A supercapacitor equivalent circuit parameter identification method for sparse data

Abstract

The present invention provides a supercapacitor equivalent circuit parameter identification method suitable for sparse data. Based on the interior point function method, under the constraint conditions of the upper and lower limits of the identification parameters, the circuit parameters are directly selected as the solution variables, and the solution variables are corrected by the model terminal voltage error to achieve parameter identification. This method avoids the intermediate link of solving the coefficients of the differential equation, and improves the stability of the algorithm under conditions of sparse data and interference. At the same time, the algorithm performs identification within the set parameter range, which ensures the rationality of the identification results to a certain extent. The parameter identification method proposed in the present invention enables a large amount of long-term accumulated supercapacitor vehicle monitoring sparse data to be utilized, provides a new idea for extracting supercapacitor aging information under sparse data, and is of great significance to the prediction and optimization management of supercapacitor service life.

Description

Technical Field

[0001] The invention relates to a supercapacitor equivalent circuit parameter identification method suitable for sparse data, which can be used in the technical field of energy storage system management. Background Art

[0002] Supercapacitors have the characteristics of high power density, long cycle life, and wide operating temperature range, and are widely used in urban buses, trams and other means of transportation. Supercapacitor on-board equipment transmits the collected voltage, current, temperature and other data to the background data center through wireless communication. Aging information can be mined from the background historical monitoring data to evaluate the degree of supercapacitor aging, and further use data-driven methods to predict the service life of supercapacitors. Accurate supercapacitor parameter identification methods can extract aging characteristic parameters such as supercapacitor internal resistance and capacitance, which is the basis for supercapacitor aging analysis.

[0003] Limited by the communication rate and economic cost, the sampling frequency of the monitoring data transmitted back by the supercapacitor vehicle management system is generally 0.1Hz, which is lower than the 2Hz sampling frequency requirement commonly used in general parameter identification methods, that is, the data has obvious sparsity. In addition, the vehicle operating conditions are complex and changeable, and there are many sampling interferences, which will bring difficulties to parameter identification. Traditional parameter identification methods such as the least squares method solve the differential equation coefficients through the voltage and current signals and then inversely calculate the model parameters. Under the condition of sparse data, the identification results have large errors and are even outside the reasonable range. Therefore, this field needs a supercapacitor parameter identification method suitable for sparse data conditions to make full use of the historical monitoring data of supercapacitors with low sampling rates. Summary of the invention

[0004] The present invention proposes a supercapacitor parameter identification method suitable for sparse data conditions, which solves the problem of large errors in traditional parameter identification methods under sparse data conditions and realizes the extraction of aging information contained in low sampling rate monitoring data.

[0005] Technical Solution

[0006] In order to solve the problem of parameter identification difficulties caused by the sparse monitoring data of actual supercapacitors, the present invention constructs a fitness function that characterizes the error of the identification result based on the first-order equivalent circuit model of the supercapacitor and the voltage and current data; and solves the optimization algorithm that minimizes the fitness function through the interior point penalty function method to achieve accurate identification of supercapacitor parameters under sparse data.

[0007] Compared with the existing methods, the present invention has the following beneficial effects:

[0008] The present invention directly selects series internal resistance, parallel capacitor and parallel resistor as optimization targets, avoids the error caused by solving intermediate parameters and improves the accuracy of parameter identification; transforms the parameter identification problem into a nonlinear optimization problem, and adopts the optimization algorithm of interior point penalty function to solve the optimization target, so that the parameter identification algorithm can be carried out within the set range, ensuring the convergence of parameter identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is a schematic diagram of the steps for implementing the method of the present invention;

[0010] Figure 2 A schematic diagram of a supercapacitor equivalent circuit model selected for a specific embodiment of the present invention;

[0011] Figure 3 A schematic diagram of the steps of the interior point penalty function method selected for a specific implementation mode of the present invention;

[0012] Figure 4 Parameter identification effect when the sampling rate is 1Hz;

[0013] Figure 5 Parameter identification effect when the sampling rate is 0.1Hz; DETAILED DESCRIPTION

[0014] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments:

[0015] The technical solution of the present invention has the following steps: Figure 1 As shown:

[0016] Step 1: Under laboratory test conditions, perform a random variable current discharge experiment on the supercapacitor to be tested, and measure the supercapacitor terminal voltage U and current I.

[0017] Step 2: Establish the state space equation for the selected supercapacitor first-order equivalent circuit model.

[0018] The first-order equivalent circuit model of the supercapacitor is as follows: Figure 2 As shown, including the series internal resistance R s , parallel resistance R p And the parallel capacitor C p ; I is the current flowing through the supercapacitor model, which has the same meaning as the measured current I; U t and U p They represent the terminal voltage of the supercapacitor model and the parallel branch voltage respectively. The discrete state space equation is shown in formula (1):

[0019]

[0020] Where k represents the discrete time mark, T sRepresents the sampling interval, which is the same as the sampling frequency f s The relationship is T s =1 / f s , in this case, the sampling frequency f s The following values ​​are taken: 1 Hz, 0.1 Hz, to verify the performance of the present invention under two sparse data conditions. From formula (1), it can be seen that when the model current I and the initial capacitor voltage U are known, p (0), the terminal voltage U of the supercapacitor model at each time k can be derived: t (k). The solution of the discrete state space equation can be obtained from the knowledge of linear control theory, as shown in equation (2).

[0021]

[0022] in,

[0023] Step 3: Construct a fitness function based on the collected data and the solution of the state-space equation.

[0024] The circuit parameters to be identified are regarded as the parameter vector to be solved The output voltage U of the model is measured by the sum of squared differences t The error between the collected voltage signal U is recorded as the fitness function f(x), as shown in formula (3), where N is the total number of voltage signal collections.

[0025]

[0026] Step 4: Optimize the parameter vector to be solved based on the interior point penalty function method to obtain the identification result.

[0027] The identification problem of the parameter vector x to be solved is equivalent to an inequality constrained optimization problem in the feasible domain of x:

[0028]

[0029] That is, optimize and solve between the upper and lower limits of x to achieve the goal of minimizing the fitness function f(x), where x m is the mth component of x, x m,lower and x m,upper x m The upper and lower limits of the value of g1(x)~g8(x) represent the constraint functions of the solution variables. The interior point penalty function method constructs an auxiliary function by taking the sum of the natural logarithms of the constraint functions as the penalty term P(x), so that the optimization process can be carried out within the feasible domain formed by the constraint conditions:

[0030]

[0031] Where μ is the penalty parameter. The following are the specific steps of the interior point function method optimization: Figure 3 As shown:

[0032] 4.1 Based on the given upper and lower limits of parameter identification and the acquisition of voltage and current signals, the optimization problem is summarized as formula (4).

[0033] 4.2 Initialization: Initial solution x(0) = [R s0 ,R p0 ,C p0 ,U p0 ] T , precision ε = 10 -8 ,

[0034] 4.2 Penalty parameter exponent takes values ​​r=0,1,2,3…10 in sequence, let penalty parameter μ=10 r , performed under different penalty parameters:

[0035] 4.2.1 Construct auxiliary functions:

[0036]

[0037] 4.2.2 Assignment: x [0] (r) = x(r), iteration flag i = 0

[0038] 4.2.3 Recursive optimization solution variable: x [i+1] (r) = x [i] (r)-H -1 (x [i] (r))G(x [i] (r)), where G(x) and H(x) are functions F μ The Jacobian matrix and Hessian matrix of (x) represent the function F μ The first-order derivative information and second-order derivative information of (x). The iterative optimization process is in the iterative step effect threshold ||x [i+1] (r)-x [i] (r)||≤ε or when the maximum number of iterations i=100 is reached, stop and assign x(r+1)=x [i+1] (r), otherwise continue the recursion i=i+1.

[0039] 4.2.4 If Or r=10, the solution process ends, otherwise the penalty parameter is increased exponentially by r=r+1 and the solution continues.

[0040] 4.3 After the optimization process is completed, x(r+1) is the parameter identification result, which is recorded as:

[0041]

[0042] Step 5: Identify the parameter results Substitute into formula (2) to obtain the terminal voltage of the supercapacitor model under this parameter: By comparing with the actual collected voltage U and calculating the average absolute error between the two, the parameter identification effect can be illustrated, as shown in formula (8).

[0043]

[0044] In an embodiment of the present invention, a supercapacitor module of model K12 is selected as the research object, with a rated capacity of 15Ah, a charge and discharge cut-off voltage of 48V and 30V respectively, and a maximum charge and discharge current of 100A. The experimental working condition is a random variable current working condition. The terminal voltage measured by the supercapacitor test system is used as a reference value to compare the terminal voltage estimate after the parameter identification result is brought into the first-order model as an error, and the OCV-SOC (open circuit voltage-state of charge) curve interpolation result is used as a reference value to analyze the identification error of the initial voltage of the supercapacitor parallel branch, and the accuracy of the algorithm is verified from the above two aspects. At the same time, the algorithm proposed in the present invention is compared with the parameter identification algorithm based on least squares in the case of sparse data to illustrate the applicability of the algorithm when the data is sparse.

[0045] from Figure 4 It can be seen that when the sampling rate is 1 Hz, both the parameter identification method based on the interior point penalty function proposed in the present invention and the traditional least squares method can achieve relatively accurate parameter identification effects. The simulated voltages of the two are basically consistent with the measured voltages. In individual data segments, the method proposed in the present invention is slightly better than the least squares method.

[0046] from Figure 5 It can be seen that when the signal sampling rate is further reduced to 0.1Hz, the parameter identification method based on the interior point penalty function proposed in the present invention can still accurately identify the parameters, and its simulated voltage is basically consistent with the measured voltage value, while the traditional least squares rule has a large voltage error. It can be seen that when the signal sampling rate is reduced, the method proposed in the present invention is an effective means for sparse data parameter identification.

[0047] This implementation case is only a preferred implementation mode of the present invention. It should be noted that without departing from the spirit and essence of the present invention, technical personnel familiar with the field can make various corresponding changes and deformations according to the present invention, but these changes and deformations should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A supercapacitor equivalent circuit parameter identification method suitable for sparse data, characterized in that: Includes steps: Step 1: Under laboratory test conditions, perform a random variable current discharge experiment on the supercapacitor to be tested, and measure the supercapacitor terminal voltage U and current I; Step 2: Establish a state space equation for the selected supercapacitor first-order equivalent circuit model; Step 3: Construct a fitness function based on the collected data and the solution of the state space equation; Step 4: Optimize the parameter vector to be solved based on the interior point penalty function method to obtain the identification result; Step 5: The parameter results obtained by identification are used to illustrate the identification effect; In step 2, specifically: The first-order equivalent circuit model of the supercapacitor includes a series internal resistance R s , parallel resistance R p And the parallel capacitor C p ; I is the current flowing through the supercapacitor model, which has the same meaning as the measured current I; U t and U p They represent the terminal voltage of the supercapacitor model and the parallel branch voltage respectively. The discrete state space equation is shown in formula (1): Where k represents the discrete time mark, T s Represents the sampling interval, which is the same as the sampling frequency f s The relationship is T s =1 / f s , it can be seen from formula (1) that when the model current I and the initial capacitor voltage U are known p (0), the terminal voltage U of the supercapacitor model at each k moment is derived. t (k); the solution of the discrete state space equation is obtained, as shown in equation (2); in, In step 3, specifically: The circuit parameters to be identified are regarded as the parameter vector to be solved x = [x1, x2, x3, x4] T =[R s ,R p ,C p ,U p (0)] T , the model output voltage U is measured by the sum of squared differences t The error between the collected voltage signal U is recorded as the fitness function f(x), as shown in formula (3), where N is the total number of voltage signal collections; In step 4, specifically: The identification problem of the parameter vector x to be solved is equivalent to an inequality constrained optimization problem in the feasible domain of x: That is, optimize and solve between the upper and lower limits of x to achieve the goal of minimizing the fitness function f(x), where x m is the mth component of x, x m,lower and x m,upper x m The upper and lower limits of the value of g1(x)~g8(x) represent the constraint functions of the solution variables; the interior point penalty function method constructs an auxiliary function through the sum of the natural logarithms of the constraint functions as the penalty term P(x), so that the optimization process can be carried out within the feasible domain formed by the constraint conditions: Where μ is the penalty parameter; In step 5, specifically: The parameter results will be identified Substitute into formula (2) to obtain the terminal voltage of the supercapacitor model under this parameter: By comparing with the actual collected voltage U and calculating the average absolute error between the two, the parameter identification effect is illustrated, as shown in formula (8); 2. The method according to claim 1, characterized in that Sampling frequency f s The following values ​​will be taken: 1Hz, 0.1Hz.

3. The method according to claim 1, characterized in that The specific steps of interior point penalty function optimization are as follows: 4.1 Based on the given upper and lower limits of parameter identification and the acquisition of voltage and current signals, the optimization problem is summarized as formula (4); 4.2 Initialization: Initial solution x(0) = [R s0 ,R p0 ,C p0 ,U p0 ] T , precision ε = 10 -8 , 4.2 Penalty parameter exponent takes values ​​r=0,1,2,3…10 in sequence, let penalty parameter μ=10 r , performed under different penalty parameters: 4.2.1 Construct auxiliary functions: 4.2.2 Assignment: x [0] (r) = x(r), iteration flag i = 0 4.2.3 Recursive optimization solution variable: x [i+1] (r) = x [i] (r)-H -1 (x [i] (r))G(x [i] (r)), where G(x) and H(x) are functions F μ The Jacobian matrix and Hessian matrix of (x) represent the function F μ (x) first-order derivative information and second-order derivative information; the iterative optimization process is at the iterative step effect threshold ||x [i+1] (r)-x [i] (r)||≤ε or when the maximum number of iterations i=100 is reached, stop and assign x(r+1)=x [i+1] (r), otherwise continue the recursion i=i+1; 4.2.4 If Or r = 10, the solution process ends, otherwise the penalty parameter exponentially increases by r = r + 1 and the solution continues; 4.3 After the optimization process is completed, x(r+1) is the parameter identification result, which is recorded as:

Images