Method and device for determining leakage current of supercapacitor

Abstract

The invention provides a method and device for determining the leakage current of a supercapacitor, and relates to the technical field of supercapacitors, and the method comprises the steps: enabling the supercapacitor to be equivalently divided into N infinitesimal elements, building a transmission line equation, and enabling the distribution parameters in the transmission line equation to comprise the distribution resistance, the distribution capacitance and the distribution leakage resistance; processing the transmission line equation to determine an impedance expression; testing the supercapacitor to obtain a plurality of impedance measurement values; determining an estimated value of the distribution parameter when a convergence condition is satisfied according to the plurality of impedance measurement values and the impedance expression; solving the transmission line equation according to the estimated value of the distribution parameter so as to determine voltage distribution; and determining the leakage current value of the supercapacitor according to the estimated values of the voltage distribution and the distributed leakage resistance. Therefore, the leakage current value of the supercapacitor can be quickly determined without waiting for a long time, and the testing efficiency of the leakage current of the supercapacitor is greatly improved.

Description

Technical Field

[0001] This application relates to the field of supercapacitor technology, and in particular to a method and apparatus for determining the leakage current of a supercapacitor. Background Technology

[0002] Supercapacitors, also known as electric double-layer capacitors (EDLCs), offer higher energy density compared to traditional electrostatic capacitors and electrolytic capacitors, and higher power density compared to batteries and fuel cells. They fill a gap in energy storage technology and are widely used in transportation, power, industrial machinery, consumer electronics, and many other fields. Leakage current is a crucial parameter for evaluating supercapacitor performance, directly affecting the device's energy retention capability and safety performance.

[0003] In related technologies, the constant voltage float charge method is commonly used to measure leakage current. This involves floating the capacitor at its rated voltage for a certain period and then directly measuring the leakage current. While this method is simple to operate, it has a long testing cycle, often requiring several days to complete. Therefore, it is crucial to achieve rapid testing of supercapacitor leakage current and improve efficiency. Summary of the Invention

[0004] This application provides a method and apparatus for determining the leakage current of a supercapacitor.

[0005] According to a first aspect of this application, a method for determining the leakage current of a supercapacitor is provided, the method comprising:

[0006] The supercapacitor is equivalently divided into N micro-elements, and a transmission line equation is established. The distributed parameters in the transmission line equation include distributed resistance, distributed capacitance, and distributed leakage resistance.

[0007] The transmission line equations are processed to determine the impedance expression;

[0008] The supercapacitor was tested to obtain multiple impedance measurements;

[0009] Based on the multiple impedance measurements and the impedance expression, the estimated value of the distributed parameter is determined when the convergence condition is met.

[0010] Based on the estimated values ​​of the distribution parameters, the transmission line equations are solved to determine the voltage distribution;

[0011] The leakage current value of the supercapacitor is determined based on the voltage distribution and the estimated value of the distributed leakage resistance.

[0012] Optionally, processing the transmission line equation to determine the impedance expression includes:

[0013] The transmission line equations are processed to determine the chain parameter matrix of each of the infinitesimal elements and the total chain parameter matrix;

[0014] Based on the chain parameter matrix and the total chain parameter matrix, the impedance expression is determined.

[0015] Optionally, determining the estimated value of the distributed parameter based on the plurality of impedance measurements and the impedance expression, when the convergence condition is met, includes:

[0016] Based on the initial distributed parameter values, the measured impedance values, and the impedance expression, determine the theoretical impedance value, the error vector value, and the objective function value;

[0017] The Jacobian matrix is ​​determined based on the initial distribution parameter values ​​corresponding to the N infinitesimal elements and the theoretical impedance values.

[0018] The parameter increment is determined based on the initial distribution parameter value, the error vector value, and the Jacobian matrix;

[0019] The initial distributed parameters are updated based on the parameter increments. The updated distributed parameter values ​​are then used to return and execute the steps of determining the theoretical impedance value, error vector value, and objective function value until the objective function converges, thereby determining the estimated value of the distributed parameters.

[0020] Optionally, determining the Jacobian matrix based on the initial distribution parameter values ​​corresponding to the N infinitesimal elements and the theoretical impedance value includes:

[0021] The initial distribution parameter values ​​are subjected to temporary positive and temporary negative perturbations with small step sizes to obtain temporary positive and temporary negative parameter values.

[0022] Using the aforementioned temporary positive and temporary negative parameter values, determine the corresponding theoretical values ​​of temporary positive and temporary negative impedances;

[0023] The theoretical values ​​of the temporary positive impedance and the temporary negative impedance are processed to determine the Jacobian matrix.

[0024] Optionally, determining the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance includes:

[0025] Based on the distributed voltage and the distributed leakage resistance at each micro-element location, determine the local leakage current density corresponding to each micro-element;

[0026] The leakage current value of the supercapacitor is determined by integrating the local leakage current density.

[0027] Optionally, after determining the estimated value of the distribution parameter, the method further includes:

[0028] Based on the frequency characteristics of each leakage mechanism, a multi-mechanism superposition model is established to determine the conductivity coefficient of each leakage mechanism.

[0029] Based on the conductivity coefficient and operating voltage of each leakage mechanism, the leakage current under each leakage mechanism is determined.

[0030] Optionally, the supercapacitor is tested to obtain multiple impedance measurements, including:

[0031] Impedance tests were performed on the supercapacitor at different frequencies to obtain multiple raw impedance measurements;

[0032] The original impedance measurements are preprocessed to determine the corresponding impedance measurements.

[0033] According to a second aspect of this application, a device for determining the leakage current of a supercapacitor is provided, comprising:

[0034] An equivalent module is used to divide a supercapacitor into N micro-elements and establish a transmission line equation, wherein the distributed parameters in the transmission line equation include distributed resistance, distributed capacitance and distributed leakage resistance.

[0035] The processing module is used to process the transmission line equation to determine the impedance expression;

[0036] The testing module is used to test the supercapacitor to obtain multiple impedance measurements.

[0037] The first determining module is used to determine the estimated value of the distributed parameter based on the plurality of impedance measurements and the impedance expression, when the convergence condition is met.

[0038] The second determining module is used to solve the transmission line equation based on the estimated values ​​of the distribution parameters to determine the voltage distribution;

[0039] The third determining module is used to determine the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance.

[0040] Optionally, the processing module is specifically used for:

[0041] The transmission line equations are processed to determine the chain parameter matrix of each of the infinitesimal elements and the total chain parameter matrix;

[0042] Based on the chain parameter matrix and the total chain parameter matrix, the impedance expression is determined.

[0043] Optionally, the first determining module includes:

[0044] The first determining unit is used to determine the theoretical impedance value, the error vector value, and the objective function value based on the initial distributed parameter value, the measured impedance value, and the impedance expression.

[0045] The second determining unit is used to determine the Jacobian matrix based on the initial distribution parameter values ​​corresponding to the N micro-elements and the theoretical impedance values;

[0046] The third determining unit is used to determine the parameter increment based on the initial distribution parameter value, the error vector value, and the Jacobian matrix;

[0047] The update unit is used to update the initial distribution parameters according to the parameter increment, and use the updated distribution parameter values ​​to return to the steps of determining the theoretical impedance value, error vector value and objective function value until the objective function converges, and to determine the estimated value of the distribution parameters.

[0048] Optionally, the second determining unit is specifically used for:

[0049] The initial distribution parameter values ​​are subjected to temporary positive and temporary negative perturbations with small step sizes to obtain temporary positive and temporary negative parameter values.

[0050] Using the aforementioned temporary positive and temporary negative parameter values, determine the corresponding theoretical values ​​of temporary positive and temporary negative impedances;

[0051] The theoretical values ​​of the temporary positive impedance and the temporary negative impedance are processed to determine the Jacobian matrix.

[0052] Optionally, the third determining module is specifically used for:

[0053] Based on the distributed voltage and the distributed leakage resistance at each micro-element location, determine the local leakage current density corresponding to each micro-element;

[0054] The leakage current value of the supercapacitor is determined by integrating the local leakage current density.

[0055] Optionally, the first determining module is further configured to:

[0056] Based on the frequency characteristics of each leakage mechanism, a multi-mechanism superposition model is established to determine the conductivity coefficient of each leakage mechanism.

[0057] Based on the conductivity coefficient and operating voltage of each leakage mechanism, the leakage current under each leakage mechanism is determined.

[0058] Optionally, the test module is specifically used for:

[0059] Impedance tests were performed on the supercapacitor at different frequencies to obtain multiple raw impedance measurements;

[0060] The original impedance measurements are preprocessed to determine the corresponding impedance measurements.

[0061] According to a third aspect of this application, an electronic device is provided, comprising: a processor and a memory storing computer program instructions; the processor, when executing the computer program instructions, implements any of the above-described methods for determining the leakage current of a supercapacitor.

[0062] According to a fourth aspect of this application, a computer-readable storage medium is provided, on which computer program instructions are stored, which, when executed by a processor, implement any of the above-described methods for determining the leakage current of a supercapacitor.

[0063] In summary, the method and apparatus for determining the leakage current of a supercapacitor provided in this application have at least the following beneficial effects: First, the supercapacitor can be equivalently divided into N micro-elements, and a transmission line equation can be established. The distributed parameters include distributed resistance, distributed capacitance, and distributed leakage resistance. Then, the transmission line equation can be processed to determine the impedance expression. Multiple impedance measurements are obtained by testing the supercapacitor. Based on these measurements and the impedance expression, the estimated values ​​of the distributed parameters are determined when the convergence condition is met. Then, the transmission line equation is solved based on the estimated values ​​of the distributed parameters to determine the voltage distribution. Finally, the leakage current value of the supercapacitor is determined based on the voltage distribution and the estimated value of the distributed leakage resistance. Therefore, by equivalently processing the supercapacitor, the corresponding transmission line equation and impedance expression can be determined. Then, by using the measured impedance values ​​and the impedance expression, the transmission line equation can be solved by inversion. This eliminates the need for a long waiting time, allowing for rapid determination of the supercapacitor's leakage current value and greatly improving the testing efficiency of the supercapacitor's leakage current. Attached Figure Description

[0064] To more clearly illustrate the specific embodiments of this application or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 A flowchart illustrating a method for determining the leakage current of a supercapacitor, provided for an embodiment of this application;

[0066] Figure 2A flowchart of another method for determining the leakage current of a supercapacitor provided for embodiments of this application;

[0067] Figure 3 A schematic diagram of a transmission line equivalent circuit model provided for an embodiment of this application;

[0068] Figure 4 A test system structure block diagram provided for embodiments of this application;

[0069] Figure 5 A structural diagram of a device for determining the leakage current of a supercapacitor provided for an embodiment of this application;

[0070] Figure 6 This is a structural diagram of an electronic device provided as an embodiment of the present application. Detailed Implementation

[0071] To make the above and other features and advantages of this application clearer, the application is further described below with reference to the accompanying drawings. It should be understood that the specific embodiments given herein are for the purpose of explanation to those skilled in the art, and are exemplary only, not restrictive.

[0072] In the following description, numerous specific details are set forth to provide a thorough understanding of this application. However, it will be apparent to those skilled in the art that the specific details are not required to practice this application. In other instances, well-known steps or operations have not been described in detail to avoid obscuring this application.

[0073] The method for determining the leakage current of a supercapacitor provided in this application embodiment can be executed by the device for determining the leakage current of a supercapacitor provided in this application embodiment, which can be configured in an electronic device.

[0074] refer to Figure 1 This application provides a method for determining the leakage current of a supercapacitor, the method comprising:

[0075] Step 101: Divide the supercapacitor into N equivalent micro-elements and establish the transmission line equation, where the distributed parameters include distributed resistance, distributed capacitance and distributed leakage resistance.

[0076] N can be any integer, such as 10, 25, 30, 50, etc., and can be adjusted as needed. Setting a reasonable value for N can effectively ensure the accuracy of subsequent data processing and improve data processing efficiency.

[0077] It is understood that, in the embodiments of this application, the supercapacitor electrode structure can be equivalent to a distributed parameter transmission line network. The electrode can be divided into N micro-elements along the electrode thickness direction (x-axis), the electrode thickness is L, and the length Δx of each micro-element can be represented by the ratio of L to N to establish a transmission line model.

[0078] In addition, distributed parameters may include distributed resistance R(x), distributed capacitance C(x), and distributed leakage resistance Rl(x). Among them, distributed resistance can be used to characterize the ohmic impedance of electrolyte and electrode materials, with the unit Ω·cm; distributed capacitance can be used to characterize the sum of double-layer capacitance and pseudocapacitance, with the unit F / cm; distributed leakage resistance can be used to characterize the equivalent resistance of various leakage current paths, with the unit Ω·cm.

[0079] In addition, transmission line equations can be established based on the transmission line model. Transmission line equations can include voltage gradient equations and current gradient equations. The voltage gradient equation can be understood as the voltage drop along the electrode thickness direction driven by Ohm's law, and the voltage drop generated when the current passes through the resistive medium. The current gradient equation can be understood as the current reduction along the electrode thickness direction, which is usually due to the charge being diverted by local admittance paths, such as charging, leakage, or reaction.

[0080]

[0081] Where Y(x,ω)=jωC(x)+1 / Rl(x)+G(x), Y(x,ω) is the distributed admittance, G(x) is other admittance terms, ω is the angular frequency, C(x) is the distributed capacitance, R(x) is the distributed resistance, Rl(x) is the distributed leakage resistance, V(x,ω) is the complex voltage at position x, R(x) is the distributed resistance at position x, and I(x,ω) is the complex current at position x.

[0082] Step 102: Process the transmission line equations to determine the impedance expression.

[0083] Optionally, after determining the transmission line equation, the chain parameter matrix of each infinitesimal element and the total chain parameter matrix can be determined by processing the transmission line equation. Then, the impedance expression can be determined based on the chain parameter matrix and the total chain parameter matrix.

[0084] The transmission line equation can be approximated as a difference equation within a differential element. Then, a Taylor expansion is performed, retaining the second-order terms, to obtain the chain parameter matrix for each differential element, which can be expressed as:

[0085]

[0086] Then, the chain parameter matrices of each infinitesimal element are multiplied together, and the total chain parameter matrix is ​​obtained by concatenating the chain parameter matrices of all infinitesimal elements:

[0087]

[0088] in,

[0089] In addition, at the input terminal (x = 0), V(0) = V0, I(0) = I0. At the output terminal (x = L), it can be determined according to the load conditions, usually the open circuit condition I(L) = 0.

[0090] Accordingly, the expression for the open-circuit impedance can be determined as Z. in =A(ω) / C(ω).

[0091] Step 103: Test the supercapacitor to obtain multiple impedance measurements.

[0092] This includes the ability to perform multiple impedance tests on a supercapacitor to obtain multiple impedance measurements, as well as to perform impedance tests on a supercapacitor at different frequencies to obtain multiple impedance measurements.

[0093] For example, the frequency range can be set between 1 mHz and 10 kHz, which can well cover the main frequency response range of the supercapacitor. Alternatively, a logarithmically uniform distribution can be used, with 15-25 test points set every ten octaves, or adjustments can be made according to actual needs; this application does not limit this.

[0094] Optionally, during the multi-frequency impedance testing of a supercapacitor, the supercapacitor can be charged to the test voltage first and left to stand for 10 minutes to reach equilibrium. Then, the test can be performed sequentially from low frequency to high frequency. At least 5 cycles are required for each frequency point to stabilize. After that, the signal quality is monitored in real time. In order to ensure the accuracy and reliability of the data, the key frequency points can be repeatedly tested to minimize the relative error.

[0095] Optionally, impedance tests can be performed on the supercapacitor at different frequencies to obtain multiple raw impedance measurements. These raw impedance measurements can then be preprocessed to determine the corresponding impedance values.

[0096] There are various methods for data preprocessing, such as outlier detection, noise filtering, causality testing, and data interpolation. For example, the 3σ criterion can be used to remove outlier data points for outlier detection; filters such as Savitzky-Golay filters and Kalman filters can be used to smooth data and filter noise; the Kramers-Kronig relationship can be used to verify data consistency for causality testing; and cubic spline interpolation can be used to fill in missing values, etc.

[0097] It is understood that one or more of the above preprocessing methods may be used, and this application does not limit the application to any particular method.

[0098] Step 104: Based on multiple impedance measurements and impedance expressions, determine the estimated values ​​of the distributed parameters when the convergence condition is met.

[0099] After obtaining multiple impedance measurements, the initial distributed parameter values ​​can be used in conjunction with the impedance expression to determine the theoretical impedance value. Then, the error vector value can be determined based on the impedance measurements and the theoretical impedance value, and the objective function value can be determined based on the error vector value. The initial distributed parameter values ​​can then be updated based on the objective function value. The updated distributed parameter values ​​can then be used in conjunction with the impedance expression to calculate the new theoretical impedance value. The new theoretical impedance value and the impedance measurements can then be used to calculate the new error vector value and the objective function value. The distributed parameter values ​​can then be updated again, and the above update process can be repeated until the objective function converges. The distributed parameter values ​​at this point are then determined as the estimated values ​​of each distributed parameter.

[0100] Step 105: Solve the transmission line equations based on the estimated values ​​of the distributed parameters to determine the voltage distribution.

[0101] The boundary conditions can be V(0) = V0, and I(L) = 0 when open-circuited. Then, based on the estimated values ​​of the distributed parameters, the transmission line equation can be discretized using the fourth-order Runge-Kutta method to obtain the voltage values ​​at each micro-element node. The voltage values ​​of each micro-element are then arranged in the order of the micro-element to form the voltage distribution V(x) across the entire electrode thickness. Alternatively, linear multistep methods, finite element analysis, or other methods can be used to discretize the transmission line equation to obtain the voltage values ​​and voltage distribution at each micro-element node, etc. This application does not limit the specific methods used.

[0102] Optionally, after dividing the electrode into N micro-elements along the electrode thickness direction (x-axis), the right endpoint or center point of each micro-element can be regarded as a calculation node x_k, in order from k=1 to k=N, etc. This application does not limit this.

[0103] Therefore, in this embodiment of the application, by performing impedance testing on the supercapacitor to obtain multiple impedance test values, and then using the impedance test values ​​to solve the transmission line equation established by the supercapacitor, the voltage distribution of the supercapacitor can be determined. This can more accurately reflect the voltage values ​​of the micro-elements at different locations of the supercapacitor, thus using a more accurate voltage distribution to ensure the accuracy of the subsequent determination of the leakage current value of the supercapacitor. At the same time, since the impedance testing and transmission line equation solving of the supercapacitor are performed in a short time, a lot of waiting time is saved.

[0104] Step 106: Determine the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance.

[0105] Optionally, after determining the voltage distribution V(x) across the entire electrode thickness, the local leakage current density corresponding to each micro-element can be determined based on the distributed voltage and the distributed leakage resistance at each micro-element location. Then, the local leakage current density is integrated to determine the leakage current value of the supercapacitor.

[0106] First, the ratio of the voltage distribution to the distributed leakage resistance at the corresponding micro-element location can be calculated, and this ratio can be determined as the local leakage current density at the corresponding location, which can be expressed as: i(x)=V(x) / R(x), in A / cm. Then, the local leakage current density can be numerically integrated along the electrode thickness direction to obtain the total leakage current value of the supercapacitor, which can be expressed as:

[0107] Therefore, in this embodiment, by performing a wideband impedance test on the supercapacitor to obtain the impedance measurement value, and then based on the impedance measurement value and the impedance expression obtained using the transmission line equation, the estimated value of the distributed parameters can be further determined. Then, by using the estimated value of the distributed parameters to inversely solve the transmission line equation, the voltage distribution of the supercapacitor in the reverse direction along the electrode thickness can be determined. Then, based on the voltage distribution and the estimated value of the distributed leakage resistance corresponding to each micro-element, the leakage current value of the supercapacitor can be quickly determined. The required time is short, saving a lot of waiting time and greatly improving efficiency.

[0108] In this embodiment, the supercapacitor can first be equivalently divided into N micro-elements, and a transmission line equation can be established. The distributed parameters include distributed resistance, distributed capacitance, and distributed leakage resistance. The transmission line equation can then be processed to determine the impedance expression. Multiple impedance measurements are obtained by testing the supercapacitor. Based on these measurements and the impedance expression, and provided the convergence condition is met, the estimated values ​​of the distributed parameters are determined. The transmission line equation is then solved using these estimated values ​​to determine the voltage distribution. Finally, the leakage current of the supercapacitor is determined based on the voltage distribution and the estimated value of the distributed leakage resistance. Thus, by equivalently processing the supercapacitor, the corresponding transmission line equation and impedance expression can be determined. Then, by using the measured impedance values ​​and the impedance expression, the transmission line equation can be solved by inversion. This allows for rapid determination of the supercapacitor's leakage current without a long waiting period, significantly improving the testing efficiency of supercapacitor leakage current.

[0109] like Figure 2 As shown, the method for determining the leakage current of the supercapacitor may include the following steps:

[0110] Step 201: Divide the supercapacitor into N equivalent micro-elements and establish the transmission line equation. The distributed parameters in the transmission line equation include distributed resistance, distributed capacitance and distributed leakage resistance.

[0111] Step 202: Process the transmission line equations to determine the impedance expression.

[0112] Step 203: Perform impedance testing on the supercapacitor at different frequencies to obtain multiple impedance measurements.

[0113] It should be noted that the specific content and implementation of steps 201 to 203 can be referred to the description of the various embodiments of this application, and will not be repeated here.

[0114] Step 204: Determine the theoretical impedance value, error vector value, and objective function value based on the initial distributed parameter values, impedance measurement values, and impedance expression.

[0115] The initial distributed parameter values ​​can be initially estimated based on empirical formulas and high-frequency impedance characteristics, or they can be determined in other ways. This application does not limit this.

[0116] In this process, after obtaining multiple impedance measurements by performing impedance tests on the supercapacitor, the theoretical impedance value can be determined using the initial distributed parameter values ​​and the impedance expression. The absolute value of the difference between the theoretical impedance value and the measured impedance value can then be defined as the error value. It is understandable that, since there are multiple impedance measurements, the impedance is a complex number, and there are multiple distributed parameters, the error value between each measured impedance value and the theoretical impedance value can be expressed as an error vector value: e = |Z| exp (f i )-Z exp (f i The objective function value can be expressed as:

[0117] Among them, Z exp (f i Z represents the impedance measurement value actually obtained at frequency fi. th (f i ,θ) is the frequency f i The theoretical impedance value obtained from the transmission line equation and impedance expression, where θ is the value containing all distributed parameters [R1, R2, ..., R2].

[0118] R N C1, C2, ..., C N Rl1, Rl2, ..., Rl N The vector of ].

[0119] Step 205: Determine the Jacobian matrix based on the initial distributed parameter values ​​and theoretical impedance values ​​corresponding to the N infinitesimal elements.

[0120] After determining the initial distributed parameter values ​​and theoretical impedance values ​​corresponding to each micro-element, the initial distributed parameter values ​​can be slightly perturbed, and the corresponding theoretical impedance values ​​can be recalculated using the slightly perturbed distributed parameter values. The results are then processed and used as elements in the Jacobian matrix to determine the Jacobian matrix.

[0121] Optionally, the initial distributed parameter values ​​can be subjected to temporary positive and temporary negative perturbations with small step sizes to obtain temporary positive and temporary negative parameter values. Then, the temporary positive and temporary negative parameter values ​​can be used to determine the corresponding temporary positive and temporary negative impedance theoretical values. The temporary positive and temporary negative impedance theoretical values ​​are then processed to determine the Jacobian matrix.

[0122] The micro-step size can be a pre-set step size value, or it can be adjusted according to actual needs, etc. This application does not limit it in this regard.

[0123] In addition, the rows of the Jacobian matrix correspond to the test frequency f for impedance testing of supercapacitors. i The column corresponds to each distribution parameter θ j .

[0124] Alternatively, temporary positive and negative perturbations can be applied to only one initial distribution parameter value at a time to obtain the corresponding temporary positive and negative parameter values. These temporary positive and negative parameter values ​​can then be substituted into the impedance expression to determine the corresponding theoretical values ​​of the temporary positive and negative impedances. Based on these theoretical values, the first-order partial derivatives of the central difference approximation can be calculated, and these results can be used as elements of the Jacobian matrix. Then, temporary positive and temporary negative perturbations can be applied to each initial distribution parameter value in sequence, and the above process can be repeated to determine each element of the Jacobian matrix and construct the Jacobian matrix.

[0125] Step 206: Determine the parameter increment based on the initial distribution parameter values, error vector values, and Jacobian matrix.

[0126] It is understandable that the following relationship can be satisfied when updating the parameters:

[0127] θ k+1 =θ k -(J T ·J+λ·I) -1 ·J T ·e

[0128] Where θ represents all distribution parameters, including [R1, R2, ..., R...]. N C1, C2, ..., C N， Rl1,Rl2,...,Rl N ], where J is the Jacobian matrix, λ is the adaptive damping factor, and e is the error vector.

[0129] The parameter increment for each distribution parameter can be determined by solving the initial distribution parameter values, error vector values, Jacobian matrix, and the relational expression satisfied during parameter update.

[0130] Step 207: Update the initial distributed parameters according to the parameter increment, and use the updated distributed parameter values ​​to return to the steps of determining the theoretical impedance value, error vector value, and objective function value, until the objective function converges and the estimated value of the distributed parameters is determined.

[0131] Understandably, after determining the parameter increment for each distributed parameter, this increment can be used to update the distributed parameters. Then, using the updated distributed parameter values, the measured impedance value, and the impedance expression, the theoretical impedance value, error vector value, and objective function value corresponding to the updated distributed parameter values ​​can be redefined. Next, the updated Jacobian matrix is ​​determined, and a new parameter increment is identified. The distributed parameters are then updated again, and this process is repeated iteratively until the objective function converges. The distributed parameter values ​​at convergence are then used as estimates of each distributed parameter. Alternatively, after reaching a preset number of iterations, the current distributed parameter values ​​can be used as estimates of each distributed parameter.

[0132] Step 208: Solve the transmission line equations based on the estimated values ​​of the distributed parameters to determine the voltage distribution.

[0133] Step 209: Determine the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance.

[0134] It is understandable that the characteristics of leakage current are closely related to the specific loss mechanism, and different loss mechanisms have significantly different frequencies. For example, ohmic leakage caused by diaphragm resistance, contact resistance, etc., is usually independent of frequency and exhibits constant loss; Faraday leakage caused by redox reactions of electrode materials is usually inversely proportional to frequency; diffusion leakage caused by the diffusion process of ions in electrode pores is usually inversely proportional to the square root of the frequency; other leakage currents, such as electrolyte decomposition and self-discharge, also exist, but this application does not limit these.

[0135] Optionally, after determining the estimated values ​​of each distribution parameter, a multi-mechanism superposition model can be established based on the frequency characteristics of each leakage mechanism to determine the conductivity coefficient of each leakage mechanism. Then, based on the conductivity coefficient of each leakage mechanism and the operating voltage, the leakage current under each leakage mechanism can be determined.

[0136] The multi-mechanism superposition model can be represented as follows:

[0137]

[0138] Where: 1 / R(f) is the total admittance, f is the frequency, G0 is the conductivity of ohmic leakage, G1 is the conductivity of Faraday leakage, G2 is the conductivity of diffuse leakage, G3 is the conductivity of other leakage mechanisms, and α is the parameter of other leakage mechanisms.

[0139] Optionally, after determining the estimated value of the distributed parameters, the total port impedance can be determined based on the estimated value of the distributed parameters and the impedance expression, and the total admittance can be obtained by inverting it. Alternatively, other methods can be used to determine the total admittance, which is not limited in this application.

[0140] Understandably, after solving the above multi-mechanism superposition model, the coefficients can be obtained. Then, based on the relationship between the coefficients and the frequency, the conductivity under various leakage mechanisms can be determined. Finally, the conductivity under various leakage mechanisms is multiplied by the operating voltage, and the resulting product is the leakage current under the corresponding leakage mechanism.

[0141] The operating voltage can be understood as the voltage applied to the supercapacitor. Its value can be the rated operating voltage or it can be adjusted according to the actual operating conditions. This application does not limit this.

[0142] Therefore, in this embodiment of the application, after determining the estimated values ​​of each distribution parameter, a multi-mechanism superposition model can be established based on the frequency characteristics of each leakage mechanism, and processed to determine the conductivity coefficient of each leakage mechanism. Then, based on the conductivity coefficient of each leakage mechanism and the operating voltage, the leakage current under each leakage mechanism can be determined. Thus, based on the leakage current under various leakage mechanisms, various losses can be clearly seen, thereby improving the accuracy of leakage current assessment.

[0143] The method for determining the leakage current of a supercapacitor provided in this application can be applied to any type of supercapacitor in any scenario, and this application does not limit it.

[0144] The following section uses a standard supercapacitor as an example to illustrate the process of determining the leakage current of the supercapacitor provided in this application.

[0145] First, the supercapacitor can be divided into N infinitesimal elements along the electrode thickness direction to establish a transmission line model. The equivalent circuit model of this transmission line is as follows: Figure 3 As shown, the distribution parameters include [R1, R2, ..., R]. N C1, C2, ..., C N , Rl1,Rl2,...,Rl N The test system block diagram used to test this supercapacitor can be shown as follows. Figure 4 As shown.

[0146] The supercapacitor has a capacitance of 3000F and a rated voltage of 2.7V. The entire measurement hardware can be supplied by...

[0147] The Solartron 1260A frequency response analyzer consists of three parts: a temperature and humidity chamber, and a four-wire Kelvin test fixture. It can perform impedance testing on supercapacitors within an extremely wide frequency band of 1μHz-32MHz, with a current resolution of 1pA, a voltage resolution of 1μV, and a phase accuracy of 0.01°. The temperature and humidity chamber provides a temperature environment of -40℃ to 160℃ with a temperature control accuracy of ±0.1℃, and humidity can be maintained at ±2%RH. The test fixture uses a four-wire Kelvin structure with shielding effectiveness exceeding 60dB (10kHz-1 GHz), contact resistance below 10mΩ, and parasitic capacitance less than 1pF, ensuring signal purity and reliable connection.

[0148] The supercapacitor can then be pre-treated. This includes a sample inspection, such as a visual inspection to confirm the capacitor casing is undamaged and undeformed; an electrical inspection to measure the static capacitance value and confirm it is within ±10% of the nominal value; and a pre-charge check by charging to the rated voltage at the rated current and allowing it to stand for 2 hours. After this, the sample can be installed. The electrode surfaces of the supercapacitor can be cleaned with anhydrous ethanol, and a Kelvin four-terminal connection can be used, separating the current and voltage terminals. The supercapacitor casing is then connected to the shielding ground of the test fixture, and the contact resistance between each terminal is measured to ensure it is <5mΩ. The required test temperature is 25.0±0.1℃, relative humidity is 45±2%RH, and the air pressure is standard atmospheric pressure. The supercapacitor must stabilize in the test environment for more than 30 minutes.

[0149] In addition, regarding the electrical parameters used, the test frequency points can be from 1mHz to 10kHz, a total of 120 frequency points. The excitation voltage is a sine wave of 10mV (RMS). The DC bias can be 1.35V, which is 50% of the rated voltage. Measurement begins after each frequency point has stabilized for 5 seconds, and the frequency is automatically adjusted according to the frequency, with longer durations for low frequencies and shorter durations for high frequencies. During data acquisition, the sampling period should exceed 10 complete signal cycles, with more than 100 sampling points per cycle. Each frequency point should be measured 3 times, and the average value can be taken. The impedance is in complex form, such as Z = Z' + jZ.

[0150] In addition, for the transmission line model parameter settings, the electrode thickness L is 200 μm, N is 20 (i.e., divided into 20 micro-elements), each micro-element has a thickness Δx of 10 μm, and the electrode area S is 500 cm². 2This refers to the effective electrode area, with a porosity ε of 0.35. Additionally, initial estimates can be made based on empirical formulas and high-frequency impedance characteristics. For example, the initial value of the distributed resistance is R0(x) = ρ_eff / (ε·S) = 1.2 mΩ·cm, where ρ_eff is the effective resistivity of the electrolyte. The initial value of the distributed capacitance is C0(x) = C_total / L = 15 F / cm, and the initial value of the distributed leakage resistance is Rl0(x) = R_leak·L = 60 Ω·cm. During the test, the distributed resistance R(x) ranges from 0.1 mΩ·cm to 100 mΩ·cm, the distributed capacitance C(x) ranges from 1 F / cm to 50 F / cm, and the distributed leakage resistance Rl(x) ranges from 1 Ω·cm to 10 kΩ·cm.

[0151] Subsequently, multi-frequency impedance testing was performed on the supercapacitor to obtain multiple impedance measurements. The method for determining the leakage current of the supercapacitor provided in this application was used, and the test results are shown below. At a rated voltage of 2.7V, the total leakage current Il = 2.50 ± 0.05mA, the ohmic leakage current is 1.63mA (65.2%), the Faraday leakage current is 0.75mA (30.0%), and the diffusion leakage current is 0.12mA (4.8%). The distributed resistance R(x) ranges from 0.8 to 1.5mΩ·cm, with a larger value near the separator; the distributed capacitance C(x) ranges from 12 to 18F / cm, with a larger value in the middle of the electrodes; the distributed leakage resistance R(x) ranges from 60 to 120Ω·cm, exhibiting a non-uniform distribution.

[0152] In addition, during data processing, the goodness of fit R... 2 The value is 0.9985, the residuals are normally distributed, there is no systematic bias, and the relative uncertainty is less than 5% at the 95% confidence level.

[0153] The following tests were conducted on supercapacitors of different capacity specifications using the method for determining the leakage current of the supercapacitor provided in this application to verify the applicability of the method.

[0154] The supercapacitors used are: Supercapacitor A (small capacity, 100F, rated voltage, 2.5V, 50μm electrode thickness, used in portable devices); Supercapacitor B (medium capacity, 1000F, rated voltage, 2.7V, 150μm electrode thickness, used in hybrid vehicles); and Supercapacitor C (5000F, 3.0V, 300μm electrode thickness, used in energy storage systems). Test parameters can be adjusted for each supercapacitor. For example, the test frequency is 10mHz-100kHz for Supercapacitor A, 1mHz-10kHz for Supercapacitor B, and 0.1mHz-1kHz for Supercapacitor C. The excitation voltage is 5mV for Supercapacitor A to avoid nonlinear effects; 10mV for Supercapacitor B; and 15mV for Supercapacitor C to improve the signal-to-noise ratio. In terms of micro-element division, supercapacitor A, due to its thinner electrodes and fewer layers, is divided into 10 micro-elements, i.e., N = 10; supercapacitor B is divided into 15 micro-elements, i.e., N = 15; and supercapacitor C, due to its thicker electrodes, requires more precise division, so it can be divided into 25 micro-elements, i.e., N = 25.

[0155] The method for determining the leakage current of the supercapacitor provided in this application was then used, and the test results are shown below. The total leakage current of supercapacitor A was 0.8 mA, the ohmic leakage current was 0.5 mA (62.5%), the Faraday leakage current was 0.25 mA (31.3%), and the leakage current of other types was 0.05 mA (6.2%). The test took 15 minutes, and the goodness of fit R0 was [value missing]. 2 The goodness-of-fit is 0.996. The total leakage current of supercapacitor B is 1.8 mA, of which ohmic leakage current is 1.1 mA (61.1%), Faraday leakage current is 0.6 mA (33.3%), and other leakage currents are 0.1 mA (5.6%). The test took 25 minutes, and the goodness-of-fit R² was 0.996. 2 The goodness-of-fit is 0.998. The total leakage current of supercapacitor C is 4.2 mA, of which ohmic leakage current is 2.8 mA (66.7%), Faraday leakage current is 1.2 mA (28.6%), and other leakage currents are 0.2 mA (4.7%). The test took 35 minutes, and the goodness-of-fit R0 was 0.998. 2 It is 0.997.

[0156] In addition, regarding the parameter distribution characteristics of the above-mentioned supercapacitors, the parameter distribution of the small-capacity supercapacitor A is relatively uniform and the electrode structure is simple. The parameters of the medium-capacity supercapacitor B show a gradient distribution and are related to the electrolyte concentration. The parameter distribution of the large-capacity supercapacitor C is complex and has obvious non-uniformity.

[0157] Therefore, through the above comparative analysis, it can be seen that the method for determining the super leakage current provided in this application is applicable to a capacity range of 100F-5000F, which can cover the main application scenarios. The voltage range used is 2.5V-3.0V, which is suitable for common voltage levels. The goodness of fit of all samples is greater than 0.995, indicating high test accuracy. The test time increases with the capacity, but is less than 40 minutes, which means the test time is short and the test efficiency is improved.

[0158] In this embodiment, the supercapacitor can first be equivalently divided into N micro-elements, and a transmission line equation can be established. The distributed parameters in the transmission line equation include distributed resistance, distributed capacitance, and distributed leakage resistance. The transmission line equation is processed to determine the impedance expression. Impedance tests are performed on the supercapacitor at different frequencies to obtain multiple impedance measurements. Then, based on the initial distributed parameter values, impedance measurements, and impedance expression, the theoretical impedance value, error vector value, and objective function value can be determined. Based on the initial distributed parameter values ​​and the theoretical impedance value corresponding to the N micro-elements, the Jacobian matrix is ​​determined. Then, based on the initial distributed parameter values, error vector values, and the Jacobian matrix, the parameter increment is determined. The initial distributed parameters are then updated based on the parameter increment. The updated distributed parameter values ​​are used to return to the steps of determining the theoretical impedance value, error vector value, and objective function value until the objective function converges and the estimated value of the distributed parameters is determined. Then, based on the estimated value of the distributed parameters, the transmission line equation is solved to determine the voltage distribution. Based on the voltage distribution and the estimated value of the distributed leakage resistance, the leakage current value of the supercapacitor is determined. Therefore, by performing equivalent processing on the supercapacitor, the corresponding transmission line equation and impedance expression can be determined. Then, by using the measured impedance value and impedance expression, the transmission line equation can be solved by inversion. Thus, the leakage current value of the supercapacitor can be quickly determined without waiting for a long time, which greatly improves the testing efficiency of supercapacitor leakage current.

[0159] According to this application, a device 500 for determining the leakage current of a supercapacitor is provided, such as... Figure 5 As shown, the device includes an equivalent module 510, a processing module 520, a testing module 530, a first determining module 540, a second determining module 550, and a third determining module 560.

[0160] The equivalent module 510 is used to divide the supercapacitor into N micro-elements and establish transmission line equations. The distributed parameters in the transmission line equations include distributed resistance, distributed capacitance, and distributed leakage resistance.

[0161] The processing module 520 is used to process the transmission line equation to determine the impedance expression.

[0162] The test module 530 is used to test the supercapacitor to obtain multiple impedance measurements.

[0163] The first determining module 540 is used to determine the estimated value of the distributed parameter based on the plurality of impedance measurements and the impedance expression, when the convergence condition is met.

[0164] The second determining module 550 is used to solve the transmission line equation based on the estimated values ​​of the distribution parameters to determine the voltage distribution.

[0165] The third determining module 560 is used to determine the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance.

[0166] Optionally, the processing module 520 is specifically used for:

[0167] The transmission line equations are processed to determine the chain parameter matrix of each of the infinitesimal elements and the total chain parameter matrix;

[0168] Based on the chain parameter matrix and the total chain parameter matrix, the impedance expression is determined.

[0169] Optionally, the first determining module 540 includes:

[0170] The first determining unit is used to determine the theoretical impedance value, the error vector value, and the objective function value based on the initial distributed parameter value, the measured impedance value, and the impedance expression.

[0171] The second determining unit is used to determine the Jacobian matrix based on the initial distribution parameter values ​​corresponding to the N micro-elements and the theoretical impedance values;

[0172] The third determining unit is used to determine the parameter increment based on the initial distribution parameter value, the error vector value, and the Jacobian matrix;

[0173] The update unit is used to update the initial distribution parameters according to the parameter increment, and use the updated distribution parameter values ​​to return to the steps of determining the theoretical impedance value, error vector value and objective function value until the objective function converges, and to determine the estimated value of the distribution parameters.

[0174] Optionally, the second determining unit is specifically used for:

[0175] The initial distribution parameter values ​​are subjected to temporary positive and temporary negative perturbations with small step sizes to obtain temporary positive and temporary negative parameter values.

[0176] Using the aforementioned temporary positive and temporary negative parameter values, determine the corresponding theoretical values ​​of temporary positive and temporary negative impedances;

[0177] The theoretical values ​​of the temporary positive impedance and the temporary negative impedance are processed to determine the Jacobian matrix.

[0178] Optionally, the third determining module 560 is specifically used for:

[0179] Based on the distributed voltage and the distributed leakage resistance at each micro-element location, determine the local leakage current density corresponding to each micro-element;

[0180] The leakage current value of the supercapacitor is determined by integrating the local leakage current density.

[0181] Optionally, the first determining module 540 is further configured to:

[0182] Based on the frequency characteristics of each leakage mechanism, a multi-mechanism superposition model is established to determine the conductivity coefficient of each leakage mechanism.

[0183] Based on the conductivity coefficient and operating voltage of each leakage mechanism, the leakage current under each leakage mechanism is determined.

[0184] Optionally, the test module 530 is specifically used for:

[0185] Impedance tests were performed on the supercapacitor at different frequencies to obtain multiple raw impedance measurements;

[0186] The original impedance measurements are preprocessed to determine the corresponding impedance measurements.

[0187] The device for determining the leakage current of a supercapacitor provided in this application can first divide the supercapacitor into N equivalent micro-elements and establish a transmission line equation, where distributed parameters include distributed resistance, distributed capacitance, and distributed leakage resistance. Then, the transmission line equation can be processed to determine the impedance expression. Multiple impedance measurements are obtained by testing the supercapacitor. Based on these measurements and the impedance expression, and provided the convergence condition is met, the estimated values ​​of the distributed parameters are determined. Then, based on these estimated values, the transmission line equation is solved to determine the voltage distribution. Finally, based on the voltage distribution and the estimated value of the distributed leakage resistance, the leakage current value of the supercapacitor is determined. Thus, by equivalent processing of the supercapacitor, the corresponding transmission line equation and impedance expression can be determined. Then, by using the measured impedance values ​​and the impedance expression, the transmission line equation can be solved by inversion, thereby quickly determining the leakage current value of the supercapacitor without waiting for a long time, greatly improving the testing efficiency of supercapacitor leakage current.

[0188] It should be understood that the specific features, operations, and details described herein with respect to the methods of this application can also be similarly applied to the apparatus and system of this application, or vice versa. Furthermore, each step of the methods of this application described above can be performed by a corresponding component or unit of the apparatus or system of this application.

[0189] It should be understood that the various modules / units of the device of this application can be implemented wholly or partially through software, hardware, firmware, or a combination thereof. Each module / unit can be embedded in the processor of the electronic device in hardware or firmware form or independent of the processor, or it can be stored in the memory of the electronic device in software form for the processor to call to execute the operation of each module / unit. Each module / unit can be implemented as an independent component or module, or two or more modules / units can be implemented as a single component or module.

[0190] like Figure 6 As shown, this application provides an electronic device 600, which includes a processor 601 and a memory 602 storing computer program instructions. The processor 601 executes the computer program instructions to implement the steps of the above-described method for determining the leakage current of a supercapacitor. This electronic device 600 can be broadly categorized as a server, terminal, or any other electronic device with the necessary computing and / or processing capabilities.

[0191] In one embodiment, the electronic device 600 may include a processor, memory, network interface, communication interface, etc., connected via a system bus. The processor of the electronic device 600 can be used to provide necessary computing, processing, and / or control capabilities. The memory of the electronic device 600 may include non-volatile storage media and internal memory. The non-volatile storage media may store an operating system, computer programs, etc. The internal memory can provide an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface and communication interface of the electronic device 600 can be used to connect and communicate with external devices via a network. When the computer program is executed by the processor, it performs the steps of the method of this application.

[0192] This application provides a computer-readable storage medium storing computer program instructions, which, when executed by a processor, implement the above-described method for determining the leakage current of a supercapacitor.

[0193] Those skilled in the art will understand that the method steps of this application can be performed by a computer program instructing related hardware, such as electronic device 600 or a processor. The computer program can be stored in a non-transitory computer-readable storage medium, and its execution causes the steps of this application to be performed. Depending on the context, any reference herein to memory, storage, or other media may include non-volatile or volatile memory. Examples of non-volatile memory include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, magnetic tape, floppy disk, magneto-optical data storage device, optical data storage device, hard disk, solid-state drive, etc. Examples of volatile memory include random access memory (RAM), external cache memory, etc.

[0194] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification, provided that such combination does not contain contradictions.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for determining the leakage current of a supercapacitor, characterized in that, include: The supercapacitor is equivalently divided into N micro-elements, and a transmission line equation is established. The distributed parameters in the transmission line equation include distributed resistance, distributed capacitance, and distributed leakage resistance. The transmission line equations are processed to determine the impedance expression; The supercapacitor was tested to obtain multiple impedance measurements; Based on the multiple impedance measurements and the impedance expression, the estimated value of the distributed parameter is determined when the convergence condition is met. Based on the estimated values ​​of the distribution parameters, the transmission line equations are solved to determine the voltage distribution; The leakage current value of the supercapacitor is determined based on the voltage distribution and the estimated value of the distributed leakage resistance.

2. The method as described in claim 1, characterized in that, The process of processing the transmission line equation to determine the impedance expression includes: The transmission line equations are processed to determine the chain parameter matrix of each of the infinitesimal elements and the total chain parameter matrix; Based on the chain parameter matrix and the total chain parameter matrix, the impedance expression is determined.

3. The method as described in claim 1, characterized in that, The step of determining the estimated value of the distributed parameter based on the plurality of impedance measurements and the impedance expression, when the convergence condition is met, includes: Based on the initial distributed parameter values, the measured impedance values, and the impedance expression, determine the theoretical impedance value, the error vector value, and the objective function value; The Jacobian matrix is ​​determined based on the initial distribution parameter values ​​corresponding to the N infinitesimal elements and the theoretical impedance values. The parameter increment is determined based on the initial distribution parameter value, the error vector value, and the Jacobian matrix; The initial distributed parameters are updated based on the parameter increments. The updated distributed parameter values ​​are then used to return and execute the steps of determining the theoretical impedance value, error vector value, and objective function value until the objective function converges, thereby determining the estimated value of the distributed parameters.

4. The method as described in claim 3, characterized in that, The step of determining the Jacobian matrix based on the initial distribution parameter values ​​corresponding to the N infinitesimal elements and the theoretical impedance value includes: The initial distribution parameter values ​​are subjected to temporary positive and temporary negative perturbations with small step sizes to obtain temporary positive and temporary negative parameter values. Using the aforementioned temporary positive and temporary negative parameter values, determine the corresponding theoretical values ​​of temporary positive and temporary negative impedances; The theoretical values ​​of the temporary positive impedance and the temporary negative impedance are processed to determine the Jacobian matrix.

5. The method as described in claim 1, characterized in that, Determining the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance includes: Based on the distributed voltage and the distributed leakage resistance at each micro-element location, determine the local leakage current density corresponding to each micro-element; The leakage current value of the supercapacitor is determined by integrating the local leakage current density.

6. The method as described in claim 1, characterized in that, After determining the estimated value of the distribution parameter, the method further includes: Based on the frequency characteristics of each leakage mechanism, a multi-mechanism superposition model is established to determine the conductivity coefficient of each leakage mechanism. Based on the conductivity coefficient and operating voltage of each leakage mechanism, the leakage current under each leakage mechanism is determined.

7. The method as described in claim 1, characterized in that, The supercapacitor is tested to obtain multiple impedance measurements, including: Impedance tests were performed on the supercapacitor at different frequencies to obtain multiple raw impedance measurements; The original impedance measurements are preprocessed to determine the corresponding impedance measurements.

8. A device for determining the leakage current of a supercapacitor, characterized in that, include: An equivalent module is used to divide a supercapacitor into N micro-elements and establish a transmission line equation, wherein the distributed parameters in the transmission line equation include distributed resistance, distributed capacitance and distributed leakage resistance. The processing module is used to process the transmission line equation to determine the impedance expression; The testing module is used to test the supercapacitor to obtain multiple impedance measurements. The first determining module is used to determine the estimated value of the distributed parameter based on the plurality of impedance measurements and the impedance expression, when the convergence condition is met. The second determining module is used to solve the transmission line equation based on the estimated values ​​of the distribution parameters to determine the voltage distribution; The third determining module is used to determine the leakage current value of the supercapacitor based on the voltage distribution and the estimated value of the distributed leakage resistance.

9. The apparatus as claimed in claim 8, characterized in that, The processing module is specifically used for: The transmission line equations are processed to determine the chain parameter matrix of each of the infinitesimal elements and the total chain parameter matrix; Based on the chain parameter matrix and the total chain parameter matrix, the impedance expression is determined.

10. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the method for determining the leakage current of the supercapacitor as described in any one of claims 1-7.

Images