A cross-scale multi-state joint estimation method for supercapacitors

Abstract

The present invention discloses a cross-scale multi-state joint estimation method suitable for supercapacitors, comprising: S1, performing characteristic testing on supercapacitors, S2, establishing a supercapacitor model, and S3, performing cross-scale multi-state joint estimation on supercapacitors. A cross-scale multi-state joint estimation method suitable for supercapacitors adopts the above technical solution, firstly optimizes the supercapacitor model and obtains the optimal parameters of the supercapacitor model, and then combines two extended Kalman filters, which can not only predict the charge state of the supercapacitor from a microscopic scale, but also update the equivalent internal resistance and capacity state from a macroscopic scale. Therefore, this method not only greatly improves the estimation accuracy, but also greatly improves the operating efficiency of the supercapacitor system.

Description

Technical Field

[0001] The present invention relates to the technical field of supercapacitors, and in particular to a cross-scale multi-state joint estimation method applicable to supercapacitors. Background Art

[0002] Supercapacitors, as a new generation of energy storage components, are widely used in electrochemical energy storage systems due to their excellent properties. However, to fully leverage the advantages of supercapacitors and optimize their performance for energy storage systems, the first challenge is how to accurately estimate their state of charge (SOC). Currently, model-based state observer methods are favored by many experts and scholars. However, in these model-based state observer methods, supercapacitor model parameters are mostly generated through offline identification or theoretical values. This does not conform to the actual usage patterns of supercapacitors. Supercapacitors are constantly affected by the operating environment and aging factors during operation, and model parameters will also change accordingly. The most direct manifestation of this is changes in their equivalent internal resistance and capacitance. Therefore, using fixed parameter values ​​will seriously affect the accuracy of SOC estimation.

[0003] Solving the above problems has become a top priority. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a cross-scale multi-state joint estimation method suitable for supercapacitors.

[0005] The technical solution is as follows:

[0006] A cross-scale multi-state joint estimation method for supercapacitors is mainly based on the following steps:

[0007] S1. Perform characteristic tests on the supercapacitor to obtain the basic parameters of the supercapacitor and determine the relationship between the maximum available capacity and temperature. Follow the steps below:

[0008] S11. Conduct a maximum available capacity test on the supercapacitor;

[0009] S12. Conducting a mixed power pulse characteristic test experiment on the supercapacitor;

[0010] S13. Conducting urban road cycle test experiments on the supercapacitor;

[0011] S14. Obtain basic parameters of the supercapacitor based on the maximum available capacity test experiment, the mixed power pulse characteristic test experiment, and the urban road cycle test experiment, thereby determining the relationship between the maximum available capacity of the supercapacitor and temperature;

[0012] S2. Build a supercapacitor model by following these steps:

[0013] S21. Based on the Thevenin model, a supercapacitor model is obtained;

[0014] S22, determining the relationship between the state of charge and the open circuit voltage;

[0015] S23. Use the simulated annealing algorithm combined with the experimental data of the mixed power pulse characteristic test experiment to obtain the optimal parameters of the model.

[0016] S3. Jointly estimate the supercapacitor's multi-state across scales by following the steps below:

[0017] S31. Establish a nonlinear system equation of supercapacitor based on supercapacitor model;

[0018] S32. Perform cross-scale multi-state joint estimation based on double extended Kalman filtering for the nonlinear system equations of supercapacitors.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] A cross-scale multi-state joint estimation method suitable for supercapacitors using the above technical solution first optimizes the supercapacitor model and obtains the optimal parameters of the supercapacitor model. Then, combined with two extended Kalman filters, it can not only predict the charge state of the supercapacitor from a microscopic scale, but also update the equivalent internal resistance and capacity state from a macroscopic scale. Therefore, this method not only greatly improves the estimation accuracy, but also greatly improves the operating efficiency of the supercapacitor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of the present invention;

[0022] Figure 2 It is the Thevenin model;

[0023] Figure 3 Graph showing the state of charge (SOC) and voltage estimation results for comparative example 1;

[0024] Figure 4 Graph showing the capacity and ohmic internal resistance estimation results for Comparative Example 1;

[0025] Figure 5 Graph showing the state of charge (SOC) and voltage estimation results of Example 1;

[0026] Figure 6 This is a diagram showing the capacity and ohmic internal resistance estimation results of Example 1. DETAILED DESCRIPTION

[0027] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0028] like Figure 1 As shown in FIG, a cross-scale multi-state joint estimation method suitable for supercapacitors is performed in the following steps:

[0029] S1. Perform characteristic test on supercapacitor.

[0030] By performing characteristic tests on supercapacitors, the basic parameters of the supercapacitor can be obtained, including a series of voltage and current data, and the relationship between the maximum available capacity and temperature can be determined. Specifically, follow the steps below:

[0031] S11. Perform a maximum available capacity test on the supercapacitor, specifically following the steps below:

[0032] S111 , leaving the supercapacitor to stand at a set temperature and time. In this embodiment, the standing time is 10 hours.

[0033] S112. Discharge the supercapacitor with a current of 1 A to a lower cutoff voltage of 0.5 V.

[0034] S113, leaving the supercapacitor to stand for a set time. In this embodiment, the standing time is 10 minutes.

[0035] S114. Charge the supercapacitor with a constant current and constant voltage of 1A to an upper cutoff voltage of 2.7V until the current is less than 0.05A.

[0036] S115, leaving the supercapacitor to stand for a set time. In this embodiment, the standing time is 60 minutes.

[0037] S116. Discharge the supercapacitor with a constant current of 1A to a lower cutoff voltage of 0.5V.

[0038] S117, leaving the supercapacitor to stand for a set time. In this embodiment, the standing time is 60 minutes.

[0039] S118. Repeat steps S111-S117 according to the set number of cycles. In this embodiment, the number of cycles is 3 times.

[0040] S12. Conduct a mixed power pulse characteristic test experiment on the supercapacitor, specifically according to the following steps:

[0041] S121. The supercapacitor is allowed to stand at a set temperature and time. In this embodiment, the standing time is 10 hours.

[0042] S122. Charge the supercapacitor with a constant current and constant voltage of 1A to an upper cutoff voltage of 2.7V until the current is less than 0.05A.

[0043] S123, first, discharge the supercapacitor with a current of 1A for a set time, the discharge time in this embodiment is 5s, and then let it stand for a set time, the standby time in this embodiment is 10s, then charge the supercapacitor with a current of 1A for a set time, the charging time in this embodiment is 5s, and then let it stand for a set time, the standby time in this embodiment is 10s, then discharge the supercapacitor with a current of 5A for a set time, the discharge time in this embodiment is 5s, and then let it stand for a set time, the standby time in this embodiment is 10s, and then charge the supercapacitor with a current of 5A for a set time, the discharge time in this embodiment is 5s, and then let it stand for a set time, the standby time in this embodiment is 10s, and then charge the supercapacitor with a current of 5A for a set time, the discharge time in this embodiment is 5s, and then let it stand for a set time, the standby time in this embodiment is 10s, and then The supercapacitor is charged with a current of 10A for a set time, the charging time in this embodiment is 5s, and then it is allowed to stand for a set time, the standing time in this embodiment is 10s. Next, the supercapacitor is discharged with a current of 10A for a set time, the discharge time in this embodiment is 5s, and then it is allowed to stand for a set time, the standing time in this embodiment is 10s. Next, the supercapacitor is charged with a current of 10A for a set time, the charging time in this embodiment is 5s, and then it is allowed to stand for a set time, the standing time in this embodiment is 10s. Finally, the supercapacitor is discharged with a current of 1A to a 10% state of charge.

[0044] S124. Repeat steps S121-S123 according to the set number of cycles. In this embodiment, the number of cycles is 10 times.

[0045] S13. Conduct an urban road cycle test experiment on the supercapacitor, specifically according to the following steps:

[0046] S131. Adjust the experimental temperature to a first set temperature.

[0047] S132. Charge the supercapacitor to 2.7V using a constant current and constant voltage of 1A until the current is less than 0.05A.

[0048] S133, leaving the supercapacitor to stand for a set time. In this embodiment, the standing time is 60 minutes.

[0049] S134. Discharge the supercapacitor to 0.5V using a constant current of 1A.

[0050] S135. Adjust the experimental temperature to the second set temperature, and repeat steps S132-S134.

[0051] S14. Based on the maximum available capacity test experiment, the mixed power pulse characteristic test experiment and the urban road cycle test experiment, the basic parameters of the supercapacitor are obtained, thereby determining the relationship between the maximum available capacity of the supercapacitor and the temperature.

[0052] Specifically, by performing the above-mentioned characteristic tests on the supercapacitor, it can be found that the maximum available capacity of the supercapacitor will continue to decrease with increasing temperature. In order to more intuitively represent the change of the maximum available capacity of the supercapacitor with temperature, the experimental results are listed in Table 1.

[0053] Table 1 Maximum available capacity of supercapacitors at four different temperatures obtained from characteristic experiments

[0054] Temperature (℃) -10 10 25 40 Capacity (Ah) 0.9452 0.9406 0.9369 0.9294

[0055] S2. Establish a supercapacitor model.

[0056] In order to estimate the state and parameters of the supercapacitor, the first task is to build a dynamic model that can represent its characteristics. The following steps are taken:

[0057] S21. Based on the Thevenin model, a supercapacitor model is obtained.

[0058] Specifically, the Thevenin model has better model accuracy and robustness than other single-cell supercapacitor equivalent circuit models. Figure 2 The Thevenin model shown is used as an equivalent circuit model of a supercapacitor cell.

[0059] Based on the Thevenin model, the continuous system equation of the supercapacitor model is obtained:

[0060] (1)

[0061] In formula (1), the time constant , U oc represents the open circuit voltage, R D Represents polarization internal resistance, C D Represents polarization capacitance, U D represents the polarization voltage, R i Indicates the ohmic internal resistance, i L Indicates current, U t Indicates terminal voltage.

[0062] After discretizing formula (1), we can obtain:

[0063] (2)

[0064] In formula (2), U D,k represents the polarization voltage of the RC network at time k, U D,k-1 represents the polarization voltage of the RC network at time k-1, and the RC network represents R D and C D The parallel circuit composed of U t,krepresents the terminal voltage at time k, U oc,k represents the open circuit voltage at time k, i L,k represents the current flowing through the supercapacitor at time k.

[0065] S22. Determine the relationship between the state of charge and the open circuit voltage.

[0066] Due to the state of charge SOC of supercapacitor and lithium-ion battery and open circuit voltage U oc The relationship is similar, so the state of charge SOC of the supercapacitor is related to the open circuit voltage U oc Therefore, first let the fully charged supercapacitor stand still and measure the terminal voltage of the supercapacitor at this time as the open circuit voltage U when the state of charge SOC is 100%. oc Then, combined with the mixed power pulse characteristic test data of supercapacitors at different temperatures, the terminal voltage measured after a long period of static state is used as the open circuit voltage U of the state of charge SOC at this moment. oc , and then use the least square fitting method to get the state of charge SOC and open circuit voltage U oc The relationship is as follows:

[0067] (3)

[0068] In formula (3), p1, p2, p3, p4, p5, p6, and p7 represent the fitting coefficients, respectively, and f(z) represents the relationship between the state of charge SOC and the open circuit voltage U oc Functional relationship, z represents SOC.

[0069] The best fitting coefficients are shown in Table 2.

[0070] Table 2 SOC-U at different temperatures oc Fitting coefficients

[0071] temperature <![CDATA[P1]]> <![CDATA[P2]]> <![CDATA[P3]]> <![CDATA[P4]]> <![CDATA[P5]]> <![CDATA[P6]]> <![CDATA[P7]]> -10℃ 0.9837 -3.1985 3.8635 -1.9189 -0.0160 2.5056 0.4552 10℃ 0.8417 -2.7729 3.4629 -1.8146 -0.0014 2.4874 0.4621 25℃ 1.0436 -3.4296 4.3360 -2.4257 0.2499 2.4219 0.4569 40℃ 1.0934 -3.8226 5.2354 -3.3113 0.6674 2.3195 0.4413

[0072] S23. Use the simulated annealing algorithm combined with the experimental data of the mixed power pulse characteristic test experiment to obtain the optimal parameters of the model.

[0073] The simulated annealing algorithm is based on the similarity between general combinatorial optimization problems and the annealing process of solid materials. It can not only solve different nonlinear problems, but also optimize non-differentiable or discontinuous functions. It has great advantages in solving global optimization problems and is therefore particularly suitable for parameter identification of supercapacitor models. The specific implementation steps are as follows:

[0074] S231, first, set the initial annealing temperature T and the number of iterations L at each temperature, then set the corresponding initial solution x, and finally, calculate the function value F(x) of the objective function at x;

[0075] S232. Generate a new feasible solution x' in the neighborhood of solution x, and calculate the objective function value F(x') of x'.

[0076] S233. Calculate the difference ΔF between F(x') and F(x). If ΔF < 0, accept x' as the current new solution. Otherwise, calculate the probability p = exp(-ΔF / T). If p > random[0,1], accept x' as the current new solution, where random[0,1] represents a random number in the interval [0,1].

[0077] S234, determine whether the number of iterations L has been reached. If not, return to S231 and continue the loop; otherwise, exit the loop and perform the annealing operation.

[0078] S235. Determine whether the termination condition T=0 is met. If not, perform a cooling operation, then return to S232 and continue the loop until the termination condition T=0 is met. Output the solution at this time as the global optimal solution, thereby obtaining the optimal parameters of the supercapacitor model.

[0079] S3. Jointly estimate the supercapacitor's multi-state across scales by following the steps below:

[0080] S31. Establish a nonlinear system equation of the supercapacitor based on the supercapacitor model.

[0081] Considering that the parameters of supercapacitors have slow-changing characteristics and the state has fast-changing characteristics in the actual working process, a discrete time-state-space equation is established using the cross-time scale method to predict the parameters θ of supercapacitors from a macroscopic perspective, including the ohmic internal resistance R i And capacity Q, predict the system state of supercapacitor from a microscopic perspective, based on which, establish the nonlinear system equation of supercapacitor:

[0082] (4)

[0083] In formula (4), X k,l Indicates that at t k,l The system state matrix of the supercapacitor at time t, where k and l represent the time scale indicators of the supercapacitor system in the microscopic state and macroscopic state respectively, k,l = t k,0 +l×△T, where △T represents the interval between two adjacent sampling points, t k,0 Indicates the initial time point; X k,l+1 Indicates that at t k,l+1 The system state matrix of the supercapacitor at time U k,l Indicates that at t k,l The system input matrix of the supercapacitor at the moment; Yk,l is the supercapacitor system at t k,l The observation matrix at time ω k,l The process noise matrix representing the state of the supercapacitor system; υ k,l represents the measurement noise matrix; ρ k The process noise matrix representing the model parameters; θ k represents the parameter matrix at the kth macroscopic scale; θ k+1 Represents the parameter matrix at the k+1th macroscale; F represents the prediction function relationship composed of the three parameters in the brackets; G represents the measurement function relationship composed of the three parameters in the brackets.

[0084] S32. Perform cross-scale multi-state joint estimation based on double extended Kalman filtering on the nonlinear system equation of the supercapacitor, according to the following steps:

[0085] S321. Estimating system parameters θ by combining a Kalman filter at a macroscopic scale k , initialize the nonlinear system equation of the supercapacitor of formula (4):

[0086] (5)

[0087] In formula (5), represents the initial parameters of the system, represents the initial estimated value of the system parameters, X 0,0 represents the initial state of the system, represents the initial estimate of the system state, and Represent the initial covariance matrix of the parameter and state filter respectively, and E represents the mathematical expectation of the elements in the brackets;

[0088] Through formula (5), we can determine The initial value of .

[0089] S322, Calculate the parameter filter at the macro scale The time update equation is:

[0090] , (6)

[0091] In formula (6), , and Represent the error covariance matrix and noise matrix of the system parameters at the previous moment, and denote the prior estimate of the system parameter matrix and the error covariance prediction value, respectively. Represents the estimated value of the system parameters at the previous moment;

[0092] Through formula (6) we can get and ;

[0093] S323, after the parameter filter is updated, the state filter is combined Calculate the state filter at each microscopic scale The time update equation is:

[0094] (7)

[0095] In formula (7), , and denote the prior estimate of the system state matrix and the error covariance estimate, respectively. Represents the partial derivative matrix of the prediction function with respect to the state, represents the estimated value of the system state at the previous moment, Indicates The external input matrix of the moment system, represents the error covariance matrix of the system at the previous moment, Represents the transposed matrix of the partial derivative of the prediction function with respect to the state, The noise covariance matrix representing the error covariance at the previous moment;

[0096] Through formula (7) we can get .

[0097] S324, at each microscopic scale, the state filter is combined with the updated terminal voltage error to calculate the state filter at the microscopic scale The measurement update equation is:

[0098] (8)

[0099] In formula (8), Indicates The Kalman gain of the state matrix at time , The error covariance prediction value of the state equation at time , Indicates The partial derivative of the measurement function with respect to the state at the moment, Indicates The noise covariance matrix at time , Indicates The external input matrix of the system at the moment;

[0100] The posterior state estimate is obtained by formula (8): and its error covariance .

[0101] S325, when the time scale sequence When the state is updated and the posterior state estimate is obtained, the micro-scale indicator l is compared with the macro-scale indicator L. If l does not reach the level of L, the state measurement update at the micro-scale is and It will be transmitted to step S321 as the initial value for parameter estimation and state estimation at the next moment. Conversely, if l reaches the level of L, the posterior state estimate and its error covariance will be measured and updated at the macro scale, that is, it can be obtained by formula (9) and :

[0102] (9)

[0103] S326, after the state measurement is updated, all micro-scale indicators are updated using formula (6). Estimated value update at time The value at the moment, that is:

[0104] (10)

[0105] In formula (10), Indicates The observation matrix at time t, Indicates The system external input matrix of the supercapacitor at all times, Indicates The posterior state estimate at time t, Indicates The error covariance matrix of the posterior state estimate at time , represents the estimated value of the system state after macro-scale conversion, represents the error covariance matrix of the state estimation of the system after macro-scale conversion, represents the observation matrix of the system after macroscopic scale transformation, Represents the external input matrix of the system after macro-scale transformation.

[0106] S327, after completing the time scale conversion, the estimated value of the state filter is transferred to the parameter filter to calculate the parameter filter at the macro scale The time update equation is:

[0107] (11)

[0108] in

[0109] (12)

[0110] In formulas (11) and (12), represents the Kalman gain of the parametric equation, represents the derivative of the measurement function with respect to the parameter, represents the covariance prediction value of the parametric equation, represents the system noise matrix, represents the a posteriori estimate of the system parameters, represents the posterior estimation error covariance matrix of the system parameters, X represents the system state matrix, U k-1,l-1 Represents the external input matrix of the system at the previous moment;

[0111] Thus, the posterior estimate of the parameter matrix is ​​obtained from formula (11): and its error covariance .

[0112] Therefore, through steps S321-S327, the charge state of the supercapacitor can be predicted from a microscopic scale, and the equivalent internal resistance and capacity state can be updated from a macroscopic scale. Therefore, not only the estimation accuracy is greatly improved, but also the operating efficiency of the supercapacitor system is greatly improved.

[0113] Comparative Example 1

[0114] First, initialize the state of charge SOC correctly, that is, the initial state of charge SOC=100%, and then set the parameter ohmic internal resistance R i and capacity Q are set to 0.0001 and 0.5556Ah respectively. Finally, the macroscale L is set to 1s, which is the same as the microscale.

[0115] The comparison curve of the estimated state of charge SOC and the reference state of charge SOC is as follows: Figure 2 As shown in (a), the state of charge SOC estimation error is as follows Figure 2 As shown in (b), the comparison curve between the estimated voltage and the measured voltage is as follows Figure 2 As shown in (c), the voltage estimation error is Figure 2 (d). Therefore, Figure 2 The results show that when there are errors in the initial parameters, the average absolute error of the state of charge (SOC) estimation is less than 0.37%, and after reaching a steady state, the absolute error of the estimated voltage is less than 7mV. The comparison curve between the measured capacity and the estimated capacity is shown in the figure. Figure 3 As shown in (a), the capacity estimation error is Figure 3 (b). Figure 3 It can be seen that due to the small micro-scale setting, the estimated capacity fluctuates greatly, but most of them are concentrated near the real capacity. Figure 2 and Figure 3It can be seen that despite the error in the parameters, this method can also achieve better state of charge SOC and parameter estimation. This is mainly due to the synergy of the two Kalman filters. First, after the prior estimation of the parameters, the state filter begins to adjust the state of charge SOC to minimize the terminal voltage estimation error. At this time, the open circuit voltage U oc The optimal state is reached. Then, combined with the state of charge SOC estimated by the state filter, the parameter filter starts to update the parameters. When the optimal parameters are found, they are passed to the state filter. At this time, the SOC estimation error will be further reduced. However, the minimum terminal voltage error mainly depends on the accurate U oc , U oc It is directly related to the state of charge (SOC). Therefore, this method can achieve accurate estimation of parameter states and SOC.

[0116] To analyze the computational efficiency of this method in this scenario, we selected an Intel Core i5-4200H CPU (2.80GHz, 16GB) and wrote and optimized the MATLAB code in MATLAB (version: MATLAB 2020b). The code was run by MATLAB itself, and the average computation time of 10 runs was used to evaluate the computational efficiency. The average computation time in this case was 0.823 seconds.

[0117] Example 1

[0118] Compared with Comparative Example 1, the difference of Example 1 is that the macroscale L is set to 131s. The estimated results of state of charge SOC and voltage are shown in Figure 1. Figure 4 As shown, the capacity and internal resistance estimation results are as follows Figure 5 As shown. Among them, Figure 4 (a) shows the comparison between the estimated state of charge SOC curve and the reference state of charge SOC curve, Figure 4 (b) shows the error distribution curve of the estimated state of charge SOC, Figure 4 (c) Comparison curve of estimated voltage and measured voltage. Figure 5 (a) shows the comparison curve of estimated capacity and measured capacity, Figure 5 (b) represents the capacity estimation error curve, Figure 5 (c) shows the estimated curve of ohmic internal resistance. Figure 4 and Figure 5 The results shown show that when the initial parameters are inaccurate, the average absolute error of the state of charge (SOC) estimation is less than 0.36%, the absolute error of the voltage estimation in the steady state is less than 5mV, and the absolute error of the capacity estimation is less than 0.06Ah. Figure 2 and 3 L=1s in Figure 4 and5 The results shown in Figure 1 show that when L=131s, the estimation accuracy of the method is better. This is because when L=1s, the estimated parameters are constantly changing, the parameters fluctuate greatly, and it is difficult to make a stable estimation of the parameters, which affects the estimation accuracy of the state of charge (SOC) and leads to poor overall estimation performance. In addition, iterative updates using inaccurate parameters will cause the parameter filter to take more time to reach a reliable estimate, thereby affecting the estimation accuracy and reliability of the method. More importantly, if the value of L is set to a large value, the parameter state of the supercapacitor will be difficult to estimate, and the accuracy of the state of charge (SOC) estimation will be even worse. In addition, the value of L should be adaptively fixed as the method is executed. Here, L=131s is selected for research.

[0119] On the other hand, when L=131s, the average running time of this method for 10 times is 0.62s. Compared with the running time of the dual EKF, the running time of the cross-scale EKF is reduced by 24.67%, which greatly reduces the operating burden of the system and is conducive to promoting the progress of practical application research.

[0120] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention. Such changes fall within the scope of protection of the present invention.

Claims

1. A cross-scale multi-state joint estimation method for supercapacitors, characterized in that: Follow these steps: S1. Perform characteristic tests on the supercapacitor to obtain the basic parameters of the supercapacitor and determine the relationship between the maximum available capacity and temperature. Follow the steps below: S11, perform a capacity test experiment on the supercapacitor; S12. Conducting a mixed power pulse characteristic test experiment on the supercapacitor; S13. Conducting urban road cycle test experiments on the supercapacitor; S14. Obtain basic parameters of the supercapacitor based on the capacity test experiment, the mixed power pulse characteristic test experiment, and the urban road cycle test experiment, thereby determining the relationship between the capacity and temperature of the supercapacitor; S2. Build a supercapacitor model by following these steps: S21. Based on the Thevenin model, a supercapacitor model is obtained; S22, determining the relationship between the state of charge and the open circuit voltage; S23, using a simulated annealing algorithm combined with experimental data from a mixed power pulse characteristic test experiment to obtain optimal parameters of the model; S3. Jointly estimate the supercapacitor's multi-state across scales by following these steps: S31. Establish a nonlinear system equation of supercapacitor based on supercapacitor model; S32. Perform cross-scale multi-state joint estimation based on double extended Kalman filtering for the nonlinear system equations of supercapacitors; The step S11 is performed according to the following steps: S111, leaving the supercapacitor at a set temperature and time; S112, discharging the supercapacitor with a current of 1A to a lower cut-off voltage of 0.5V; S113, leaving the supercapacitor to stand for a set time; S114, charging the supercapacitor with a constant current and constant voltage of 1A to an upper cut-off voltage of 2.7V, until the current is less than 0.05A; S115, leaving the supercapacitor to stand for a set time; S116, discharge the supercapacitor with a constant current of 1A to a lower cut-off voltage of 0.5V; S117, leaving the supercapacitor to stand for a set time; S118. Repeat steps S111-S117 according to the set number of cycles.

2. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 1, characterized in that: Step S12 is performed according to the following steps: S121, leaving the supercapacitor at a set temperature and time; S122, charge the supercapacitor with a constant current and constant voltage of 1A to an upper cut-off voltage of 2.7V, until the current is less than 0.05A; S123. First, discharge the supercapacitor with a current of 1A for a set time, and after completion, let it stand for a set time. Then, charge the supercapacitor with a current of 1A for a set time, and after completion, let it stand for a set time. Then, discharge the supercapacitor with a current of 5A for a set time, and after completion, let it stand for a set time. Then, charge the supercapacitor with a current of 5A for a set time, and after completion, let it stand for a set time. Next, discharge the supercapacitor with a current of 10A for a set time, and after completion, let it stand for a set time. Next, charge the supercapacitor with a current of 10A for a set time, and after completion, let it stand for a set time. Finally, discharge the supercapacitor with a current of 1A to a 10% state of charge. S124. Repeat steps S121-S123 according to the set number of cycles.

3. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 1, characterized in that: Step S13 is performed according to the following steps: S131, adjusting the experimental temperature to a first set temperature; S132, charge the supercapacitor to 2.7V using a constant current and constant voltage of 1A until the current is less than 0.05A; S133, leaving the supercapacitor at rest for a set time; S134, discharge the supercapacitor to 0.5V with a constant current of 1A; S135. Adjust the experimental temperature to the second set temperature, and repeat steps S132-S134.

4. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 1, characterized in that: In step S21, based on the Thevenin model, the continuous system equation of the supercapacitor model is obtained: （1） In formula (1), the time constant , U oc represents the open circuit voltage, R D Represents polarization internal resistance, C D Represents polarization capacitance, U D represents the polarization voltage, R i Indicates the ohmic internal resistance, i L Indicates current, U t Indicates terminal voltage; After discretizing formula (1), we can obtain: （2） In formula (2), U D,k represents the polarization voltage of the RC network at time k, U D,k-1 represents the polarization voltage of the RC network at time k-1, and the RC network represents R D and C D The parallel circuit composed of U t,k represents the terminal voltage at time k, U oc,k represents the open circuit voltage at time k, i L,k represents the current flowing through the supercapacitor at time k.

5. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 4, characterized in that: In step S22, the fully charged supercapacitor is first allowed to stand still, and the terminal voltage of the supercapacitor is measured as the open circuit voltage U when the state of charge (SOC) is 100%. oc Then, combined with the mixed power pulse characteristic test data of supercapacitors at different temperatures, the terminal voltage measured after a long period of static state is used as the open circuit voltage U of the state of charge SOC at this moment. oc , and then use the least square fitting method to get the state of charge SOC and open circuit voltage U oc The relationship is as follows: （3） In formula (3), p1, p2, p3, p4, p5, p6, and p7 represent the fitting coefficients, respectively, and f(z) represents the relationship between the state of charge SOC and the open circuit voltage U oc Functional relationship, z represents SOC.

6. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 5, characterized in that: Step S23 is performed according to the following steps: S231, first, set the initial annealing temperature T and the number of iterations M at each temperature, then set the corresponding initial solution x, and finally, calculate the function value F(x) of the objective function at x; S232. Generate a new feasible solution x' in the neighborhood of solution x, and calculate the objective function value F(x') of x'. S233. Calculate the difference ΔF between F(x') and F(x). If ΔF < 0, accept x' as the current new solution. Otherwise, calculate the probability p = exp(-ΔF / T). If p > random[0,1], accept x' as the current new solution, where random[0,1] represents a random number in the interval [0,1]. S234, determine whether the number of iterations M has been reached. If not, return to S231 and continue the loop; otherwise, exit the loop and perform the annealing operation. S235. Determine whether the termination condition T=0 is met. If not, perform a cooling operation, then return to S232 and continue the loop until the termination condition T=0 is met. Output the solution at this time as the global optimal solution, thereby obtaining the optimal parameters of the supercapacitor model.

7. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 6, characterized in that: In step S31, considering that the parameters of the supercapacitor have slow-changing characteristics and the state has fast-changing characteristics during actual operation, a discrete time-state-space equation is established using a cross-time scale method to predict the parameters θ of the supercapacitor from a macroscopic perspective, including the ohmic internal resistance R i And capacity Q, predict the system state of supercapacitor from a microscopic perspective, based on which, establish the nonlinear system equation of supercapacitor: （4） In formula (4), X k,l Indicates that at t k,l The system state matrix of the supercapacitor at time t, where k and l represent the time scale indicators of the supercapacitor system in the microscopic state and macroscopic state respectively, k,l = t k,0 +l×△T, where △T represents the interval between two adjacent sampling points, t k,0 Indicates the initial time point; X k,l+1 Indicates that at t k,l+1 The system state matrix of the supercapacitor at time U k,l Indicates that at t k,l The system input matrix of the supercapacitor at the moment; Y k,l is the supercapacitor system at t k,l The observation matrix at time ω k,l The process noise matrix representing the state of the supercapacitor system; υ k,l represents the measurement noise matrix; ρ k The process noise matrix representing the model parameters; θ k represents the parameter matrix at the kth macroscopic scale; θ k+1 Represents the parameter matrix at the k+1th macroscale; F represents the prediction function relationship composed of the three parameters in the brackets; G represents the measurement function relationship composed of the three parameters in the brackets.

8. The cross-scale multi-state joint estimation method applicable to supercapacitors according to claim 7, characterized in that: Step S32 is performed according to the following steps: S321. Estimating system parameters θ by combining a Kalman filter at a macroscopic scale k , initialize the nonlinear system equation of the supercapacitor of formula (4): （5） In formula (5), represents the initial parameters of the system, represents the initial estimated value of the system parameters, X 0,0 represents the initial state of the system, represents the initial estimate of the system state, and Represent the initial covariance matrix of the parameter and state filter respectively, and E represents the mathematical expectation of the elements in the brackets; Through formula (5), we can determine The initial value of S322, Calculate the parameter filter at the macro scale The time update equation is: ， （6） In formula (6), , and Represent the error covariance matrix and noise matrix of the system parameters at the previous moment, and denote the prior estimate of the system parameter matrix and the error covariance prediction value, respectively. Represents the estimated value of the system parameters at the previous moment; Through formula (6) we can get and ; S323, after the parameter filter is updated, the state filter is combined Calculate the state filter at each microscopic scale The time update equation is: （7） In formula (7), , and denote the prior estimate of the system state matrix and the error covariance estimate, respectively. Represents the partial derivative matrix of the prediction function with respect to the state, represents the estimated value of the system state at the previous moment, Indicates The external input matrix of the moment system, represents the error covariance matrix of the system at the previous moment, Represents the transposed matrix of the partial derivative of the prediction function with respect to the state, The noise covariance matrix representing the error covariance at the previous moment; Through formula (7) we can get and ; S324, at each microscopic scale, the state filter is combined with the updated terminal voltage error to calculate the state filter at the microscopic scale The measurement update equation is: （8） In formula (8), Indicates The Kalman gain of the state matrix at time , Indicates The error covariance prediction value of the state equation at time , Indicates The partial derivative of the measurement function with respect to the state at the moment, Indicates The noise covariance matrix at time , Indicates The external input matrix of the system at the moment; The posterior state estimate is obtained by formula (8): and its error covariance ; S325, when the time scale sequence When the state is updated and the posterior state estimate is obtained, the micro-scale indicator l is compared with the macro-scale indicator L. If l does not reach the level of L, the state measurement update at the micro-scale is and It will be transmitted to step S321 as the initial value for parameter estimation and state estimation at the next moment. Conversely, if l reaches the level of L, the posterior state estimate and its error covariance will be measured and updated at the macro scale, that is, it can be obtained by formula (9) and : （9） S326, after the state measurement is updated, all micro-scale indicators are updated using formula (6). Estimated value update at time The value at the moment, that is: （10） In formula (10), Indicates The observation matrix at time t, Indicates The system external input matrix of the supercapacitor at all times, Indicates The posterior state estimate at time t, Indicates The error covariance matrix of the posterior state estimate at time , represents the estimated value of the system state after macro-scale conversion, represents the observation matrix of the system after macroscopic scale transformation, Represents the external input matrix of the system after macro-scale transformation; S327, after completing the time scale conversion, the estimated value of the state filter is transferred to the parameter filter to calculate the parameter filter at the macro scale The time update equation is: （11） in （12） In formulas (11) and (12), represents the Kalman gain of the parametric equation, represents the derivative of the measurement function with respect to the parameter, represents the covariance prediction value of the parametric equation, represents the system noise matrix, represents the a posteriori estimate of the system parameters, represents the posterior estimation error covariance matrix of the system parameters, X represents the system state matrix, U k-1,l-1 Represents the external input matrix of the system at the previous moment; Thus, the posterior estimate of the parameter matrix is ​​obtained from formula (11): and its error covariance .

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