A method for estimating the state of charge of lithium-ion batteries for energy storage considering the influence of multiple factors

Abstract

This invention discloses a method for estimating the state of charge (SOC) of energy storage lithium-ion batteries considering the influence of multiple factors. The method includes constructing a second-order RC equivalent circuit model equation for the lithium-ion battery, discretizing the equivalent circuit model equation to obtain the discretized state equation and observation equation; conducting actual maximum usable capacity tests on the lithium-ion battery at different temperatures and current rates to fit the relationship between the actual usable capacity of the lithium-ion battery and temperature and current rate; performing pulse discharge experiments on the lithium-ion battery at different temperatures to establish the relationship between temperature and various parameters in the state and observation equations; and improving the state and observation equations for use in the volumetric Kalman filter algorithm to estimate the SOC of the lithium-ion battery. This invention combines the influence of temperature and current rate for SOC estimation and employs the volumetric Kalman filter algorithm for SOC estimation, resulting in higher accuracy and more reliable practicality.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery state of charge estimation technology, and relates to a method for estimating the state of charge of energy storage lithium-ion batteries that takes into account the influence of multiple factors. Background Technology

[0002] The current energy structure, primarily based on clean and renewable energy, faces a series of challenges. Firstly, its power supply is volatile and intermittent; secondly, it puts pressure on the absorption end, leading to wind and solar power curtailment; and finally, it struggles to address load fluctuations caused by increased electricity consumption from residents and the tertiary sector. Energy storage systems play a crucial role in addressing these challenges. They can not only smooth out the volatility of renewable energy grid connection but also effectively handle peak power demand, saving grid investment and compensating for the relatively poor frequency regulation capabilities of renewable energy generation. Currently, the main energy storage technology is mechanical energy storage, while electrochemical energy storage offers advantages such as fast response speed, strong environmental adaptability, bidirectional regulation, and decentralized configuration. As the technology matures, electrochemical energy storage is increasingly being applied. The main technologies for electrochemical energy storage include lithium-ion batteries, lead-acid batteries, sodium-ion batteries, and flow batteries, with lithium batteries currently being the mainstream and the focus of industry research.

[0003] Scholars have proposed various methods for accurately estimating the state of charge (SOC) of lithium-ion batteries, which can be categorized into data-driven methods and battery model-based methods. Data-driven methods primarily utilize neural networks and their derivative models, offering high computational accuracy and strong nonlinear processing capabilities. However, these methods suffer from high computational complexity, and their accuracy relies heavily on extensive historical training data, making it impossible to guarantee SOC estimation accuracy outside the data range. Battery model-based methods, on the other hand, currently represent the most promising approach for lithium-ion battery SOC estimation in terms of both research and practical application. In practice, a suitable lithium-ion battery model is first selected and its parameters identified. Then, a state estimation algorithm is used to estimate the lithium-ion battery SOC, demonstrating excellent estimation accuracy and robustness.

[0004] Traditional single-filter algorithms perform well in battery SOC estimation, but they do not consider factors affecting battery conditions such as temperature and current rate. Compensation for current rate and temperature effects is crucial for lithium-ion battery model parameters and SOC estimation. Although many studies have explored the impact of operating temperature on lithium-ion battery model parameters and SOC estimation, evaluating the state of charge of lithium-ion batteries based solely on temperature effects results in low accuracy and significant errors when applied to actual production. Summary of the Invention

[0005] The purpose of this invention is to provide a method for estimating the state of charge (SOC) of energy storage lithium-ion batteries that considers the influence of multiple factors, thereby solving the problem that the accuracy of the SOC assessment results is low when only considering the temperature effect.

[0006] The technical solution adopted in this invention is a method for estimating the state of charge of energy storage lithium-ion batteries considering the influence of multiple factors, including the following steps:

[0007] Step 1: Construct the second-order RC equivalent circuit model equation of lithium-ion battery, and discretize the equivalent circuit model equation to obtain the discretized state equation and observation equation.

[0008] Step 2: Test the actual maximum usable capacity of lithium-ion batteries at different temperatures and current rates, fit the relationship between the actual usable capacity of lithium-ion batteries and temperature and current rate, conduct pulse discharge experiments on lithium-ion batteries at different temperatures, establish the relationship between temperature and various parameters in the state equation and observation equation, and improve the state equation and observation equation.

[0009] Step 3: The improved state equation and observation equation are used in the volumetric Kalman filter algorithm to estimate the SOC of the lithium-ion battery.

[0010] The specific process of step 1 is as follows:

[0011] Step 1.1: Construct the second-order RC equivalent circuit model equations for a lithium-ion battery, as follows:

[0012]

[0013]

[0014] In the formula, R0 is the battery's ohmic resistance, i.e., the battery's internal resistance; R1 is the electrochemical polarization internal resistance; R2 is the concentration polarization internal resistance; C1 is the electrochemical polarization capacitance; C2 is the concentration polarization capacitance; U1 is the voltage across R1 and C1 connected in parallel; U2 is the voltage across R2 and C2 connected in parallel; U ocv I is the battery open-circuit voltage. t Let U be the battery operating current at time t. t Let Q be the battery terminal voltage at time t. n The capacity is the lithium-ion battery capacity, and the state of charge (SOC) is the state of charge of the lithium-ion battery.

[0015] Step 1.2, discretize equation (1) at time k:

[0016]

[0017] In the formula, U 1,k U represents the voltage across the parallel connection of R1 and C1 at time k. 1,k-1 T represents the voltage across the parallel connection of R1 and C1 at time k-1. s U represents the sampling time interval. 2,kU represents the voltage across the parallel connection of R2 and C2 at time k. 2,k-1 SOC represents the voltage across the parallel connection of R2 and C2 at time k-1. k Represents the SOC value at time k, SOC k-1 This represents the SOC value at time k-1;

[0018] Step 1.3, simplify equation (3) to obtain:

[0019]

[0020] Step 1.4, let x = [U1, U2, SOC], y = U t Substituting into equation (4) yields the discretized equivalent circuit model equations, including the state equations x k and observation equation y k ,as follows:

[0021]

[0022] Where, x k x is the system's state variable at time k. k-1 It is the system's state variable at time k-1; y k It is the observed variable of the system, I t,k Let w be the battery operating current collected at time k. k It is a random signal of system process noise, v k A is the random signal of system observation noise, B is the system state transfer matrix, C is the system observation matrix, and D is the feedforward matrix.

[0023] Let C = [-1, -1, 0], D = -R0, then we get:

[0024]

[0025]

[0026] Step 2 is as follows:

[0027] Step 2.1: Test the actual maximum usable capacity of the lithium-ion battery at different temperatures and current rates, fit the relationship between the actual usable capacity of the lithium-ion battery and temperature and current rate, and improve the system control matrix B in the state equation based on the fitted relationship.

[0028] Step 2.2: Conduct pulse discharge experiments on lithium-ion batteries at different temperatures to establish the fitting relationship between temperature and various parameters in the state equation and observation equation, in order to improve the state equation and observation equation.

[0029] Step 2.1 The specific process is as follows:

[0030] Step 2.1.1: Under different temperatures and current rates, test the actual maximum usable capacity of the lithium-ion battery, and fit the relationship between the actual maximum usable capacity of the lithium-ion battery and the temperature and current rate. The fitted relationship is as follows:

[0031] Q real (T,I)=a1T+b1I+a2T 2 +b2I 2 +cTI+d+e (8)

[0032] In the above formula, Q real (T, I) represents the actual maximum usable capacity of the lithium-ion battery, T represents the current ambient temperature, I represents the current rate, and a1, a2, b1, b2, c, d, and e are all fitting coefficients of the formula.

[0033] Step 2.1.2, improve the system control matrix B based on the fitted relationship:

[0034]

[0035] Step 2.2 The specific process is as follows:

[0036] Step 2.2.1: Conduct pulse discharge experiments on the lithium-ion battery at different temperatures to obtain the open-circuit voltage U of the battery. ocv The relationship between temperature and battery state of charge (SOC) is shown in the figure. The SOC-OCV at each temperature is fitted using an eighth-order polynomial, and the fitting formula is as follows:

[0037] U ocv (SOC)=z8SOC 8 +z7SOC 7 +z6SOC 6 +z5SOC 5

[0038] +z4SOC 4 +z3SOC 3 +z2SOC 2 +z1SOC+z0(10)

[0039] In the above formula: z i The fitting parameters are i = 0, 1, 2, ..., 8;

[0040] Step 2.2.2: According to formula (10), the fitting coefficients of the model parameters fitted at different temperatures are fitted with the corresponding temperatures, and a cubic polynomial is selected for fitting z. i Relationship coefficient with temperature T:

[0041] z i =k 3iT 3 +k 2i T 2 +k 1i T+k 0i (11)

[0042] Where, k ji Temperature and open-circuit voltage U ocv The fitting coefficients of the relationship between the battery state of charge (SOC) and the battery state of charge (SOC), j = 0, 1, 2, 3, i = 0, 1, 2, ..., 8;

[0043] Step 2.2.3: At the start or end of pulse discharge, the voltage on the two parallel RC loops in the second-order RC network model will not change abruptly. The voltage change is only related to the battery's internal resistance R0. Therefore, the R0 identification formula can be obtained:

[0044]

[0045] In the formula, t a t represents the time when the pulsed discharge current occurs. b The time t is 1 second after the occurrence of the pulse discharge current. b =t a +1s,t c t is the time it takes for the pulsed discharge current to disappear. d t is the time 1 second after the pulse discharge current disappears. d =t c +1s;

[0046] Step 2.2.4: After the current disappears, the two RC circuits lose their external excitation, which is equivalent to a zero-input response. At this time, the battery terminal voltage equation is:

[0047]

[0048] In the formula, τ i τ represents the time constant. i =R i ×C i i = 1, 2; t c Given the time it takes for the pulse discharge current to disappear, the voltage data for this stage are fitted using the least squares method to obtain U1, U2, τ1, and τ2.

[0049] After a lithium-ion battery has been left to rest, it undergoes pulse discharge. At this time, the RC polarization of the battery can be represented as a zero-state response, as shown in the following expression:

[0050]

[0051] Step 2.2.5: Select a specific temperature as the reference temperature, denoted as T. BLet the coefficient of influence of temperature on lithium-ion battery parameters be S. Ti The calculation formula is as follows:

[0052]

[0053] In the above formula, V Ti This represents the average value of the parameter at the i-th temperature. Reference temperature T B The average value of the parameter under the following conditions;

[0054] The influence coefficient of each temperature on the parameter is fitted with a mathematical relationship to the actual temperature:

[0055]

[0056] In the formula, h3, h2, h1, and h0 are the fitting coefficients of the formula;

[0057] Step 2.2.6: According to equation (16), perform polynomial fitting on R0, R1, C1, R2, and C2 at different temperatures to establish the expressions for each parameter in the equivalent mathematical model considering the influence of temperature:

[0058]

[0059] In the formula, h 0,R0 h 0,R1 h 0,R2 h 0,C1 h 0,C2 These represent the fitting coefficients h0 and h1 corresponding to R0, R1, C1, R2, and C2 obtained according to formula (16); j,R0 h j,R1 h j,R2 h j,C1 h j,C2 This indicates that the fitting coefficients h for R0, R1, C1, R2, and C2 are obtained according to formula (16). j j = 1, 2, 3; R TB，R0 R TB,R1 R TB,R2 C TB,C1 C TB,C2 The reference temperature T B The average values ​​of R0, R1, C1, R2, and C2 under given conditions; T is the current ambient temperature. j Let T be the power of j, where j = 1, 2, 3.

[0060] Step 3 includes using the model established in Step 2 to establish the relationship between temperature, current rate and actual maximum usable capacity of lithium-ion battery, the parameter identification in the equivalent circuit model under different temperature effects, and the parameter-temperature relationship fitting model for estimating the state of charge (SOC) of energy storage lithium-ion battery, and using the volumetric Kalman filter algorithm (CKF) for SOC estimation.

[0061] Step 3 is as follows:

[0062] Step 3.1: Based on the state equation and observation equation from Step 1, perform SOC estimation using the capacitive Kalman filter algorithm. The corresponding state equation and observation equation are as follows:

[0063]

[0064]

[0065] In the formula, Ts is the sampling period, i.e., the time required to go from time k to time k+1, and U i,k (SOC,T,I) represents the voltages of the two parallel RC circuits after parameter improvements considering temperature effects, where i = 1, 2; I k Let be the battery terminal current at time k, where k = 1, 2, ...;

[0066] Step 3.2: Substitute the state equation and observation equation from step 3.1 into the capacitive Kalman filter algorithm to estimate the state of charge (SOC) of the lithium battery.

[0067] Step 3.2 The specific process is as follows:

[0068] Step 3.2.1, assume the state equation and observation equation are as follows:

[0069]

[0070] x k+1 Let x be the state variable of the system at time k+1. k Let u be the state variable of the system at time k. k Let f(x) be the input of the system at time k. k ,u k g(x) is a nonlinear state transfer function. k ,u k ) is a nonlinear measurement function;

[0071] Step 3.2.2, Initialize state variables Error covariance P k Process noise Q and measurement noise matrix R;

[0072] Step 3.2.3: Update the battery capacity according to the relationship between the actual maximum usable capacity of the lithium-ion battery and temperature and current rate (8) fitted in step 2, and update the model parameters at the current temperature according to the parameter expressions (10) and (17) in the equivalent mathematical model that considers the influence of temperature.

[0073] Step 3.2.4, calculate the volume point at time k:

[0074]

[0075]

[0076] In the formula, P k Let S represent the error covariance matrix at time k. k =chol{P k}, chol{} denotes the Koleski decomposition of the matrix. S represents k It is for P k The matrix obtained by performing Koleski decomposition. S represents k The transpose of the matrix, Represents a sigma point set. Let ξ be the state variable at time k, n be the dimension of the state vector, and ξ be the state variable at time k. i The set of volume points is as follows:

[0077]

[0078] In the formula, [1] represents the identity matrix;

[0079] Step 3.2.5, Propagation Volume Point:

[0080]

[0081] The subscript k+1|k indicates that the value of k+1 is based on the value at time k, representing the calculation backward from the value at time k.

[0082] Step 3.2.6: Calculate the predicted values ​​of the state variables and their error covariance prediction values.

[0083]

[0084]

[0085] In the formula, P represents the predicted value of the state variable. k+1|k This represents the predicted value of the error covariance;

[0086] Step 3.2.7, calculate the volume point at time k+1.

[0087]

[0088]

[0089] Step 3.2.8, Propagation Volume Point:

[0090]

[0091] In the formula, This represents the updated sigma point set;

[0092] Step 3.2.9, Calculate the predicted measurement value:

[0093]

[0094] In the formula, To measure the predicted value;

[0095] Step 3.2.10, calculate the measurement error covariance and cross-covariance:

[0096]

[0097] In the formula, This represents the measurement error covariance of the observed variable at time k+1. The cross-covariance between state variables and observed variables;

[0098] Step 3.2.11: Calculate the Kalman gain, update the state variables and the corresponding error covariance:

[0099]

[0100]

[0101] In the formula, K k+1 Indicates Kalman gain, P represents the updated state variable. k+1 This represents the updated error covariance.

[0102] The beneficial effects of this invention are that it combines the influence of temperature and current rate for SOC estimation. By establishing a second-order RC equivalent circuit model of a lithium-ion battery, a mathematical model of battery capacity-temperature-discharge rate is established based on the different actual battery capacities caused by temperature and current rate. The polynomials related to capacity in the system control matrix of the model equation are improved, and the influence of temperature on the circuit model parameters is analyzed. A reference temperature is taken, and the parameter values ​​at different temperatures are corrected and a new parameter-temperature model equation is fitted. This makes the model parameters more adaptable to temperature changes. The volumetric Kalman filter algorithm is used for SOC estimation. The battery parameters are updated by the estimated lithium-ion battery SOC and experimental temperature, resulting in higher accuracy and more reliable practicality. Attached Figure Description

[0103] Figure 1 This is a flowchart illustrating the method for estimating the state of charge of energy storage lithium-ion batteries that considers the influence of multiple factors according to the present invention.

[0104] Figure 2 This is a structural diagram of the second-order RC equivalent circuit model of a lithium-ion battery in this invention;

[0105] Figure 3 This invention is based on establishing fitting graphs of the actual maximum usable capacity of lithium-ion batteries under different temperatures and rates;

[0106] Figure 4 This is a flowchart of the SOC estimation based on the capacitive Kalman filter algorithm of this invention. Detailed Implementation

[0107] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0108] Example 1

[0109] A method for estimating the state of charge (SOC) of energy storage lithium-ion batteries that considers the influence of multiple factors, referring to... Figure 1 This includes the following steps:

[0110] Step 1: Construct the second-order RC equivalent circuit model equation of lithium-ion battery, and discretize the equivalent circuit model equation to obtain the discretized state equation and observation equation.

[0111] The second-order RC equivalent circuit model can provide information about battery dynamics, adapt to various dynamic operating conditions, intuitively analyze the characteristics of lithium batteries, list the corresponding model state equations, and facilitate the addition of variables such as temperature and discharge rate into the model, making the analysis more accurate and easier to express mathematically.

[0112] Step 2: Test the actual maximum usable capacity of lithium-ion batteries at different temperatures and current rates, fit the relationship between the actual usable capacity of lithium-ion batteries and temperature and current rate, conduct pulse discharge experiments on lithium-ion batteries at different temperatures, establish the relationship between temperature and various parameters in the state equation and observation equation, and update the state equation and observation equation.

[0113] Step 3: The improved state equation and observation equation are used in the volumetric Kalman filter algorithm to estimate the SOC of the lithium-ion battery.

[0114] Example 2

[0115] A method for estimating the state of charge (SOC) of energy storage lithium-ion batteries that considers the influence of multiple factors is described below:

[0116] Step 1: Construct and discretize the second-order RC equivalent circuit model equations for a lithium-ion battery. The structure of the constructed second-order RC equivalent circuit model is as follows: Figure 2 As shown;

[0117] Step 1.1: Construct the second-order RC equivalent circuit model equations for a lithium-ion battery, as follows:

[0118]

[0119]

[0120] In the formula, R0 is the battery's ohmic resistance, i.e., the battery's internal resistance; R1 is the electrochemical polarization internal resistance; R2 is the concentration polarization internal resistance; C1 is the electrochemical polarization capacitance; C2 is the concentration polarization capacitance; U1 is the voltage across R1 and C1 connected in parallel; U2 is the voltage across R2 and C2 connected in parallel; U ocv I is the battery open-circuit voltage. t Let U be the battery operating current at time t. t Let Q be the battery terminal voltage at time t. n The capacity is the lithium-ion battery capacity, and the state of charge (SOC) is the state of charge of the lithium-ion battery.

[0121] Step 1.2, discretize equation (1) at time k:

[0122]

[0123] In the formula, U 1,k U represents the voltage across the parallel connection of R1 and C1 at time k. 1,k-1 T represents the voltage across the parallel connection of R1 and C1 at time k-1. s U represents the sampling time interval. 2,k U represents the voltage across the parallel connection of R2 and C2 at time k. 2,k-1SOC represents the voltage across the parallel connection of R2 and C2 at time k-1. k Represents the SOC value at time k, SOC k-1 This represents the SOC value at time k-1;

[0124] Step 1.3, simplify equation (3) to obtain:

[0125]

[0126] Step 1.4, let x = [U1, U2, SOC], y = U t Substituting into equation (4) yields the discretized equivalent circuit model equations, including the state equations x k and observation equation y k ,as follows:

[0127]

[0128] Where, x k x is the system's state variable at time k. k-1 It is the system's state variable at time k-1; y k It is the observed variable of the system, I t,k Let w be the battery operating current collected at time k. k It is a random signal of system process noise, v k A is the random signal of system observation noise, B is the system state transfer matrix, C is the system observation matrix, and D is the feedforward matrix.

[0129] Let C = [-1, -1, 0], D = -R0, then we get:

[0130]

[0131]

[0132] Step 2: Based on the input-output equations obtained from the discretized equivalent circuit in Step 1, i.e., the state equation and the observation equation, the lithium-ion battery capacity Q in the equation is... n Capacity experiments were conducted at different temperatures and current rates to obtain the relationship between the actual maximum usable capacity of lithium-ion batteries and temperature and current rate. This relationship was then used to update the input-output equations of the model, i.e., to update the state equation and observation equation. The specific process is as follows:

[0133] Step 2.1: Test the actual maximum usable capacity of the lithium-ion battery at different temperatures and current rates, fit the relationship between the actual usable capacity of the lithium-ion battery and temperature and current rate, and improve the system control matrix B in the state equation based on the fitted relationship.

[0134] Step 2.2: Conduct pulse discharge experiments on lithium-ion batteries at different temperatures to establish the fitting relationship between temperature and various parameters in the state equation and observation equation, in order to update the state equation and observation equation.

[0135] Step 3: The parameter identification and parameter-temperature relationship model established in Step 2, which relates temperature, current rate and actual maximum usable capacity of lithium-ion battery, as well as the equivalent circuit model under different temperature effects, are used for the state of charge (SOC) estimation of energy storage lithium-ion battery. The volumetric Kalman filter algorithm (CKF) is used for SOC estimation.

[0136] Example 3

[0137] A method for estimating the state of charge (SOC) of energy storage lithium-ion batteries that considers the influence of multiple factors is described below:

[0138] Step 1: Construct the second-order RC equivalent circuit model equation of the lithium-ion battery and discretize it;

[0139] Step 1.1: Construct the second-order RC equivalent circuit model equations for a lithium-ion battery, as follows:

[0140]

[0141]

[0142] In the formula, R0 is the battery's ohmic resistance, i.e., the battery's internal resistance; R1 is the electrochemical polarization internal resistance; R2 is the concentration polarization internal resistance; C1 is the electrochemical polarization capacitance; C2 is the concentration polarization capacitance; U1 is the voltage across R1 and C1 connected in parallel; U2 is the voltage across R2 and C2 connected in parallel; U ocv I is the battery open-circuit voltage. t Let U be the battery operating current at time t. t Let Q be the battery terminal voltage at time t. n The capacity is the lithium-ion battery capacity, and the state of charge (SOC) is the state of charge of the lithium-ion battery.

[0143] Step 1.2, discretize equation (1) at time k:

[0144]

[0145] In the formula, U 1,k U represents the voltage across the parallel connection of R1 and C1 at time k. 1,k-1 T represents the voltage across the parallel connection of R1 and C1 at time k-1. s U represents the sampling time interval. 2,k U represents the voltage across the parallel connection of R2 and C2 at time k. 2,k-1 SOC represents the voltage across the parallel connection of R2 and C2 at time k-1. kRepresents the SOC value at time k, SOC k-1 This represents the SOC value at time k-1;

[0146] Step 1.3, simplify equation (3) to obtain:

[0147]

[0148] Step 1.4, let x = [U1, U2, SOC], y = U t Substituting into equation (4) yields the discretized equivalent circuit model equations, including the state equations x k and observation equation y k ,as follows:

[0149]

[0150] Where, x k x is the system's state variable at time k. k-1 It is the system's state variable at time k-1; y k It is the observed variable of the system, I t,k Let w be the battery operating current collected at time k. k It is a random signal of system process noise, v k A is the random signal of system observation noise, B is the system state transfer matrix, C is the system observation matrix, and D is the feedforward matrix.

[0151] Let C = [-1, -1, 0], D = -R0, then we get:

[0152]

[0153]

[0154] Step 2: Based on the input-output equations obtained from the discretized equivalent circuit in Step 1, i.e., the state equation and the observation equation, the lithium-ion battery capacity Q in the equation is... n Capacity experiments were conducted at different temperatures and current rates to obtain the relationship between the actual maximum usable capacity of lithium ions and temperature and current rate, which was used to update the input-output equations of the model, i.e., to update the state equation and observation equation.

[0155] Step 2.1: Under different temperatures and current rates, test the actual maximum usable capacity of the lithium-ion battery, fit the relationship between the actual usable capacity of the lithium-ion battery and temperature and current rate, and improve the system control matrix B in the state equation based on the fitted relationship. The specific process is as follows:

[0156] Step 2.1.1, refer to Figure 3The actual maximum usable capacity of lithium-ion batteries was tested at different temperatures and current rates. The relationship between the actual maximum usable capacity of lithium-ion batteries and temperature and current rate was fitted, and the fitted relationship is as follows:

[0157] Q real (T,I)=a1T+b1I+a2T 2 +b2I 2 +cTI+d+e (8)

[0158] In the above formula, Q real (T, I) represents the actual maximum usable capacity of the lithium-ion battery, T represents the current temperature, I represents the current rate, and a1, a2, b1, b2, c, d, and e are all formula fitting coefficients. In this embodiment, a1 = 0.06518, a2 = -0.001158, b1 = -0.3758, b2 = -0.05971, c = -3.244e+14, d = -17.77, and e = -1.324.

[0159] Step 2.1.2, improve the system control matrix B based on the fitted relationship:

[0160]

[0161] Step 2.2: Identify the remaining parameters in the second-order RC equivalent circuit model of the lithium-ion battery obtained from the above steps. Conduct pulse discharge experiments on the lithium-ion battery at different temperatures to identify the values ​​of each parameter in the model at different temperatures. Establish the fitting relationship between temperature and each parameter in the state equation and observation equation to update the state equation and observation equation. The specific process is as follows:

[0162] Step 2.2.1: Conduct pulse discharge experiments on the lithium-ion battery at different temperatures to obtain the open-circuit voltage U of the battery. ocv The relationship between temperature and battery state of charge (SOC) is shown in the figure. The SOC-OCV at each temperature is fitted using an eighth-order polynomial, and the fitting formula is as follows:

[0163] U ocv (SOC)=z8SOC 8 +z7SOC 7 +z6SOC 6 +z5SOC 5

[0164] +z4SOC 4 +z3SOC 3 +z2SOC 2 +z1SOC+z0(10)

[0165] In the above formula: z iThe fitting parameters are i = 0, 1, 2, ..., 8;

[0166] Step 2.2.2: Based on the relevant data of open-circuit voltage, temperature, and SOC at different temperatures, considering the influence of temperature, it is necessary to fit the temperature-open-circuit voltage-SOC relationship according to the experimental data. According to formula (10), the fitting coefficients of the model parameters fitted at different temperatures are respectively fitted with the temperature at which they are located. A cubic polynomial is selected for fitting z. i Relationship coefficient with temperature T:

[0167] z i =k 3i T 3 +k 2i T 2 +k 1i T+k 0i (11)

[0168] Where, k ji Temperature and open-circuit voltage U ocv The fitting coefficients of the relationship between the battery state of charge (SOC) and the battery state of charge (SOC), j = 0, 1, 2, 3, i = 0, 1, 2, ..., 8;

[0169] Step 2.2.3: The parameters that still need to be identified in the equivalent circuit model are: R0, R1, C1, R2, and C2.

[0170] At the start or end of pulse discharge, the voltage on the two parallel RC loops in the second-order RC network model will not change abruptly. The voltage change is only related to the battery's internal resistance R0. Therefore, the R0 identification formula can be obtained:

[0171]

[0172] In the formula, t a t represents the time when the pulsed discharge current occurs. b The time t is 1 second after the occurrence of the pulse discharge current. b =t a +1s,t c t is the time it takes for the pulsed discharge current to disappear. d t is the time 1 second after the pulse discharge current disappears. d =t c +1s;

[0173] Step 2.2.4: After the current disappears, the two RC circuits lose their external excitation, which is equivalent to a zero-input response. At this time, the battery terminal voltage equation is:

[0174]

[0175] In the formula, τ i τ represents the time constant.i =R i ×C i i = 1, 2; t c Given the time it takes for the pulse discharge current to disappear, the voltage data for this stage are fitted using the least squares method to obtain U1, U2, τ1, and τ2.

[0176] After a lithium-ion battery has been left to rest, it undergoes pulse discharge. At this time, the RC polarization of the battery can be represented as a zero-state response, as shown in the following expression:

[0177]

[0178] Combining equations (12) and (14) yields the optimal identification results for R0, R1, C1, R2, and C2.

[0179] Step 2.2.5: Based on the R0, R1, C1, R2, and C2 data identified at different temperatures, when considering the influence of temperature, it is necessary to fit model equations for different temperatures and parameters.

[0180] Choose a specific temperature as the reference temperature, denoted as T. B Let the coefficient of influence of temperature on lithium-ion battery parameters be S. Ti The calculation formula is as follows:

[0181]

[0182] In the above formula, V Ti This represents the average value of the parameter at the i-th temperature. Reference temperature T B The average value of the parameter under the following conditions;

[0183] The influence coefficient of each temperature on the parameter is fitted with a mathematical relationship to the actual temperature:

[0184]

[0185] In the formula, h3, h2, h1, and h0 are the fitting coefficients of the formula;

[0186] Step 2.2.6: According to equation (16), perform polynomial fitting on R0, R1, C1, R2, and C2 at different temperatures to establish the expressions for each parameter in the equivalent mathematical model considering the influence of temperature:

[0187]

[0188] In the formula, h 0,R0 h 0,R1 h 0,R2 h 0,C1 h 0,C2These represent the fitting coefficients h0 and h1 corresponding to R0, R1, C1, R2, and C2 obtained according to formula (16); j,R0 h j,R1 h j,R2 h j,C1 h j,C2 This indicates that the fitting coefficients h for R0, R1, C1, R2, and C2 are obtained according to formula (16). j j = 1, 2, 3; R TB，R0 R TB,R1 R TB,R2 C TB,C1 C TB,C2 The reference temperature T B The average values ​​of R0, R1, C1, R2, and C2 under given conditions; T is the current ambient temperature. j Let T be the power of j, where j = 1, 2, 3.

[0189] Step 3: The parameter identification and parameter-temperature relationship model established in Step 2, which relates temperature, current rate and actual maximum usable capacity of lithium-ion battery, as well as the equivalent circuit model under different temperature effects, are used for the state of charge (SOC) estimation of energy storage lithium-ion battery. The volumetric Kalman filter algorithm (CKF) is used for SOC estimation.

[0190] The CKF algorithm does not require linearization of the established state and observation equations. It is based on numerical integration theory, using the third-order spherical radial volume criterion to approximate the Gaussian integral. It has a rigorous and complete theoretical foundation, making the algorithm stable and highly accurate. The CKF algorithm flowchart is shown below. Figure 4 As shown.

[0191] Step 3 is as follows:

[0192] Step 3.1: Based on the state equation and observation equation from Step 1, perform SOC estimation using the capacitive Kalman filter algorithm. The corresponding state equation and observation equation are as follows:

[0193]

[0194]

[0195] In the formula, Ts is the sampling period, i.e., the time required to go from time k to time k+1, and U i,k (SOC,T,I) represents the voltages of the two parallel RC circuits after parameter improvements considering temperature effects, where i = 1, 2; I k Let be the battery terminal current at time k, where k = 1, 2, ...;

[0196] Step 3.2: Substitute the state equation and observation equation from step 3.1 into the capacitive Kalman filter algorithm to estimate the state of charge (SOC) of the lithium battery.

[0197] Step 3.2.1, assume the state equation and observation equation are as follows:

[0198]

[0199] x k+1 Let x be the state variable of the system at time k+1. k Let u be the state variable of the system at time k. k Let f(x) be the input of the system at time k. k ,u k g(x) is a nonlinear state transfer function. k ,u k ) is a nonlinear measurement function;

[0200] Step 3.2.2, Initialize state variables Error covariance P k Process noise Q and measurement noise matrix R;

[0201] Step 3.2.3: Update the battery capacity according to the relationship between the actual maximum usable capacity of the lithium-ion battery and temperature and current rate (8) fitted in step 2, and update the model parameters at the current temperature according to the parameter expressions (10) and (17) in the equivalent mathematical model that considers the influence of temperature.

[0202] Step 3.2.4, calculate the volume point at time k:

[0203]

[0204]

[0205] In the formula, P k Let S represent the error covariance matrix at time k. k =chol{P k}, chol{} denotes the Koleski decomposition of the matrix. It is for P k The matrix obtained by performing Koleski decomposition. S represents k The transpose of the matrix, Let ξ represent the sigma point set, where n is the dimension of the state vector, and ξ is the sigma point set. i Given a set of volume points, the expression is as follows:

[0206]

[0207] In the formula, [1] represents the identity matrix;

[0208] Step 3.2.5, Propagation Volume Point:

[0209]

[0210] The subscript k+1|k indicates that the value of k+1 is based on the value at time k, representing the calculation backward from the value at time k.

[0211] Step 3.2.6: Calculate the predicted values ​​of the state variables and their error covariance prediction values.

[0212]

[0213]

[0214] In the formula, P represents the predicted value of the state variable. k+1|k This represents the predicted value of the error covariance;

[0215] Step 3.2.7, calculate the volume point at time k+1.

[0216]

[0217]

[0218] Step 3.2.8, Propagation Volume Point:

[0219]

[0220] In the formula, This represents the updated sigma point set;

[0221] Step 3.2.9, Calculate the predicted measurement value:

[0222]

[0223] In the formula, To measure the predicted value;

[0224] Step 3.2.10, calculate the measurement error covariance and cross-covariance:

[0225]

[0226] In the formula, This represents the measurement error covariance of the observed variable at time k+1. The cross-covariance between state variables and observed variables;

[0227] Step 3.2.11: Calculate the Kalman gain, update the state variables and the corresponding error covariance:

[0228]

[0229]

[0230] In the formula, K k+1 This represents the Kalman gain.

Claims

1. A method for estimating the state of charge (SOC) of energy storage lithium-ion batteries considering the influence of multiple factors, characterized in that, Includes the following steps: Step 1: Construct the second-order RC equivalent circuit model equation of lithium-ion battery, and discretize the equivalent circuit model equation to obtain the discretized state equation and observation equation. The specific process of step 1 is as follows: Step 1.1: Construct the second-order RC equivalent circuit model equations for a lithium-ion battery, as follows: （1） （2） In the formula, R 0 represents the battery's ohmic resistance, i.e., its internal resistance. R 1 represents the electrochemical polarization internal resistance. R 2 represents the concentration polarization internal resistance. C 1 is an electrochemically polarized capacitor. C 2 is the concentration polarization capacitor. U 1 is R 1 and C 1. The voltage across the parallel terminals, U 2 is R 2 and C 2. The voltage across the parallel terminals, U ocv This is the battery open-circuit voltage. I t Let be the battery operating current at time t. U t Let be the battery terminal voltage at time t. Q n The capacity is the lithium-ion battery capacity, and the state of charge (SOC) is the state of charge of the lithium-ion battery. Step 1.2, discretize equation (1) at time k: （3） In the formula, Represents time k R 1 and C 1. The voltage across the parallel terminals, U 1,k-1 Represents time k-1 R 1 and C The voltage across the parallel terminals, T s Indicates the sampling time interval. U 2,k Represents time k R 2 and C 2. The voltage across the parallel terminals, U 2,k-1 Represents time k-1 R 2 and C 2. The voltage across the parallel terminals, express k SOC value at time t, express k SOC value at time -1; Step 1.3, simplify equation (3) to obtain: （4） Step 1.4, let , Substituting into equation (4), we obtain the discretized equivalent circuit model equations, including the state equations. x k and observation equations y k ,as follows: （5） in, x k It is the system's state variable at time k. It is the system's state variable at time k-1; y k These are the observed variables of the system. Let k be the battery operating current collected at time k. w k It is a random signal of system process noise. v k It is a random signal of system observation noise. A For the system state transfer matrix, B The control matrix of the system. C The system's observation matrix, D It is a feedforward matrix; make , We can obtain: （6） （7） Step 2: Test the actual maximum usable capacity of lithium-ion batteries at different temperatures and current rates, fit the relationship between the actual usable capacity of lithium-ion batteries and temperature and current rate, conduct pulse discharge experiments on lithium-ion batteries at different temperatures, establish the relationship between temperature and various parameters in the state equation and observation equation, and improve the state equation and observation equation. The specific process of step 2 is as follows: Step 2.1: Test the actual maximum usable capacity of the lithium-ion battery at different temperatures and current rates, fit the relationship between the actual usable capacity of the lithium-ion battery and temperature and current rate, and improve the system control matrix B in the state equation based on the fitted relationship. The specific process of step 2.1 is as follows: Step 2.1.1: Under different temperatures and current rates, test the actual maximum usable capacity of the lithium-ion battery, and fit the relationship between the actual maximum usable capacity of the lithium-ion battery and the temperature and current rate. The fitted relationship is as follows: （8） In the above formula, (T, I) represents the actual maximum usable capacity of the lithium-ion battery. T Indicates the current ambient temperature. I Indicates the current ratio. a 1. a 2. b 1. b 2. c , d , e All are formula fitting coefficients; Step 2.1.2, improve the system control matrix B based on the fitted relationship: （9） Step 2.2: Conduct pulse discharge experiments on lithium-ion batteries at different temperatures to establish the fitting relationship between temperature and various parameters in the state equation and observation equation, in order to improve the state equation and observation equation. The specific process of step 2.2 is as follows: Step 2.2.1: Conduct pulse discharge experiments on the lithium-ion battery at different temperatures to obtain the open-circuit voltage of the battery. The relationship between temperature and battery state of charge (SOC) is shown in the figure. The SOC-OCV at each temperature is fitted using an eighth-order polynomial, and the fitting formula is as follows: （10） In the above formula: For the fitting parameters, i =0,1,2,...,8; Step 2.2.2: According to formula (10), the fitting coefficients of the model parameters fitted at different temperatures are fitted with the corresponding temperatures, and a cubic polynomial is selected for fitting. z i Relationship coefficient with temperature T: （11） in, k ji For temperature and open circuit voltage The fitting coefficients of the relationship between the battery's state of charge (SOC) and the battery's state of charge (SOC). j =0,1,2,3 i =0,1,2,...,8; Step 2.2.3: At the start or end of pulse discharge, the voltage on the two parallel RC loops in the second-order RC network model will not change abruptly. The voltage change is only related to the battery's internal resistance R0. Therefore, the R0 identification formula can be obtained: （12） In the formula, t a t represents the time when the pulsed discharge current occurs. b One second after the occurrence of the pulse discharge current, i.e. t b = t a +1s, t c t is the time it takes for the pulsed discharge current to disappear. d One second after the pulse discharge current disappears, i.e. t d = t c +1s; Step 2.2.4: After the current disappears, the two RC circuits lose their external excitation, which is equivalent to a zero-input response. At this time, the battery terminal voltage equation is: （13） In the formula, τ i Represents the time constant. τ i = R i × C i , i =1, 2; t c Let be the time when the pulse discharge current disappears. Using the least squares method to fit the voltage data during this stage, we can obtain... U 1. U 2. τ 1. τ 2; After a lithium-ion battery has been left to rest, it undergoes pulse discharge. At this time, the RC polarization of the battery can be represented as a zero-state response, as shown in the following expression: （14） Step 2.2.5: Select a specific temperature as the reference temperature, denoted as T. B Let the coefficient of influence of temperature on lithium-ion battery parameters be S. Ti The calculation formula is as follows: （15） In the above formula, Indicates the first i The average value of the parameters at each temperature. Reference temperature T B The average value of the parameter under the following conditions; The influence coefficient of each temperature on the parameter is fitted with a mathematical relationship to the actual temperature: （16） In the formula, h 3. h 2. h 1. h 0 represents the fit coefficient of the formula; Step 2.2.6, according to equation (16), for different temperatures R 0、 R 1. C 1. R 2. C 2. Perform polynomial fitting to establish the expressions for each parameter in the equivalent mathematical model that considers the influence of temperature: （17） In the formula, h 0,R0 , h 0,R1 , h 0,R2 , h 0,C1 , h 0,C2 They respectively represent the results obtained from formula (16) regarding... R 0、 R 1. C 1. R 2. C The fitting coefficient h0 corresponding to 2; h j,R0 , h j,R1 , h j,R2 , h j,C1 , h j,C2 This means that according to formula (16), we can obtain information about... R 0、 R 1. C 1. R 2. C The fitting coefficient h of 2 j j=1, 2, 3; R TB，R0 , R TB, R1 , R TB,R2 , C TB,C1 , C TB,C2 The reference temperature T B Below R 0、 R 1. C 1. R 2. C The average value of 2; T is the current ambient temperature, T j Let T be the power of j, where j = 1, 2, or 3; Step 3: The improved state equation and observation equation are used in the volumetric Kalman filter algorithm to estimate the SOC of the lithium-ion battery.

2. The method for estimating the state of charge of energy storage lithium-ion batteries considering the influence of multiple factors according to claim 1, characterized in that, Step 3 includes using the relationship model between temperature, current rate and actual maximum usable capacity of lithium-ion battery established in step 2, parameter identification in the equivalent circuit model under different temperature effects, and parameter-temperature relationship fitting model for energy storage lithium-ion battery state of charge (SOC) estimation, and using the volumetric Kalman filter algorithm (CKF) for SOC estimation.

3. The method for estimating the state of charge of energy storage lithium-ion batteries considering the influence of multiple factors according to claim 2, characterized in that, The specific process of step 3 is as follows: Step 3.1: Based on the state equation and observation equation from Step 1, perform SOC estimation using the capacitive Kalman filter algorithm. The corresponding state equation and observation equation are as follows: （18） （19） In the formula, Ts is the sampling period, which is the time required to go from time k to time k+1. This represents the voltage of two RC parallel circuits after adjusting the parameters to account for the influence of temperature. i =1,2; I k Let be the battery terminal current at time k, where k = 1, 2, ...; Step 3.2: Substitute the state equation and observation equation from step 3.1 into the capacitive Kalman filter algorithm to estimate the state of charge (SOC) of the lithium battery.

4. The method for estimating the state of charge of energy storage lithium-ion batteries considering the influence of multiple factors according to claim 3, characterized in that, The specific process of step 3.2 is as follows: Step 3.2.1, assume the state equation and observation equation are as follows: （20） UK for k The input of the time system, ƒ( xk , UK ) is a nonlinear state transfer function ，g ( xk , UK ) is a nonlinear measurement function; Step 3.2.2, Initialize state variables Error covariance P k Process noise Q and measurement noise matrix R; Step 3.2.3: Update the battery capacity according to the relationship between the actual maximum usable capacity of the lithium-ion battery and temperature and current rate fitted in Step 2; update the model parameters at the current temperature according to the parameter expressions in the equivalent mathematical model that considers the influence of temperature. Step 3.2.4, calculate the volume point at time k: （21） （22） In the formula, Pk represents the error covariance matrix at time k. Sk = chol { Pk }, chol {} denotes the Koleski decomposition of the matrix. This is the matrix obtained by performing Koleski decomposition on Pk. Denotes the transpose of Sk. express sigma Point set, Let n be the state variable at time k, and n be the dimension of the state vector. The set of volume points is as follows: （23） In the formula, [1] represents the identity matrix; Step 3.2.5, Propagation Volume Point: （24） Among them, subscript k +1| k express k The value of +1 is built on k Based on the time, it represents the result of k The value at that moment is extrapolated backwards; Step 3.2.6: Calculate the predicted values ​​of the state variables and their error covariance prediction values; （25） In the formula, This represents the predicted value of the state variable. This represents the predicted value of the error covariance; Step 3.2.7, calculate the volume point at time k+1. : （26） Step 3.2.8, Propagation Volume Point: （27） In the formula, Indicates the updated sigma Point set; Step 3.2.9, Calculate the predicted measurement value: （28） In the formula, To measure the predicted value; Step 3.2.10, calculate the measurement error covariance and cross-covariance: （29） In the formula, express k The measurement error covariance of the observed variable at time +1, The cross-covariance between state variables and observed variables; Step 3.2.11: Calculate the Kalman gain, update the state variables and the corresponding error covariance: （30） In the formula, Indicates Kalman gain, This represents the updated state value. P k+1 This represents the updated error covariance matrix.

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