Method for estimating state of charge of lithium battery based on electrochemical model and particle filter

Abstract

The invention discloses a method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering. First, SPME is adopted to reduce the computational burden of the electrochemical model while fully reflecting the internal state changes during the charge and discharge process of the lithium battery. Then, sensitive parameters are selected through basic effect tests, and the sensitive parameters that are difficult to directly measure are identified through a particle swarm optimization algorithm to improve the accuracy of the model. Finally, a particle swarm optimization algorithm is used to construct an SOC estimation model based on the electrochemical model, and voltage correction of the SOC value is introduced to reduce the errors introduced by long-term operation, so as to achieve accurate online estimation of SOC. Compared with the estimation method based on the extended Kalman filter of ECM, the method of the invention has higher accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of power lithium battery applications, and particularly to a method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering. Background Art

[0002] With the increasingly serious global energy crisis and environmental pollution, electric vehicles and smart grids have received extensive attention worldwide, and energy storage systems play a crucial role in electric vehicles and smart grids. Among the existing energy storage devices, lithium-ion batteries have been widely used due to their advantages such as high specific energy density, high power density, long life, low self-discharge rate, and no memory effect. In order to ensure the safety and reliability of the energy storage system and achieve the best working performance with an optimal management strategy, the battery management system (BMS) must monitor the battery state. The battery state usually includes the state of charge (SOC), state of health (SOH), functional state, and power state. The state of charge of the battery, which is the ratio of the remaining battery charge to its maximum value, is a key variable that must be estimated in the BMS.

[0003] However, the SOC cannot be directly measured by the BMS. It must be estimated through some related measurable variables such as current, voltage, and temperature. Commonly used SOC estimation methods include the ampere-hour integration method, the OCV look-up table method, the model-based method, etc. The ampere-hour integration method is the most commonly used method in SOC estimation and has the advantages of simplicity and reliability. However, due to the cumulative measurement errors during long-term operation and the uncertainty of the initial SOC, and this method calculates the SOC only based on current measurement and cannot use voltage measurement for any correction, so it has significant disadvantages. Although the OCV look-up table method can overcome the above disadvantages, this method cannot achieve online estimation of the SOC when the battery is working. The model-based method generally uses an equivalent circuit model (ECM) and an electrochemical model. The equivalent circuit model uses resistors, inductors, and capacitors to simulate the external characteristics of lithium batteries. However, the parameters of the equivalent circuit model have no direct relationship with the electrochemical reaction process, lack clear physical meaning, and cannot reflect the internal state changes during the battery charge and discharge process. The initial electrochemical model is the pseudo-2D (P2D) model proposed by Doyle, Fuller, and Newman, which consists of four partial differential equations and an algebraic equation and can be used to describe the thermodynamic and electrochemical processes of the battery with high accuracy. However, the solution of the partial differential equations is very complex, so some simplified models have been developed. The most representative one is the single particle model (SPM). This model assumes that the current distribution in the electrode is uniform, ignores the electrolyte dynamics, and simplifies the calculation of the electrochemical model. However, due to the neglect of the electrolyte dynamics, this model cannot be applied in scenarios with high currents.

[0004] The electrochemical model has high accuracy in SOC estimation because it can accurately describe the state changes inside the battery. The calculation accuracy of the electrochemical model depends to a large extent on the accuracy of the parameters. Therefore, it is crucial to find accurate battery parameter values. Some electrochemical model parameter values can be directly measured by disassembling the battery, such as geometric parameters and the OCV curves of the positive and negative electrodes. The remaining parameters need to be obtained through parameter identification. At the same time, although the electrochemical model itself has the ability to monitor the change of lithium-ion concentration inside the solid-phase particles, it lacks correction of the terminal voltage during long-term operation and will introduce a large amount of errors. Summary of the Invention

[0005] Aiming at the above problems, the purpose of the present invention is to provide a method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering. Based on the extended single particle model and combined with the particle filtering algorithm, it realizes the online estimation of the state of charge of the battery, and can make the output SOC value have high accuracy. The technical solution is as follows:

[0006] A method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering, comprising the following steps:

[0007] Step 1: Establish a single-particle model of the lithium battery with liquid-phase potential, estimate the state variables inside the battery through the charge and discharge current, and thus simulate the output voltage;

[0008] Step 2: Conduct a sensitivity analysis on the parameters of the single-particle model with liquid-phase potential using the elementary effect test;

[0009] Step 3: Use the particle swarm optimization algorithm for sensitive parameter identification;

[0010] Step 4: Based on the single-particle model with liquid-phase potential, using the charge and discharge current as the input and the voltage across the battery as the observation, estimate the state variables related to the SOC through particle filtering, and calculate the SOC value of the battery accordingly.

[0011] Furthermore, the single-particle model with liquid-phase potential includes six sets of mathematical equations: the liquid-phase diffusion equation of lithium ions, the solid-phase diffusion equation of lithium ions, the liquid-phase Ohm's law, the solid-phase Ohm's law, the charge conservation equation, and the Butler-Vomer kinetic equation.

[0012] Even further, the sensitivity analysis in Step 2 specifically includes:

[0013] Step 2.1: Calculate the elementary effect of the i-th parameter on the j-th trajectory as:

[0014]

[0015] where, is the i-th parameter for the j-th change; y(·) represents the output equation of the system; is the change amount of the i-th parameter at the j-th change; i = 1, 2,....n, j = 1, 2,..., r; n is the total number of parameters, and r is the total number of trajectories;

[0016] Step 2.2: Assume the state-space equation of the system is:

[0017]

[0018] y = h(x, t, u, p) (3)

[0019] where, x is the system state vector, y is the output vector, t represents time, u is the system input, and p represents the parameter;

[0020] Step 2.3: Use the mean value μ i and the standard deviation σ i to measure the elementary effect test with two sensitivity metrics

[0021]

[0022]

[0023] If the average value μ i is greater than the average value setting threshold, it means that the parameter p i has a significant impact on the output of the model;

[0024] If the standard deviation σ i is greater than the standard deviation setting threshold, it indicates that the parameter p i will interact with other parameters, or the impact of the parameter p i on the model output is non - linear.

[0025] Furthermore, the specific steps of step 3 include:

[0026] Step 3.1: Initialization

[0027] Randomly initialize the particle swarm, where the position of the k - th particle in the m - dimensional space is A k =(a k1 ,a k2 ,...,a km ), and the velocity is V k =(v k1 ,v k2 ,...,v kn );

[0028] Step 3.2: Select the best particle

[0029] Record the individual fitness, individual best fitness, and population best fitness, and record the particle with the individual best fitness, that is, the position P k =(p k1 ,p k2 ,...,p km ), and the particle with the population best fitness, that is, the position G k =(g k1 ,g k2 ,...,g km );

[0030] Step 3.3: State update

[0031] Update the velocity and state of the particle flight;

[0032] V′ k =w×V k +c1×Rand×(P k -A k) + c2 × Rand × (G k -A k ) (5)

[0033] a′ k =a k +V′ k (6)

[0034] Wherein, a k is the individual position, V k is the individual flight speed, w is the inertia coefficient, c1 and c2 are learning factors, Rand is a random number between 0 and 1; V′ k is the updated speed, a′ k is the updated individual position;

[0035] Step 3.4: Iteration

[0036] Calculate the fitness of the new position. If the fitness is higher than the preset value, update the best fitness and the best position. Otherwise, continue to loop and determine whether the termination condition is satisfied;

[0037] Step 3.5: Through the particle swarm optimization algorithm of Steps 3.1 - 3.4, identify the sensitive parameters; meanwhile, for the parameters related to SOC calculation: the negative electrode solid-phase lithium-ion concentration c s,n0％ when the battery charge is 0% and the positive electrode solid-phase lithium-ion concentration c s,p100％ when the battery charge is 100% are identified.

[0038] Furthermore, the specific steps of Step 4 include:

[0039] Step 4.1: The positive electrode SOC SOC p represents the number of lithium ions that can be extracted from the active material in the electrode before depletion; the negative electrode SOC SOC n represents the number of lithium ions that can be absorbed by the active material in the electrode before saturation, and are respectively expressed as:

[0040]

[0041]

[0042] Wherein, and are the average negative electrode and positive electrode solid-phase lithium-ion concentrations respectively; c s,p0％ is the positive electrode solid-phase lithium-ion concentration when the battery charge is 0%, c s,n100％ is the negative electrode solid-phase lithium-ion concentration when the battery charge is 100%; take the average of the two, that is

[0043]

[0044] Step 4.2: Fit the partial differential equation of solid-phase diffusion using the three-parameter parabola approximation method. The simplified solid-phase diffusion equation is:

[0045]

[0046]

[0047]

[0048] where, is the average value of the gradient of the solid-phase lithium-ion concentration c s along the r direction; is the average solid-phase lithium-ion concentration; R s is the radius of the solid-phase particle; D s is the solid-phase diffusion coefficient; c ss is the lithium-ion concentration on the surface of the solid-phase particle; j n is the lithium-ion flux on the surface of the active particle;

[0049] Then the state-space equation of the system is:

[0050]

[0051] where, and are the average solid-phase lithium-ion concentrations of the negative and positive electrodes, respectively; and are the average values of the gradients of the solid-phase lithium-ion concentration c s along the R direction of the negative and positive electrodes, respectively; D s,n and D s,p are the solid-phase diffusion coefficients of the negative and positive electrodes, respectively; R s,n and R s,p are the radii of the solid-phase particles of the negative and positive electrodes, respectively; F is the Faraday constant; S n and S p are the surface areas of the negative and positive electrodes, respectively; L n and L p are the lengths of the negative and positive electrodes, respectively; ε s,n and ε s,p are the solid-phase volume fractions of the negative and positive electrodes, respectively; I(t) is the external current density;

[0052] The output equation is expressed as:

[0053] V(t) = h(c ss,n (t), c ss,p (t), c e,n (t), c e,p (t), I(t)) (14)

[0054] where, h(·) represents the system observation equation; css,n (t) and c ss,p (t) are the lithium-ion concentrations on the surfaces of the negative and positive solid-phase particles, respectively; c e,n (t) and c e,p (t) are the lithium-ion concentrations in the liquid phases of the negative and positive electrodes, respectively;

[0055] Step 4.3: Use particle filtering to estimate the state value, and estimate the posterior probability density using random samples in the state space.

[0056] Furthermore, the steps of the particle filtering in Step 4.3 are as follows:

[0057] Step 4.3.1: Initialization

[0058] Let the initial value x0 follow a normal distribution N(μ, σ 2 ), and generate random samples g = 1, 2, … z, and the corresponding weights where the weights are allocated proportionally or set z is the number of random samples;

[0059] Step 4.3.2: Prediction step

[0060] According to the state-space equation of the system, predict each sample point to generate the initial sample points at time t = 1

[0061] Step 4.3.3: Update step

[0062] Use the state sample points generated in the prediction step and the observation equation of the system to generate observation sample points Update the weight values of the sample points according to the observation sample points, the true observation value, and the observation error, and normalize all the obtained weight values; obtain new particles and their weight values

[0063] Step 4.3.4: Resampling

[0064] Use resampling to mitigate the problem of potential failure of the next update caused by particle degeneracy;

[0065] Step 4.3.5: Recursively according to the above steps, finally obtain the predicted value at time t

[0066] The beneficial effects of the present invention are as follows: Based on the extended single-particle model and combined with the particle filter algorithm, the present invention realizes the online estimation of the state of charge of the battery; an extended single-particle model including electrolyte kinetics is adopted to reflect the internal state changes during the charge and discharge process of the battery, and the state variables affecting the SOC value are monitored; the sensitivity analysis of parameters is realized by basic effect tests to verify the influence of specific parameters in the model on the output and determine the sensitive parameters; the sensitive parameters are identified by the particle swarm optimization algorithm to establish an electrochemistry model with higher accuracy; combined with the particle filter, the voltage across the battery is used as a correction to reduce the errors generated during long-term operation. Therefore, compared with the SOC estimation methods based on ECM and SPME, the present invention has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flowchart of the online estimation model of SOC in an embodiment of the present invention.

[0068] Figure 2(a) is the result of parameter sensitivity analysis in an embodiment of the present invention: discharge rate 0.5C.

[0069] Figure 2(b) is the result of parameter sensitivity analysis in an embodiment of the present invention: discharge rate 1C.

[0070] Figure 3(a) is the experimental verification result under NEDC working conditions in an embodiment of the present invention: SOC comparison.

[0071] Figure 3(b) is the experimental verification result under NEDC working conditions in an embodiment of the present invention: SOC error comparison. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0073] To improve the accuracy of online SOC estimation of the SOC, the present invention analyzes the prediction model required for battery SOC estimation, and based on SPME and particle filter, proposes a high-precision lithium battery SOC estimation method based on an electrochemical model, adopting a single particle model with electrolyte (SPME). Compared with the estimation method based on ECM and the role of SPME itself in estimating SOC, this method has higher accuracy. At the same time, by selecting and identifying sensitive parameters, the accuracy of this method is further improved. This method first adopts SPME, while fully reflecting the internal state transformation during the charge and discharge process of the lithium battery, reducing the computational burden of the electrochemical model. Then, sensitive parameters are selected through basic effect tests, and the sensitive parameters that are difficult to directly measure are identified through the particle swarm optimization algorithm to improve the accuracy of the model. Finally, a particle swarm optimization algorithm is used to construct an SOC estimation model based on the electrochemical model, introducing voltage correction for the SOC value to reduce the error introduced by long-term operation to achieve accurate online SOC estimation. Compared with the estimation method of extended Kalman filter (EKF) based on ECM, the method of the present invention has higher accuracy. The overall flowchart of the method proposed by the present invention is as Figure 1 shown.

[0074] The following will introduce each key link of the present invention one by one in the form of embodiments:

[0075] (1) Establishment of the electrochemical model

[0076] Establish an SPME model. The P2D model includes six groups of mathematical equations, namely the liquid-phase diffusion equation of lithium ions, the solid-phase diffusion equation of lithium ions, the liquid-phase Ohm's law, the solid-phase Ohm's law, the charge conservation equation, and the Butler-Vomer kinetic equation. This model can estimate the state variables inside the battery through the charge and discharge current, so as to simulate the output voltage.

[0077] The P2D model takes the current as the input, and according to the above six groups of mathematical equations, simulates and emulates the output voltage at the corresponding moment and the information such as the lithium ion concentration in the solid phase and the liquid phase. The SPME model simplifies each electrode into a porous spherical particle, and at the same time takes into account the polarization voltage and conductance voltage generated by electrolyte kinetics; it is assumed that the solid-phase lithium ion concentration, exchange current density, total molar number of lithium ions, and activity coefficient are constant on the x-axis of space, which reduces the computational burden while having high accuracy and application range.

[0078] (2) Parameter sensitivity analysis

[0079] Sensitivity analysis of the parameters of the electrochemical model is carried out using the elementary effect test, and the elementary effect of the \(i\)th parameter is calculated as:

[0080]

[0081] where is the \(i\)th parameter for the \(j\)th change; \(y(\cdot)\) represents the output equation of the system; is the change in the \(i\)th parameter at the \(j\)th change; \(i = 1, 2, \ldots, n\), \(j = 1, 2, \ldots, r\); \(n\) is the total number of parameters, and \(r\) is the total number of trajectories.

[0082] The sensitivity of the parameters is analyzed using the average value of the EE. A higher average value indicates that the parameter has a significant impact on the output of the model.

[0083] Sensitivity analysis of the parameters in the electrochemical model is carried out using the elementary effect test. Assume that the state - space equation of the system is:

[0084]

[0085] \(y = h(x, t, u, p)\ (3)\)

[0086] where \(x\) is the system state vector, \(y\) is the output vector, \(t\) represents time, \(u\) is the system input, and \(p\) represents the parameter. Assume that each parameter \(p\) i \((i = 1, 2, \ldots, n)\) is independent in the system and varies in the \(n\) - dimensional space. Then, the definition (1) is the elementary effect of the \(i\)th parameter for the \(j\)th (\(j = 1, 2, \ldots, r\)) trajectory.

[0087] The elementary effect test uses two sensitivity metrics, namely the average value \(\mu\) i and the standard deviation \(\sigma\) i :

[0088]

[0089] If the average value \(\mu\) i is high, it means that the parameter \(p\) i has a significant impact on the output of the model. If the standard deviation \(\sigma\) i is high, it indicates that the parameter interacts with other parameters or the impact of the parameter on the model output is non - linear.

[0090] Experiments are carried out using Samsung ICR18650 - 26J batteries. Sensitivity analysis of 14 parameters of the electrochemical model is carried out respectively under the conditions of discharge rates of 0.5C and 1C. The average value and standard deviation of the elementary effect are shown in Table 1, and the results are shown in Figures 2(a) and 2(b). The solid - phase particle radius \(R\) s and the solid - phase volume fraction \(\varepsilon\)s As a sensitive parameter.

[0091] Table 1 Basic effect test results

[0092]

[0093]

[0094] (3) Parameter identification based on the particle swarm optimization algorithm

[0095] The particle swarm optimization algorithm regards each individual particle as a particle without weight and volume in an n-dimensional search space, and flies at a certain speed in the search space. This flying speed is dynamically adjusted by the flying experience of the individual and the flying experience of the group.

[0096] Step 3.1: Initialization

[0097] Randomly initialize the particle population, where the position of the k-th particle in the m-dimensional space is A k =(a k1 , a k2 ,..., a km ), and the speed is V k =(v k1 , v k2 ,..., v kn );

[0098] Step 3.2: Select the best particle

[0099] Record the individual fitness, the individual best fitness, and the population best fitness, and record the particle with the individual best fitness, that is, the position P k =(p k1 , p k2 ,..., p km ), and the particle with the population best fitness, that is, the position G k =(g k1 , g k2 ,..., g km ).

[0100] Step 3.3: State update

[0101] Update the speed and state of the particle flight;

[0102] V′ k =w × V k + c1 × Rand × (P k - A k ) + c2 × Rand × (G k - A k ) (5)

[0103] a′ k = a k + V′ k (6)

[0104] where a k is the individual position, vV k is the individual flight speed, w is the inertia coefficient, c1 and c2 are learning factors, Rand is a random number between 0 and 1; V′ k is the updated speed, and a′ k is the updated individual position.

[0105] Step 3.4: Iteration

[0106] Calculate the fitness of the new position. If the fitness is high, update the best fitness and the best position; otherwise, continue to loop and determine whether the termination condition is met. The termination condition can be that the number of iterations reaches a specified value, or the fitness does not change after n generations.

[0107] Through the above particle swarm optimization algorithm, the identification of sensitive parameters; meanwhile, the parameters related to SOC calculation - the solid-phase lithium-ion concentrations c s,n0％ and c s,p100％ at 0% and 100% battery charge are identified.

[0108] (4) SOC Estimation Based on Particle Filter

[0109] The SOC of a lithium battery is related to the solid-phase lithium-ion concentration. The negative and positive electrode SOCs can be expressed in the forms of Equations (7) and (8) respectively. The negative electrode SOC represents the number of lithium ions that can be extracted from the active material in the electrode before depletion; the positive electrode SOC represents the number of lithium ions that can be absorbed by the active material in the electrode before saturation.

[0110]

[0111]

[0112] where and are the average solid-phase lithium-ion concentrations of the negative and positive electrodes respectively; c s,p0％ is the solid-phase lithium-ion concentration of the positive electrode at 0% battery charge, and c s,n100％ is the solid-phase lithium-ion concentration of the negative electrode at 100% battery charge; theoretically, the SOC values of the negative and positive electrodes should be the same. Considering the calculation error, generally, the average of the two is taken, that is

[0113]

[0114] To obtain the above two state variables, the solid-phase lithium-ion diffusion equation needs to be simplified. In this method, the three-parameter parabola approximation method is used to fit the partial differential equation of solid-phase diffusion. The simplified solid-phase diffusion equation:

[0115]

[0116]

[0117]

[0118] where, is the average value of the gradient of the solid-phase lithium-ion concentration c s along the r direction. Then the state-space equation of the system

[0119]

[0120] where, and are the average solid-phase lithium-ion concentrations of the negative and positive electrodes respectively; and are the average values of the gradients of the solid-phase lithium-ion concentration c s along the R direction of the negative and positive electrodes respectively; D s,n and D s,p are the solid-phase diffusion coefficients of the negative and positive electrodes respectively; R s,n and R s,p are the solid-phase particle radii of the negative and positive electrodes respectively; F is the Faraday constant; S n and S p are the surface areas of the negative and positive electrodes respectively; L n and L p are the lengths of the negative and positive electrodes respectively; ε s,n and ε s,p are the solid-phase volume fractions of the negative and positive electrodes respectively; I(t) is the external current density.

[0121] The output equation can be expressed as

[0122] V(t) = h(c ss,n (t), c ss,p (t), c e,n (t), c e,p (t), I(t)) (14)

[0123] Particle filtering is a recently developed statistical filtering method with high potential, based on the sequential Monte Carlo method and recursive Bayesian estimation. This algorithm estimates the state value using the Monte Carlo method and estimates the posterior probability density using random samples in the state space. Generally speaking, the steps of particle filtering are as follows

[0124] Step a1: Initialization

[0125] Let the initial value \(x_0\) follow a normal distribution \(N(\mu,\sigma 2 ), and generate random samples for \(g = 1,2,\cdots,z\), and the corresponding weights where the weights are allocated proportionally or set and \(z\) is the number of random samples.

[0126] Step a2: Prediction step

[0127] Predict for each sample point according to the state - space equation of the system to generate the initial sample points at \(t = 1\)

[0128] Step a3: Update step

[0129] Use the state sample points generated in the prediction step and the observation equation of the system to generate observation sample points Update the weight values of the sample points according to the observation sample points, the true observation values and the observation errors, and normalize all the obtained weight values; obtain new particles and their weight values

[0130] Step a4: Resampling

[0131] In the particle filter recursion process, there may be a problem of particle degeneracy, that is, the weight values of a few particles are high, while the weight values of the remaining large number of particles are extremely low. Even after a few steps of recursion, there may be only one particle with a non - zero weight value. Therefore, resampling is used to weaken the problem of the next update failure caused by possible particle degeneracy.

[0132] Step a5: Recursively according to the above steps, and finally obtain the predicted value at time \(t\)

[0133] Experiments were carried out using the Samsung ICR18650 - 26J battery under the NEDC working condition, and the results are shown in Figure 3(a) and Figure 3(b). Among them, the ECM - based EKF method has a relatively high error, with the mean absolute error \(MAE=0.0292\) and the root mean square error \(RMSE = 0.0346\); in the SPME - based method, \(MAE = 0.0122\) and \(RMSE = 0.0142\); the proposed method based on SPME and particle filter reduces most of the errors, with \(MAE = 0.0025\) and \(RMSE = 0.0039\). In the long - term operation of the SPME - based method, the error shows an increasing trend, and the proposed method introduces voltage correction to weaken this kind of error.

[0134] After all the above steps, the lithium battery state of charge estimation model based on the electrochemical model and particle filter can be established.

Claims

1. A method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering, characterized in that It includes the following steps: Step 1: Establish a single-particle model of a lithium battery with a liquid-phase potential, estimate the state variables inside the battery through the charge and discharge current, and thus simulate the output voltage; Step 2: Conduct a sensitivity analysis on the parameters of the single-particle model with a liquid-phase potential using a basic effect test; Step 3: Use a particle swarm optimization algorithm to identify sensitive parameters; Step 4: Based on the single-particle model with a liquid-phase potential, with the charge and discharge current as the input and the voltage across the battery as the observation, estimate the state variables related to the SOC through particle filtering, and calculate the SOC value of the battery accordingly; The specific content of Step 4 includes: Step 4.1: Positive electrode SOC SOC p represents the number of lithium ions that can be extracted from the active material in the electrode before depletion; negative electrode SOC SOC n represents the number of lithium ions that can be absorbed by the active material in the electrode before saturation, and are respectively expressed as: Wherein, and are the average solid-phase lithium-ion concentrations of the negative electrode and the positive electrode, respectively; c s,p0％ is the solid-phase lithium-ion concentration of the positive electrode when the battery charge is 0%, and c s,n100％ is the solid-phase lithium-ion concentration of the negative electrode when the battery charge is 100%; taking the average of the two, that is Step 4.2: Use the three-parameter parabola approximation method to fit the partial differential equation of solid-phase diffusion. The simplified solid-phase diffusion equation is: Among them, is the average value of the gradient of the solid-phase lithium-ion concentration c s along the particle radius R direction; is the average solid-phase lithium-ion concentration; R s is the solid-phase particle radius; D s is the solid-phase diffusion coefficient; c ss is the lithium-ion concentration on the surface of the solid-phase particle; j n is the lithium-ion flux on the surface of the active particle; Then the state-space equation of the system is: Wherein, and are the average negative and positive solid-phase lithium-ion concentrations, respectively; and are the average gradients of the negative and positive solid-phase lithium-ion concentration c s along the R direction; D s,n and D s,p are the negative and positive solid-phase diffusion coefficients, respectively; R s,n and R s,p are the negative and positive solid-phase particle radii respectively; F is the Faraday constant; S n and S p are the negative and positive surface areas respectively; L n and L p are the lengths of the negative and positive electrodes respectively; ε s,n and ε s,p are the solid-phase volume fractions of the negative and positive electrodes respectively; I(t) is the external current density; The output equation is expressed as: V(t) = h(c ss,n (t), c ss,p (t), c e,n (t), c e,p (t), I(t)) (14) where h(·) represents the system observation equation; c ss,n (t) and c ss,p (t) are the lithium-ion concentrations on the surfaces of the negative and positive solid-phase particles, respectively; c e,n (t) and c e,p (t) are the lithium-ion concentrations in the negative and positive liquid phases, respectively; Step 4.3: Use particle filtering to estimate the state value, and use the random samples in the state space to estimate the posterior probability density.

2. The method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering according to claim 1, wherein The single-particle model with a liquid-phase potential includes six sets of mathematical equations: the liquid-phase diffusion equation of lithium ions, the solid-phase diffusion equation of lithium ions, the liquid-phase Ohm's law, the solid-phase Ohm's law, the charge conservation equation, and the Butler-Vomer kinetic equation.

3. The method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering according to claim 1, wherein The specific content of the sensitivity analysis in Step 2 includes: Step 2.1: Calculate the basic effect of the i-th parameter on the j-th trajectory as: Among them, is the i-th parameter of the j-th change; y(·) represents the output equation of the system; is the change amount of the i-th parameter at the j-th change; i = 1, 2, …, n, j = 1, 2, …, r; n is the total number of parameters, and r is the total number of trajectories; Step 2.2: Assume the state-space equation of the system is: y = h(x, t, u, p) (3) where x is the system state vector, y is the output vector, t represents time, u is the system input, and p represents the parameter; Step 2.3: Use the mean value μ i and the standard deviation σ i to perform two sensitivity measure basic effect tests, where If the average value μ i is greater than the average value setting threshold, it means that the parameter p i has a significant impact on the output of the model; If the standard deviation σ i is greater than the standard deviation setting threshold, it means that the parameter p i will interact with other parameters, or the parameter p i has a non-linear impact on the model output.

4. The method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering according to claim 1, wherein The specific content of Step 3 includes: Step 3.1: Initialization Randomly initialize the particle swarm, where the position of the k-th particle in the m-dimensional space is A k =(a k1 , a k2 ,..., a km ), and the velocity is V k =(v k1 , v k2 ,..., v kn ); Step 3.2: Select the best particle Record the individual fitness, the individual best fitness, and the population best fitness, and record the particles with the individual best fitness, i.e., the positions P of the individual best particles k =(p k1 ,p k2 ,...,p km ), and the particles with the population best fitness That is, the position G of the best particle in the population k =(g k1 , g k2 ,..., g km ); Step 3.3: State update Update the velocity and state of the particle flight; V k ′ = w × V k + c1 × Rand × (P k - A k ) + c2 × Rand × (G k - A k ) (5) a ′ k = a k + V k ′ (6) where a k is the individual position, V k is the individual flying speed, w is the inertia coefficient, c1 and c2 are the learning factors, and Rand is a random number between 0 and 1; V k ′ is the updated speed, a ′ k is the updated individual position; Step 3.4: Iteration Calculate the fitness of the new position. If the fitness is higher than the preset value, update the best fitness and the best position. Otherwise, continue to loop and determine whether the termination condition is met; Step 3.5: Identify the sensitive parameters through the particle swarm optimization algorithm in Steps 3.1 - 3.4; meanwhile, identify the parameters related to SOC calculation: the negative electrode solid-phase lithium-ion concentration c when the battery charge is 0% s,n0％ and the positive electrode solid-phase lithium-ion concentration c when the battery charge is 100%. s,p100％ Perform identification.

5. The method for estimating the state of charge of a lithium battery based on an electrochemical model and particle filtering according to claim 1, characterized in that The steps of particle filtering in Step 4.3 are as follows: Step 4.3.1: Initialization Let the initial value \(x_0\) follow a normal distribution \(N(\mu,\sigma 2 )\), and generate random samples \(g = 1,2,\cdots,z\), and the corresponding weights where the weights are allocated proportionally or set \(z\) is the number of random samples; Step 4.3.2: Prediction step For each sample point according to the state-space equation of the system make a prediction to generate the initial sample point at time t = 1 Step 4.3.3: Update step State sample points generated using the prediction step and the observation equation of the system to generate observation sample points Update the weight values of the sample points based on the observation sample points, the true observation values, and the observation errors, and normalize all the obtained weight values; obtain new particles and their weight values Step 4.3.4: Resampling Use resampling to weaken the possible problem of the next update failure caused by particle degeneracy; Step 4.3.5: By recursively calculating according to the above steps, the predicted value at time t is finally obtained.

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