阅读说明：本技术 一种混合电容器等效电路模型及在线参数辨识方法 (Hybrid capacitor equivalent circuit model and online parameter identification method ) 是由 王康丽 陈文欣 蒋凯 徐成 陈曼琳 于 2020-12-04 设计创作，主要内容包括：本发明公开了一种混合电容器等效电路模型及在线参数辨识方法,属于混合电容器应用技术领域。模型包括1个可变电容,1个欧姆内阻,n个RC电路,每个RC电路包括一个电阻R-i和一个电容C-i,得到n阶多模型融合的等效电路模型的状态空间方程。本发明构建的混合电容器多模型融合等效电路模型,结合了电池和双电层电容器的特点,能够较好地表征混合电容器的外部特性。与传统电容器等效电路模型相比,该模型能够有效提高混合电容器的仿真精度；与电化学模型相比,该模型结构简单,在实际应用中的计算效率高。(The invention discloses a hybrid capacitor equivalent circuit model and an online parameter identification method, and belongs to the technical field of hybrid capacitor application. The model comprises 1 variable capacitor, 1 ohm internal resistance and n RC circuits, wherein each RC circuit comprises a resistor R i And a capacitor C i And obtaining the state space equation of the equivalent circuit model fused by the n-order multi-model. The multi-model fusion equivalent circuit model of the hybrid capacitor constructed by the invention combines the characteristics of the battery and the double electric layer capacitor, and can well represent the external characteristics of the hybrid capacitor. Compared with the traditional capacitor equivalent circuit model, the model can effectively improve the simulation precision of the hybrid capacitor; compared with an electrochemical model, the model is simple in structure and high in calculation efficiency in practical application.)

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 isComprising a resistor R_iAnd a capacitor C_iThe state space equation of the equivalent circuit model of the n-order multi-model fusion is expressed as follows:

wherein, C₀Is a variable capacitance, R₀Is ohmic internal resistance, R_iIs the resistance of an RC circuit, C_iBeing the capacitance of an RC circuit, RC_iDenotes the ith RC circuit, I is 1,2,3, …, n, I is the load current, U_tTerminal voltage of hybrid capacitor, U_C0And U_RCiAre respectively a variable capacitance C₀And the voltage of the ith RC circuit,representing the differential over time.

2. The hybrid capacitor equivalent circuit model of claim 1, wherein the state space equation is discretized to be represented as:

where Δ t is the system sampling period, I_kLoad current at time k, U_t,kTerminal voltage of the hybrid capacitor at time k, U_C0,kIs a variable capacitance C at time k₀Voltage of U_RCi,kIs the voltage of the ith RC circuit at time k.

3. The hybrid capacitor equivalent circuit model of claim 2, wherein Z transform and Z inverse transform are performed on the discretized state space equation to obtain a differential equation with time delay:

U_t,k＝θ₁U_t,k-1+…+θ_n+1U_t,k-n-1+θ_n+2I_k+…+θ_2n+3I_k-n-1 (3)

wherein, theta_jIs a variable for the model parameter, j ═ 1,2,3, …,2n + 3.

4. A hybrid capacitor equivalent circuit model according to claim 3, characterized in that the presence of colored noise e in the model is taken into account_kThe difference equation with time delay is expressed as:

U′_t,k＝θ₁U_t,k-1+…+θ_n+1U_t,k-n-1+θ_n+2I_k+…+θ_2n+3I_k-n-1+e_k (4)

e_k＝w_k+c₁w_k-1+c₂w_k-2+…+c_rw_k-r (5)

wherein, U'_t,kTo take into account the terminal voltage of the hybrid capacitor at the time k after colored noise, e_kColored noise of the system at time k, w_kWhite noise at time k, r is the order of the white noise moving average model, c_lIs the coefficient of the model, l ═ 1,2,3, …, r.

5. The hybrid capacitor equivalent circuit model of claim 4, wherein the output measurement of the system at time k is represented as:

y_k＝H_kθ_k+w_k (6)

wherein, y_kIs the output measurement of the system at time k, H_kAnd theta_kRespectively a data matrix and a parameter matrix at time k.

6. A parameter determination method based on the equivalent circuit model of the hybrid capacitor as claimed in any one of claims 1 to 5, characterized in that the Chi cell information criterion AIC is used to determine the order of the hybrid capacitor model, the order with the smallest AIC value is the 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 the unknown parameters of the n-order model is 2(n + 1).

7. The method for determining parameters of a hybrid capacitor equivalent circuit model according to claim 6, wherein when the model error satisfies the independent normal distribution, equation (8) is rewritten as:

AIC＝Nln(s²/N)+2T (9)

where N is the number of data, s²Represents the sum of the squared residuals under the optimal parameters:

wherein, y_kThe terminal voltage predicted value of the multi-model fusion equivalent circuit model is obtained.

8. 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 used for storing executable instructions;

the processor is used for reading executable instructions stored in the computer readable storage medium and executing the parameter determination method of the hybrid capacitor equivalent circuit model of any one of claims 6 to 7.

9. An online parameter identification method based on the equivalent circuit model of the hybrid capacitor as claimed in any one of claims 1 to 5, characterized in that a forgetting factor is adopted to solve the problem of data saturation occurring along with the increase of data volume in the operation of the system; obtaining unbiased estimation of parameters under colored noise by adopting an augmented least square method; and realizing parameter online identification in a recursion mode.

10. The method for online parameter identification of the equivalent circuit model of the hybrid capacitor as claimed in claim 9, wherein the online parameter identification by using the recursive augmented least squares with forgetting factor is performed as follows:

(1) parameter initialization

(2) Constructing a System matrix H_kWherein

(3) Gain matrix calculation

(4) Model parameter updating

(5) Model covariance update

Wherein, λ is forgetting factor, K_kAs a gain matrix, P_kIs an error covariance matrix of the parameter estimates, I is an identity matrix, δ²Is a constant.

Technical Field

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

Background

At present, supercapacitors can be broadly classified into electric double layer capacitors, hybrid capacitors and pseudo-capacitance capacitors. The hybrid capacitor is used as an energy storage device with a dual electrochemical reaction mechanism of a battery and an electric double layer capacitor, has higher power density and longer cycle life than the battery, has higher energy density than the electric double layer capacitor, can better meet the overall requirements on the power supply energy density and the power density in practical application, and has wide application prospects in the fields of smart power grids, electric automobiles and the like.

The establishment of the hybrid capacitor model has important significance for researching the characteristics, the state of charge estimation, the state of health estimation, the algorithm development of a management system and the rapid real-time simulation of the hybrid capacitor model. Currently, the commonly used hybrid capacitor models are mainly classified into two types: electrochemical models and equivalent circuit models. The electrochemical model can describe the electrochemical reaction process in the hybrid capacitor in detail, has high precision, but contains complex partial differential equation calculation, has low calculation efficiency and is difficult to meet the real-time requirement of the system. The equivalent circuit model adopts basic circuit elements to describe the external characteristics of the hybrid capacitor, has simple structure and high calculation efficiency, and is widely applied.

Patent CN110096780A discloses a supercapacitor first-order RC network equivalent circuit model and a parameter determination method, which constructs a circuit model containing a controlled current source, and identifies model parameters by a recursive least square method. According to the method, the effect generated by residual charge in the super capacitor is simulated by introducing the controlled current source, so that the model precision is improved, but the determination of the controlled current source parameters is more complicated, and the controlled current source parameters are not considered to be updated in time in the aging process, so that the model is difficult to always maintain higher precision in the whole life cycle of the super capacitor. In addition, the model is mainly directed to an electric double layer supercapacitor, and for a hybrid capacitor, the external characteristics thereof cannot be well characterized.

Due to the defects and shortcomings, further improvement and improvement are urgently needed in the field, an equivalent circuit model capable of well representing the external characteristics of the hybrid capacitor is constructed according to the double electrochemical reaction mechanism of the hybrid capacitor, and model parameters are updated on line so as to improve the precision of the equivalent circuit model in the whole life cycle of the hybrid capacitor.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide a hybrid capacitor equivalent circuit model and an online parameter identification method, which combine the characteristics of a battery and a double electric layer capacitor and aim to solve the problem that the traditional capacitor model cannot well represent the external characteristics of the hybrid capacitor, thereby improving the model precision of the hybrid capacitor in the whole life cycle and laying a foundation for the state estimation and integrated management of the hybrid capacitor.

To achieve the above object, according to one aspect of the present invention, there is provided a hybrid capacitor equivalent circuit model including 1 variable capacitor, 1 ohmic internal resistance, and n RC circuits connected in series. The variable capacitor C₀Characterizing a hybrid capacitor dual electrochemical energy storage mechanism; the ohmic internal resistance R₀Characterizing electrode materials, electrolyte, diaphragm resistance and contact resistance of parts; the RC circuits are circuit structures formed by connecting resistors and capacitors in parallel and represent the polarization characteristics of the hybrid capacitor, and each RC circuit comprises a resistor R_iAnd a capacitor C_i。

According to kirchhoff's law, establishing a state space equation of an equivalent circuit model of n-order multi-model fusion:

wherein, C₀Is a variable capacitance, R₀Is ohmic internal resistance, R_iIs the resistance of an RC circuit, C_iBeing the capacitance of an RC circuit, RC_iThe ith RC circuit is shown, I is 1,2,3, …, n, I is the load current, U_tTerminal voltage of hybrid capacitor, U_C0And U_RCiAre respectively a variable capacitance C₀And the voltage of the ith RC circuit,representing its differential over time.

Discretizing the state equation to obtain:

in the formula, Δ t is a system sampling period. I is_kLoad current at time k, U_t,kIs the terminal voltage of the hybrid capacitor at time k. U shape_C0,kIs a variable capacitance C at time k₀Voltage of U_RCi,kIs the voltage of the ith RC circuit at time k.

Under the zero initial condition, Z transformation and Z inverse transformation are carried out on the formula (2), and a difference equation with time delay can be obtained:

U_t,k＝θ₁U_t,k-1+…+θ_n+1U_t,k-n-1+θ_n+2I_k+…+θ_2n+3I_k-n-1 (16)

in the formula, theta_jIs a variable for the model parameter, j ═ 1,2,3, …,2n + 3.

Preferably, in the present invention, in order to improve the model accuracy, the presence of colored noise e in the model is taken into account_k。

U’_t,k＝θ₁U_t,k-1+…+θ_n+1U_t,k-n-1+θ_n+2I_k+…+θ_2n+3I_k-n-1+e_k (17)

In formula (II) U'_t,kTo take into account the terminal voltage of the hybrid capacitor at the time k after colored noise, e_kIs the colored noise of the time k system.

Preferably, in the present invention, the colored noise e_kBy calculating white noise w_kIs obtained as a running average of. White noise w_kIs the random error of the system at time k.

e_k＝w_k+c₁w_k-1+c₂w_k-2+…+c_rw_k-r (18)

Where r is the order of the moving average model, c_lIs the coefficient of the model, l ═ 1,2,3, …, r.

Further, equation (4) can be written as:

y_k＝H_kθ_k+w_k (19)

in the formula, y_kIs the output measurement of the system at time k. H_kAnd theta_kThe data matrix and the parameter matrix of the k-time system are respectively, namely:

preferably, the Chi-cell information criterion AIC is used in the present invention to determine the optimum order of the hybrid capacitor model. The calculation formula is as follows:

AIC＝-2lnL+2T (21)

where 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 of the n-order model is 2(n + 1).

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

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

AIC＝Nln(s²/N)+2T (22)

in the formula, N is the number of data. s²Representing the sum of the squares of the residuals under optimal parameters, i.e.

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

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

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

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

the processor is used for reading the executable instructions stored in the computer readable storage medium and executing the parameter determination method of the hybrid capacitor equivalent circuit model.

According to another aspect of the invention, an online parameter identification method of a hybrid capacitor multi-model fusion equivalent circuit model is provided, and a forgetting factor is adopted to solve the problem of data saturation along with the increase of data volume in the operation of a system; obtaining unbiased estimation of parameters under colored noise by adopting an augmented least square method; and realizing parameter online identification in a recursion mode.

Preferably, the method adopts a recursive augmented least square method with forgetting factors to perform online parameter identification. And the precision of the model in the whole life cycle is ensured through real-time parameter correction and updating. The algorithm recursion process is as follows:

(1) parameter initialization

(2) Constructing a System matrix H_kWherein

(3) Gain matrix calculation

(4) Model parameter updating

(5) Model covariance update

In the formula, λ is forgetting factor, K_kAs a gain matrix, P_kIs an error covariance matrix of the parameter estimates, I is an identity matrix, δ²Is a constant, usually taken as 10¹²～10¹⁵。

Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:

1. the multi-model fusion equivalent circuit model of the hybrid capacitor constructed by the invention combines the characteristics of the battery and the double electric layer capacitor, and can well represent the external characteristics of the hybrid capacitor. Compared with the traditional capacitor equivalent circuit model, the model can effectively improve the simulation precision of the hybrid capacitor; compared with an electrochemical model, the model is simple in structure and high in calculation efficiency in practical application.

2. The optimal order of the hybrid capacitor multi-model fusion equivalent circuit model is determined by a Chichi information quantity criterion order determination method through balancing the precision and the complexity of the model. The optimal model has the lowest calculation complexity under the condition of equal precision; and under the condition of equal complexity, the model precision is highest.

3. The recursive augmented least square method with forgetting factors is adopted by the method, so that real-time online updating of the model parameters of the hybrid capacitor multi-model fusion equivalent circuit can be realized. Compared with an off-line parameter identification method, the method can effectively track the parameter change of the model under various working conditions, and enhances the adaptability and robustness of the model, thereby improving the precision of the equivalent circuit model of the hybrid capacitor in the whole life cycle.

Drawings

FIG. 1 is a schematic diagram of a hybrid capacitor test platform according to the present invention;

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

FIG. 3 is a flow chart of a hybrid capacitor multi-model fusion equivalent circuit model construction provided by the present invention;

FIG. 4 is a diagram of the calculation result of the hybrid capacitor multi-model fusion equivalent circuit model AIC value provided by the present invention;

FIG. 5(a) is a graph of current curves for a hybrid capacitor operating condition provided by the present invention;

FIG. 5(b) is a voltage profile of a hybrid capacitor operating condition provided by the present invention;

FIG. 6(a) shows a variable capacitance C in the equivalent circuit model of the hybrid capacitor provided by the present invention₀Comparing the identification result with a graph;

FIG. 6(b) shows the polarization capacitance C in the equivalent circuit model of the hybrid capacitor provided by the present invention₁Comparing the identification result with a graph;

FIG. 6(c) is the ohm internal resistance R in the equivalent circuit model of the hybrid capacitor provided by the present invention₀Comparing the identification result with a graph;

FIG. 6(d) is the polarization internal resistance R in the equivalent circuit model of the hybrid capacitor provided by the present invention₁Comparing the identification result with a graph;

FIG. 7(a) is a comparison graph of the predicted voltage of the equivalent circuit model of the hybrid capacitor provided by the present invention;

fig. 7(b) is a comparison graph of the predicted voltage error of the equivalent circuit model of the hybrid capacitor provided by the present invention.

Detailed Description

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

Fig. 1 is a schematic diagram of a hybrid capacitor test platform provided in the present invention, which includes 1 hybrid capacitor unit, 1 power module, 1 test module, and 1 microprocessor module. The power supply module is used for supplying power to the test module; the testing module is a programmable battery tester and is used for controlling charging and discharging of the hybrid capacitor and collecting a voltage value and a current value; and the microprocessor module is used for carrying out program control on the test module and storing the acquired voltage value and current value.

In one embodiment of the invention, the hybrid capacitor cell tested was a lithium ion capacitor with a rated capacity of 160mAh and a model number of EVE SPC 1550.

FIG. 2 is a schematic diagram of a hybrid capacitor multi-model fusion equivalent circuit model provided by the present invention, which includes 1 variable capacitor C₀1 ohm internal resistance R₀And n RC circuits. The variable capacitor C₀Characterizing a hybrid capacitor dual electrochemical energy storage mechanism; the ohmic internal resistance R₀Characterizing electrode materials, electrolyte, diaphragm resistance and contact resistance of parts; the RC circuit is a circuit structure formed by connecting a resistor and a capacitor in parallel and represents the polarization characteristic of the hybrid capacitor.

Fig. 3 is a flow chart of a hybrid capacitor multi-model fusion equivalent circuit model construction provided by the present invention, which mainly comprises the following steps:

(1) building a universal hybrid capacitor multi-model fusion equivalent circuit model as shown in fig. 2;

(2) calculating the information quantity AIC (information value) of the Chichi pool of the multi-model fusion equivalent circuit model with different orders of the hybrid capacitor, and selecting the optimal model order according to the AIC value;

(3) testing the working condition of the hybrid capacitor, and collecting the voltage value and the current value of the hybrid capacitor;

(4) and substituting the voltage value and the current value into the model, and adopting a recursive augmented least square method with forgetting factors to identify the parameters of the model on line.

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

Specifically, n is 1, the AIC value is minimum, i.e. the first-order multi-model fusion equivalent circuit model is the optimal model of the tested lithium ion capacitor.

Fig. 5(a) and 5(b) are graphs illustrating the testing of the working condition of the hybrid capacitor according to the present invention.

In one embodiment of the present invention, Dynamic Stress Test (DST) conditions are used, as shown, fig. 5(a) is a voltage curve of the hybrid capacitor under the DST conditions, and fig. 5(b) is a current curve of the hybrid capacitor under the DST conditions.

In one embodiment of the invention, the forgetting factor λ is taken to be 0.996, δ²Is taken as 10¹²。

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

Fig. 6(a) -6 (d) are comparison graphs of the parameter identification results of the equivalent circuit model of the hybrid capacitor provided by the present invention. By the online parameter identification method provided by the invention, the parameters of the equivalent circuit model are updated online in real time, and compared with an offline method, the method has the advantages that the adaptability and robustness are enhanced, and the precision of the whole life cycle of the equivalent circuit model of the hybrid capacitor can be effectively improved.

Fig. 7(a) and fig. 7(b) are graphs comparing the accuracy effect of the equivalent circuit model of the hybrid capacitor provided by the present invention. The average absolute error of the output voltage of the model obtained by the online parameter identification method provided by the invention is 2.9mV, and the root mean square error is 6 mV; the average absolute error of the output voltage of the model obtained by the off-line parameter identification method is 1.54mV, and the root mean square error is 3.3 mV. It can be seen that the model obtained by the online parameter identification method provided by the invention has higher precision than the model obtained by the offline parameter identification method, namely the hybrid capacitor equivalent circuit model and the online parameter identification method provided by the invention can effectively improve the precision of the hybrid capacitor simulation model.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.