CN112580284B - Hybrid capacitor equivalent circuit model and online parameter identification method - Google Patents

Abstract

The invention discloses a hybrid capacitor equivalent circuit model and an on-line parameter identification method, belonging to the technical field of hybrid capacitor applicationDomain. The model comprises 1 variable capacitor, 1 ohm internal resistance, n RC circuits, each RC circuit comprises a resistor R _i And a capacitor C _i And obtaining a state space equation of the n-order multi-model fused equivalent circuit model. The hybrid capacitor multi-model fusion equivalent circuit model constructed by the invention combines the characteristics of a battery and an electric double layer capacitor, and can better characterize the external characteristics of the hybrid capacitor. Compared with the traditional capacitor equivalent circuit model, the simulation precision of the hybrid capacitor can be effectively improved; compared with an electrochemical model, the model has a simple structure and high calculation efficiency in practical application.

Description

A hybrid capacitor equivalent circuit model and online parameter identification method

Technical field

The invention belongs to the field of hybrid capacitor application technology, and more specifically, relates to a hybrid capacitor equivalent circuit model and an online parameter identification method.

Background technique

At present, supercapacitors can be roughly divided into electric double layer capacitors, hybrid capacitors and pseudocapacitive capacitors. As an energy storage device that combines the dual electrochemical reaction mechanisms of batteries and electric double layer capacitors, hybrid capacitors have higher power density and longer cycle life than batteries, and higher energy density than electric double layer capacitors. It can better meet the overall requirements for power energy density and power density in practical applications, and has broad application prospects in smart grids, electric vehicles and other fields.

The establishment of hybrid capacitor model is of great significance for studying its characteristics, state of charge estimation, health state estimation, management system algorithm development and rapid real-time simulation. Currently, commonly used hybrid capacitor models are mainly divided into two categories: electrochemical models and equivalent circuit models. The electrochemical model can describe the electrochemical reaction process inside the hybrid capacitor in detail with high accuracy, but it contains complex partial differential equation calculations, which has low computational efficiency and is difficult to meet the real-time requirements of the system. The equivalent circuit model uses basic circuit components to describe the external characteristics of the hybrid capacitor. It has a simple structure and high calculation efficiency, and has been widely used.

Patent CN110096780A discloses a supercapacitor first-order RC network equivalent circuit model and parameter determination method. It constructs a circuit model containing a controlled current source and identifies the model parameters through the recursive least squares method. This invention introduces a controlled current source to simulate the effect of the residual charge inside the supercapacitor to improve the accuracy of the model. However, the determination of the controlled current source parameters is relatively cumbersome and does not consider the timely updating of the controlled current source parameters during the aging process. , so it is difficult for the model to maintain high accuracy throughout the entire life cycle of the supercapacitor. In addition, this model is mainly aimed at electric double layer supercapacitors, and cannot well characterize the external characteristics of hybrid capacitors.

Due to the above defects and shortcomings, this field urgently needs to make further improvements and improvements. According to the dual electrochemical reaction mechanism of hybrid capacitors, an equivalent circuit model that can better characterize the external characteristics of hybrid capacitors is constructed, and the model is updated online. parameters to improve the accuracy of the equivalent circuit model over the entire life cycle of the hybrid capacitor.

Contents of the invention

In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a hybrid capacitor equivalent circuit model and an online parameter identification method, which combines the characteristics of batteries and electric double layer capacitors and aims to solve the problem that traditional capacitor models cannot be well characterized. Problems with the external characteristics of hybrid capacitors, thereby improving the model accuracy during the entire life cycle of hybrid capacitors and laying the foundation for hybrid capacitor state estimation and integrated management.

In order to achieve the above object, according to one aspect of the present invention, a hybrid capacitor equivalent circuit model is provided, including a variable capacitor, an ohmic internal resistance and n RC circuits in series. The variable capacitance C ₀ represents the dual electrochemical energy storage mechanism of the hybrid capacitor; the ohmic internal resistance R ₀ represents the electrode material, electrolyte, diaphragm resistance and contact resistance of each part; the RC circuit is composed of resistance and capacitance The circuit structure formed in parallel represents the polarization characteristics of the hybrid capacitor. Each RC circuit includes a resistor _Ri and a capacitor _Ci .

According to Kirchhoff's law, the state space equation of the equivalent circuit model of n-order multi-model fusion is established:

Among them, C ₀ is the variable capacitance, R ₀ is the ohmic internal resistance, R _i is the resistance of the RC circuit, C _i is the capacitance of the RC circuit, RC _i represents the i-th RC circuit, i=1,2,3 ,...,n, I is the load current, U _t is the terminal voltage of the hybrid capacitor, U _C0 and U _RCi are the voltage of the variable capacitor C ₀ and the voltage of the i-th RC circuit respectively, represents its derivative with respect to time.

After discretizing the state equation, we can get:

In the formula, Δt is the system sampling period. I _k is the load current at time k, and U _t,k is the terminal voltage of the hybrid capacitor at time k. U _C0,k is the voltage of the variable capacitor C ₀ at time k, and U _RCi,k is the voltage of the i-th RC circuit at time k.

Under zero initial conditions, Z transform and inverse Z transform are performed on equation (2), and the difference equation with time delay can be obtained:

U _t,k ＝θ ₁ U _t,k-1 +…+θ _n+1 U _t,kn-1 +θ _n+2 I _k +…+θ _2n+3 I _kn-1 (16)

In the formula, θ _j is a variable related to the model parameters, j=1,2,3,…,2n+3.

Preferably, in the present invention, in order to improve the accuracy of the model, the presence of colored noise e _k in the model is considered.

U' _t,k ＝θ ₁ U _t,k-1 +…+θ _n+1 U _t,kn-1 +θ _n+2 I _k +…+θ _2n+3 I _kn-1 +e _k (17 )

In the formula, U' _t,k is the terminal voltage of the hybrid capacitor at time k after considering colored noise, and e _k is the colored noise of the system at time k.

Preferably, in the present invention, the colored noise e _k is obtained by calculating the sliding average of the white noise w _k . White noise w _k is the random error of the system at time k.

e _k ＝w _k +c ₁ w _k-1 +c ₂ w _k-2 +…+c _r w _kr (18)

In the formula, r is the order of the moving average model, c _l is the coefficient of the model, l = 1, 2, 3,..., r.

Furthermore, formula (4) can be written as:

y _k =H _k θ _k +w _k (19)

In the formula, y _k is the output measurement value of the system at time k. H _k and θ _k are the data matrix and parameter matrix of the system at time k respectively, namely:

Preferably, the Akaike Information Criterion (AIC) is used in the present invention to determine the optimal order of the hybrid capacitor model. The calculation formula is:

AIC＝-2lnL+2T (21)

In the formula, L is the maximum likelihood function of the model. T represents the number of unknown parameters in the model, and the number of unknown parameters in the n-order model is 2(n+1).

Preferably, the smaller the model AIC value, the better the model.

Furthermore, when the model error satisfies the independent normal distribution, equation (8) can be rewritten as:

AIC＝Nln(s ² /N)+2T (22)

In the formula, N is the number of data. s ² represents the sum of squares of the residuals under optimal parameters, that is

In the formula, y _k is the terminal voltage predicted value of the multi-model fusion equivalent circuit model.

Furthermore, by comparing the AIC values of the multi-model fusion equivalent circuit model at different orders, the optimal order of the hybrid capacitor equivalent circuit model is determined.

According to another aspect of the present invention, a parameter determination system for a hybrid capacitor equivalent circuit model is provided, including: a computer-readable storage medium and a processor;

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

The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the above method for determining parameters of the hybrid capacitor equivalent circuit model.

According to another aspect of the present invention, an online parameter identification method for a hybrid capacitor multi-model fusion equivalent circuit model is provided, using a forgetting factor to solve the data saturation problem that occurs as the amount of data increases during system operation; The generalized least squares method is used to obtain unbiased estimates of parameters under colored noise; the recursive form is used to realize parameter online identification.

Preferably, the present invention uses the recursive augmented least squares method with a forgetting factor for online parameter identification. Through real-time parameter correction and updating, the accuracy of the model is guaranteed throughout its life cycle. The algorithm recursion process is as follows:

(1) Parameter initialization

(2) Construct the system matrix H _k , where

(3) Gain matrix calculation

(4)Model parameter update

(5)Model covariance update

In the formula, λ is the forgetting factor, K _k is the gain matrix, P _k is the error covariance matrix of parameter estimates, I is the identity matrix, and δ ² is a constant, usually 10 ¹² to 10 ¹⁵ .

Through the above technical solutions conceived by the present invention, compared with the existing technology, the following beneficial effects can be achieved:

1. The hybrid capacitor multi-model fusion equivalent circuit model constructed by the present invention combines the characteristics of batteries and electric double layer capacitors, and can better characterize the external characteristics of the hybrid capacitor. Compared with the traditional capacitor equivalent circuit model, this model can effectively improve the simulation accuracy of hybrid capacitors; compared with the electrochemical model, this model has a simple structure and high computational efficiency in practical applications.

2. The Akaike Information Criterion order determination method adopted in this invention determines the optimal order of the hybrid capacitor multi-model fusion equivalent circuit model by weighing the accuracy and complexity of the model. The optimal model has the lowest computational complexity under the same accuracy conditions; the highest model accuracy under the same complexity conditions.

3. The recursive augmented least squares method with forgetting factor used in the present invention can realize real-time online updating of hybrid capacitor multi-model fusion equivalent circuit model parameters. Compared with the offline parameter identification method, this method can effectively track the parameter changes of the model under various working conditions, enhance the adaptability and robustness of the model, and thereby improve the accuracy of the hybrid capacitor equivalent circuit model throughout its life cycle.

Description of the drawings

Figure 1 is a schematic diagram of the hybrid capacitor testing platform provided by the present invention;

Figure 2 is a schematic diagram of the hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention;

Figure 3 is a flow chart for building a hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention;

Figure 4 is a diagram showing the calculation results of the AIC value of the hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention;

Figure 5(a) is a current curve diagram of the working condition of the hybrid capacitor provided by the present invention;

Figure 5(b) is a voltage curve diagram of the working condition of the hybrid capacitor provided by the present invention;

Figure 6(a) is a comparison diagram of the identification results of the variable capacitance C ₀ in the hybrid capacitor equivalent circuit model provided by the present invention;

Figure 6(b) is a comparison chart of the identification results of polarization capacitance C ₁ in the hybrid capacitor equivalent circuit model provided by the present invention;

Figure 6(c) is a comparison chart of the identification results of ohmic internal resistance R ₀ in the hybrid capacitor equivalent circuit model provided by the present invention;

Figure 6(d) is a comparison chart of the identification results of polarization internal resistance R ₁ in the hybrid capacitor equivalent circuit model provided by the present invention;

Figure 7(a) is a comparison chart of predicted voltages of the hybrid capacitor equivalent circuit model provided by the present invention;

Figure 7(b) is a comparison chart of predicted voltage errors of the hybrid capacitor equivalent circuit model provided by the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

Figure 1 is a schematic diagram of a hybrid capacitor test platform provided by the present invention, which includes a hybrid capacitor unit, a power module, a test module and a microprocessor module. The power module is used to provide power to the test module; the test module refers to a programmable battery tester, which is used to control the charge and discharge of the hybrid capacitor and collect voltage values and current values; the microprocessor module is used to Perform program control on the test module and save the collected voltage and current values.

In one embodiment of the present invention, the tested hybrid capacitor is a lithium-ion capacitor with a rated capacity of 160mAh and a model of EVE SPC1550.

Figure 2 is a schematic diagram of the hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention, which includes a variable capacitor C ₀ , an ohm internal resistance R ₀ and n RC circuits in series. The variable capacitance C ₀ represents the dual electrochemical energy storage mechanism of the hybrid capacitor; the ohmic internal resistance R ₀ represents the electrode material, electrolyte, diaphragm resistance and contact resistance of each part; the RC circuit is composed of resistance and capacitance The circuit structure formed in parallel represents the polarization characteristics of the hybrid capacitor.

Figure 3 is a flow chart for building a hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention. The main steps include:

(1) Build a universal hybrid capacitor multi-model fusion equivalent circuit model, as shown in Figure 2;

(2) Calculate the AIC value of the Akaike information content of the multi-model fusion equivalent circuit model of different orders of the hybrid capacitor, and select the optimal model order based on the AIC value;

(3) Test the hybrid capacitor under working conditions and collect its voltage and current values;

(4) Substitute the voltage and current values into the model, and use the recursive augmented least squares method with a forgetting factor to identify the parameters of the model online.

Figure 4 is a diagram showing the calculation results of the AIC value of the hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention.

Specifically, when n=1, the AIC value is the smallest, that is, the first-order multi-model fusion equivalent circuit model is the optimal model of the tested lithium-ion capacitor.

Figure 5(a) and Figure 5(b) are hybrid capacitor working condition test curves provided by the present invention.

In one embodiment of the present invention, the dynamic stress test (DST) working condition is adopted, as shown in the figure. Figure 5(a) is the voltage curve of the hybrid capacitor under the DST working condition, and Figure 5(b) is the voltage curve of the hybrid capacitor under the DST working condition. Current curve of hybrid capacitor.

In one embodiment of the present invention, the forgetting factor λ is set to 0.996, and δ ² is set to 10 ¹² .

Specifically, the first-order multi-model fusion equivalent circuit model parameters of the hybrid capacitor can be calculated and obtained, namely

Figures 6(a) to 6(d) are comparison diagrams of parameter identification results of the hybrid capacitor equivalent circuit model provided by the present invention. Through the online parameter identification method provided by the present invention, the parameters of the equivalent circuit model are updated online in real time. Compared with the offline method, the adaptability and robustness are enhanced, and the performance of the hybrid capacitor equivalent circuit model throughout the life cycle can be effectively improved. Accuracy.

Figure 7(a) and Figure 7(b) are comparison diagrams of accuracy effects of the hybrid capacitor equivalent circuit model provided by the present invention. The average absolute error of the model output voltage obtained by using the online parameter identification method provided by the present invention is 2.9mV, and the root mean square error is 6mV; while the average absolute error of the model output voltage obtained by using the offline parameter identification method is 1.54mV, with a root mean square error of 1.54mV. Root error is 3.3mV. It is not difficult to see that the model obtained by using the online parameter identification method provided by the present invention is more accurate than the model obtained by using the offline parameter identification method. That is, the hybrid capacitor equivalent circuit model and the online parameter identification method provided by the present invention can effectively improve Hybrid capacitor simulation model accuracy.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements, etc., made within the spirit and principles of the present invention, All should be included in the protection scope of the present invention.

Claims (6)

1. A hybrid capacitor equivalent circuit model is characterized by comprising 1 variable capacitor, 1 ohm internal resistance and n RC circuits which are connected in series, wherein each RC circuit comprises a resistor R _i And a capacitor C _i The state space equation of the n-order multimode fused equivalent circuit model is expressed as:

wherein C is ₀ R is a variable capacitance ₀ Is ohm internal resistance, R _i Resistance of RC circuit, C _i Capacitance of RC circuit, RC _i Represents an ith RC circuit, i=1, 2,3, …, n, I is the load current, U _t U is the terminal voltage of the hybrid capacitor _C0 And U _RCi Respectively variable capacitance C ₀ And the voltage of the ith RC circuit,representing differentiation over time; the discretized state space equation is expressed as:

wherein Deltat is the sampling period of the system, I _k For the load current at time k, U _t,k Is the terminal voltage of the mixed capacitor at the moment k, U _C0,k Is the variable capacitance C at time k ₀ Voltage of U _RCi,k Is the voltage of the ith RC circuit at the moment k; performing Z transformation and Z inverse transformation on the discretized state space equation to obtain a differential equation with time delay:

U _t,k ＝θ ₁ U _t,k-1 +…+θ _n+1 U _t,k-n-1 +θ _n+2 I _k +…+θ _2n+3 I _k-n-1 (3)

wherein θ _j Is a variable for model parameters, j=1, 2,3, …,2n+3; consider the presence of colored noise e in the model _k The differential equation with delay is expressed as:

U′ _t,k ＝θ ₁ U _t,k-1 +…+θ _n+1 U _t,k-n-1 +θ _n+2 I _k +…+θ _2n+3 I _k-n-1 +e _k (4)

e _k ＝w _k +c ₁ w _k-1 +c ₂ w _k-2 +…+c _r w _k-r (5)

wherein U 'is' _t,k E for the terminal voltage of the hybrid capacitor at k time after the colored noise is taken into account _k Is the colored noise of the k-moment system, w _k For white noise at time k, r is the order of the white noise moving average model, c _l Is a coefficient of the model, l=1, 2,3, …, r; the output measurement of the system at time k is expressed as:

y _k ＝H _k θ _k +w _k (6)

wherein y is _k Is the output measurement of the system at time k,H _k and theta _k The data matrix and the parameter matrix at the time k are respectively.

2. A method for determining parameters of a hybrid capacitor equivalent circuit model according to claim 1, characterized in that the order of the hybrid capacitor model is determined by adopting a red pool information amount criterion AIC, the minimum order of the AIC value is an optimal solution, and the calculation formula is:

AIC＝-2lnL+2T (8)

wherein L is the maximum likelihood function of the equivalent circuit model of the hybrid capacitor, T represents the number of unknown parameters in the model, and the number of unknown parameters of the n-order model is 2 (n+1).

3. The parameter determination method of a hybrid capacitor equivalent circuit model according to claim 2, characterized in that when the model error satisfies the independent normal distribution, the formula (8) is rewritten as:

AIC＝Nl _n (s ² n) +2T (9) wherein N is the number of data, s ² Representing the sum of squares of residuals at optimal parameters:

wherein,is the terminal voltage predicted value of the multimode fusion equivalent circuit model.

4. A parameter determination system for a hybrid capacitor equivalent circuit model, comprising: a computer readable storage medium and a processor;

the computer-readable storage medium is for storing executable instructions;

the processor is configured to read executable instructions stored in the computer-readable storage medium and execute the parameter determination method of the hybrid capacitor equivalent circuit model according to claim 2 or 3.

5. An online parameter identification method based on the hybrid capacitor equivalent circuit model of claim 1, which is characterized in that a forgetting factor is adopted to solve the problem of data saturation which occurs along with the increase of data volume in the system operation; obtaining unbiased estimation of parameters under colored noise by adopting an augmentation least square method; and realizing the on-line identification of the parameters by adopting a recursive form.

6. The method for on-line parameter identification of hybrid capacitor equivalent circuit model according to claim 5, wherein the process of on-line parameter identification by using a recursive augmentation least square method with forgetting factors is as follows:

(1) Parameter initialization

(2) Construction of System matrix H _k Wherein

(3) Gain matrix calculation

(4) Model parameter update

(5) Model covariance update

Wherein lambda isForgetting factor, K _k Is a gain matrix, P _k Is the error covariance matrix of the parameter estimation value, I is the identity matrix, delta ² Is a constant.