CN112580284B - Hybrid capacitor equivalent circuit model and online parameter identification method - Google Patents
Hybrid capacitor equivalent circuit model and online parameter identification method Download PDFInfo
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- 239000003990 capacitor Substances 0.000 title claims abstract description 107
- 238000000034 method Methods 0.000 title claims abstract description 33
- 230000004927 fusion Effects 0.000 claims abstract description 18
- 238000004364 calculation method Methods 0.000 claims abstract description 13
- 239000011159 matrix material Substances 0.000 claims description 14
- 230000003416 augmentation Effects 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 4
- 238000010276 construction Methods 0.000 claims description 3
- 238000005259 measurement Methods 0.000 claims description 3
- 230000008569 process Effects 0.000 claims description 3
- 238000007476 Maximum Likelihood Methods 0.000 claims description 2
- 230000004069 differentiation Effects 0.000 claims description 2
- 238000005070 sampling Methods 0.000 claims description 2
- 238000004088 simulation Methods 0.000 abstract description 4
- 238000012360 testing method Methods 0.000 description 9
- 238000010586 diagram Methods 0.000 description 6
- 230000009977 dual effect Effects 0.000 description 4
- 230000007246 mechanism Effects 0.000 description 4
- 238000003487 electrochemical reaction Methods 0.000 description 3
- 230000010287 polarization Effects 0.000 description 3
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000012983 electrochemical energy storage Methods 0.000 description 2
- 239000007772 electrode material Substances 0.000 description 2
- 239000003792 electrolyte Substances 0.000 description 2
- 229910001416 lithium ion Inorganic materials 0.000 description 2
- ULGZDMOVFRHVEP-RWJQBGPGSA-N Erythromycin Chemical compound O([C@@H]1[C@@H](C)C(=O)O[C@@H]([C@@]([C@H](O)[C@@H](C)C(=O)[C@H](C)C[C@@](C)(O)[C@H](O[C@H]2[C@@H]([C@H](C[C@@H](C)O2)N(C)C)O)[C@H]1C)(C)O)CC)[C@H]1C[C@@](C)(OC)[C@@H](O)[C@H](C)O1 ULGZDMOVFRHVEP-RWJQBGPGSA-N 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 238000004146 energy storage Methods 0.000 description 1
- 230000036541 health Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000000178 monomer Substances 0.000 description 1
- 230000035882 stress Effects 0.000 description 1
- 239000000758 substrate Substances 0.000 description 1
- 238000005303 weighing Methods 0.000 description 1
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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
Technical Field
The invention belongs to the technical field of application of hybrid capacitors, and particularly relates to a hybrid capacitor equivalent circuit model and an online parameter identification method.
Background
Currently, supercapacitors can be broadly classified into electric double layer capacitors, hybrid capacitors, and pseudocapacitance 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 of power supply energy density and power density in practical application, and has wide application prospects in the fields of smart grids, electric automobiles and the like.
The establishment of the hybrid capacitor model has important significance for researching the characteristics, the charge state estimation, the health state estimation and the algorithm development of a management system and quick real-time simulation. Currently, the 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 in the hybrid capacitor in detail, and has high precision, but the electrochemical model comprises complex partial differential equation calculation, has low calculation efficiency and is difficult to meet the real-time requirement of a 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 determining method, which construct a circuit model containing a controlled current source, and identify model parameters by a recursive least square method. According to the invention, the effect generated by residual charges in the super capacitor is simulated by introducing the controlled current source, so that the model accuracy is improved, the determination of the parameters of the controlled current source is complicated, and the parameters of the controlled current source are not updated in time in the aging process, so that the model is difficult to maintain higher accuracy all the time 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.
Because of the above-mentioned drawbacks and shortcomings, there is a need in the art to make further improvements and improvements, and to construct an equivalent circuit model capable of better characterizing external characteristics of a hybrid capacitor, and update model parameters online, so as to improve the accuracy of the equivalent circuit model in the whole life cycle of the hybrid capacitor, aiming at the dual electrochemical reaction mechanism 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 an electric double layer capacitor, and aim to solve the problem that the traditional capacitor model cannot better represent the external characteristics of the hybrid capacitor, thereby improving the model precision in the whole life cycle of the hybrid capacitor 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 capacitance, 1 ohmic internal resistance, and n RC circuits connected in series. The variable capacitance C 0 Characterizing a dual electrochemical energy storage mechanism of the hybrid capacitor; the ohmic internal resistance R 0 Characterizing electrode materials, electrolyte, diaphragm resistance and contact resistance of parts of each part; the RC circuit is a circuit structure formed by parallel connection of a resistor and a capacitor and represents a hybrid capacitorPolarization characteristics of the device, each RC circuit including a resistor R i And a capacitor C i 。
According to kirchhoff's law, a state space equation of an n-order multi-model fused equivalent circuit model is established:
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 The I-th RC circuit is represented, 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 its differentiation over time.
The state equation is discretized to obtain:
where Δt is the system sampling period. I k For the load current at time k, U t,k Is the terminal voltage of the hybrid capacitor at time k. U (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 time k.
Under the zero initial condition, performing Z transformation and Z inverse transformation on the formula (2) 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 (16)
in θ j Is a variable for model parameters, j=1, 2,3, …,2n+3.
Preferably, in the present invention, the first and second substrates,to improve the model accuracy, consider the presence of colored noise e in the model k 。
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 (17)
In U's' 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 system at time k.
Preferably, in the present invention, the colored noise e k By calculating white noise w k Is obtained from the running average of (a). 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 k-r (18)
Where r is the order of the moving average model, c l Is a coefficient of the model, l=1, 2,3, …, r.
Further, formula (4) may be written as:
y k ＝H k θ k +w k (19)
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 of the k moment system are respectively:
preferably, the red-cell information content criterion AIC is employed in the present invention to determine the optimal 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, the expression (8) can be rewritten as:
AIC＝Nln(s 2 /N)+2T (22)
wherein N is the number of data. s is(s) 2 Representing the sum of squares of residuals at optimal parameters, i.e
Wherein y is k Is the terminal voltage predicted value of the multimode fusion equivalent circuit model.
Further, the optimal order of the hybrid capacitor equivalent circuit model is determined by comparing AIC values of the multi-model fusion equivalent circuit model at different orders.
According to another aspect of the present invention, there is provided a parameter determination system of 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 above-described method for determining parameters of the hybrid capacitor equivalent circuit model.
According to the invention, the invention further provides an on-line parameter identification method for the hybrid capacitor multi-model fusion equivalent circuit model, which adopts forgetting factors to solve the problem of data saturation which occurs along with the increase of data quantity 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.
Preferably, the invention adopts a recursive augmentation least square method with forgetting factors to carry out online parameter identification. And the accuracy 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) Construction of System matrix H k Wherein
(3) Gain matrix calculation
(4) Model parameter update
(5) Model covariance update
Wherein lambda is forgetting 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, usually 10 12 ～10 15 。
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. 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.
2. According to the method for determining the order of the erythro pool information quantity criterion, the optimal order of the hybrid capacitor multi-model fusion equivalent circuit model is determined by weighing the precision and the complexity of the model. The optimal model has the lowest calculation complexity under the condition of equal precision; with equal complexity, the model accuracy is highest.
3. The recursive augmentation least square method with the forgetting factor adopted by the invention can realize the real-time online updating of the parameters of the hybrid capacitor multi-model fusion equivalent circuit model. Compared with an offline parameter identification method, the method can effectively track the parameter changes of the model under various working conditions, and the adaptability and the robustness of the model are enhanced, so that the accuracy of the equivalent circuit model of the hybrid capacitor in the whole life cycle is improved.
Drawings
FIG. 1 is a schematic diagram of a hybrid capacitor test platform provided by the present invention;
FIG. 2 is a schematic diagram of a hybrid capacitor multi-model fusion equivalent circuit model provided by the invention;
FIG. 3 is a flow chart of the construction of the hybrid capacitor multi-model fusion equivalent circuit model provided by the invention;
FIG. 4 is a graph of AIC value calculation results of a mixed capacitor multi-model fusion equivalent circuit model provided by the invention;
FIG. 5 (a) is a graph of current versus operating conditions for a hybrid capacitor provided by the present invention;
FIG. 5 (b) is a voltage plot for a hybrid capacitor operating mode provided by the present invention;
FIG. 6 (a) shows the variable capacitance C in the equivalent circuit model of the hybrid capacitor according to the present invention 0 Is a comparison graph of the identification results;
FIG. 6 (b) shows the polarization capacitance C in the equivalent circuit model of the hybrid capacitor according to the present invention 1 Is a comparison graph of the identification results;
FIG. 6 (c) shows the Europe internal resistance R in the equivalent circuit model of the hybrid capacitor according to the present invention 0 Is a comparison graph of the identification results;
FIG. 6 (d) shows the internal resistance R of polarization in the equivalent circuit model of the hybrid capacitor according to the present invention 1 Is a comparison graph of the identification results;
FIG. 7 (a) is a graph showing the comparison of predicted voltages of the equivalent circuit model of the hybrid capacitor according to the present invention;
fig. 7 (b) is a comparison diagram of the predicted voltage error of the equivalent circuit model of the hybrid capacitor provided by the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not interfere with each other.
Fig. 1 is a schematic diagram of a hybrid capacitor test platform provided by 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 providing power supply for the test module; the test module refers to a programmable battery tester and is used for controlling the charge and discharge of the hybrid capacitor and collecting a voltage value and a current value; the microprocessor module is used for performing program control on the test module and storing the acquired voltage value and current value.
In one embodiment of the invention, the hybrid capacitor monomer tested was a lithium ion capacitor with a rated capacity of 160mAh and model No. EVE SPC1550.
FIG. 2 is a schematic diagram of a hybrid capacitor multi-model fusion equivalent circuit model according to the present invention, which includes 1 variable capacitor C 0 1 ohm internal resistance R 0 And n RC circuits are connected in series. The variable capacitance C 0 Characterizing a dual electrochemical energy storage mechanism of the hybrid capacitor; the ohmic internal resistance R 0 Characterizing electrode materials, electrolyte, diaphragm resistance and contact resistance of parts of each part; the RC circuit is a circuit structure formed by parallel connection of a resistor and a capacitor and represents the polarization characteristic of the hybrid capacitor.
Fig. 3 is a flow chart for constructing a hybrid capacitor multi-model fusion equivalent circuit model, which mainly comprises the following steps:
(1) Building a general hybrid capacitor multi-model fusion equivalent circuit model, as shown in fig. 2;
(2) Calculating the AIC value of the information quantity of the red pool of the multi-model fusion equivalent circuit model of the hybrid capacitor with different orders, and selecting the optimal model order according to the AIC value;
(3) The working condition test is carried out on the hybrid capacitor, and the voltage value and the current value of the hybrid capacitor are collected;
(4) Substituting the voltage value and the current value into the model, and adopting a recursive augmentation least square method with forgetting factors to identify parameters of the model on line.
Fig. 4 is a graph of the calculation result of the AIC value of the mixed capacitor multi-model fusion equivalent circuit model provided by the invention.
Specifically, n=1, the aic value is the smallest, i.e., the first-order multi-model fusion equivalent circuit model is the optimal model for the lithium ion capacitor tested.
Fig. 5 (a) and fig. 5 (b) are graphs for testing the working condition of the hybrid capacitor provided by the invention.
In one embodiment of the present invention, a Dynamic Stress Test (DST) regime is employed, as shown, fig. 5 (a) is a voltage curve of the hybrid capacitor under the DST regime, and fig. 5 (b) is a current curve of the hybrid capacitor under the DST regime.
In one embodiment of the invention, the forgetting factor λ is taken to be 0.996, δ 2 Taken as 10 12 。
In particular, the hybrid capacitor first-order multimode fusion equivalent circuit model parameters can be obtained by calculation, namely
Fig. 6 (a) -fig. 6 (d) are comparison diagrams of the parameter identification results of the equivalent circuit model of the hybrid capacitor provided by the invention. By the online parameter identification method provided by the invention, the parameters of the equivalent circuit model are updated online in real time, so that compared with an offline method, the adaptability and the robustness are enhanced, and the accuracy of the full life cycle of the equivalent circuit model of the hybrid capacitor can be effectively improved.
Fig. 7 (a) and fig. 7 (b) are graphs showing comparison of the accuracy effects of the equivalent circuit model of the hybrid capacitor provided by the invention. The average absolute error of the model output voltage obtained by the online parameter identification method provided by the invention is 2.9mV, and the root mean square error is 6mV; the average absolute error of the model output voltage obtained by the off-line parameter identification method is 1.54mV, and the root mean square error is 3.3mV. It is clear 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 readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the 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.
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| CN113687241A (en) * | 2021-09-28 | 2021-11-23 | 淮河能源(集团)股份有限公司 | Method and device for estimating state of charge of lithium ion battery for multi-mode model mine |
| CN114186522B (en) * | 2021-12-08 | 2024-06-18 | 华中科技大学 | Construction method and application of hybrid capacitor power state on-line estimation model |
| CN114509677A (en) * | 2022-01-30 | 2022-05-17 | 北京西清能源科技有限公司 | Multi-factor evaluation method and system for residual capacity of battery and electronic equipment |
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