A method and apparatus for estimating the SOC value of a lithium battery based on three-state variables.

Abstract

This invention relates to the field of battery management technology, and provides a method for estimating the State of Charge (SOC) of a lithium battery based on three-state variables. The method includes: initializing the SOC value of a single-event model of the lithium battery; the single-event model includes a single-event model and its extended models, as well as a thermally coupled model based on the single-event correlation model; inputting a measured current value into the single-event model of the lithium battery to generate the output voltage value of the lithium battery; comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain an initial SOC estimate of the three-state variables of the lithium battery; the three-state variables include the volume average concentration of lithium ions diffused in the positive electrode or the volume average concentration of lithium ions diffused in the negative electrode, the volume average concentration of lithium ions diffused in the positive electrode, and the volume average concentration of lithium ions diffused in the negative electrode; and filtering the initial SOC estimate of the three-state variables using an extended Kalman filter to obtain a target SOC estimate of the three-state variables.

Description

Technical Field

[0001] This invention relates to the field of battery management technology, and more particularly to a method and apparatus for estimating the SOC value of a lithium battery based on three state variables. Background Technology

[0002] Energy storage power stations use a large number of lithium batteries. Estimating their state of charge (SOC) is not only an important function of the battery management system (BMS), but the SOC value is also an important parameter of the performance of energy storage power stations. Accurate estimation of SOC can significantly improve the performance of batteries and maximize the regulation role and economic value of power stations in frequency regulation energy storage and "peak shaving and valley filling".

[0003] Currently, mainstream SOC estimation methods rely on macroscopic physical quantities such as current and voltage for prediction. Commonly used methods include the open-circuit voltage method and the ampere-hour integration method. The ampere-hour integration method requires integrating the charging or discharging current over a period of time and summing it with the initial charge level. Its accuracy depends on the accuracy of the initial SOC, but in real-world operating conditions, it's difficult to know the battery's initial SOC, thus reducing its accuracy. The open-circuit voltage method measures the battery's open-circuit voltage (OCV) corresponding to each SOC value, establishing a mapping relationship between the battery's OCV and SOC. However, because measuring the open-circuit voltage requires disconnecting the battery from the external circuit and measuring after a certain time interval, it's not suitable for online prediction.

[0004] Currently, there are algorithms based on battery models, such as Kalman filtering and neural network methods, that can predict battery SOC, but none of them involve the complex electrochemical changes inside the battery. Summary of the Invention

[0005] The purpose of this invention is to provide a method for estimating the SOC value of a lithium battery based on three state variables, in order to solve the above-mentioned problems.

[0006] The technical solution provided by this invention is as follows:

[0007] In some embodiments, the present invention provides a method for estimating the SOC value of a lithium battery based on three-state variables, comprising:

[0008] Initialize the SOC value of the single-particle model of the lithium battery; the single-particle model includes single-particle and its extended models, as well as a thermally coupled model based on the single-particle correlation model;

[0009] Input the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery;

[0010] By comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery, the initial SOC estimate of the three state variables of the lithium battery is obtained; the three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase.

[0011] The initial SOC estimates of the three-state variables are filtered by extended Kalman filtering to obtain the target SOC estimates of the three-state variables.

[0012] In some implementations, inputting the measured current value to the single-particle model of the lithium battery to generate the output voltage value of the lithium battery includes:

[0013] The volume-average concentration of lithium ions in the positive electrode solid phase or the volume-average concentration of lithium ions in the negative electrode solid phase, the volume-average diffusion flux of lithium ions in the positive electrode solid phase, and the volume-average diffusion flux of lithium ions in the negative electrode solid phase are selected as system state variables.

[0014] The system state variables are calculated based on the governing equations and boundary conditions of the solid phase concentration using the single-particle model of the lithium battery.

[0015] The output voltage value of the lithium battery is calculated based on the system state variables.

[0016] In some embodiments, the calculation of the system state variables based on the governing equations for solid phase concentration and boundary conditions using the single-particle model of the lithium battery includes:

[0017] The governing equation for the solid phase concentration in the single-particle model of the lithium battery is:

[0018]

[0019] Where r is the length along the radial direction of the solid-phase active material, and D s Where C is the diffusion coefficient, C is the solid concentration, and t is time;

[0020] The boundary conditions are as follows:

[0021]

[0022] Where j is the molar flux of lithium ions per unit area per unit time; R is the radius of the active material;

[0023] The system state variable x = [C] is obtained by approximation using three parameters. n,avg Q n,avg Q p,avg Let the lithium ion concentration on the negative electrode surface be C. n,s ,but:

[0024]

[0025] Among them, C n,avg R represents the volume average concentration of lithium ions in the negative electrode solid phase. n Where is the negative radius, and t is time;

[0026]

[0027] Solving the equation discretically yields the following:

[0028]

[0029] Where, j n D represents the molar flux of lithium ions per unit time and unit area at the negative electrode. s,n Let Q be the negative electrode solid-phase diffusion coefficient, τ represent the time difference between time k+1 and time k, and Q be the negative electrode solid-phase diffusion coefficient. n,avg This represents the volume-average diffusion flux of lithium ions in the negative electrode solid phase. Let be the volume-average diffusion flux of lithium ions in the negative electrode solid phase at time k. The negative electrode solid-phase lithium ion volume average diffusion flux at time k+1;

[0030]

[0031] Solving the equation discretically yields the following:

[0032]

[0033] Where, j p D represents the molar flux of lithium ions per unit time and per unit area at the positive electrode. s,p Let Q be the solid-phase diffusion coefficient of the positive electrode, τ represent the time difference between time k+1 and time k, and Q be the solid-phase diffusion coefficient of the positive electrode. p,avg This represents the volume-average diffusion flux of lithium ions in the solid phase of the cathode. Let be the volume-average diffusion flux of lithium ions in the positive electrode solid phase at time k. Rp is the volume-average diffusion flux of lithium ions in the solid phase of the cathode at time k+1; Rp is the cathode radius.

[0034] In some implementations, it also includes:

[0035] Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery.

[0036] The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery.

[0037] Based on the initialized initial volume concentration of lithium ions in the negative electrode solid phase and the initialized initial volume concentration of lithium ions in the positive electrode solid phase, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

[0038] In some embodiments, the initialization process of the initial volume concentration of lithium ions in the positive and negative electrodes of the lithium battery based on the SOC value of the initialized lithium battery includes:

[0039] The formula for initialization is:

[0040] C n,ini =C n,0 +SOC×(C n,100 -C n,0 )

[0041] C p,ini =C p,0 +SOC×(C p,100 -C p,0 )

[0042] Among them, C n,ini C represents the initial volume concentration of lithium ions in the negative electrode solid phase after initialization. n,100 C represents the volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%. n,0 The volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value = 0; C p,ini C represents the initial volume concentration of lithium ions in the positive electrode solid phase after initialization. p,100 C is the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%. p,0 The actual SOC value is the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 0; SOC is the actual SOC value.

[0043] In some implementations, calculating the output voltage value of the lithium battery based on the system state variables includes:

[0044] The formula for calculating the output voltage of the lithium battery is as follows:

[0045] V = U P -U n +η p -η n -I*R Ω

[0046] V = h(x, u)

[0047] Where x is the state variable and u is the input; U P U n The equilibrium potential between the positive and negative electrodes, ηp This is the overpotential of the positive electrode reaction; η n The overpotential of the negative electrode reaction is given by I, where I is the current value and R is the overpotential of the negative electrode Ω Let h be the empirical resistance, and h be a function.

[0048] Select [C] n,avg Q n,avg Q p,avg If ] represents the system state variable, then matrix A is:

[0049]

[0050] Where is the sampling time, i.e., the time difference between two voltage values;

[0051] The observation matrix H is:

[0052]

[0053] Where V = U P -U n +η p -η n -I*R Ω The equation is the observation equation.

[0054] In some embodiments, the step of comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three-state variables of the lithium battery includes:

[0055] Based on the negative electrode solid phase lithium ion volume average concentration C n,avg Calculate the volume average concentration C of lithium ions in the solid phase of the cathode. p,avg The formula is as follows:

[0056]

[0057] Among them, L n For the thickness of the negative electrode active material, L p ε represents the thickness of the positive electrode active material. n εp is the volume fraction of the negative electrode active material, and c is the volume fraction of the positive electrode active material. p,100 c represents the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%. n,100 This represents the volume-average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%.

[0058] Based on the initialized positive electrode solid-phase lithium ion volume average concentration and the output voltage value, the initial SOC estimate of the three state variables is calculated.

[0059] The extended Kalman filter formula is as follows:

[0060]

[0061] Where x is the state variable, - indicates prior estimate, + indicates posterior estimate, and k represents time.

[0062] Calculate the prior error covariance:

[0063]

[0064] Where P is the state variable error covariance matrix, which outputs the initial SOC estimate during initialization; Q is the process noise covariance, which outputs the initial SOC estimate when updating the state variable error; A T Let be the transpose of matrix A.

[0065] In some implementations, the step of filtering the initial SOC estimates of the three-state variables using an extended Kalman filter to obtain the target SOC estimates of the three-state variables includes:

[0066] The state variables are updated using the extended Kalman filter, and the update formula for the state variables is as follows:

[0067]

[0068] Among them, z k This is the actual voltage value. The voltage value is obtained by substituting the initial SOC estimate and the actual SOC value at time k into the observation equation;

[0069] Among them, K k To simplify the coefficients, they are calculated using the following formula:

[0070]

[0071] Where R is the measurement error covariance, and H T Let H be the transpose of matrix H.

[0072] In some embodiments, the present invention also provides a device for estimating the SOC value of a lithium battery based on three-state variables, comprising:

[0073] The data initialization module is used to initialize the SOC value of the single-particle model of the lithium battery; the single-particle model includes single-particle and its extended models, as well as a thermally coupled model based on the single-particle correlation model.

[0074] A voltage output module is used to input the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery.

[0075] The initial estimation module is used to compare the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three state variables of the lithium battery; the three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase.

[0076] The filtering estimation module is used to filter the initial SOC estimates of the three-state variables through extended Kalman filtering to obtain the target SOC estimates of the three-state variables.

[0077] In some implementations, an initial processing module is also included, for:

[0078] Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery.

[0079] The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery.

[0080] Based on the initialized initial volume concentration of lithium ions in the negative electrode solid phase and the initialized initial volume concentration of lithium ions in the positive electrode solid phase, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

[0081] Compared with the prior art, the SOC value estimation method and apparatus for lithium batteries based on three-state variables provided by the present invention can bring the following beneficial effects:

[0082] This invention is based on a single-particle model and its extended model, an electrochemical model (or its electrothermal coupling model). First, the concentration values ​​of the model are initialized. The measured current values ​​are input into the electrochemical model. The output voltage of the electrochemical model is compared with the actual voltage of the battery. The volume average concentration of solid lithium ions in the positive electrode or the volume average concentration of solid lithium ions in the negative electrode, as well as the volume average diffusion flux of solid lithium ions in the positive and negative electrodes, are corrected by extended Kalman filtering to obtain a more accurate SOC. Attached Figure Description

[0083] The preferred embodiments will be described below in a clear and easy-to-understand manner, with reference to the accompanying drawings, to further explain the above-mentioned characteristics, technical features, advantages, and implementation methods of a method and apparatus for estimating the SOC value of a lithium battery based on three state variables.

[0084] Figure 1This is a flowchart of an embodiment of a method for estimating the SOC value of a lithium battery based on three-state variables according to the present invention;

[0085] Figure 2 This is a schematic diagram of voltage changes according to the present invention;

[0086] Figure 3 This is a schematic diagram of the SOC value calculated by the EKF algorithm according to the present invention;

[0087] Figure 4 This is a schematic diagram of an embodiment of a lithium battery SOC value estimation device based on three state variables according to the present invention. Detailed Implementation

[0088] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0089] To keep the drawings concise, only the parts relevant to the invention are shown schematically in each figure, and they do not represent the actual structure of the product. Furthermore, for ease of understanding, in some figures, only one of components with the same structure or function is shown schematically, or only one is labeled. In this document, "one" can mean not only "only one" but also "more than one".

[0090] In one embodiment, such as Figure 1 As shown, this invention provides a method for estimating the SOC value of a lithium battery based on three-state variables, including:

[0091] S101 initializes the SOC value of a single-particle model of a lithium battery.

[0092] Among them, single-particle models include single-particle and its extended models, as well as thermally coupled models based on single-particle related models, such as SPM, SPME, and ESPM.

[0093] Single particle model

[0094] single particle model with electrolyte,

[0095] Enhanced single particle model, etc.

[0096] S102 inputs the measured current value to the single-particle model of the lithium battery to generate the output voltage value of the lithium battery.

[0097] S103 compares the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three state variables of the lithium battery. The three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase.

[0098] Specifically, in this embodiment, the volume-average concentration of lithium ions in the negative electrode solid phase, the volume-average diffusion flow rate of lithium ions in the positive electrode solid phase, and the volume-average diffusion flow rate of lithium ions in the negative electrode solid phase are selected as the three-state variables, or the volume-average concentration of lithium ions in the positive electrode solid phase, the volume-average diffusion flow rate of lithium ions in the positive electrode solid phase, and the volume-average diffusion flow rate of lithium ions in the negative electrode solid phase are selected as the three-state variables.

[0099] S104 filters the initial SOC estimates of the three-state variables using an extended Kalman filter to obtain the target SOC estimates of the three-state variables.

[0100] In this embodiment, the present invention accurately estimates the internal volume average concentration and SOC value of lithium battery active materials based on the single-particle model and its extended model electrochemical model (or its electrothermal coupling model).

[0101] In one embodiment, inputting the measured current value to the single-particle model of the lithium battery to generate the output voltage value of the lithium battery includes:

[0102] The volume-average concentration of lithium ions in the positive electrode solid phase or the volume-average concentration of lithium ions in the negative electrode solid phase, the volume-average diffusion flux of lithium ions in the positive electrode solid phase, and the volume-average diffusion flux of lithium ions in the negative electrode solid phase are selected as system state variables.

[0103] The system state variables are calculated based on the governing equations and boundary conditions of the solid phase concentration using the single-particle model of the lithium battery.

[0104] The output voltage value of the lithium battery is calculated based on the system state variables.

[0105] In one embodiment, the calculation of the system state variables based on the governing equations and boundary conditions for the solid phase concentration using the single-particle model of the lithium battery includes:

[0106] The governing equation for the solid phase concentration in the single-particle model of the lithium battery is:

[0107]

[0108] Where r is the length along the radial direction of the solid-phase active material, and D s Where C is the diffusion coefficient, C is the solid concentration, and t is time;

[0109] The boundary conditions are as follows:

[0110]

[0111] Where j is the molar flux of lithium ions per unit area per unit time; R is the radius of the active material;

[0112] The system state variable x = [C] is obtained by approximation using three parameters. n,avg Q n,avg Q p,avg Let the lithium ion concentration on the negative electrode surface be C. n,s ,but:

[0113]

[0114] Among them, C n,avg R represents the volume average concentration of lithium ions in the negative electrode solid phase. n Where is the negative radius, and t is time;

[0115]

[0116]

[0117] Solving the equation discretically yields the following:

[0118]

[0119] Where, j n D represents the molar flux of lithium ions per unit time and unit area at the negative electrode. s,n Let Q be the negative electrode solid-phase diffusion coefficient, τ represent the time difference between time k+1 and time k, and Q be the negative electrode solid-phase diffusion coefficient. n,avg This represents the volume-average diffusion flux of lithium ions in the negative electrode solid phase. Let be the volume-average diffusion flux of lithium ions in the negative electrode solid phase at time k. The negative electrode solid-phase lithium ion volume average diffusion flux at time k+1;

[0120]

[0121] Solving the equation discretically yields the following:

[0122]

[0123] Where, j p D represents the molar flux of lithium ions per unit time and per unit area at the positive electrode. s,pLet Q be the solid-phase diffusion coefficient of the positive electrode, τ represent the time difference between time k+1 and time k, and Q be the solid-phase diffusion coefficient of the positive electrode. p,avg This represents the volume-average diffusion flux of lithium ions in the solid phase of the cathode. Let be the volume-average diffusion flux of lithium ions in the positive electrode solid phase at time k. Rp is the volume-average diffusion flux of lithium ions in the solid phase of the cathode at time k+1; Rp is the cathode radius.

[0124] In this embodiment, the solution method for the volume-average concentration of lithium ions in the positive electrode solid phase is the same as that for the volume-average concentration of lithium ions in the negative electrode solid phase mentioned above, except that the parameters used are positive electrode parameters, such as the state variable: x = [C p,avg Q n,avg Q p,avg ].

[0125] In one embodiment, it also includes:

[0126] Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery.

[0127] The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery.

[0128] Based on the initialized initial volume concentration of lithium ions in the negative electrode solid phase and the initialized initial volume concentration of lithium ions in the positive electrode solid phase, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

[0129] In one embodiment, the initialization process of the initial volume concentration of lithium ions in the positive and negative electrodes of the lithium battery based on the SOC value of the initialized lithium battery includes:

[0130] The formula for initialization is:

[0131] C n,ini =C n,0 +SOC×(C n,100 -C n,0 )

[0132] C p,ini =C p,0 +SOC×(C p,100 -C p,0 )

[0133] Among them, C n,ini C represents the initial volume concentration of lithium ions in the negative electrode solid phase after initialization. n,100C represents the volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%. n,0 The volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value = 0; C p,ini C represents the initial volume concentration of lithium ions in the positive electrode solid phase after initialization. p,100 The volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%; C p,0 The actual SOC value is the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 0; SOC is the actual SOC value.

[0134] In one embodiment, calculating the output voltage value of the lithium battery based on the system state variables includes:

[0135] The formula for calculating the output voltage of the lithium battery is as follows:

[0136] V = U P -U n +η p -η n -I*R Ω

[0137] V = h(x, u)

[0138] Where x is the state variable and u is the input; U P U n The equilibrium potential between the positive and negative electrodes, η p This is the overpotential of the positive electrode reaction; η n The overpotential of the negative electrode reaction is given by I, where I is the current value and R is the overpotential of the negative electrode Ω Let h be the empirical resistance, and h be a function.

[0139] Select [C] n,avg Q n,avg Q p,avg If ] represents the system state variable, then matrix A is:

[0140]

[0141] Where is the sampling time, i.e., the time difference between two voltage values;

[0142] The observation matrix H is:

[0143]

[0144] Where V = U P -U n +η p -η n -I*R Ω The equation is the observation equation.

[0145] In one embodiment, the step of comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three-state variables of the lithium battery includes:

[0146] Based on the negative electrode solid phase lithium ion volume average concentration C n,avg Calculate the volume average concentration C of lithium ions in the solid phase of the cathode. p,avg The formula is as follows:

[0147]

[0148] Among them, L n For the thickness of the negative electrode active material, L p ε represents the thickness of the positive electrode active material. n εp is the volume fraction of the negative electrode active material, and c is the volume fraction of the positive electrode active material. p,100 c represents the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%. n,100 This represents the volume-average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%.

[0149] Based on the initialized positive electrode solid-phase lithium-ion volume average concentration and the output voltage value, the initial SOC estimate of the three state variables is calculated.

[0150] The extended Kalman filter formula is as follows:

[0151]

[0152] Where x is the state variable, - indicates prior estimate, + indicates posterior estimate, and k represents time.

[0153] Calculate the prior error covariance:

[0154]

[0155] Where P is the state variable error covariance matrix, which outputs the initial SOC estimate during initialization; Q is the process noise covariance, which outputs the initial SOC estimate when updating the state variable error; A T Let be the transpose of matrix A.

[0156] In one embodiment, filtering the initial SOC estimates of the three-state variables using an extended Kalman filter to obtain the target SOC estimates of the three-state variables includes:

[0157] The state variables are updated using the extended Kalman filter, and the update formula for the state variables is as follows:

[0158]

[0159] Among them, z k This is the actual voltage value. The voltage value is obtained by substituting the initial SOC estimate and the actual SOC value at time k into the observation equation;

[0160] Among them, K k To simplify the coefficients, they are calculated using the following formula:

[0161]

[0162] Where R is the measurement error covariance, and H T Let H be the transpose of matrix H.

[0163] In one embodiment, the present invention also provides a method for estimating the SOC value of a lithium battery based on three-state variables, comprising:

[0164] This invention provides a method for accurately estimating the internal volume average concentration and SOC value of active materials in lithium batteries based on a single-particle (SPM) electrochemical model (or its electrothermal coupling model).

[0165] First, an electrochemical model is established for the battery, and the electrochemical model parameters are obtained. These electrochemical model parameters are generally identified through parameter identification. Finally, the concentration, i.e., the state of charge (SOC), is estimated by EKF filtering.

[0166] The specific implementation method is as follows:

[0167] Taking a certain lithium cobalt oxide battery as an example:

[0168] Step 1:

[0169] An electrochemical model of the battery was established to obtain the battery SPM model parameters, focusing on the average concentrations of the positive and negative electrodes at SOC = 100% and SOC = 0, and C. n,100 C n,0 C p,100 C p,0 .

[0170] Step 2:

[0171] The positive and negative electrode concentrations of the model are initialized based on the battery data used for SOC estimation: If the data includes the SOC values ​​uploaded by the BMS, the initial concentrations of the positive and negative electrodes are initialized using the following formula:

[0172] C n,ini =C n,0 +SOC×(C n,100 -C n,0 )

[0173] C p,ini =C p,0 +SOC×(Cp,100 -C p,0 )

[0174] If the data does not contain SOC values, the positive and negative electrodes can be initialized to SOC = 100% or the concentration corresponding to any SOC value, as shown in the formula above.

[0175] Step 3:

[0176] SOC is estimated using EKF filtering:

[0177] 3.1 State Variables

[0178] The positive or negative electrode volume-average concentration and the positive or negative electrode volume-average diffusion flux are selected as system state variables. This patent takes the negative electrode volume-average concentration as an example, denoted by C. n,avg C p,avg Q n,avg Q p,avg Right now:

[0179] x = [C n,avg Q n,avg Q p,avg

[0180] 3.2 Approximate Solution of SPM Model

[0181] The SPM model neglects changes in liquid phase concentration and liquid phase potential, considering only solid phase concentration. Its governing equation is:

[0182]

[0183] The concentrations of the positive and negative electrode solids both follow the formula above, where r is the radius of the solid active material, and D... s Let C be the diffusion coefficient and C be the concentration. The boundary conditions are:

[0184]

[0185] Where, j n This represents the molar flux of lithium ions per unit area per unit time.

[0186] It is obtained through a three-parameter approximation, assuming the surface lithium ion concentration is C. n,s ,but:

[0187] Formula 1:

[0188]

[0189] Formula 2:

[0190]

[0191] Formula 3:

[0192]

[0193] Solving the equation discretically yields the following:

[0194]

[0195] Where, j n D represents the molar flux of lithium ions per unit time and unit area at the negative electrode. s,n Let Q be the negative electrode solid-phase diffusion coefficient, τ represent the time difference between time k+1 and time k, and Q be the negative electrode solid-phase diffusion coefficient. n,avg This represents the volume-average diffusion flux of lithium ions in the negative electrode solid phase. Let be the volume-average diffusion flux of lithium ions in the negative electrode solid phase at time k. The negative electrode solid-phase lithium ion volume average diffusion flux at time k+1;

[0196]

[0197] Solving the equation discretically yields the following:

[0198]

[0199] Where, j p D represents the molar flux of lithium ions per unit time and per unit area at the positive electrode. s,p Let Q be the solid-phase diffusion coefficient of the positive electrode, τ represent the time difference between time k+1 and time k, and Q be the solid-phase diffusion coefficient of the positive electrode. p,avg This represents the volume-average diffusion flux of lithium ions in the solid phase of the cathode. Let be the volume-average diffusion flux of lithium ions in the positive electrode solid phase at time k. Rp is the volume-average diffusion flux of lithium ions in the solid phase of the cathode at time k+1; Rp is the cathode radius.

[0200] Formula 4: Voltage is calculated using the following formula:

[0201] V = U P -U n +η p -η n -I*R Ω

[0202] Let v = h(x,u);

[0203] Where x is the state variable and u is the input current.

[0204] Among them, U P U n The equilibrium potential between the positive and negative electrodes, η p This is the overpotential of the positive electrode reaction; η n The overpotential of the negative electrode reaction is I, where I is the current and R is the overpotential of the negative electrode reaction. Ω This is an empirical resistance.

[0205] 3.3 State transition matrix A, observation matrix H.

[0206] Select [C] n,avg Q n,avg Q p,avg If ] is a system state variable, then:

[0207]

[0208] Where τ is the sampling time, i.e. the time difference between two voltage values.

[0209] V = U P -U n +η p -η n -I*R Ω

[0210] For the observation equation

[0211]

[0212] Specifically, such as Figure 2 As shown, the battery SOC is initialized to 100% through the model, but the actual SOC value of the battery is not 1. Therefore, it can be seen from the voltage that there is a difference between ekf_v and the measured voltage value measure_v. By filtering the data through EKF, it can be seen that ekf_v gradually approaches the true voltage value true_v, and the SOC value also gradually approaches the true SOC value.

[0213] It should be noted that:

[0214] 1. This is simulation data. In real-world conditions, the measured voltage value will also have errors compared to the actual voltage value, which is the measurement error. Therefore, the simulated measured voltage value fluctuates around the actual value. Hence, there will be both the actual value and the measured value.

[0215] 2. Kalman filtering can fuse model values ​​and measured values ​​to obtain data that more closely approximates the true value. This means that ekf_v is even closer to the true voltage value than the measured value, resulting in a more accurate SOC estimate. Specifically, as shown... Figure 3 As shown.

[0216] 3.4 Prior Estimation

[0217] Based on the initialized volume average concentration C n,avg The positive electrode volume average concentration C is calculated using the following formula. p,avg :

[0218]

[0219] Ln ε represents the thickness of the negative electrode active material. n denoted as the volume fraction of the negative electrode active material, and p represents the positive electrode material.

[0220] Because initially, C n,s C p,s with C n,ini C p,ini The prior estimated voltage value is calculated using Formula 3.

[0221] Then, prior estimation of the state variables is performed according to formulas 1, 2, and 3, namely:

[0222]

[0223] Where, - sign represents prior estimation, + sign represents posterior estimation, f represents the operation of formulas 1, 2, and 3, k represents time, and u is the input current.

[0224] Calculate the prior error covariance:

[0225]

[0226] Where P is the state variable error covariance matrix, given an initial value during initialization, and Q is the process noise covariance, which is the error introduced when updating the state variables according to formulas 1, 2, and 3, given an initial value during initialization.

[0227] 3.5 Posterior estimation

[0228] According to EKF filtering, the update formula for the state variables is as follows:

[0229]

[0230] Update the state variables, where z k This refers to the measured voltage value, specifically the voltage value from the battery data described in step 2. The voltage value is obtained by substituting the prior estimate and the input value (current) at time k into the observation equation.

[0231] Among them, K k Calculated using the following formula:

[0232]

[0233] Where R is the measurement error covariance, which is the error in measuring the voltage and current values ​​in the battery data described in step 2 using a measuring instrument or sensor.

[0234] 3.6 SOC Estimation

[0235] By repeatedly calculating 3.4 and 3.5, the battery SOC value can be estimated through EKF filtering.

[0236] In one embodiment, such as Figure 4 As shown, the present invention also provides a device for estimating the SOC value of a lithium battery based on three-state variables, comprising:

[0237] The data initialization module 101 is used to initialize the SOC value of the single-particle model of the lithium battery; the single-particle model includes single-particle and its extended models, as well as a thermally coupled model based on the single-particle correlation model.

[0238] The voltage output module 102 is used to input the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery;

[0239] The initial estimation module 103 is used to compare the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three state variables of the lithium battery; the three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase.

[0240] The filtering estimation module 104 is used to filter the initial SOC estimates of the three-state variables through extended Kalman filtering to obtain the target SOC estimates of the three-state variables.

[0241] In one embodiment, it further includes: an initial processing module, configured to:

[0242] Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery.

[0243] The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery.

[0244] Based on the initialized initial volume concentration of lithium ions in the negative electrode solid phase and the initialized initial volume concentration of lithium ions in the positive electrode solid phase, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

[0245] It should be noted that the above embodiments can be freely combined as needed. The above description is only a preferred embodiment of the present invention. It should be pointed out that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the SOC value of a lithium battery based on three-state variables, characterized in that, include: Initialize the SOC value of the single-particle model of the lithium battery; The single-particle model includes single-particle and extended models, as well as a thermally coupled model based on the single-particle correlation model; Input the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery; By comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery, the initial SOC estimate of the three state variables of the lithium battery is obtained; the three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase. The initial SOC estimates of the three-state variables are filtered by extended Kalman filtering to obtain the target SOC estimates of the three-state variables.

2. The SOC value estimation method for lithium batteries based on three-state variables according to claim 1, characterized in that, The process of inputting the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery includes: The volume-average concentration of lithium ions in the positive electrode solid phase or the volume-average concentration of lithium ions in the negative electrode solid phase, the volume-average diffusion flux of lithium ions in the positive electrode solid phase, and the volume-average diffusion flux of lithium ions in the negative electrode solid phase are selected as system state variables. The system state variables are calculated based on the governing equations and boundary conditions of the solid phase concentration using the single-particle model of the lithium battery. The output voltage value of the lithium battery is calculated based on the system state variables.

3. The SOC value estimation method for lithium batteries based on three-state variables according to claim 2, characterized in that, The control equations for solid phase concentration and boundary conditions based on the single-particle model of the lithium battery are used to calculate the system state variables, including: The governing equation for the solid phase concentration in the single-particle model of the lithium battery is: Where r is the length along the radial direction of the solid-phase active material, and D s Where C is the diffusion coefficient, C is the solid concentration, and t is time; The boundary conditions are as follows: Where j is the molar flux of lithium ions per unit area per unit time; R is the radius of the active material; The system state variable x = [C] is obtained by approximation using three parameters. n,avg Q n,avg Q p,avg Let the lithium ion concentration on the negative electrode surface be C. n,s ,but: Among them, C n,avg R represents the volume average concentration of lithium ions in the negative electrode solid phase. n is the negative radius, and t is time; Solving the equation discretically yields the following: Where, j n D represents the molar flux of lithium ions per unit time and unit area at the negative electrode. s,n Let Q be the negative electrode solid-phase diffusion coefficient, τ represent the time difference between time k+1 and time k, and Q be the negative electrode solid-phase diffusion coefficient. n,avg This represents the volume-average diffusion flux of lithium ions in the negative electrode solid phase. Let be the volume-average diffusion flux of lithium ions in the negative electrode solid phase at time k. The negative electrode solid-phase lithium ion volume average diffusion flux at time k+1; Solving the equation discretically yields the following: Where, j p D represents the molar flux of lithium ions per unit time and per unit area at the positive electrode. s,p Let Q be the solid-phase diffusion coefficient of the positive electrode, τ represent the time difference between time k+1 and time k, and Q be the solid-phase diffusion coefficient of the positive electrode. p,avg This represents the volume-average diffusion flux of lithium ions in the solid phase of the cathode. Let be the volume-average diffusion flux of lithium ions in the positive electrode solid phase at time k. R is the volume-average diffusion flux of lithium ions in the positive electrode solid phase at time k+1; p The radius is the positive polarity.

4. The SOC value estimation method for lithium batteries based on three-state variables according to claim 2, characterized in that, Before inputting the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery, the process further includes: Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery. The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery. Based on the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase after initialization, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

5. The SOC value estimation method for lithium batteries based on three-state variables according to claim 4, characterized in that, Based on the SOC value of the initialized lithium battery, the initial volume concentration of solid-phase lithium ions in the positive electrode and the initial volume concentration of solid-phase lithium ions in the negative electrode of the lithium battery are initialized, including: The formula for initialization is: C n,ini =C n,0 +SOC×(C n,100 -C n,0 ) C p,ini =C p,0 +SOC×(C p,100 -C p,0 ) Among them, C n,ini The initial volume concentration of lithium ions in the negative electrode solid phase after initialization; C n,100 The volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%; C n,0 The volume average concentration of lithium ions in the negative electrode solid phase when the actual SOC value = 0; C p,ini The initial volume concentration of lithium ions in the positive electrode solid phase after initialization; C p,100 The volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%; C p,0 The actual SOC value is the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 0; SOC is the actual SOC value.

6. The SOC value estimation method for lithium batteries based on three-state variables according to claim 5, characterized in that, The calculation of the output voltage value of the lithium battery based on the system state variables includes: The formula for calculating the output voltage of the lithium battery is as follows: V=U P -U n +n p -or n -I*R Ω V = h(x, u) Where x is the state variable and u is the input; U P 、U n The equilibrium potential between the positive and negative electrodes, η p The positive electrode reaction overpotential, η n The overpotential of the negative electrode reaction is given by I, where I is the current value and R is the overpotential of the negative electrode Ω Let h be the empirical resistance, and h be a function. Select [C] n,avg Q n,avg Q p,avg ] represents the system state variable, where C n,avg Q represents the volume average concentration of lithium ions in the negative electrode solid phase. n,avg Q represents the volume-average diffusion flux of lithium ions in the negative electrode solid phase. p,avg The volume-average diffusion flux of lithium ions in the positive electrode solid phase; Then matrix A is: Where τ is the sampling time, i.e. the time difference between two samplings; D s,n D is the positive electrode solid-phase diffusion coefficient; s,p R is the diffusion coefficient of the negative electrode solid phase; n R is the negative radius; p The positive radius; The observation matrix H is: Where V is the observation equation, V = U P -U n +η p -η n -I*R Ω .

7. The SOC value estimation method for lithium batteries based on three-state variables according to claim 6, characterized in that, The process of comparing the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three-state variables of the lithium battery includes: Based on the negative electrode solid phase lithium ion volume average concentration C n,avg Calculate the volume average concentration C of lithium ions in the solid phase of the cathode. p,avg , the formula is as follows: Among them, L n For the thickness of the negative electrode active material, L p ε represents the thickness of the positive electrode active material. n ε represents the volume fraction of the negative electrode active material. p c is the volume fraction of the positive electrode active material. p,100 c represents the volume average concentration of lithium ions in the solid phase of the cathode when the actual SOC value is 100%. n,100 This represents the volume-average concentration of lithium ions in the negative electrode solid phase when the actual SOC value is 100%. Based on the average volume concentration of lithium ions in the positive electrode solid phase and the output voltage value, the initial SOC estimate of the three state variables is calculated. The extended Kalman filter formula is as follows: Where x is the state variable, - indicates prior estimate, + indicates posterior estimate, and k represents time. Calculate the prior error covariance: Where P is the state variable error covariance matrix, which outputs the initial SOC estimate during initialization; Q is the process noise covariance, which outputs the initial SOC estimate when updating the state variable error; A T Let be the transpose of matrix A.

8. The SOC value estimation method for lithium batteries based on three-state variables according to claim 7, characterized in that, The process of filtering the initial SOC estimates of the three-state variables using an extended Kalman filter to obtain the target SOC estimates of the three-state variables includes: The state variables are updated using the extended Kalman filter, and the update formula for the state variables is as follows: Among them, z k This is the actual voltage value. The voltage value is obtained by substituting the initial SOC estimate and the actual SOC value at time k into the observation equation; Among them, K k To simplify the coefficients, they are calculated using the following formula: Where R is the measurement error covariance, and H T Let H be the transpose of matrix H.

9. A device for estimating the SOC value of a lithium battery based on three-state variables, characterized in that, include: The data initialization module is used to initialize the SOC value of the single-particle model of the lithium battery. The single-particle model includes single-particle and extended models, as well as a thermally coupled model based on the single-particle correlation model; A voltage output module is used to input the measured current value into the single-particle model of the lithium battery to generate the output voltage value of the lithium battery. The initial estimation module is used to compare the output voltage value of the lithium battery with the actual voltage value of the lithium battery to obtain the initial SOC estimate of the three state variables of the lithium battery; the three state variables include the volume average concentration of lithium ions in the positive electrode solid phase or the volume average concentration of lithium ions in the negative electrode solid phase, the volume average diffusion flux of lithium ions in the positive electrode solid phase, and the volume average diffusion flux of lithium ions in the negative electrode solid phase. The filtering estimation module is used to filter the initial SOC estimates of the three-state variables through extended Kalman filtering to obtain the target SOC estimates of the three-state variables.

10. The SOC value estimation device for a lithium battery based on three-state variables according to claim 9, characterized in that, Also includes: The initial processing module is used for: Input the initial SOC value of the lithium battery and the actual current value of the lithium battery into the single-particle model of the lithium battery to obtain the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase of the lithium battery. The initial volume concentration of solid lithium ions in the positive electrode and the initial volume concentration of solid lithium ions in the negative electrode of the lithium battery are initialized based on the SOC value of the initialized lithium battery. Based on the initial volume concentration of lithium ions in the positive electrode solid phase and the initial volume concentration of lithium ions in the negative electrode solid phase after initialization, the average volume concentration of lithium ions in the positive electrode solid phase and the average volume concentration of lithium ions in the negative electrode solid phase are obtained.

Images