CN109408865B - Non-solid-state aluminum electrolytic capacitor equivalent circuit model and parameter identification method - Google Patents
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Abstract
An equivalent circuit model of non-solid-state aluminum electrolytic capacitor and its parameter identification method, the equivalent circuit model is composed of fractional order capacitor C representing infinite self-similar structure on the surface of capacitor electrode α The sum R of the electrolyte resistance in the capacitor and the resistance of the auxiliary lead wire Ω And a fractional order capacitor representing complex movement of ions in the capacitor electrolyte
And (4) forming. The parameter identification method of the equivalent circuit model is a fractional order multi-target off-line parameter identification method based on a differential evolution algorithm. The equivalent circuit model provided by the invention can accurately describe the characteristic that the equivalent series resistance of the non-solid aluminum electrolytic capacitor changes along with the working frequency, and can predict the change trend of the actual capacitance of the capacitor under different working frequencies, thereby providing a reference basis for the design and reliability analysis of a circuit system containing the element.
Description
Technical Field
The invention relates to the field of modeling and parameter identification of electrochemical elements, in particular to an equivalent circuit model of a non-solid-state aluminum electrolytic capacitor and a parameter identification method thereof.
Background
The conventional capacitors mainly comprise an aluminum electrolytic capacitor, a tantalum electrolytic capacitor, a niobium electrolytic capacitor, a ceramic capacitor, a film capacitor and the like, and the aluminum electrolytic capacitor occupies the largest market share due to the advantages of unit volume capacity and cost performance, and is widely applied to a switching power supply.
The non-solid aluminum electrolytic capacitor is mainly composed of an anode foil with a compact nonporous alumina film surface, a cathode foil with a natural oxidation layer surface and electrolyte, paper soaked with the electrolyte is used as a gasket between a cathode and an anode, wherein the anode is formed into an uneven surface through an optical and electrical two-step corrosion process, an Al2O3 compact dielectric layer with a fixed thickness d is generated in a formation process, the layer has unidirectional conductivity, and the capacitance value and the service life of the capacitor are determined by using the layer as an insulating layer between the cathode and the anode. And the cathode only passes through the electrical corrosion process, and the surface of the cathode only has a natural oxide layer with a very thin thickness. Therefore, the spacing between the cathode and the anode is generally considered to be the thickness of the dielectric layer. The electrolyte carried by the liner layer permeates into the corrosion grooves of the aluminum foils at the anode and the cathode to respectively form two substructure of anode aluminum foil/Al 2O3 dielectric layer/electrolyte, electrolyte/natural oxide layer/cathode aluminum foil. After the element is electrified, the anions and cations in the electrolyte are attached to the surfaces of the rough and porous bipolar aluminum foils to form a Helmholtz layer, the other part of the anions and cations is dissociated in the electrolyte to form a diffusion layer, and the two parts of the anions and cations act together to form an electric field in the element.
The nominal value of the current commercial aluminum electrolytic capacitor shell is measured by a manufacturer technician under the temperature condition of 100/120Hz working frequency of 20 ℃/25 ℃. In practice, however, due to the influence of the manufacturing process, the error between the actual capacity value and the nominal value of a single product with the same type of electrolytic capacitors with the precision of E3 and E6 under the IEC 60062 standard is usually about 20%; on the other hand, due to the influence of factors such as non-uniform mass transfer in the electrolyte of the electrolytic capacitor, non-uniform current caused by different pore structures on the electrode surface, non-uniform potential distribution, and ion concentration variation caused by electrolyte evaporation, and the dielectric constant is influenced by the frequency, for example, when the electrolytic capacitor is used for a switching converter, the working frequency is usually in kHz, so that when the nominal value of the electrolytic capacitor is directly adopted to perform modeling and analysis of a circuit system, the wrong estimation of the circuit operation state is caused, the deviation of the analysis result is caused, and the performance of the designed circuit system is further reduced. Taking 50V 10 muF Rubycon PX series capacitance as an example, the impedance of the capacitor is measured in a frequency band of 25 ℃ (100Hz, 1MHz) by a Wayne Kerr WK65120B precision impedance analyzer, and the variation trend of the impedance along with the working frequency is shown in figure 1 of the attached drawing of the specification:
based on the above situation, various equivalent circuit models of aluminum electrolytic capacitors are proposed. In the technical manuals provided by capacitance manufacturers TDK and Rubycon, considering the self-resonance phenomenon of capacitance under high-frequency operating conditions, an RLC model including equivalent series inductance is used (reference 1"TDK. Aluminum Electrolytic capacitors,
https: tdk. Eu/download/530704/5f33d2619fa73419e2a4af562122e90 c/pdf-genetic engineering for formation. Pdf ", reference 2 'rubycon, technical nodes for electronic capacitors. Http:// www.rubycon.co.jp/en/products/aluminum/pdf/performance. Pdf"), but this model does not take into account the influence of electrolytic capacitor leakage current, and therefore an equivalent model of capacitors and equivalent series inductors connected in parallel with leakage current resistors 45 zxft 3245 and RpL, respectively, on the RLC model is proposed (reference 3' braham, a. Lavian, a. Vector, p.net, 3265. Electronic circuits 3232, IEEE 3732. Conversion, and 3. Conversion 3732. Sub., "power of electric capacitors". For the same purpose, a leakage current resistance Rp is connected in parallel to the capacitance in an Electrolytic capacitance equivalent circuit model proposed by a manufacturer Nichicon (reference 4"Nichicon, general Description of Aluminum Electrolytic Capacitors).
<xnotran> https:// 5754 zxft 5754/～ reese/electrolytics/tec1.pdf. "), ( 5"Zhao,K., ciufo, P., perera, S.Rectifier capacitor filter stress analysis when subject to regular voltage fluctuations [ J ], IEEE Trans.Power Electron., 3252 zxft 3252, (7), pp.3627-3635.", 6"Gasperi,M.L.A method for predicting the expected life of bus capacitors[J ]. IEEE Industry Applications Society Annual Meeting, new Orleans, LA, october 1997.", 7"Abdennadher,K., venet, P., rojat, G., et al.A real-time predictive-maintenance system of aluminum electrolytic capacitors used in uninterrupted power supplies [ J ], IEEE Trans.Ind.Appl., 3532 zxft 3532, (4), pp.1644-1652.", 8"Rendusara,D., cengelci, E., enjeti, P., et al.An evaluation of the DC-link capacitor heating in adjustable speed drive systems with different utility interface options [ C ].14th Annual Applied Power Electronics Conf.and Exposition (APEC' 99), march 1999,vol.2,pp.781-787.", 9"Kieferndorf,F., forster, M., lipo, T.Reduction of DC-bus capacitor ripple current with PAM/PWM converter [ J ], IEEE Trans.Ind.Appl., 3425 zxft 3425, (2), pp.607-614 "). </xnotran> The manufacturer KEMET proposed a model considering dielectric absorption and molecular polarization effects based on the internal reaction mechanism of electrolytic Capacitors (reference 10 ″ -KEMET.
http://www.dialelectrolux.ru/files/file/Kemet/f3102.pdf”)。
In the manufacturer Cornell Dublier's technical manual, it is believed that a Zener diode needs to be added to the equivalent circuit model to reflect the reverse voltage characteristics of the Electrolytic Capacitor (reference 11"CDM Cornell Dubilier, aluminum electronic Capacitor Application guide. Http:// www.cde.com/resources/targets/AEapppGUIDE. Pdf"). Some research works suggest that more complex ladder network models can be used to describe the capacitance characteristics (ref. 12' parler, s.g. improved characteristics of aluminum electrolytic capacitors for inverter Applications, j. IEEE industrial Applications Society of the same, october 2002. ") because a large number of plate capacitors are formed between ions and electrodes on the electrode surface roughened by the aluminum electrolytic capacitors, and the electron resistance formed by the electrode material and the ion resistance of the electrolyte correspond to the self-similar fractal structure of the parallel combination of infinite capacitors and resistor strings. Furthermore, a fractional order equivalent circuit model of aluminum electrolytic capacitor has been proposed in recent years for the characteristic that the impedance of the aluminum electrolytic capacitor varies with the operating frequency (reference 13"Hadi Malek, sara Dadras and Yangquan Chen. Fractional order equivalent circuit model of electronic capacitor and fractional order approximation with application to prediction main J." IET Power Electronics,2016, vol.9, iss.8, pp.1608-1613 ").
It can be seen that new circuit elements and new branches are continually added based on the existing model in order to more accurately characterize the capacitance. It is anticipated that more elements may be used in the model to improve the prediction accuracy of the model. However, an overly complex structure would inconvenience the modeling of the circuitry.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art, provides an equivalent circuit model of a non-solid-state aluminum electrolytic capacitor and a parameter identification method, and provides a new thought for the equivalent circuit model modeling and parameter identification of electrochemical elements, thereby providing a reference basis for the design and reliability analysis of a circuit system containing the elements.
The technical scheme adopted by the invention is as follows:
an equivalent circuit model topology structure of a non-solid-state aluminum electrolytic capacitor, comprising:
fractional order capacitor C representing infinite self-similar structure of capacitor electrode surface α The sum R of the electrolyte resistance in the capacitor and the resistance of the auxiliary lead wire Ω Fractional order capacitors representing complex movement of ions in the capacitor electrolyte
Wherein C is the nominal value of the capacitor case, [ alpha, R [ ] Ω ,β,C 1 ]Is a parameter to be identified;
sum R of electrolyte resistance and auxiliary conductor resistance in capacitor Ω And a fractional order capacitor representing complex movement of ions within the electrolyte
Parallel connection with a fractional order capacitor C representing infinite self-similar structure on the surface of the capacitor electrode α And the equivalent circuit model topological structure is formed by connecting the two circuits in series.
The equivalent circuit model impedance expression is as follows:
the invention discloses an equivalent circuit model of a non-solid-state aluminum electrolytic capacitor and a parameter identification method, which have the following technical effects:
1. according to the equivalent circuit model provided by the invention, the traditional electrolytic capacitor equivalent circuit model has more and more elements in order to achieve higher prediction accuracy. In contrast, the capacitance fractional order model of the invention has a great reduction of the parameters to be determined, and is easier to establish the model.
2. The non-solid aluminum electrolytic capacitor equivalent circuit model provided by the invention can describe the characteristic that the impedance value of the non-solid aluminum electrolytic capacitor changes along with the working frequency, and can obtain the expression of the equivalent series resistance and the equivalent capacitance value of the capacitor according to the impedance formula.
3. According to the parameter identification process of the model, in the process of constructing the parameter identification target function, the influence of the equivalent series resistance and the equivalent capacitance value of the capacitor is considered, so that the model and the method provided by the invention can be further applied to predicting the capacitor life of the non-solid-state aluminum electrolytic capacitor. Therefore, reference basis can be provided for the design and reliability analysis of a circuit system containing the element.
4. The equivalent circuit model provided by the invention can accurately describe the characteristic that the equivalent series resistance of the non-solid aluminum electrolytic capacitor changes along with the working frequency, and can predict the change trend of the actual capacitance value of the capacitor under different working frequencies, thereby providing a reference basis for the design and reliability analysis of a circuit system containing the element.
Drawings
The invention is further illustrated with reference to the following figures and examples:
FIG. 1 is a curve of the impedance value of 10 μ F Rubycon PX series aluminum electrolytic capacitor measured by a precision impedance analyzer along with the variation of operating frequency.
FIG. 2 (a) is a TDK/Rubycon model of aluminum electrolytic capacitor.
Fig. 2 (b) is a model of the aluminum electrolytic capacitor considering leakage current.
FIG. 2 (c) is an aluminum electrolytic capacitor Nichicon model.
FIG. 2 (d) shows a KEMET model of aluminum electrolytic capacitor.
FIG. 2 (e) shows a Cornell Dubilier model of an aluminum electrolytic capacitor.
FIG. 2 (f) is a model of an aluminum electrolytic capacitor ladder network.
Fig. 2 (g) is an aluminum electrolytic capacitor fractional order model.
Fig. 3 is a fractional order equivalent circuit diagram of an aluminum electrolytic capacitor.
FIG. 4 is a flow chart of aluminum electrolytic capacitor parameter identification.
FIG. 5 (a) is a comparison chart of the identification results of the equivalent circuit model impedance values of various aluminum electrolytic capacitors in the embodiment.
FIG. 5 (b) is a comparison chart of the equivalent series resistance values of the equivalent circuit models of various aluminum electrolytic capacitors in the embodiment.
FIG. 5 (c) is a comparison chart of the equivalent capacitance value identification results of the equivalent circuit models of various aluminum electrolytic capacitors in the specific embodiment.
Detailed Description
As shown in fig. 3 and 4, an equivalent circuit model and a parameter identification method for a non-solid aluminum electrolytic capacitor includes the following features:
s1, an equivalent circuit model of a non-solid-state aluminum electrolytic capacitor is composed of a fractional order capacitor C representing an infinite self-similar structure on the surface of a capacitor electrode α The sum R of the electrolyte resistance in the capacitor and the resistance of the auxiliary lead wire Ω And a fractional order capacitor representing complex movement of ions in the capacitor electrolyte
Wherein C is the nominal value of the capacitor case, [ alpha, R [ ] Ω ,β,C 1 ]Is the parameter to be identified. The step S1 includes:
s11, resistance R representing sum of electrolyte resistance and auxiliary lead resistance in equivalent circuit model of non-solid-state aluminum electrolytic capacitor Ω And a fractional order capacitor representing complex movement of ions within the electrolyte
Parallel connection with fractional order capacitor C representing infinite self-similar structure of electrode surface α The series connection forms the topological structure of the equivalent circuit model.
S12, according to the circuit principle and the working principle of the fractional order energy storage element, the equivalent circuit model impedance expression is as follows:
R Ω and C 1 The values are defined as S11, and represent the corresponding resistance of the electrolyte and the auxiliary lead, and the fractional order capacitance of the complex motion of ions in the electrolyte, alpha and beta are the fractional order capacitance C of the complex motion of ions in the electrolyte 1 And the order of fractional order capacitance C of the infinite self-similar structure on the surface of the electrode.
S2, identifying parameters of the non-solid-state aluminum electrolytic capacitor based on a differential algorithm fractional order multi-target off-line parameter identification method. The step 2 comprises the following steps:
s21, measuring and obtaining the impedance value of the non-solid aluminum electrolytic capacitor in a frequency band of (100Hz, 100kHz), and preprocessing data;
s22, according to the equivalent circuit model impedance expression (1), column writing of the Equivalent Series Resistance (ESR) of the non-solid-state aluminum electrolytic capacitor is as follows:
R Ω and C 1 The values are defined as S11, and represent the corresponding resistance of the electrolyte and the auxiliary lead, and the fractional order capacitance of the complex motion of ions in the electrolyte, alpha and beta are the fractional order capacitance C of the complex motion of ions in the electrolyte 1 And the order of fractional order capacitance C of the infinite self-similar structure at the electrode surface.
Column-written non-solid aluminum electrolytic capacitor equivalent capacitance value C eq Comprises the following steps:
R Ω and C 1 The values are defined as step S11, and represent the corresponding resistance of the electrolyte and the attached lead, and the fractional order capacitance of the complex motion of ions in the electrolyte, respectively, and alpha and beta are respectively the complex motion of ions in the electrolyteFractional order capacitor C 1 And the order of fractional order capacitance C of the infinite self-similar structure on the surface of the electrode.
S23, respectively endowing the equivalent series resistance value and the equivalent capacitance value with a weight factor lambda 1 、λ 2 Considering that the influence of the resistance value of the equivalent series resistor on the service life of the aluminum electrolytic capacitor is more obvious, the weight coefficient lambda of the mean square error is predicted for the equivalent series resistor in the parameter optimization process 1 More, in this embodiment, λ is taken 1 ＝0.7，λ 2 And =0.3. Carrying out square sum operation and square opening on the equivalent series resistance value multiplied by the weighting factor and the equivalent capacitance value to construct a multi-target prediction function Z E ；
S24, utilizing the prediction function Z E And the mean-square error (MSE) of the impedance value of the aluminum electrolytic capacitor actually measured at the N points constructs a target function of the parameter identification method:
in the above formula, N is the number of measured data, omega k For the corresponding operating angular frequency, i.e. ω, at the point of kth data k ＝2πf s Wherein f is s I.e. the operating frequency shown on the abscissa in fig. 1:
s25, selecting a population scale of a differential evolution algorithm to be 40 times according to the number of parameters to be estimated of a model in S11, selecting a scaling factor of a differential evolution algorithm variation operation and a probability of a cross operation to be 0.85 and 0.8 respectively, simultaneously selecting a variation strategy of DE/rand-to-best/1 and a cross strategy of binomial distribution, and adding a parameter limiting measure based on a Bounce-Back strategy (refer to' Carlos A. Coello. Thermal constraint-handling techniques: a surfy of the state in the variation and cross process in order to prevent parameter vectors in the variation and cross processes from jumping out of a predetermined parameter space the art[J]Computer Methods in Applied Mechanics and Engineering, vol.191, no.11,2002, pp.1245-1287. "), and fitting data to the objective function (5) to obtain a set of model parameters [ alpha, R ] under the condition that the objective function (5) is minimum Ω ,β,C 1 ]＝[0.9883,1.2430Ω,0.2808,5mF]；
S26, obtaining model parameters [ alpha, R ] in the S25 Ω ,β,C 1 ]＝[0.9883,1.2430Ω,0.2808,5mF]And substituting the expressions (2) and (3) in the step S22 to obtain the equivalent series resistance value and the equivalent capacitance value of the non-solid aluminum electrolytic capacitor under different working frequencies.
Comparing the model parameter identification result provided by the present invention with the model provided by the manufacturer KEMET and the fractional order model parameter identification result in reference 13, as shown in fig. 5 (a), 5 (b), and 5 (C), the three sub-graphs are curves of the impedance value, the ESR value, and the equivalent capacitance value C _ eq of the 10 μ F Rubycon PX series aluminum electrolytic capacitor with the operating frequency. Wherein: the red curve is the measured data, the blue curve is the model parameter identification result provided by the present invention, the black curve is the KEMET model parameter identification result, and the yellow curve is the model parameter identification result provided by the document 13.
From fig. 5 (a), fig. 5 (b), and fig. 5 (c), it can be seen that the model of the present invention fits well to the parameters of the capacitance, which indicates that the method of the present invention is effective.
The parameter variation trend shows that the equivalent series resistance value and the equivalent capacitance value of the aluminum electrolytic capacitor are both reduced along with the increase of the working frequency in the frequency band (100Hz, 100kHz); the parameters obtained by the model identification provided by the invention show that the electrode surface of the non-solid aluminum electrolytic capacitor has weak fractional order characteristics, and the electric field in the electrolyte has strong fractional order characteristics.
Therefore, compared with the traditional scheme, the model with the two fractional order capacitance elements can be used for predicting the capacitance service life of the accurate non-solid-state aluminum electrolytic capacitor, and further can provide reference basis for the design and reliability analysis of a circuit system containing the elements.
Claims (3)
1. An equivalent circuit model topological structure of a non-solid-state aluminum electrolytic capacitor is characterized by comprising:
fractional order capacitor C representing infinite self-similar structure on surface of capacitor electrode α The sum R of the electrolyte resistance in the capacitor and the resistance of the auxiliary lead wire Ω Fractional order capacitors representing complex movement of ions in the capacitor electrolyte
Wherein C is the nominal value of the capacitor case, [ alpha, R [ ] Ω ,β,C 1 ]Is a parameter to be identified;
sum R of electrolyte resistance in capacitor and auxiliary lead resistance Ω And a fractional order capacitor representing complex movement of ions within the electrolyte
Parallel connection with a fractional order capacitor C representing infinite self-similar structure on the surface of the capacitor electrode α And the equivalent circuit model topological structure is formed by connecting the two circuits in series.
2. The equivalent circuit model topology structure of the non-solid aluminum electrolytic capacitor according to claim 1, wherein: the equivalent circuit model impedance expression is as follows:
3. the method for identifying parameters of a non-solid aluminum electrolytic capacitor using the topological structure of the equivalent circuit model according to claim 2, comprising the steps of:
step 1, measuring and obtaining the impedance value of a non-solid aluminum electrolytic capacitor in a frequency band of (100Hz, 100kHz), and preprocessing data;
step 2, according to the equivalent circuit model impedance expression (1), the equivalent series resistance ESR of the column-written non-solid aluminum electrolytic capacitor is as follows:
column-written non-solid aluminum electrolytic capacitor equivalent capacitance value C eq Comprises the following steps:
step 3, respectively endowing the equivalent series resistance value and the equivalent capacitance value with a weight factor lambda 1 、λ 2 ，λ 1 、λ 2 Values are all in the range of 0 to 1, the equivalent series resistance value multiplied by the weight factor and the equivalent capacitance value are subjected to square sum operation and squared to construct a multi-target prediction function Z E ；
Step 4, utilizing the prediction function Z E And (3) constructing a target function of the parameter identification method by using the mean square error MSE of the impedance value of the aluminum electrolytic capacitor actually measured at the N points:
in the above formula: n is the number of measured data, omega k For the corresponding operating angular frequency, i.e. ω, at the point k k ＝2πf s Wherein f is s As the operating frequency:
step 5, selecting the population scale of the differential evolution algorithm to be 40 times according to the number of the parameters to be estimated of the model in the step 1, selecting the scaling factor of the differential evolution algorithm variation operation and the probability of the cross operation to be 0.85 and 0.8 respectively, simultaneously selecting the variation strategy of DE/rand-to-best/1 and the cross strategy of binomial distribution, adding a parameter limiting measure based on the Bounce-Back strategy in the variation and cross processes, and performing data fitting on the objective function (5)Obtaining a set of model parameters [ alpha, R ] under the condition of minimum objective function (5) Ω ,β,C 1 ]；
Step 6, obtaining the model parameters [ alpha, R ] in the step 5 Ω ,β,C 1 ]Substituting the expressions (2) and (3) in the step 2 to obtain the equivalent series resistance value and the equivalent capacitance value of the non-solid aluminum electrolytic capacitor.
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