An online parameter identification method for sodium-ion energy storage batteries based on maximum correlation entropy

Abstract

The present invention belongs to the field of parameter identification technology and discloses a method for online parameter identification of sodium-ion energy storage batteries based on maximum correlation entropy. The method comprises: establishing a first-order Thevenin model of the sodium-ion energy storage battery; obtaining a discrete time-domain model of the sodium-ion energy storage battery based on the first-order Thevenin model; and constructing a cost function using a maximum correlation entropy criterion based on a Gaussian kernel function to estimate the parameters of the discrete time-domain model, thereby obtaining the sodium-ion energy storage battery parameters and completing parameter identification of the sodium-ion energy storage battery. The identification method of the present invention can suppress impulse noise under energy storage conditions, achieve accurate and robust parameter estimation, and simultaneously ensure the convergence speed of the parameter estimator.

Description

Technical Field

[0001] The present invention belongs to the technical field of parameter identification, and more specifically, relates to an online parameter identification method for sodium ion energy storage batteries based on maximum correlation entropy. Background Art

[0002] In recent years, with resource and environmental issues becoming increasingly prominent, accelerating energy transformation is imperative. The integration of a high proportion of renewable energy sources poses severe challenges to the power-energy balance of power systems across multiple timescales. Large-scale application of energy storage technologies is an effective means of addressing the issue of power supply and demand balance. Among these, electrochemical energy storage technology, with its advantages of flexible configuration, rapid response, and efficient energy conversion, has taken the lead in achieving large-scale application. Currently, lithium-ion batteries dominate both the power battery and energy storage battery sectors due to their high energy density, long cycle life, low self-discharge rate, and lack of memory effect. However, safety performance and production costs remain two key issues that hinder the large-scale application of lithium-ion batteries in the energy storage sector. Sodium-ion energy storage batteries, with their high safety, low cost, and long life, are expected to become an important complement to lithium-ion battery technology. Therefore, online identification of sodium-ion energy storage battery parameters is of great research significance.

[0003] Currently, research on sodium-ion energy storage battery modeling and parameter identification is just beginning, and essentially still follows the research methods used in the lithium-ion battery field. Battery model performance verification is mostly conducted under constant current conditions, standard dynamic conditions, and actual vehicle driving conditions. However, changes in battery systems and application scenarios indicate different optimization requirements for models and algorithms. Energy storage battery operating conditions are completely different from power battery operating conditions, and the current magnitude and direction frequently undergo sudden changes, which places higher demands on the convergence and robustness of parameter identification algorithms.

[0004] Currently, online parameter identification methods for power battery operation include the least squares method and the Kalman filter, all of which are based on the minimum mean square error (MMSE) criterion. These filters share a common characteristic: they place strict demands on the statistical distribution of noise. While they achieve optimal filtering performance under Gaussian noise conditions, they suffer from severe performance degradation under impulse noise. Under energy storage battery operation, the frequent sudden changes in current magnitude and direction make it difficult for the statistical distribution of noise to conform to a Gaussian noise distribution. Furthermore, current spikes in energy storage frequency modulation (FSM) operation can generate impulse noise in the voltage prediction error, compromising the accuracy and robustness of estimation algorithms based on the MMSE criterion. Consequently, directly employing an MMSE-based estimation algorithm under sodium-ion battery operation can have two negative consequences: First, the impulse noise generated under sodium-ion battery conditions can perturb converged model parameters, causing short-lived, large-amplitude oscillations in parameter estimates, or even significant deviations from their normal values. Second, impulse noise can lead to an abnormal growth of the covariance matrix in the state estimator, weakening the stability of the recursive filter or observer. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy, which aims to improve the accuracy and identification stability of online identification of sodium ion energy storage battery parameters.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy is provided, comprising:

[0007] S1. Establish a first-order Thevenin model of sodium-ion energy storage battery: including the series voltage source U OC , ohmic internal resistance R0 and R1C1 circuit consisting of resistor C1 and capacitor C1 in parallel; where U OC It represents the open circuit voltage of the sodium ion energy storage battery, and R0 represents the resistance of the electrodes, electrolyte, and diaphragm to Na + The R1C1 circuit represents the polarization effect of the sodium ion energy storage battery;

[0008] S3. Based on the first-order Thevenin model, a discrete time domain model of the sodium ion energy storage battery is obtained:

[0009] U t,k -U OC,k =a0I k +a1I k-1 +b1(U t,k-1 -U OC,k-1 ), k≥2

[0010] Among them, U t,k、U OC,k , I k Corresponding to the terminal voltage U of the sodium ion energy storage battery t , open circuit voltage U OC , the kth sampling value of the current I; and the parameters a0, a1, b1 satisfy:

[0011]

[0012] Where T is the preset sampling period, τ1=R1C1;

[0013] S3. A cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to estimate the parameters a0, a1, and b1 of the discrete time domain model, thereby obtaining the parameters R0, R1, and C1 of the sodium-ion energy storage battery and completing the parameter identification of the sodium-ion energy storage battery.

[0014] Furthermore, in S3, the cost function constructed using the maximum correlation entropy criterion based on the Gaussian kernel function is:

[0015]

[0016] Where, represents the correlation entropy based on the Gaussian kernel function, σ is the kernel length of the Gaussian kernel function, and λ represents the forgetting factor; represents θ k The estimated value of θ k 、φ k 、y k The parameter matrix, input matrix and output matrix corresponding to the discrete time domain model are: θ k =[a 0,k a 1,k b 1,k ] T ,φ k =[I k I k-1 U t,k-1 -U OC,k-1 ] T ,y k =U t,k -U OC,k ; Among them, a 0,k 、a 1,k 、b 1,k Correspondingly represents the estimated values ​​of parameters a0, a1, and b1 at the kth sampling time.

[0017] Furthermore, the cost function is used to estimate the parameters a0, a1, and b1 of the discrete time domain model, including:

[0018] With the related entropy The maximum is the optimization goal, and the following recursive formula is used to solve θ in real time k Estimates

[0019]

[0020] Among them, P k represents the covariance matrix of the kth sampling; K k is the gain matrix,

[0021] Furthermore, in S2, based on the first-order Thevenin model, a discrete time domain model of the sodium ion energy storage battery is obtained, including:

[0022] Determine the continuous time domain model of sodium-ion energy storage batteries based on the first-order Thevenin model;

[0023] Performing a Laplace transform on the continuous time-domain model to obtain a corresponding continuous transfer function H(s); and performing a bilinear transform on the continuous transfer function H(s) to obtain a corresponding discrete transfer function H(z);

[0024] The discrete time domain model is determined using the discrete transfer function H(z).

[0025] Furthermore, the input matrix φ k Middle,U OC,k-1 Determined as follows:

[0026] Obtain the OCV-SoC function relationship of the sodium ion energy storage battery; where OCV represents the open circuit voltage U OC , SoC represents the state of charge;

[0027] The open circuit voltage value U is obtained by the OCV-SoC function relationship OC,k-1 .

[0028] Furthermore, the OCV-SoC function relationship of the sodium-ion energy storage battery is obtained, including:

[0029] Conduct low-current charge and discharge experiments on sodium-ion energy storage batteries to obtain the relationship between the open-circuit voltage and state of charge during discharge, and the relationship between the open-circuit voltage and state of charge during charge.

[0030] The open circuit voltage during charging and the open circuit voltage during discharging at the same state of charge are averaged to obtain a curve showing the relationship between the average open circuit voltage and the state of charge.

[0031] A polynomial fitting is performed on the relationship curve between the average open circuit voltage and the state of charge to obtain the OCV-SoC function relationship.

[0032] Furthermore, performing polynomial fitting on the relationship curve between the average open circuit voltage and the state of charge includes:

[0033] Between 10% and 95% of the SoC, with 35% SoC as the boundary, a piecewise second-order polynomial fitting is performed on the relationship curve between the average open circuit voltage and the state of charge.

[0034] According to a second aspect of the present invention, there is provided an electronic device comprising a computer-readable storage medium and a processor;

[0035] The computer-readable storage medium is used to store executable instructions;

[0036] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the online identification method of sodium-ion energy storage battery parameters as described in any one of the first aspects.

[0037] According to a third aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the method for online identification of sodium-ion energy storage battery parameters as described in any one of the first aspects is implemented.

[0038] According to a fourth aspect of the present invention, a computer program product is provided, comprising a computer program, which, when executed on a computer, enables the computer to execute the method for online identification of sodium ion energy storage battery parameters according to any one of the first aspects.

[0039] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0040] (1) The present invention's method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy, for sodium ion energy storage battery, first establishes a first-order Thevenin model of sodium ion energy storage battery, and converts the open circuit voltage U OC , electrodes, electrolytes, and diaphragms have a great influence on the Na + The obstruction effect of the sodium ion energy storage battery and the polarization effect of the sodium ion energy storage battery are characterized as a first-order equivalent circuit, and the discrete time domain model of the sodium ion energy storage battery is determined based on the first-order equivalent circuit. The cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to perform online identification of the sodium ion energy storage battery parameters. When the impulse noise comes, that is, the input parameters in the discrete time domain model of the sodium ion energy storage battery [I k I k-1 U t,k-1 -U OC,k-1 ] TAfter the Gaussian kernel function (exponential function) is applied to the impulse noise caused by the current spikes contained in , the corresponding cost function increment tends to 0, thus having no substantial impact on parameter estimation. Thus, the cost function constructed using the maximum correlation entropy criterion based on the Gaussian kernel function effectively suppresses impulse noise, thereby achieving accurate and robust parameter estimation, improving the accuracy and stability of online parameter identification for sodium-ion energy storage batteries.

[0041] (2) Furthermore, the present invention uses the correlation entropy based on the Gaussian kernel function to measure the output measurement value y under the working condition of the sodium ion energy storage battery. k and output estimates The cost function for parameter identification of sodium ion energy storage batteries is defined based on the maximum correlation entropy criterion of the Gaussian kernel function. That is, the model error at the current moment is evaluated under the correlation entropy induced distance based on the Gaussian kernel function. In this way, when the impulse noise comes, Rapidly increases, after the exponential function, the corresponding cost function tends to 0, The contribution of can be ignored, thus achieving the suppression of impulse noise.

[0042] (3) Furthermore, the present invention uses the correlation entropy The maximum is the optimization objective, and a corresponding recursive formula is designed. This formula is used for iterative solution, and the newly obtained data is used to correct the original estimated value. This can achieve real-time online parameter updates without storing large amounts of data, occupying a small amount of computer memory. It can achieve real-time, high-precision, robust parameter estimation of sodium-ion energy storage battery models under energy storage frequency modulation conditions. At the same time, the data selection mechanism established by the maximum relevant entropy criterion is spontaneous, without introducing any new parameters or steps into the recursive formula. The algorithm complexity is the same as that of the traditional least squares algorithm. That is, the method of the present invention improves the accuracy and stability of online identification of sodium-ion energy storage battery parameters while not affecting the identification speed compared to traditional methods.

[0043] (4) As a preference, considering that the batteries in the battery energy storage system serve as a frequency control backup, the SoC operating range is limited to between 10% and 95% of the SoC, and within this range, the OCV-SoC curve of the sodium-ion energy storage battery is close to linear, which is convenient for fitting; a piecewise second-order polynomial fitting is adopted, and the order of the polynomial fitting is low, and the amount of calculation is small.

[0044] In summary, the online parameter identification method of the sodium-ion energy storage battery of the present invention is based on the constructed first-order Thevenin model of the sodium-ion energy storage battery and its discrete time domain model, and uses the maximum correlation entropy criterion to construct a cost function, so that under the battery energy storage condition, when a current spike occurs, the identification algorithm can suppress the pulse noise, achieve accurate and robust parameter estimation, and ensure the convergence speed of the parameter estimator. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of an online parameter identification method for sodium-ion energy storage batteries based on maximum correlation entropy in an embodiment of the present invention.

[0046] Figure 2 This is a schematic diagram of a specific process for identifying unknown parameters of a sodium-ion battery using the maximum correlation entropy algorithm in an embodiment of the present invention.

[0047] Figure 3 This is the OCV-SoC curve fitting result in the embodiment of the present invention.

[0048] Figure 4 Graphs showing changes in load current, battery voltage, and SoC during testing of an embodiment of the present invention; (a)-(h) in the figure correspond to curves showing current and voltage changes over time for randomly selected days 82, 318, 76, and 336 of the annual reference current operating condition for energy storage frequency regulation; (i) shows curves showing SoC changes over time for days 82, 318, 76, and 336.

[0049] Figure 5 Graphs showing the identification results of the ohmic internal resistance R0 obtained using different identification methods in an embodiment of the present invention; (a)-(d) respectively represent the identification results of the ohmic internal resistance R0 on the 82nd day, the 318th day, the 76th day, and the 336th day. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0051] Example 1

[0052] like Figure 1 As shown, an embodiment of the present invention provides a method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy, which mainly includes:

[0053] S1. Establish a first-order Thevenin model of sodium-ion energy storage battery. The model includes a voltage source U OC , an ohmic internal resistance R0 and an R1C1 circuit consisting of a resistor R1 and a capacitor C1 in parallel; wherein the voltage source U OC , an ohmic internal resistor R0 and R1C1 circuit connected in series; voltage source U OC It represents the open circuit voltage of the sodium ion energy storage battery, and the ohmic internal resistance R0 represents the resistance of the electrodes, electrolyte, and diaphragm in the sodium ion energy storage battery to Na + The R1C1 network represents the polarization effect of sodium ion energy storage batteries;

[0054] S2. Based on the first-order Thevenin model, the discrete time domain model of the sodium-ion energy storage battery is obtained:

[0055] U t,k -U OC,k =a0I k +a1I k-1 +b1(U t,k-1 -U OC,k-1 ), k≥2

[0056] Among them, U t,k Indicates the terminal voltage U of the sodium ion energy storage battery t The value of the kth sampling, U OC,k Indicates the open circuit voltage U of the sodium ion energy storage battery OC The value of the k-th sampling, I k represents the value of the kth sampling of the current I of the sodium ion energy storage battery. Correspondingly, U t,k-1 、U OC,k-1 , I k-1 Respectively represent the t 、U OC , I performs the k-1th sampling value; parameters a0, a1, b1 satisfy:

[0057]

[0058] Where T is the preset sampling period, which represents the time interval between two adjacent samplings.

[0059] As a preferred implementation method, based on the first-order Thevenin model, a discrete time domain model of the sodium ion energy storage battery is obtained, including:

[0060] S21. Based on the first-order Thevenin model, the continuous time domain model of the sodium-ion energy storage battery is determined as:

[0061]

[0062] Among them, U1(t) is the polarization voltage of the sodium ion energy storage battery at time t, Ut (t) is the terminal voltage of the sodium ion energy storage battery at time t, U OC (t) is the open circuit voltage of the sodium ion energy storage battery at time t, and I(t) is the current of the sodium ion energy storage battery at time t.

[0063] S22. Perform Laplace transform on the continuous time domain model of the sodium ion energy storage battery to obtain the corresponding continuous transfer function H(s):

[0064]

[0065] Where U t (s), U OC (s), I(s) correspond to U t (t), U OC (t), U OC Laplace transform of (t); s is a complex variable, τ1 is the time constant, τ1 = R1C1.

[0066] S23. Perform bilinear transformation on the continuous transfer function H(s) to obtain the corresponding discrete transfer function H(z):

[0067]

[0068]

[0069] Where T is the preset sampling period, which represents the time interval between two adjacent samplings; a0, a1, and b1 are the parameters to be identified.

[0070] S23. Determine the discrete time domain model of the sodium ion energy storage battery based on the discrete transfer function H(z):

[0071] U t,k -U OC,k =a0I k +a1I k-1 +b1(U t,k-1 -U OC,k-1 ), k≥2

[0072] Among them, the parameter mapping relationship between the discrete time domain model and the continuous time domain model is:

[0073]

[0074] S3. A cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to estimate the parameters a0, a1, and b1, thereby obtaining the sodium-ion energy storage battery parameters R0, R1, and C1, and completing the sodium-ion energy storage battery parameter identification.

[0075] As a preferred implementation, Figure 2As shown, in the embodiment of the present invention, a cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to estimate the parameters a0, a1, and b1, including:

[0076] S31. Write the discrete time domain model of the sodium ion energy storage battery in matrix form:

[0077] System parameter matrix: θ k =[a 0,k a 1,k b 1,k ] T ;

[0078] System input matrix: φ k =[I k I k-1 U t,k-1 -U OC,k-1 ] T ;

[0079] System output matrix: y k =U t,k -U OC,k ;

[0080] System news:

[0081] Among them, a 0,k 、a 1,k 、b 1,k The corresponding values ​​are the estimated values ​​of a0, a1, and b1 at the kth iteration, that is, the parameters to be identified corresponding to the kth sampling. The kth iteration corresponds to the kth sampling. θ k-1 estimate.

[0082] Among them, the system input matrix φ k Middle,U OC,k-1 Determined as follows:

[0083] Obtain the OCV-SoC function relationship of the sodium ion energy storage battery; where OCV represents the open circuit voltage U OC , SoC represents the state of charge;

[0084] The open circuit voltage value U is obtained through the OCV-SoC function relationship OC,k-1 .

[0085] As a preferred implementation, a low current method is used to establish the OCV-SoC function relationship, including:

[0086] Carry out a small current charge and discharge experiment. The specific process is as follows:

[0087] Fully charge the sodium ion energy storage battery using the standard charging method and let it sit for a period of time tm After a period of 30 minutes (for example, 30 minutes), the battery is discharged at a low rate (for example, 0.05C) to a preset lower cutoff voltage V1 (for example, 2V), and the relationship between the open circuit voltage OCV and the state of charge SoC of the sodium ion energy storage battery during discharge is obtained; wherein, the open circuit voltage OCV is the above-mentioned U OC ;

[0088] Let the sodium ion energy storage battery stand for a period of time t m Then, the voltage is charged from the preset lower cut-off voltage V1 to the preset upper cut-off voltage V2 (for example, 3.95V) at the same rate to obtain the relationship between the open circuit voltage OCV and the state of charge SoC when the sodium ion energy storage battery is charged;

[0089] The average open circuit voltage (OCV) during charging and the open circuit voltage (OCV) during discharging under the same state of charge (SoC) are taken to obtain the average OCV-SoC curve.

[0090] The average OCV-SoC curve was fitted with a polynomial to obtain the desired OCV-SoC functional relationship.

[0091] Preferably, a polynomial fitting is performed on the average OCV-SoC curve to obtain the desired OCV-SoC functional relationship, including:

[0092] Because the batteries in the battery energy storage system serve as a backup for frequency control, the SoC operating range is limited to between 10% and 95% of the SoC. Furthermore, within this range, the OCV-SoC curve of the sodium-ion energy storage battery is close to linear, making it easy to fit. Therefore, when fitting the average OCV-SoC curve, the fitting range is 10% ≤ SoC ≤ 95%;

[0093] A piecewise second-order polynomial fit was performed on the average OCV-SoC curve, using 35% SoC as the boundary, to obtain the desired OCV-SoC curve. In the embodiments of the present invention, experimental measurements showed that a piecewise second-order polynomial fit of the average OCV-SoC curve, using 35% SoC as the boundary, resulted in a lower order polynomial fit and a smaller computational effort.

[0094] In the embodiment of the present invention, a piecewise second-order polynomial fitting is performed on the average OCV-SoC curve with 35% SoC as the boundary, that is:

[0095]

[0096] Among them, k1, k2, ..., k6 are fitting coefficients, OCV represents the open circuit voltage U OC (t).

[0097] The fitted OCV-SOC curve is as follows: Figure 3 shown.

[0098] S32. The cost function constructed using the maximum correlation entropy criterion based on the Gaussian kernel function is:

[0099]

[0100] Where, represents the correlation entropy based on the Gaussian kernel function, represents θ k , σ is the kernel length of the Gaussian kernel function, and λ represents the forgetting factor.

[0101] S33, with correlation entropy The maximum optimization goal is:

[0102]

[0103] S34. Use the following recursive formula to solve the parameter value that maximizes the correlation entropy and obtain the estimated values ​​of a0, a1, and b1 at each sampling time:

[0104]

[0105] Among them, P k represents the covariance matrix of the kth iteration, P k-1 It represents the covariance matrix of the k-1th iteration. Its initial value is assigned through experience and is usually the unit matrix. The kth iteration corresponds to the kth sampling, that is, one iteration is performed for each sampling. When performing online parameter identification, the parameters can be updated in real time according to this iterative formula. The initial value of can be any value in theory, usually 0, or it can be calculated as the initial value by the existing conventional offline identification algorithm to speed up the convergence of the model; k is an intermediate variable, representing the gain matrix. ω represents the parameter related to the core length σ,

[0106] According to the above recursive formula, the estimated values ​​of a0, a1, and b1 for each sampling can be obtained , and put it into the following formula to obtain the unknown parameters R0, R1 and C1 of the first-order equivalent circuit of the sodium ion energy storage battery:

[0107]

[0108] In the embodiment of the present invention, the correlation entropy of two random variables can be used to measure the closeness between the two random variables X and Y. It is defined as:

[0109]

[0110] Where x and y are the values ​​of random variables X and Y; E[·] is the expected value; F X,Y (x,y) is the joint distribution function of X and Y; G σ (·) is a kernel function with a kernel length of σ. If the kernel function is a Gaussian kernel function, then:

[0111]

[0112] Based on this, under the working condition of sodium ion energy storage battery, the output measurement value y is measured by the correlation entropy based on Gaussian kernel function. k and output estimates The cost function for parameter identification of sodium ion energy storage batteries is defined based on the maximum correlation entropy criterion of the Gaussian kernel function. for:

[0113]

[0114] In this way, the embodiment of the present invention no longer uses the Euclidean distance to measure the model error at a certain moment. Instead of evaluating the size of the model at the current moment, the model error is evaluated based on the correlation entropy induced distance of the Gaussian kernel function. When the impulse noise comes, Increases rapidly, and after the exponential function is applied, the corresponding cost function increment tends to 0. The contribution of is negligible and therefore has no substantial impact on parameter estimation, effectively automatically filtering out the noise data. In other words, after constructing the cost function using the maximum correlation entropy criterion, the parameter estimator implicitly incorporates data selection capabilities. This feature is crucial for real-time parameter estimation of battery models under energy storage frequency regulation conditions. The impulse noise suppression it provides is a crucial prerequisite for accurate and robust parameter estimation.

[0115] The kernel length σ is a key parameter that determines the algorithm's performance. When σ approaches infinity, the maximum correlated entropy algorithm degenerates into a least squares algorithm and loses its ability to filter noise. Conversely, when σ approaches zero, all noise is filtered indiscriminately, halting real-time parameter updates. By controlling the kernel length σ, reducing it can enhance noise suppression capabilities, but it also slows the convergence of the parameter estimator. Therefore, the kernel length selection requires a trade-off between the algorithm's real-time performance and stability based on actual needs.

[0116] The recognition effect of the method of the present invention is further illustrated below with specific examples.

[0117] From the annual reference current conditions for energy storage frequency regulation established in existing technologies, we randomly selected the current curves of four days and scaled them to the single cell scale for testing. Figure 4The changes in load current, battery voltage, and SoC during the test are shown. The model parameters are identified online using the Recursive Least Square (RLS) algorithm with a forgetting factor and the Recursive Maximum Correntropy (RMC) algorithm designed by the present invention. Both methods are initialized according to Table 1, with the kernel lengths set to σ1 = 0.5912 mV, σ2 = 0.9008 mV, and σ3 = 1.5877 mV, respectively. The identification results of the ohmic internal resistance R0 are shown in Figure 1. Figure 5 As shown in the figure, RMC demonstrates its excellent anti-interference performance. When using RLS for online parameter identification, the estimated R0 value often experiences jitter due to abnormal noise, and in severe cases, can even deviate significantly from the normal range. However, RMC completely eliminates this jitter, maintaining a smooth curve.

[0118] Based on the identification results, voltage prediction was performed. Table 2 shows the prediction results, using mean absolute error (MAE) and root mean square error (RMSE) as metrics. This evaluates the voltage prediction accuracy of the battery model when using RLS and RMC for online parameter identification. Compared to RLS, at low noise suppression strength (σ = σ3), RMC not only significantly improves the robustness of the parameter estimation algorithm but also achieves further improvements in model accuracy. Therefore, RMC is a more reasonable and appropriate choice for parameter estimation of battery models under energy storage frequency regulation conditions.

[0119] Table 1 Parameter identification initial value setting

[0120]

[0121] Table 2 Voltage prediction results

[0122]

[0123] The present invention takes into account that directly using an estimation algorithm based on the minimum mean square error criterion under the operating conditions of sodium-ion energy storage batteries will result in serious performance degradation under impulse noise conditions. This is because the minimum mean square error criterion is based on a cost function designed based on second-order statistics, which inevitably experiences explosive growth at the moment of the current spike. Since forgetting is gradual, this instantaneous change will have a lasting impact for a period of time afterwards, forcing the parameter estimator to re-enter the dynamic convergence process. Directly applying it to the identification of sodium-ion energy storage battery parameters will affect the accuracy and identification stability of the online identification of sodium-ion energy storage battery parameters.

[0124] Based on this, for sodium ion energy storage batteries, the present invention first establishes a first-order Thevenin model of sodium ion energy storage batteries, and converts the open circuit voltage U OC , electrodes, electrolytes, and diaphragms have a great influence on the Na + The obstruction effect of the sodium ion energy storage battery and the polarization effect of the sodium ion energy storage battery are characterized as a first-order equivalent circuit, and the discrete time domain model of the sodium ion energy storage battery is determined based on the first-order equivalent circuit. The cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to perform online identification of the sodium ion energy storage battery parameters. When the impulse noise comes, that is, the input parameters in the discrete time domain model of the sodium ion energy storage battery [I k I k-1 U t,k-1 -U OC,k-1 ] T After the Gaussian kernel function (exponential function) is applied to the impulse noise caused by the current spikes contained in , the corresponding cost function increment tends to 0, thus having no substantial impact on parameter estimation. Thus, the cost function constructed using the maximum correlation entropy criterion based on the Gaussian kernel function effectively suppresses impulse noise, thereby achieving accurate and robust parameter estimation, improving the accuracy and stability of online parameter identification for sodium-ion energy storage batteries.

[0125] The present invention uses the maximum correlation entropy criterion to identify the parameters of sodium-ion energy storage batteries. After constructing the cost function using the maximum correlation entropy criterion, the parameter estimator implicitly contains the ability to select data and has the ability to suppress impulse noise. This not only significantly improves the robustness of the parameter estimation algorithm, but also achieves further improvement in model accuracy. Real-time, high-precision, robust parameter estimation of the sodium-ion energy storage battery model can be achieved under energy storage frequency modulation conditions. At the same time, the data selection mechanism established by the maximum correlation entropy criterion is spontaneous, and there is no need to introduce any new parameters or steps into the recursive algorithm. The algorithm complexity is the same as the traditional least squares algorithm. That is, the method of the present invention improves the accuracy and stability of online identification of sodium-ion energy storage battery parameters while not affecting the identification speed compared with traditional methods.

[0126] Example 2

[0127] An embodiment of the present invention provides an electronic device including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the above-mentioned method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy.

[0128] The electronic device may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The processor may be a central processing unit (CPU), or other general-purpose processors, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory may be used to store computer programs and / or modules, and the processor may perform various functions of the electronic device by running or executing the computer programs and / or modules stored in the memory, and calling the data stored in the memory.

[0129] The relevant technical solutions are the same as above and will not be repeated here.

[0130] Example 3

[0131] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the above-mentioned method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy is implemented.

[0132] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0133] The relevant technical solutions are the same as above and will not be repeated here.

[0134] Example 4

[0135] The present application provides a computer program product, including a computer program, which, when executed on a computer, enables the computer to execute the above-mentioned method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy.

[0136] The relevant technical solutions are the same as above and will not be repeated here.

[0137] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for online identification of sodium ion energy storage battery parameters based on maximum correlation entropy, characterized in that: include: S1. Establish a first-order Thevenin model of sodium-ion energy storage battery: including the series voltage source U OC , ohmic internal resistance R0 and R1C1 circuit consisting of resistor R1 and capacitor C1 in parallel; Among them, U OC represents the open circuit voltage of the sodium ion energy storage battery, R0 represents the resistance of the electrodes, electrolyte, and diaphragm to Na + The R1C1 circuit represents the polarization effect of the sodium ion energy storage battery; S2. Based on the first-order Thevenin model, a discrete time domain model of the sodium ion energy storage battery is obtained: IN t,k -IN OC,k =a0I k +a1I k-1 +b1(U t,k-1 -IN OC,k-1 ),k≥2 Among them, U t,k 、U OC,k , I k Corresponding to the terminal voltage U of the sodium ion energy storage battery t , open circuit voltage U OC , the kth sampling value of the current I; and the parameters a0, a1, b1 satisfy: Where T is the preset sampling period, τ1=R1C1; S3. A cost function is constructed using the maximum correlation entropy criterion based on the Gaussian kernel function to estimate the parameters a0, a1, and b1 of the discrete time domain model, thereby obtaining the parameters R0, R1, and C1 of the sodium-ion energy storage battery and completing the parameter identification of the sodium-ion energy storage battery.

2. The method for online identification of sodium ion energy storage battery parameters according to claim 1, characterized in that: In S3, the cost function constructed using the maximum correlation entropy criterion based on the Gaussian kernel function is: Where, represents the correlation entropy based on the Gaussian kernel function, σ is the kernel length of the Gaussian kernel function, and λ represents the forgetting factor; represents θ k The estimated value of θ k 、φ k 、y k The parameter matrix, input matrix and output matrix corresponding to the discrete time domain model are: θ k =[a 0,k a 1,k b 1,k ] T ,φ k =[I k I k-1 U t,k-1 -U OC,k-1 ] T ,y k =U t,k -U OC,k ; Among them, a 0,k 、a 1,k 、b 1,k Correspondingly represents the estimated values ​​of parameters a0, a1, and b1 at the kth sampling time.

3. The method for online identification of sodium ion energy storage battery parameters according to claim 2, characterized in that: The cost function is used to estimate the parameters a0, a1, and b1 of the discrete time domain model, including: With the related entropy The maximum is the optimization goal, and the following recursive formula is used to solve θ in real time k Estimates Among them, P k represents the covariance matrix of the kth sampling; K k is the gain matrix, 4. The method for online parameter identification of a sodium ion energy storage battery according to any one of claims 1 to 3, characterized in that: In S2, based on the first-order Thevenin model, a discrete time domain model of the sodium ion energy storage battery is obtained, including: Determine the continuous time domain model of sodium-ion energy storage batteries based on the first-order Thevenin model; Performing a Laplace transform on the continuous time-domain model to obtain a corresponding continuous transfer function H(s); and performing a bilinear transform on the continuous transfer function H(s) to obtain a corresponding discrete transfer function H(z); The discrete time domain model is determined using the discrete transfer function H(z).

5. The method for online identification of sodium ion energy storage battery parameters according to claim 2 or 3, characterized in that: Input matrix φ k Middle,U OC,k-1 Determined as follows: Obtain the OCV-SoC function relationship of the sodium ion energy storage battery; where OCV represents the open circuit voltage U OC , SoC represents the state of charge; The open circuit voltage value U is obtained by the OCV-SoC function relationship OC,k-1 .

6. The method for online identification of sodium ion energy storage battery parameters according to claim 5, characterized in that Obtain the OCV-SoC function relationship of sodium-ion energy storage batteries, including: Conduct low-current charge and discharge experiments on sodium-ion energy storage batteries to obtain the relationship between the open-circuit voltage and state of charge during discharge, and the relationship between the open-circuit voltage and state of charge during charge. The open circuit voltage during charging and the open circuit voltage during discharging at the same state of charge are averaged to obtain a curve showing the relationship between the average open circuit voltage and the state of charge. A polynomial fitting is performed on the relationship curve between the average open circuit voltage and the state of charge to obtain the OCV-SoC function relationship.

7. The method for online identification of sodium ion energy storage battery parameters according to claim 6 is characterized in that: Performing a polynomial fitting on the relationship curve between the average open circuit voltage and the state of charge includes: Between 10% and 95% of the SoC, with 35% SoC as the boundary, a piecewise second-order polynomial fitting is performed on the relationship curve between the average open circuit voltage and the state of charge.

8. An electronic device, characterized in that: comprising a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the online identification method for sodium ion energy storage battery parameters according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the online parameter identification method of a sodium ion energy storage battery according to any one of claims 1 to 7 is implemented.

10. A computer program product, characterized in that The invention comprises a computer program, which, when running on a computer, enables the computer to execute the method for online identification of sodium ion energy storage battery parameters according to any one of claims 1 to 7.

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