Sodium-ion battery state-of-charge and state-of-health joint estimation method

Abstract

The invention relates to the technical field of new energy battery management, and discloses a sodium ion battery state-of-charge and state-of-health joint estimation method, which comprises the following steps: acquiring a state equation and an observation equation of a sodium ion battery; initializing a state estimation value, a state covariance, a capacity estimation value and a capacity covariance; performing unscented transformation on the state equation to obtain a plurality of key points and weights; a state equation and an observation equation are utilized to spread key points at the # imgabs0 # moment, the state at the # imgabs1 # moment, an observation nonlinear transmission result, a prediction state, an observation estimation value, a corresponding prediction state covariance and a corresponding prediction observation covariance are obtained, Kalman gain at the # imgabs2 # moment is constructed, and an extended Kalman gain matrix is obtained; presetting an innovation length, calculating a historical observation residual error, and constructing a multi-innovation matrix; and based on the extended Kalman gain matrix, the multi-information matrix and the actual observation value at the # imgabs3 # moment, correcting to obtain the sodium ion battery charge state and the battery health state at the # imgabs4 # moment.

Description

Technical Field

[0001] The present invention relates to the technical field of new energy battery management, and in particular to a method for jointly estimating the state of charge and state of health of a sodium ion battery. Background Art

[0002] Accurately estimating battery state of charge (SOC) and state of health (SOH) is a key technology for improving the efficiency of electric vehicle powertrains. Accurate SOC and SOH prediction not only optimizes battery life but also ensures vehicle safety through scientific control of charge and discharge behavior. As sodium-ion batteries cycle, their SOH degrades, leading to parameter drift such as ohmic impedance changes and capacity decay. This can cause battery model inaccuracies and severely impact SOC estimation accuracy.

[0003] The paper "Zhang Fujian, Zhao Xi, Zheng Xinyue, et al. SOC estimation of sodium-ion batteries based on extended Kalman filter [J]. Battery, 2025, 55(01): 99-103. DOI: 10.19535 / j.1001-1579.2025.01.015." takes 18650 sodium-ion batteries as the research object. Based on the laboratory sodium-ion battery stage discharge experimental data, a second-order RC equivalent circuit model is established. The SOC curve is simulated using PyCharm software. The SOC curve estimated by the extended Kalman filter (EKF) algorithm is compared with the actual curve to verify the effectiveness and robustness of the algorithm. After adding the compensation voltage, the average error of the battery SOC estimated by the EKF algorithm is 1.79%. The paper uses a single Kalman filter (such as EKF) to estimate the state of charge of sodium-ion batteries. The accuracy is insufficient, the historical observation data is not fully utilized, the cumulative error cannot be effectively suppressed, and it is susceptible to model nonlinear errors and noise interference under dynamic loads, resulting in SOC drift.

[0004] Current sodium-ion battery SOH assessments rely primarily on offline testing and deep learning methods. Offline testing requires data to be acquired through charge-discharge cycle experiments after standing still, which presents bottlenecks in engineering applications such as poor timeliness and difficulty in real-time monitoring. Deep learning SOH prediction, on the other hand, presents problems such as large data requirements, weak generalization capabilities, and high computational complexity. Patent CN202411423425.3 discloses a sodium-ion battery health status prediction method, device, and storage medium, relating to the field of battery health management technology. This method sets a prediction time starting point to obtain the measured state parameters of the sodium-ion battery at the prediction time starting point. The measured state parameters are then input into an exponential decay model to obtain the predicted state parameters of the sodium-ion battery after the prediction time starting point, as output by the exponential decay model. Finally, the health status of the sodium-ion battery is determined based on the predicted state parameters. This method directly learns the degradation laws of battery performance through battery status measurement data, constructs an exponential decay model that can capture the characteristics of battery performance changes, and predicts the health status of the sodium-ion battery. The exponential decay model in the above method is trained based on the historical state parameters of the sodium-ion battery before the starting point of the prediction time. This will lead to the problem of insufficient model generalization, and the predictive ability will be reduced under completely new discharge conditions. This patent is a health status prediction method based on deep learning. Deep learning needs to cover the entire life cycle and multiple operating conditions (temperature, charge and discharge rate) data, while battery aging experiments require thousands of cycles, which is time-consuming and the data acquisition cost is extremely high. In addition, the performance of the deep learning method may drop drastically in unseen charge and discharge strategies (such as non-standard fast charging protocols) or new battery chemical systems (such as solid-state batteries). The deep learning method model is difficult to provide an explanation for the degradation mechanism, such as whether the dominant aging factor is SEI growth or lithium deposition, which is not conducive to fault diagnosis and design improvement; at the same time, some prediction results may violate basic electrochemical principles, such as predicting that the capacity first increases and then decreases with the number of cycles, leading to engineering application risks.

[0005] In summary, the existing SOC estimation only uses the observation data at the current moment, and the utilization rate of the single new observation information is insufficient. It cannot effectively suppress the accumulated error and noise interference during the battery SOH decay process, which easily leads to SOC drift; the existing SOC estimation requires thousands of cycle aging data, which is highly data-dependent and has poor timeliness. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problems in the prior art of estimation of state of charge and state of health, which are affected by the degree of battery aging, resulting in poor accuracy, and the need for offline detection, resulting in low timeliness.

[0007] To solve the above technical problems, the present invention provides a method for jointly estimating the state of charge and health state of a sodium ion battery, comprising: Based on the second-order RC equivalent circuit model of the sodium-ion battery, the state equation and observation equation of the sodium-ion battery are obtained; Initialize the state estimation value, state covariance, capacity estimation value and capacity covariance of the sodium ion battery; Use unscented Kalman filtering to perform unscented transformation on the state equation to obtain multiple key points and their corresponding weights; Propagation using state equation and observation equation respectively The key point of the moment, get The state nonlinear transfer result and the observation nonlinear transfer result at the moment; based on The nonlinear transfer result of the state at the moment is obtained The estimated value of the predicted state at the moment and its corresponding predicted state covariance; based on The nonlinear transfer result of the observation at the moment is obtained The estimated value of the forecast observation at time t, and its corresponding forecast observation covariance; based on The state nonlinear transfer result at the moment, the observation nonlinear transfer result, the predicted state estimate, the predicted observation estimate and the observation noise covariance are calculated. Cross covariance and innovation covariance at each moment, construct The Kalman gain at the moment; based on The Kalman gain at the moment is integrated with the Kalman gain of the preset innovation length using a sliding window to obtain the extended Kalman gain matrix; Based on the preset innovation length, The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations are used to calculate the historical observation residuals and construct a multi-innovation matrix; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction The estimated value of the predicted state at the moment is obtained The state of charge of the sodium-ion battery at the moment; Based on the extended Kalman gain matrix and The actual observation value at the time, corrected The predicted observation estimate at time t, get The health status of sodium-ion batteries at all times.

[0008] Preferably, based on the second-order RC equivalent circuit model of the sodium ion battery, the state equation and observation equation of the sodium ion battery are obtained, including: Based on the electrochemical polarization effect and concentration polarization effect of sodium ion batteries, a second-order RC equivalent circuit model corresponding to sodium ion batteries is constructed to obtain a continuous-time state space model, which is expressed as: ; ; ; ; in, represents the terminal voltage of the sodium ion battery, represents the open circuit voltage, represents the input current, represents the ohmic internal resistance, express time; 、 and They represent the capacitor voltage, internal resistance, and capacitance corresponding to the electrochemical polarization effect respectively; 、 and They represent the capacitor voltage, internal resistance and capacitance corresponding to the concentration polarization effect respectively; Based on the continuous-time state-space model, the operating current is used as input, the terminal voltage is used as output, the electrochemical polarization capacitor voltage and the concentration polarization capacitor voltage are used as system state variables, and the sampling interval is preset. The forward Euler method is used to discretize the continuous-time state-space model of the sodium-ion battery and construct a discretized state-space model, which can be expressed as: ; ; ; ; ; in, , , , ; is the time constant, , ; Indicates the preset sampling time interval, express The state of charge of the sodium-ion battery at the moment; Based on the discretized state space model, the state equation and observation equation of the sodium ion battery are obtained.

[0009] Preferably, the state equation and observation equation of the sodium ion battery are expressed as: Equation of state: ; Observation equation: ; in, represents the time step in the discretization process, and are the time constants of electrochemical polarization and concentration polarization, respectively. represents the charge and discharge efficiency of sodium-ion batteries at room temperature. represents the electrochemical polarization internal resistance, represents the concentration polarization internal resistance, express The operating current of the sodium ion battery at time t, Indicates nominal capacity; represents the system noise matrix, represents the observation noise matrix; express The open circuit voltage of the sodium ion battery at time t, and express and exist The voltage across the two terminals at time t; Indicates the The actual time corresponding to each discrete sampling point.

[0010] Preferably, an unscented Kalman filter is used to perform an unscented transformation on the state equation to obtain multiple key points and their corresponding weights, including: ; ; in, represents the state estimate of the initial key point, Indicates the The state estimation of key points, represents the number of state variables, An adjustable scale parameter to adjust the distance between key points and the mean, The first List, and Indicates the The mean weight and covariance weight of key points; represents the diffusion range control parameter, Represents the high-order moment information parameter.

[0011] Preferably, the state equation and observation equation are used to propagate The key point of the moment, get The state nonlinear transfer result and the observation nonlinear transfer result at the moment; based on The nonlinear transfer result of the state at the moment is obtained The estimated value of the predicted state at the moment and its corresponding predicted state covariance; based on The nonlinear transfer result of the observation at the moment is obtained The estimated value of the forecast observation at time , and its corresponding forecast observation covariance, include: Based on the The key point is The state nonlinear transfer result at the moment is calculated. The key point is The nonlinear transfer result of the state at time ; Based on the The key point is The nonlinear transfer results and mean weight of the state at the moment , calculate the The estimated value of the predicted state at time ; Based on the The key point is The nonlinear transfer result of the state at the moment The estimated value and covariance weight of the predicted state at time , calculate the The predicted state covariance at time ; Based on the The key point is The observed nonlinear transfer results at time t are calculated. The key point is The nonlinear transfer results of observations at time ; Based on the The key point is Nonlinear transmission results and mean weights of observations at time , calculate the The estimated value of the forecast observation at time ; Based on the The key point is The nonlinear transmission results of the observation at the moment The estimated value and covariance weight of the predicted observation at time , calculate the The predicted observation covariance at time ; in, represents the nonlinear state transfer function of the second-order RC equivalent circuit model, represents the state noise matrix, represents the observation noise matrix.

[0012] Preferably, the acquisition of the extended Kalman gain matrix includes: Based on the The key point is The state nonlinear transfer result and the observation nonlinear transfer result at the moment The estimated value of the predicted state and the estimated value of the predicted observation at the moment are calculated Cross covariance at time , expressed as: ; Based on the The key point is The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations, as well as the observation noise covariance ,calculate Innovation covariance at time , expressed as: ; based on Cross covariance and innovation covariance at each moment, construct Kalman gain at time ; based on The Kalman gain at the moment, using the sliding window to integrate the preset innovation length Kalman gain, get the extended Kalman gain matrix , expressed as: ; in, express The Kalman gain at time t.

[0013] Preferably, based on the preset innovation length, The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations are used to calculate the historical observation residuals and construct the multi-innovation matrix, which can be expressed as: ; in, express The forecast residual at time t, express The battery terminal voltage actually measured by the sensor at all times, Indicates based on The state estimation prediction at the moment The terminal voltage value at the moment.

[0014] Preferably, obtain The state of charge of the sodium-ion battery at the moment, including: Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction The estimated value of the predicted state at the moment is obtained The optimal forecast estimate at time , as Sodium ion charge state at time ; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction State covariance at time .

[0015] Preferably, obtain The health status of sodium-ion batteries at all times, including: using actual observations right The predicted observation estimate at the moment is corrected to obtain The best observed estimate at time ; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction Capacity covariance at time ; Low-pass filter the optimal observation estimate to obtain the current sodium-ion battery capacity estimate ; in, Indicates the actual measured value, represents the number of low-pass filter iterations, represents the smoothing factor.

[0016] Preferably, after obtaining the current state of charge of the sodium ion battery, the method further includes using the ambient temperature State of Charge Compensation is performed, which is expressed as: ; in, Indicates state of charge and ambient temperature The ohmic internal resistance after compensation.

[0017] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0018] The method for jointly estimating the state of charge and state of health of a sodium-ion battery described in the present invention simulates electrochemical polarization and concentration polarization, constructs a second-order RC model of the sodium-ion battery, utilizes a multi-innovation unscented Kalman filter, constructs an innovation matrix, and optimizes the posterior measurement correction process by introducing a multidimensional observation information matrix. The error of historical observation data is integrated into the state correction process, effectively solving the problem of limited estimation accuracy caused by information loss in traditional algorithms, significantly improving the system error correction capability, effectively reducing the state of charge estimation error, and improving estimation stability.

[0019] After using untraceable transformation to generate key points, this application transmits them through state equations and observation equations to update the predicted state estimate and predicted observation estimate; and introduces observation residuals to calculate the Kalman gain matrix to further correct the predicted state estimate and predicted observation estimate, and uses the SOC estimation error to correct the capacity, and uses the terminal voltage error to correct the SOC, forming a closed-loop feedback to achieve dynamic coupling of SOC and SOH, and synchronously update SOC and SOH, avoiding model inaccuracy caused by parameter drift in traditional methods, ensuring the consistency of battery state estimation from the initial stage to the retirement stage, reducing the average error fluctuation of SOC throughout the cycle, and improving estimation stability.

[0020] The present invention takes into account the temperature sensitivity of sodium-ion batteries and the SOC prediction value under the influence of temperature. Based on the capacity attenuation coefficient in the absence of temperature influence, compensation is performed through ohmic internal resistance. A temperature compensation factor is added when estimating the ohmic internal resistance, and dynamic temperature compensation is introduced to ensure real-time and accurate estimation of the state of charge (SOC) of the sodium-ion battery.

[0021] The present invention utilizes low-pass filtering to smooth the capacity estimation, suppresses random noise such as short-term capacity regeneration phenomenon, and further improves the stability of capacity estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein: Figure 1 It is a flowchart of the steps of the method for jointly estimating the state of charge and health status of a sodium ion battery of the present invention; Figure 2 This is a schematic diagram of the second-order RC equivalent circuit model corresponding to the sodium-ion battery; Figure 3 It is a flowchart of the steps of the MIUKF-UKF joint estimation method; Figure 4 This is a schematic diagram of the fitting results of the ternary function of ohmic internal resistance, ambient temperature and state of charge; Figure 5 This is a schematic diagram of the SOC estimation error fluctuation range after adding temperature compensation in a high temperature environment of 35°C. DETAILED DESCRIPTION

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0024] This embodiment addresses the problem of insufficient utilization of single-innovation observation information in SOC estimation in traditional unscented Kalman filters (UKFs). By integrating multi-innovation identification theory, an improved multi-innovation unscented Kalman filter (MIUKF) algorithm is constructed. By introducing a multidimensional observation information matrix to optimize the posterior measurement correction process, this algorithm effectively addresses the limited estimation accuracy caused by information loss in traditional algorithms and significantly improves the system's error correction capability. Furthermore, considering the temperature sensitivity of sodium-ion batteries, a temperature compensation factor is added when estimating the ohmic internal resistance, providing a new technical solution for accurate real-time SOC estimation of power batteries. Furthermore, by using the identified ohmic internal resistance parameter and the capacity decay coefficient as a joint state variable and combining it with a dynamic parameter optimization mechanism, this invention achieves simultaneous online estimation of the SOC and SOH of sodium-ion batteries.

[0025] Reference Figure 1 As shown in FIG, a flowchart of the method for jointly estimating the state of charge and health state of a sodium ion battery of the present invention includes the following steps: S101: Based on the second-order RC equivalent circuit model of the sodium-ion battery, obtain the state equation and observation equation of the sodium-ion battery; S102: Initializing the state estimation value, state covariance, capacity estimation value and capacity covariance of the sodium ion battery; S103: Using an unscented Kalman filter to perform an unscented transformation on the state equation to obtain multiple key points and their corresponding weights, including: ; ; in, represents the state estimate of the initial key point, Indicates the The state estimation of key points, represents the number of state variables, An adjustable scale parameter to adjust the distance between key points and the mean, The first List, and Indicates the The mean weight and covariance weight of key points; represents the diffusion range control parameter, Represents the high-order moment information parameter; S104: Propagation using state equation and observation equation respectively The key point of the moment, get The state nonlinear transfer result and the observation nonlinear transfer result at the moment; based on The nonlinear transfer result of the state at the moment is obtained The estimated value of the predicted state at the moment and its corresponding predicted state covariance; based on The nonlinear transfer result of the observation at the moment is obtained The estimated value of the forecast observation at time t, and its corresponding forecast observation covariance; S105: Based on The state nonlinear transfer result at the moment, the observation nonlinear transfer result, the predicted state estimate, the predicted observation estimate and the observation noise covariance are calculated. Cross covariance and innovation covariance at each moment, construct The Kalman gain at the moment; based on The Kalman gain at the moment is integrated with the Kalman gain of the preset innovation length using a sliding window to obtain the extended Kalman gain matrix; S106: Based on the preset innovation length, The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations are used to calculate the historical observation residuals and construct the multi-innovation matrix, which can be expressed as: ; in, express The forecast residual at time t, express The battery terminal voltage actually measured by the sensor at all times, Indicates based on The state estimation prediction at the moment The terminal voltage value at the moment; S107: Based on the extended Kalman gain matrix and the multi-innovation matrix, correct The estimated value of the predicted state at the moment is obtained The state of charge of the sodium-ion battery at the moment, including: S107-1: Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction The estimated value of the predicted state at the moment is obtained The optimal forecast estimate at time , as Sodium ion charge state at time ; S107-2: Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction State covariance at time ; S108: Based on the extended Kalman gain matrix and The actual observation value at the time, corrected The predicted observation estimate at time t, get The health status of the sodium-ion battery at all times, including: S108-1: Using actual observations right The predicted observation estimate at the moment is corrected to obtain The best observed estimate at time ; S108-2: Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction Capacity covariance at time ; S108-3: Low-pass filter the optimal observation estimate to obtain the current sodium-ion battery capacity estimate ; in, Indicates the actual measured value, represents the number of low-pass filter iterations, represents the smoothing factor.

[0026] Reference Figure 2 , which is a schematic diagram of a second-order RC equivalent circuit model corresponding to a sodium-ion battery; specifically, in step S101, obtaining the state equation and observation equation of the sodium-ion battery includes: S101-1: Based on the electrochemical polarization effect and concentration polarization effect of sodium-ion batteries, a second-order RC equivalent circuit model corresponding to sodium-ion batteries is constructed to obtain a continuous-time state-space model, which is expressed as: ; ; ; ; in, represents the terminal voltage of the sodium ion battery, represents the open circuit voltage, represents the input current, represents the ohmic internal resistance, express time; 、 and They represent the capacitor voltage, internal resistance, and capacitance corresponding to the electrochemical polarization effect respectively; 、 and They represent the capacitor voltage, internal resistance and capacitance corresponding to the concentration polarization effect respectively; S101-2: Based on the continuous-time state-space model, with the operating current as input and the terminal voltage as output, the electrochemical polarization capacitor voltage and the concentration polarization capacitor voltage as system state variables, and a preset sampling interval, the forward Euler method is used to discretize the continuous-time state-space model of the sodium-ion battery to construct a discretized state-space model, which can be expressed as: ; ; ; ; ; in, , , , ; is the time constant, , ; Indicates the preset sampling time interval, express The state of charge of the sodium-ion battery at the moment; S101-3: Based on the discretized state space model, the state equation and observation equation of the sodium ion battery are obtained, which are expressed as: Equation of state: ; Observation equation: ; in, represents the time step in the discretization process, and are the time constants of electrochemical polarization and concentration polarization, respectively. represents the charge and discharge efficiency of sodium-ion batteries at room temperature. represents the electrochemical polarization internal resistance, represents the concentration polarization internal resistance, express The operating current of the sodium ion battery at time t, Indicates nominal capacity; represents the system noise matrix, represents the observation noise matrix; express The open circuit voltage of the sodium ion battery at time t, and express and exist The voltage across the two terminals at time t; Indicates the The actual time corresponding to each discrete sampling point.

[0027] This embodiment uses dual RC networks to simulate electrochemical polarization and concentration polarization respectively. Compared with the first-order model, the voltage characteristic simulation accuracy is improved by about 15%. In particular, in the fast charge and discharge scenario, the terminal voltage prediction error is reduced to within 2mV.

[0028] Specifically, in step S104, the state equation and the observation equation are used to propagate Key moments include: S104-1: Based on The key point is The state nonlinear transfer result at the moment is calculated. The key point is The nonlinear transfer result of the state at time ; S104-2: Based on The key point is The nonlinear transfer results and mean weight of the state at the moment , calculate the The estimated value of the predicted state at time ; S104-3: Based on The key point is The nonlinear transfer result of the state at the moment The estimated value and covariance weight of the predicted state at time , calculate the The predicted state covariance at time ; S104-4: Based on The key point is The observed nonlinear transfer results at time t are calculated. The key point is The nonlinear transfer results of observations at time ; S104-5: Based on The key point is Nonlinear transmission results and mean weights of observations at time , calculate the The estimated value of the forecast observation at time ; S104-6: Based on The key point is The nonlinear transmission results of the observation at the moment The estimated value and covariance weight of the predicted observation at time , calculate the The predicted observation covariance at time ; in, represents the nonlinear state transfer function of the second-order RC equivalent circuit model, represents the state noise matrix, represents the observation noise matrix.

[0029] Specifically, in step S105, the acquisition of the extended Kalman gain matrix includes: S105-1: Based on The key point is The state nonlinear transfer result and the observation nonlinear transfer result at the moment The estimated value of the predicted state and the estimated value of the predicted observation at the moment are calculated Cross covariance at time , expressed as: ; S105-2: Based on The key point is The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations, as well as the observation noise covariance ,calculate Innovation covariance at time , expressed as: ; S105-3: Based on Cross covariance and innovation covariance at each moment, construct Kalman gain at time ; S105-4: Based on The Kalman gain at the moment, using the sliding window to integrate the preset innovation length Kalman gain, get the extended Kalman gain matrix , expressed as: ; in, express The Kalman gain at time t.

[0030] The method for jointly estimating the state of charge and state of health of a sodium-ion battery described in the present invention simulates electrochemical polarization and concentration polarization, constructs a second-order RC model of the sodium-ion battery, utilizes a multi-innovation unscented Kalman filter, constructs an innovation matrix, and optimizes the posterior measurement correction process by introducing a multidimensional observation information matrix. The error of historical observation data is integrated into the state correction process, effectively solving the problem of limited estimation accuracy caused by information loss in traditional algorithms, significantly improving the system error correction capability, effectively reducing the state of charge estimation error, and improving estimation stability.

[0031] Based on the above embodiment, in this embodiment, after obtaining the current state of charge of the sodium ion battery, it also includes using the ambient temperature State of Charge Compensation is performed, which is expressed as: ; in, Indicates state of charge and ambient temperature The ohmic internal resistance after compensation.

[0032] The present invention takes into account the temperature sensitivity of sodium-ion batteries and the SOC prediction value under the influence of temperature. Based on the capacity attenuation coefficient in the absence of temperature influence, compensation is performed through ohmic internal resistance. A temperature compensation factor is added when estimating the ohmic internal resistance, and dynamic temperature compensation is introduced to ensure real-time and accurate estimation of the state of charge (SOC) of the sodium-ion battery.

[0033] In this embodiment, for the characteristics of sodium-ion batteries, the second-order RC model can effectively characterize multiple polarization effects through a dual RC parallel structure: the open-circuit voltage source characterizes the static characteristics of the battery, the ohmic internal resistance reflects the instantaneous impedance, and two RC networks with different time constants simulate different polarization processes respectively. Compared with basic models such as first-order RC or Rint, this structure significantly improves the simulation accuracy of the voltage characteristics of the charge and discharge process through multi-time scale dynamic response, while maintaining a balance between parameter identifiability and computational economy. Specifically, the steps of the sodium-ion battery SOC and SOH joint estimation method include:

[0034] S201: The present invention is based on a second-order RC equivalent circuit model, and constructs Figure 2 The battery characteristic analysis framework shown in the figure; the core parameters of the model include terminal voltage , working current And the nominal capacitance ; The model structure works synergistically through an open-circuit voltage source, an ohmic internal resistance, and a dual RC polarization network; among them, the open-circuit voltage source maps the static energy storage characteristics, the ohmic internal resistance characterizes the transient impedance effect, and the two RC networks with different time constants correspond to the dynamic response processes of electrochemical polarization and concentration polarization, respectively.

[0035] The battery state of charge (SOC) is defined as the percentage of available capacity to nominal capacity, expressed as: ; The initial value is recorded as SOC, which is related to the open circuit voltage There is a nonlinear mapping relationship; represents the ohmic impedance, and Parameters that represent the network simulation of electrochemical polarization effects (such as the double layer response of the electrode / electrolyte interface), and Represents the parameters of the network describing the dynamics of concentration polarization (e.g., the evolution of ion concentration gradients);

[0036] S202: The electrical behavior of the system can be characterized by a set of differential equations, including: ; ; ; ;

[0037] S203: Based on the above equations, a discretized state space model is established, and the terminal voltage and current are used as the output and input of the equivalent circuit model respectively. The continuous equation is processed with a step size of Discretize , and obtain the system dynamics equations, including: ; ; ; ; ; in, , , , ; is the sampling time interval, is the time constant, , .

[0038] Specifically, based on the above-mentioned second-order RC model of sodium-ion batteries, the operating current is the input variable, terminal voltage is the output variable, the voltage across the two polarized capacitors 、 is the system state variable, with sampling interval time The system is discretized to obtain the state equation of the sodium ion battery model, which is expressed as: ; The observation equation is: ; in, express The open circuit voltage across the battery at this moment, and Represents the polarization resistance at each moment and The voltage across the terminals, and They are the polarization resistance caused by electrochemical reaction and the polarization resistance caused by concentration difference during the charge and discharge process, Indicates the charge and discharge efficiency of the battery at room temperature. and are system noise and observation noise, respectively.

[0039] S204: Based on the above MIUKF algorithm, the influence of SOH on the SOC estimation of sodium-ion batteries is considered, and a MIUKF-UKF joint estimation method is proposed. A low-pass filter is added to the SOH estimation to smooth it. Figure 3 The figure shows the flow chart of the steps of the MIUKF-UKF joint estimation method. The specific algorithm steps are as follows: ① Initialize state estimation and capacity estimation parameters, including: ; ; ; ; ②Construct the Sigma points and weights of UKF, including: ; ; ③ The moment capacity estimation and its error covariance are expressed as: ; ; ④ The momentary state estimate and its error covariance include: ; ; ; ⑤ Predict the observed mean and covariance, including: ; ; ; ; ⑥Multi-innovation matrix, expressed as: ; ⑦ Update the state and error covariance, and obtain the extended Kalman gain matrix, ; ; ; ⑧ Update the multi-innovation Kalman gain, state, and error covariance of the capacity estimate, including: ; ; ; ⑨Add low-pass filtering and smoothing, expressed as: .

[0040] The traditional UKF algorithm only uses single-time observation information, which makes it susceptible to noise interference and accumulation of model nonlinear errors under dynamic loads. The MIUKF-UKF algorithm proposed in this paper constructs a multi-dimensional new information matrix to dynamically integrate historical observation data into the state correction process, effectively suppressing error drift. Experiments show that under normal temperature HPPC experiments, the MIUKF algorithm has the lowest mean absolute error and root mean square error. Compared with EKF, the SOC estimation MAE is reduced by 17% and the root mean square error is reduced by 40%, further indicating that its estimated value is closer to the true value and has smaller fluctuations, proving the excellent estimation accuracy of the algorithm.

[0041] This embodiment uses the equivalent circuit model and UKF algorithm to achieve SOH estimation. The prediction results are consistent with electrochemical principles (such as monotonous decay of capacity with cycle number), avoiding the possible anti-physical law predictions (such as abnormal capacity recovery) that may occur in deep learning methods, and meeting functional safety certification requirements. Using MIUKF-UKF as a joint state variable, the SOC and SOH are synchronously updated using the capacity decay coefficient, avoiding model inaccuracy caused by parameter drift in traditional methods. Compared to deep learning methods that require thousands of cycles of aging data, this solution requires only a small amount of initial data (<100 cycles) to complete model parameter calibration, reducing data acquisition costs by over 90%. Experiments show that the SOH estimation error is kept within 2% (over the entire battery lifecycle) without relying on offline calibration. Furthermore, a low-pass filter is introduced into the capacity estimation to effectively suppress random noise during the cycle aging process (such as short-term capacity regeneration), making it more consistent with actual degradation trends. Through a dynamic parameter optimization mechanism, the system can adapt to different charging and discharging strategies (such as fast charging and pulsed loading) and temperature ranges while reducing errors. The combined SOC and SOH estimation forms a closed-loop feedback loop, which allows real-time correction of model parameters (such as the increase in R0 due to aging). This ensures consistent state estimation from the initial stage to the end of the battery lifecycle and reduces fluctuations in the average SOC error over the entire battery lifecycle. The SOH estimation results based on the physical model in this embodiment can be verified through voltage-capacity curve inversion, directly associated with aging mechanisms (such as ohmic impedance growth dominating capacity decay), and support root cause analysis of faults. High-precision SOC estimation combined with real-time SOH monitoring can avoid the risk of thermal runaway.

[0042] Based on the above embodiment, this embodiment takes into account the sensitivity of sodium ion batteries to temperature and needs to consider the impact of ambient temperature on battery capacity and the effect of temperature on ohmic internal resistance when estimating SOC. The impact of is much greater than that of SOC. At the same temperature, The change with SOC is not obvious, but the change of temperature will cause obvious fluctuation. The variation range at low temperature is obviously greater than that at high temperature. The relationship between SOC and T is Make a ternary function of SOC and T, refer to Figure 4 The figure shows the fitting result of the ternary function of ohmic internal resistance, ambient temperature and state of charge. The expression is: ;

[0043] According to the fitting ternary function, the SOC estimation is performed Compensation is added to address the impact of ambient temperature changes on sodium-ion battery SOC estimation. As the battery's SOH decreases through repeated charge and discharge cycles, the internal resistance of the sodium-ion battery also changes significantly. As the battery ages, the mean R0 value increases significantly, indicating that aging is a factor influencing the ohmic internal resistance.

[0044] Reference Figure 5 As shown in the figure, it is a schematic diagram of the SOC estimation error fluctuation range after adding temperature compensation in a high temperature environment of 35°C; A temperature compensation factor, a ternary function of temperature (T) and SOC, is introduced into the ohmic internal resistance estimation to address the SOC estimation drift caused by the drastic change in internal resistance at low temperatures in sodium-ion batteries. At 35°C, the SOC estimation error fluctuation is reduced to ±0.8% after temperature compensation, significantly improving SOC estimation accuracy to compensate for the temperature sensitivity of sodium-ion batteries.

[0045] The present invention relates to a method for jointly estimating the state of charge (SOC) and state of health (SOH) of a sodium-ion battery online, and its real-time deployment technology on an embedded hardware platform. This patent is applicable to battery management systems (BMS) in fields such as electric vehicles and energy storage systems, and is particularly designed for the high temperature sensitivity and aging characteristics of sodium-ion batteries. Based on the above embodiments, in this embodiment, the method for jointly estimating the state of charge and health of a sodium-ion battery provided by the present invention is implemented using an embedded BMS system based on an STM32F407. Specifically, the system includes: The main control chip is STM32F407 (ARM Cortex-M4, 168MHz main frequency, 1MB Flash, 192KB SRAM); The sensor module includes: Battery cell monitoring uses Linear's LTC6811 automotive-grade chip, which reads battery status via isolated SPI communication. Chip features include a maximum measurement error of 1.2mV, a stackable architecture, a built-in isoSPI™ interface, 1Mb isolated serial communication, and the ability to complete measurements of all batteries in the system within 290μs. AD total voltage and total current detection chip: The detection of the total voltage and total current of the battery pack uses a 24-bit ADI chip; the chip has a voltage acquisition channel and a current acquisition channel; Temperature detection: NTC thermistor (MF52AT 10kΩ, B value 3950K); The communication interface includes an isolated CAN chip, a non-isolated CAN chip and an RS485 chip, which are used to exchange data with the host controller.

[0046] The algorithm deployment process includes: ① Model parameter initialization: Second-order RC equivalent circuit parameters (calibrated at 25°C): R0=50mΩ, R p =120mΩ, C p =1200F, R_c=50mΩ, C_c=8000F; UKF parameters: state variable dimension n=3 (SOC,U p ,U_c); process noise covariance Q=diag([1e-5,1e-4,1e-4]); observation noise covariance R=1e-3; ②Algorithm real-time operation process, including: Initialize SOC=100%, SOH=100%, capacity Q n =100Ah; Generate Sigma points (α=1e-3, β=2, κ=0) The joint estimation loop is executed every 100ms:

[0047] In this embodiment, a multi-dimensional innovation-identified Kalman filter is used to obtain the state of charge of a sodium-ion battery, including: inputting a matrix containing capacity parameters, performing Sigma point generation prediction (α, β, κ), state prediction, weighted mean, covariance prediction, observation prediction, Kalman gain calculation, and multi-innovation correction (state update + covariance update);

[0048] In this embodiment, the health status of the sodium ion battery is obtained using Kalman filtering, including: generating parameter Sigma points, parameter prediction, observation prediction based on SOC estimation parameters, Kalman update parameters, and low-pass filter smoothing parameters.

[0049] The UKF is used in the present invention to estimate the SOH of sodium-ion batteries. The computational complexity of the UKF is O(n3), where n is the dimension of the state variable, which is much lower than the particle filter (O(N⋅n3), where N is the number of particles). This method is suitable for real-time operation of the embedded system in the present invention and meets the application requirements of low-cost sodium-ion battery scenarios.

[0050] In this embodiment, the SOC display resolution is 0.1%, and the status is updated every 1 second via CAN; when SOH < 80%, a battery replacement warning is triggered and the charging current is limited to 0.5C.

[0051] The method for jointly estimating the state of charge and state of health of a sodium-ion battery described in the present invention simulates electrochemical polarization and concentration polarization, constructs a second-order RC model of the sodium-ion battery, utilizes a multi-innovation unscented Kalman filter, constructs an innovation matrix, and optimizes the posterior measurement correction process by introducing a multidimensional observation information matrix. The error of historical observation data is integrated into the state correction process, effectively solving the problem of limited estimation accuracy caused by information loss in traditional algorithms, significantly improving the system error correction capability, effectively reducing the state of charge estimation error, and improving estimation stability. After the key points are generated by the traceless transformation, the application transmits them through the state equation and the observation equation to update the predicted state estimate and the predicted observation estimate; and introduces the observation residual to calculate the Kalman gain matrix, further corrects the predicted state estimate and the predicted observation estimate, uses the SOC estimation error to correct the capacity, and uses the terminal voltage error to correct the SOC, forming a closed-loop feedback, realizing the dynamic coupling of SOC and SOH, synchronously updating SOC and SOH, avoiding the model inaccuracy caused by parameter drift in traditional methods, ensuring the consistency of battery state estimation from the initial stage to the retirement stage, reducing the fluctuation of the average error of SOC throughout the whole cycle, and improving the estimation stability. The present invention takes into account the temperature sensitivity of sodium-ion batteries, considers the SOC prediction value under the influence of temperature, and compensates by ohmic internal resistance based on the capacity attenuation coefficient without temperature influence. When estimating the ohmic internal resistance, a temperature compensation factor is added, and dynamic temperature compensation is introduced to ensure the real-time and accurate estimation of the state of charge SOC of the sodium-ion battery. The present invention uses low-pass filtering to smooth the capacity estimation, suppresses random noise such as short-term capacity regeneration, and further improves the stability of capacity estimation.

[0052] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0053] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0054] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0055] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0056] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for jointly estimating the state of charge and health status of a sodium ion battery, characterized in that: include: Based on the second-order RC equivalent circuit model of the sodium-ion battery, the state equation and observation equation of the sodium-ion battery are obtained; Initialize the state estimation value, state covariance, capacity estimation value and capacity covariance of the sodium ion battery; Use unscented Kalman filtering to perform unscented transformation on the state equation to obtain multiple key points and their corresponding weights; Propagation using state equation and observation equation respectively The key point of the moment, get The state nonlinear transfer result and the observation nonlinear transfer result at the moment; based on The nonlinear transfer result of the state at the moment is obtained The estimated value of the predicted state at the moment and its corresponding predicted state covariance; based on The nonlinear transfer result of the observation at the moment is obtained The estimated value of the forecast observation at time t, and its corresponding forecast observation covariance; based on The state nonlinear transfer result at the moment, the observation nonlinear transfer result, the predicted state estimate, the predicted observation estimate and the observation noise covariance are calculated. Cross covariance and innovation covariance at each moment, construct The Kalman gain at the moment; based on The Kalman gain at the moment is integrated with the Kalman gain of the preset innovation length using a sliding window to obtain the extended Kalman gain matrix; Based on the preset innovation length, The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations are used to calculate the historical observation residuals and construct a multi-innovation matrix; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction The estimated value of the predicted state at the moment is obtained The state of charge of the sodium-ion battery at the moment; Based on the extended Kalman gain matrix and The actual observation value at the time, corrected The predicted observation estimate at time t, get The health status of sodium-ion batteries at all times.

2. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 1, characterized in that: Based on the second-order RC equivalent circuit model of the sodium-ion battery, the state equation and observation equation of the sodium-ion battery are obtained, including: Based on the electrochemical polarization effect and concentration polarization effect of sodium ion batteries, a second-order RC equivalent circuit model corresponding to sodium ion batteries is constructed to obtain a continuous-time state space model, which is expressed as: ； ； ； ； in, represents the terminal voltage of the sodium ion battery, represents the open circuit voltage, represents the input current, represents the ohmic internal resistance, express time; 、 and They represent the capacitor voltage, internal resistance, and capacitance corresponding to the electrochemical polarization effect respectively; 、 and They represent the capacitor voltage, internal resistance and capacitance corresponding to the concentration polarization effect respectively; Based on the continuous-time state-space model, the operating current is used as input, the terminal voltage is used as output, the electrochemical polarization capacitor voltage and the concentration polarization capacitor voltage are used as system state variables, and the sampling interval is preset. The forward Euler method is used to discretize the continuous-time state-space model of the sodium-ion battery and construct a discretized state-space model, which can be expressed as: ； ； ； ； ； in, , , , ; is the time constant, , ; Indicates the preset sampling time interval, express The state of charge of the sodium-ion battery at the moment; Based on the discretized state space model, the state equation and observation equation of the sodium ion battery are obtained.

3. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 2, wherein: The state equation and observation equation of sodium ion battery are expressed as: Equation of state: ； Observation equation: ; in, represents the time step in the discretization process, and are the time constants of electrochemical polarization and concentration polarization, respectively. represents the charge and discharge efficiency of sodium-ion batteries at room temperature. represents the electrochemical polarization internal resistance, represents the concentration polarization internal resistance, express The operating current of the sodium ion battery at time t, Indicates nominal capacity; represents the system noise matrix, represents the observation noise matrix; express The open circuit voltage of the sodium ion battery at time t, and express and exist The voltage across the two terminals at time t; Indicates the The actual time corresponding to each discrete sampling point.

4. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 3, characterized in that: The unscented Kalman filter is used to perform an unscented transformation on the state equation to obtain multiple key points and their corresponding weights, including: ； ； in, represents the state estimate of the initial key point, Indicates the The state estimation of key points, represents the number of state variables, An adjustable scale parameter to adjust the distance between key points and the mean, The first List, and Indicates the The mean weight and covariance weight of key points; represents the diffusion range control parameter, Represents the high-order moment information parameter.

5. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 4, characterized in that: Propagation using state equation and observation equation respectively The key point of the moment, get The state nonlinear transfer result and the observation nonlinear transfer result at the moment; based on The nonlinear transfer result of the state at the moment is obtained The estimated value of the predicted state at the moment and its corresponding predicted state covariance; based on The nonlinear transfer result of the observation at the moment is obtained The estimated value of the forecast observation at time , and its corresponding forecast observation covariance, include: Based on the The key point is The state nonlinear transfer result at the moment is calculated. The key point is The nonlinear transfer result of the state at time ; Based on the The key point is The nonlinear transfer results and mean weight of the state at the moment , calculate the The estimated value of the predicted state at time ; Based on the The key point is The nonlinear transfer result of the state at the moment The estimated value and covariance weight of the predicted state at time , calculate the The predicted state covariance at time ； Based on the The key point is The observed nonlinear transfer results at time t are calculated. The key point is The nonlinear transfer results of observations at time ; Based on the The key point is Nonlinear transmission results and mean weights of observations at time , calculate the The estimated value of the forecast observation at time ; Based on the The key point is The nonlinear transmission results of the observation at the moment The estimated value and covariance weight of the predicted observation at time , calculate the The predicted observation covariance at time ； in, represents the nonlinear state transfer function of the second-order RC equivalent circuit model, represents the state noise matrix, represents the observation noise matrix.

6. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 5, characterized in that: Acquisition of the extended Kalman gain matrix, including: Based on the The key point is The state nonlinear transfer result and the observation nonlinear transfer result at the moment The estimated value of the predicted state and the estimated value of the predicted observation at the moment are calculated Cross covariance at time , expressed as: ； Based on the The key point is The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations, as well as the observation noise covariance ,calculate Innovation covariance at time , expressed as: ； based on Cross covariance and innovation covariance at each moment, construct Kalman gain at time ; based on The Kalman gain at the moment, using the sliding window to integrate the preset innovation length Kalman gain, get the extended Kalman gain matrix , expressed as: ； in, express The Kalman gain at time t.

7. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 6, characterized in that: Based on the preset innovation length, The nonlinear transfer results of the observations at the moment and the estimated values ​​of the predicted observations are used to calculate the historical observation residuals and construct the multi-innovation matrix, which can be expressed as: ； in, express The forecast residual at time t, express The battery terminal voltage actually measured by the sensor at all times, Indicates based on The state estimation prediction at the moment The terminal voltage value at the moment.

8. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 7, characterized in that: Get The state of charge of the sodium-ion battery at the moment, including: Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction The estimated value of the predicted state at the moment is obtained The optimal forecast estimate at time , as Sodium ion charge state at time ; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction State covariance at time .

9. The method for jointly estimating the state of charge and health status of a sodium ion battery according to claim 8, characterized in that: Get The health status of the sodium-ion battery at all times, including: Using actual observations right The predicted observation estimate at the moment is corrected to obtain The best observed estimate at time ; Based on the extended Kalman gain matrix and the multi-innovation matrix, the correction Capacity covariance at time ; Low-pass filter the optimal observation estimate to obtain the current sodium-ion battery capacity estimate ; in, Indicates the actual measured value, represents the number of low-pass filter iterations, represents the smoothing factor.

10. The method for jointly estimating state of charge and state of health of a sodium ion battery according to claim 8, characterized in that: After obtaining the current state of charge of the sodium ion battery, it also includes using the ambient temperature State of Charge Compensation is performed, which is expressed as: ； in, Indicates state of charge and ambient temperature The ohmic internal resistance after compensation.

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