariance matrix of the battery are set to provide a basis for subsequent state estimation; Next, the state is updated using variable structure filtering technology, and the parameters are dynamically adjusted to adapt to changes in the battery state. In the noise adaptive estimation stage, the filter gain is adaptively adjusted according to the noise characteristics to enhance the robustness of the algorithm; Subsequently, by combining the idea of ​​strong tracking filters, the tracking capability for rapidly changing states is enhanced, ensuring accurate state estimation in complex environments. Finally, through iterative smoothing technology, the state estimation is iteratively optimized multiple times to further improve the accuracy of the estimation, and finally outputs the SOC estimate of the battery, providing accurate state information for the battery management system.

[0083] 3.3 Technical Implementation Steps and Results This invention discloses a method for estimating the state of energy storage (SOC) based on iterative smoothing variable structure filtering and adaptive Kalman algorithm. The technical implementation steps and results are as follows: First, this invention employs variable structure filtering technology, dynamically adjusting filter parameters to adapt to nonlinear systems under different operating conditions. Specifically, the variable structure filter can adjust filter parameters in real time according to the battery's operating conditions, thereby addressing the uncertainties of the battery model and the complexity of external operating conditions; Secondly, this invention introduces the concept of a strong tracking filter (STF), enabling the adaptive Kalman filter to possess stronger tracking capabilities under rapidly changing system models. By dynamically adjusting the filter's gain parameters, the response speed and stability of the filter under complex operating conditions are ensured. In specific implementation, the strong tracking filter dynamically adjusts its gain parameters using the following formula: ; Furthermore, iterative smoothing technology further optimizes the filtering results, effectively suppressing estimation errors that may be introduced during a single filtering process, thereby improving the accuracy of SOC estimation. Iterative smoothing technology iteratively corrects previous filtering results, making the final estimation result more accurate. Its mathematical expression is: ; in, This represents the smoothed state estimate. For measured values, This is the estimated state before smoothing.

[0084] Through the above technical steps, this invention can estimate the SOC of energy storage batteries in real time and accurately, significantly improving the performance of battery management systems. Experimental results show that this method has higher estimation accuracy, response speed, and robustness under dynamic conditions, making it suitable for widespread application in electric vehicles, smart grids, and other energy storage fields.

[0085] IV. Testing and Verification Based on Specific Implementation Examples To verify the effectiveness of this invention in a multi-sensor fusion and filtering method for energy storage battery systems, tests and verifications were conducted based on specific embodiments. The test environment included hardware configuration and software tools to ensure the comprehensiveness and accuracy of the tests.

[0086] 4.1 Test Environment Setup The simulation software environment configuration included an Intel Xeon Gold 6248 processor (2.5 GHz), 256 GB DDR4 RAM, and 1 TB NVMe SSD storage. The state-of-charge (SOC) estimation method for energy storage batteries based on iterative smoothing variable structure filtering and adaptive Kalman filtering was simulated and tested using the MATLAB / Simulink platform to verify the effectiveness of the control strategy and optimization algorithm. The simulation model includes key components such as a battery model module, a variable structure filtering module, a strong tracking filtering module, an adaptive Kalman filtering module, and an iterative smoothing module, realistically reflecting the operating characteristics and control behavior of multi-sensor fusion and filtering methods in energy storage battery systems. The parameter settings of the simulation model referenced the technical specifications and operating data of multi-sensor fusion and filtering methods applied to energy storage battery systems, ensuring the simulation results have practical significance. Various operating conditions were simulated on the simulation model, including different discharge rates, temperature variations, and noise interference, to test the system's adaptability and robustness. By comparing the SOC estimation accuracy, convergence speed, and robustness of different algorithms under various operating conditions, the superior performance of the proposed method under dynamic conditions was verified.

[0087] 4.2 Simulation Parameters The key simulation parameters are set as shown in Table 1. The dataset for the multi-sensor fusion and filtering method applied to the energy storage battery system is set to actual laboratory data, ranging from 0% to 100% of the State of Charge (SOC).

[0088] Table 1 Parameter Settings

[0089]

[0090] 4.3 Results Analysis 4.3.1 Test Result Analysis Figure 2 The paper presents a comparison of SOC estimation accuracy under different operating conditions, including the mean square error (MSE) performance of traditional Kalman filtering (KF), extended Kalman filtering (EKF), unscented Kalman filtering (UKF), and the proposed method at four discharge rates (0.5C, 1C, 1.5C, and 2C). The figures clearly show that the estimation error of all methods increases with the discharge rate, reflecting the increased difficulty of SOC estimation under high discharge rate conditions.

[0091] However, this invention exhibits significant advantages under all operating conditions, consistently maintaining the lowest MSE value. Specifically, at a discharge rate of 0.5C, the proposed method achieves an MSE of 0.015, representing reductions of 66.67%, 57.14%, and 40.00% compared to KF, EKF, and UKF, respectively. Even at a high discharge rate of 2C, the proposed method achieves an MSE of only 0.020, still maintaining a significant advantage, representing reductions of 63.64%, 53.49%, and 39.39% compared to KF, EKF, and UKF, respectively.

[0092] Further analysis revealed that the present invention not only demonstrates superior estimation accuracy but also exhibits higher stability under various operating conditions. From 0.5C to 2C, the MSE increase of the proposed method was only 0.005, representing a growth rate of 33.33%, while the MSE increases of KF, EKF, and UKF were 0.010, 0.008, and 0.008, respectively, with growth rates of 22.22%, 22.86%, and 32.00%. This indicates that the present invention can maintain relatively stable estimation performance when facing complex and changing operating conditions. Furthermore, the error bars show the standard deviation of each method under different operating conditions; the standard deviation of the proposed method is generally smaller than that of other methods, further confirming the reliability and consistency of its estimation results.

[0093] Figure 3The paper compares the convergence speed of SOC estimation using Adaptive Kalman Filtering (AKF), Particle Filtering (PF), and the proposed method. The figures clearly show that all three methods initially estimate 60% of the SOC, while the actual SOC is 80%. Over time, the estimates of the three methods gradually converge towards the true value, but significant differences exist in convergence speed and stability. The proposed method exhibits the fastest convergence speed, reaching 95% of the true SOC in approximately 3 seconds, while AKF and PF require approximately 5 and 4 seconds, respectively. Furthermore, the proposed method demonstrates superior estimation accuracy after reaching a steady state compared to the other two methods, consistently maintaining a deviation from the true SOC value within ±0.5%. Further data analysis reveals that at 1 second after the simulation begins, the proposed method's SOC estimate is 71.35%, closer to the true value than AKF's 65.27% and PF's 67.47%. At 5 seconds, the proposed method's estimate reaches 79.85%, while AKF and PF achieve 76.32% and 77.89%, respectively. This demonstrates that the proposed method not only exhibits faster convergence in the initial stage but also maintains high accuracy throughout the estimation process. It is noteworthy that while the PF method shows a faster convergence trend than AKF in the mid-stage (approximately 2-4 seconds), its final stability is slightly lower than AKF, likely due to particle degeneration. In contrast, this invention successfully overcomes this limitation, achieving significant improvements in both convergence speed and stability.

[0094] 4.3.2 Comparison with existing methods Figure 4 The results show a comparison of the SOC estimation accuracy of different algorithms under dynamic noise conditions. It is clearly observed from the figures that the SOC estimation error of all three methods decreases with increasing signal-to-noise ratio (SNR), but the magnitude of the decrease and the overall performance differ significantly. The traditional Kalman filter (KF) performs the worst across the entire SNR range, with its estimation error decreasing from 0.080 at 10 dB to 0.032 at 30 dB. The unscented Kalman filter (UKF) shows improvement over KF, with an estimation error ranging from 0.060 to 0.024. Notably, the proposed method exhibits the best performance under all SNR conditions, with an estimation error ranging from 0.040 to 0.016, significantly lower than the other two methods.

[0095] Further analysis of the data reveals that the present invention has significant advantages over traditional methods. At a signal-to-noise ratio (SNR) of 10 dB, the proposed method reduces estimation errors by 50% and 33.33% compared to KF and UKF, respectively. This advantage further expands when the SNR increases to 30 dB, reducing errors by another 50% and 33.33% compared to KF and UKF, respectively. Particularly under lower SNR conditions (e.g., 10 dB), the estimation error of the proposed method (0.040) is only slightly higher than that of UKF at high SNR (30 dB) (0.024), highlighting the robustness of the proposed method in harsh noise environments. This result fully demonstrates that the proposed method has higher estimation accuracy and stronger anti-interference capability in dynamic noise environments, providing strong support for improving the reliability and performance of battery management systems.

[0096] Figure 5 This paper presents a comparative analysis of the robustness of SOC estimation using Kalman filtering (KF), extended Kalman filtering (EKF), and the proposed method. Box plots clearly show significant differences in the SOC estimation error distributions of the three methods. The traditional KF method exhibits the largest error range, with a median of approximately 0.050 and an error range between 0.045 and 0.055. The EKF method shows improvement over KF, reducing the median to approximately 0.040 and narrowing the error range to between 0.035 and 0.045. The proposed method demonstrates significant advantages in both SOC estimation accuracy and stability, with a median of only around 0.020 and a further reduction in the error range to between 0.015 and 0.025. Quantitative analysis shows that the proposed method reduces the median SOC estimation error by approximately 60% and 50% compared to KF and EKF, respectively. Meanwhile, its upper limit of error (0.025) is 0.010 lower than the lower limit of EKF (0.035), fully demonstrating the significant effect of this method in improving the accuracy of SOC estimation and enhancing the robustness of the algorithm. This result not only reflects the superiority of this invention in handling nonlinear systems and dealing with complex noise environments, but also highlights its potential value in practical applications, such as extending battery life and improving the efficiency of energy management systems.

[0097] Overall, this invention has achieved substantial breakthroughs in the accuracy and reliability of SOC estimation, providing a new research direction for the optimization of lithium-ion battery management systems.

[0098] Figure 6This paper demonstrates the improvement effect of multi-sensor fusion on the accuracy of lithium-ion battery state of charge (SOC) estimation. The figure uses a grouped bar chart to visually compare the impact of different sensor combinations on the root mean square error (RMSE) of SOC estimation in the cases of no sensor fusion and with sensor fusion. It is clearly observed from the figure that for all sensor combinations, the SOC estimation error is significantly reduced after sensor fusion. Taking a single sensor as an example, the RMSEs of voltage (V), current (I), and temperature (T) sensors without fusion are 0.030, 0.028, and 0.029, respectively, while after fusion, they drop to 0.010, 0.009, and 0.009, respectively, with an average reduction of 66.67%. This result highlights the significant advantage of multi-sensor fusion technology in improving SOC estimation accuracy. Further analysis shows that the SOC estimation accuracy continues to improve with the increase in the number of fused sensors. Especially when all three sensors (V, I, and T) are fused, the RMSE drops to a minimum of 0.005, compared to 0.020 without fusion, representing a 75% improvement in accuracy. It is noteworthy that even when combining two sensors (such as V+I, V+T, or I+T), the estimation error is significantly lower than that of a single sensor, with RMSE values ​​of 0.007, 0.006, and 0.006, respectively. This phenomenon fully demonstrates the superiority of multi-sensor fusion methods in integrating different information sources and mitigating the limitations of single sensors. By comprehensively utilizing data from multiple sensors, this method effectively improves the robustness and reliability of SOC estimation, providing strong support for the optimization of lithium-ion battery management systems.

Claims

1. A method for estimating the state of charge (SOC) of an energy storage battery system, characterized in that, Includes the following steps: Step 1, Initialization: Set the initial state estimate of the energy storage battery system under test and its corresponding initial covariance matrix to provide a basis for subsequent state of charge estimation; The initial covariance matrix is ​​used to characterize the uncertainty of the initial state estimation and the initial noise level, serving as the starting point for the subsequent filtering process. Step 2, State of Charge Update: The state of charge is updated through a variable structure filter, and the parameters of the variable structure filter are dynamically adjusted according to the operating conditions of the energy storage battery system to adapt to changes in the state of the energy storage battery. Step 3, Noise Adaptive Estimation: Based on the changes in noise characteristics during system operation, an adaptive mechanism is introduced into the variable structure filter to adjust the process noise covariance matrix and the observation noise covariance matrix in real time. Among them, the process noise covariance matrix is ​​dynamically optimized based on the statistical characteristics of the historical state estimation error to adapt to the uncertainty generated by the evolution of the system state over time. The observation noise covariance matrix is ​​updated in real time based on the variance characteristics of the sensor measurement data to reflect the changes in observation error under different measurement conditions; Step 4, Strong Tracking Filter: Based on Step 3, a strong tracking factor is introduced into the variable structure filter to enhance the tracking ability of rapidly changing states and ensure accurate state of charge estimation in complex environments. Step 5, iterative smoothing and output of the energy storage battery state of charge estimate: Based on step 4, the energy storage battery state of charge estimate is performed using a variable structure filter with a strong tracking factor. The tracking ability of the rapidly changing state is enhanced by adjusting the dynamic parameters of the filter in real time, ensuring the accuracy and robustness of the estimate. If the estimation error exceeds the set threshold, return to step four and readjust the filter parameters until the error converges to an acceptable range, thus completing the current stage of state of charge estimation.

2. The method for estimating the state of charge of an energy storage battery system as described in claim 1, characterized in that, The status of an energy storage battery system is represented as follows: （19）； in, Indicates the system status. Indicates control input, Indicates process noise; The measurement equation is then: （20）； in, Indicates the measured value. Indicates measurement noise; This refers to the system status; Therefore, in step three, the formula for calculating the filter gain of the variable structure filter is: (21)； in, Indicates time The prediction error covariance matrix, Represents the measurement matrix. Let T denote the observation noise covariance matrix, and let T denote the transpose of the matrix.

3. The method for estimating the state of charge of an energy storage battery system as described in claim 2, characterized in that, The iterative smoothing process in step five is represented as follows: (22)； in, Indicates the smooth time interval Inside, for time The obtained smoothed estimate; Indicates time The filtered estimate; Indicates time The smoothed estimate; For time The filtered estimate; The smoothing gain matrix is ​​represented by the following formula: (23)； in, This represents the state transition matrix, used to describe the dynamic evolution model of the energy storage battery system within a small range. The filter error covariance matrix at time k is defined as the covariance of the state estimation error during the state of charge estimation process of the energy storage battery, and is used to measure the uncertainty of the current estimation result. Indicates time The prediction error covariance matrix is ​​given by T, where T represents the transpose of the matrix.

4. The method for estimating the state of charge of an energy storage battery system as described in claim 3, characterized in that, In step four, the formula for updating the variable structure filter by introducing a strong tracking factor is: (24)； in, The filtered state estimate is used to represent the system state estimate updated based on the observed and predicted states at the current time k. The predicted state estimate represents the estimated state of the system at time $k-1$ based on the state transition equation, and is used as the initial input for the filter update. Let k be the observation value at time k. For the observation matrix, Kalman gain after introducing a strong tracking factor; The strong tracking factor adjusts the Kalman gain, enabling the filter to respond quickly to changes in the system state.

5. The method for estimating the state of charge of an energy storage battery system as described in claim 4, characterized in that, The dynamic adjustment of the noise covariance matrix in step three specifically includes the process noise covariance matrix and the observation noise covariance matrix, and their update formulas are as follows: (25)； (26)； in, and Let these represent the updated process noise covariance matrix and the observation noise covariance matrix, respectively. and It is an adaptive factor, and its value range is within ; Here is the state transition matrix. The observation matrix; , These are the filtered state estimates for the current time and the previous time, respectively. Let T represent the current observation value, and let T denote the transpose of the matrix.

6. The method for estimating the state of charge of an energy storage battery system as described in claim 5, characterized in that, The update formula used in step five to estimate the state of charge of the energy storage battery and obtain the initial estimate is as follows: (2)； Among them, Kalman gain By introducing a strong tracking factor for dynamic adjustment, its calculation formula is as follows: (3)； Among them, the prediction error covariance matrix The calculation expression is: (4)； in, The state prediction estimate at time k; These are measured values; The observation matrix; This is the state transition matrix; and These are the process noise covariance matrix and the observation noise covariance matrix, respectively. Their values ​​are dynamically adjusted by introducing an adaptive factor, and T represents the transpose of the matrix.

7. The method for estimating the state of charge of an energy storage battery system as described in claim 1, characterized in that, The iterative smoothing process in step five involves iteratively correcting the previous filtering results to obtain a more accurate final state estimation result. Its mathematical expression is: (5)； in, This represents the smoothed state estimate. For measured values, This is the estimated state before smoothing.

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