CN110096780B - Super capacitor first-order RC network equivalent circuit and parameter determination method - Google Patents

Super capacitor first-order RC network equivalent circuit and parameter determination method Download PDF

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CN110096780B
CN110096780B CN201910328983.4A CN201910328983A CN110096780B CN 110096780 B CN110096780 B CN 110096780B CN 201910328983 A CN201910328983 A CN 201910328983A CN 110096780 B CN110096780 B CN 110096780B
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王朝晖
王知雨
王斌
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Xian Jiaotong University
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Abstract

The invention discloses a super capacitor first-order RC network equivalent circuit containing a controlled current source and a parameter determination method, wherein the super capacitor first-order RC network equivalent circuit comprises an electrode-electrolyte equivalent resistor R1And an equivalent capacitance C1Controlled current source IchSelf-discharge resistor R2(ii) a Wherein, the equivalent capacitance C1Equivalent resistance R with electrode-electrolyte1Connected in series as a first-order RC branch, self-discharging resistor R2Is independently used as a self-discharge branch and is connected in parallel after a first-order RC branch, and a controlled current source IchAs a branch of the controlled current source, the anode is connected with an equivalent capacitor C1The anode and the cathode are connected with a self-discharge resistor R2The sliding end is used for simulating the influence of residual charge in the super capacitor on self-discharge. The super-capacitor first-order RC network equivalent circuit is simple in structure and easy to determine parameters, and the model precision can be effectively improved by introducing a controlled current source to simulate the effect generated by residual charges in the super-capacitor.

Description

Super capacitor first-order RC network equivalent circuit and parameter determination method
Technical Field
The invention belongs to the technical field of super capacitors, and particularly relates to a first-order RC network super capacitor equivalent circuit structure comprising a controlled current source and a parameter determination method thereof.
Background
With the development of new energy technology, new energy is utilized without departing from energy storage technology, and therefore, high-performance energy storage devices and related technologies become important. As a pollution-free double electric layer electrochemical energy storage device, the super capacitor has the advantages of high charging/discharging efficiency, large power density, wide working temperature range and the like, and is widely applied to the fields of new energy generation, braking energy recovery, motor power starting and the like.
The accurate control of the working state of the super capacitor energy storage system is the basis and key for ensuring the safety and reliability of the super capacitor energy storage system. In practical application, the super capacitor has extremely high charging/discharging speed and complex working voltage dynamic characteristics, and the super capacitor is respectively influenced by different electrochemical characteristics of the super capacitor at different working stages: residual charge exists in a cave of the super-capacitor multi-level hole electrode due to the ion diffusion phenomenon in the initial charging and discharging stages, and the residual charge is represented as the steep rise and the steep fall of terminal voltage; the self-recovery phenomenon of terminal voltage is shown after the charging and discharging are finished; the redistribution effect of residual charges after the charge and discharge ends causes obvious ion concentration gradient, so that the internal electromotive force of the ion concentration gradient is reversely changed. At present, a super capacitor equivalent circuit is generally used for representing the terminal characteristics of the super capacitor in practical application. The super capacitor equivalent circuit is derived according to experience and experimental data, has a simple structure and a mathematical model with certain precision, and describes the terminal dynamic characteristic of the super capacitor by forming an RC network through parameterized resistance-capacitance elements. However, the current super capacitor equivalent circuit does not describe the current compensation effect generated by the residual charge well. Since the internal mechanism of the residual charge effect is complex and has an important role in accurately describing the dynamic voltage variation characteristics of the supercapacitor in the standing stage, it is necessary to provide an equivalent circuit for simulating the effect caused by the residual charge in the supercapacitor.
In addition, the super-capacitor equivalent circuit has important significance for super-capacitor energy management and state of charge estimation, and therefore, the establishment of an accurate super-capacitor equivalent model is very important.
Disclosure of Invention
The invention aims to provide a supercapacitor first-order RC network equivalent circuit containing a controlled current source and a parameter determination method thereof, wherein the controlled current source is used for simulating the residual charge effect in the supercapacitor to improve the model precision; a first-order RC network structure is adopted, so that the model structure is simple and the model parameters are convenient to determine; and determining model parameters by a recursive least square method by sampling the charging/discharging current i (t) and the terminal voltage u (t) of the super capacitor under the constant-current charging/discharging condition.
In order to realize the task, the invention adopts the following technical solution:
a super capacitor first-order RC network equivalent circuit comprises an electrode-electrolyte equivalent resistor R1And an equivalent capacitance C1Controlled current source IchAnd a self-discharge resistor R2(ii) a Equivalent capacitance C1And equivalent resistance R1Connected in series to form a first-order RC branch; self-discharge resistor R2Independently used as a self-discharge branch and arranged behind the first-order RC branch in parallel; controlled current source IchAs a branch of a controlled current source, a controlled current source IchIs connected with an equivalent capacitor C1The anode and the cathode are connected with a self-discharge resistor R2The sliding end of (a).
The equivalent capacitance C1The capacitance value of (a) satisfies: c1＝C0+kV*U+kI*ΔC1Wherein, C0Is a constant representing the constant capacity portion of the supercapacitor; k is a radical ofV*U+kI*ΔC1＝CV,IIs a variable related to the open-circuit voltage u and the charge/discharge current i of the super capacitor, representing the dynamic change capacity, deltaC, of the super capacitor1The actual capacity of the supercapacitor changes due to changes in the charge/discharge current i.
The controlled current source IchIs expressed as
Figure BDA0002037104440000021
Wherein τ ═ (R)1+R2)C1The circuit time constant of the equivalent model circuit after the generation of the compensation current is shown, t represents the time elapsed in the standing phase after the end of charging, and η is a compensation coefficient.
The self-discharge resistor R2Is divided into a first resistor R21And a second resistor R22Compensation coefficient η is self-discharge resistance R through sliding end pair2Is determined and the sliding end pair R2Does not affect the circuit time constant τ of the equivalent model circuit.
The delta Q satisfies: Δ Q ═ C1And delta u, wherein the delta u is divided into a charging standing stage and a discharging standing stage and represents the difference between the measured value of the end voltage of the super capacitor at the end of the standing stage and the end voltage of the equivalent model before the compensation current is not generated by the controlled current source.
The super capacitor is a monomer double electric layer super capacitor.
A parameter determination method for a super-capacitor first-order RC network equivalent circuit comprises the following steps:
the method comprises the following steps: testing the working voltage and the working current of the super capacitor under the conditions of constant current charging/discharging and standing to obtain the charging/discharging current and terminal voltage sampling values under the current conditions;
step two: according to the charging/discharging current and terminal voltage sampling values measured by experiments, parameter determination is carried out on the super capacitor first-order RC network equivalent circuit, and model parameters are further calculated and identified by adopting a recursive least square method;
step three: calculating the parameters of the controlled current source according to the data obtained by identification;
step four: after parameters of the model are determined according to a super-capacitor experiment and a recursive least square method, relevant parameters are substituted into the super-capacitor first-order RC network equivalent circuit, a voltage value obtained by model calculation and a voltage value measured by the experiment are compared and analyzed, and the parameters of the super-capacitor first-order RC network equivalent circuit containing the controlled current source are determined or corrected.
Preferably, the step two further calculating and identifying the model parameters by using a recursive least square method comprises the following specific steps:
the transfer function of the circuit Laplace transform of the super capacitor first-order RC network equivalent circuit comprising the controlled current source is as follows:
Figure BDA0002037104440000041
wherein U(s) is terminal voltage as system output, I(s) is charging/discharging current as system input;
discretizing, i.e. substituting, the transfer function by means of a bilinear transformation
Figure BDA0002037104440000042
Wherein T represents the sampling period of the system;
the discretization transfer function of the first-order RC equivalent circuit is as follows:
Figure BDA0002037104440000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002037104440000044
the difference equation corresponding to the discretized transfer function is as follows:
U(z)＝-a1U(z-1)+b0I(z)+b1I(z-1)
the above equation is written as:
Figure BDA0002037104440000045
in the formula, the parameter to be identified
Figure BDA0002037104440000046
System measurement value h (z) ═ U (z-1) I (z-1)]T；
Estimating the parameters of the formula by using a recursive least square method, wherein the recursive process comprises the following steps:
Figure BDA0002037104440000047
in the formula, k and k +1 respectively represent the values of each parameter in the kth iterative process and y (k) represents the kth measured value of the terminal voltage of the system;
in the formula, PkAnd
Figure BDA0002037104440000051
determining an iteration initial value;
determining an iteration termination condition by using the minimum mean square error;
and after determining the identification parameters when the iteration is terminated, obtaining the equivalent circuit parameters by using the identification result.
Preferably, the third step comprises the following specific steps:
computationally controlled current source Ich(t) circuit time constant τ ═ R1+R2)C1，ΔQ＝C1Δ u, where Δ u represents the maximum value of the difference between the model-calculated voltage value and the experimentally measured voltage value before the controlled current source generates the compensation current, the compensation factor η is determined by applying a self-discharge resistance R to the current2Carrying out segmentation, and comparing simulation with experimental curve calculation to obtain the result;
computing
Figure BDA0002037104440000052
And the controlled current source is equivalent only in the standing stage after the charge/discharge is finishedSimulating the effect of residual charge in a circuit, wherein τ ═ (R)1+R2)C1The circuit time constant of the equivalent model circuit after the generation of the compensation current is shown, t represents the time elapsed in the standing phase after the end of charging, and η is a compensation coefficient.
Compared with the prior art, the invention has the following advantages:
the equivalent circuit of the super capacitor first-order RC network comprises an electrode-electrolyte equivalent resistor R1And an equivalent capacitance C1Controlled current source IchAnd a self-discharge resistor R2The composition is used for simulating the influence of residual charge inside the super capacitor on self-discharge. With the consumption of residual charge, the equivalent capacitance C1The stored charge is also consumed, and IchIt is used to simulate the effect of residual charge. A super capacitor first-order RC network equivalent circuit containing a controlled current source samples a charging/discharging current i (t) and a terminal voltage u (t) of a super capacitor under a constant current charging/discharging condition, and model parameters are determined through a recursive least square method. The supercapacitor first-order RC network equivalent circuit is simple in structure and easy in parameter determination, and model accuracy can be effectively improved by introducing a controlled current source to simulate the effect generated by residual charges in the supercapacitor. The super capacitor first-order RC network equivalent circuit is simple in structure, and circuit parameters are easy to determine by adopting the first-order RC network; a controlled current source is added to simulate the residual charge effect in the super capacitor, so that the model precision is improved; self-discharge resistor R by using sliding end pair2The division of (a) enables adjustment of the controlled current source parameters. The method for determining the parameters by adopting the recursive least squares is easy to realize in principle, can identify the parameters on line, and is more convenient and quicker in actual engineering application occasions.
According to the method, after parameters are determined according to the voltage value and the current value obtained by the super capacitor experiment, the equivalent circuit parameters are calculated according to the parameter determination result and are substituted into the super capacitor equivalent circuit structure, the voltage value obtained by model simulation and the voltage value obtained by the experiment are compared and analyzed, the effect generated by simulating residual charges in the super capacitor by the super capacitor first-order RC network equivalent circuit with the controlled current source is verified, and the model precision is improved.
Drawings
FIG. 1 is a first-order super capacitor equivalent circuit structure with controlled current source and its branch description.
FIG. 2 shows an equivalent capacitor C1The specific structure is shown schematically.
Fig. 3 is a change curve of terminal voltage obtained by simulation and experimental measurement of a common first-order super capacitor equivalent model.
Fig. 4 is a schematic diagram of the operating principle of the controlled current source.
FIG. 5 is a block diagram of a model parameter identification process.
Fig. 6 is a diagram of an equivalent circuit of the controlled current source in operation.
Fig. 7 is a variation curve of terminal voltage obtained by the simulation and experimental measurement of the equivalent model of the super capacitor according to the present invention.
FIG. 8 is a graph showing the variation of the amount of charge of the controlled current source to compensate for the residual charge effect; in which FIG. 8(a) is a graph showing a charge-standing phase, and FIG. 8(b) is a graph showing a discharge-standing phase.
Detailed Description
The present invention will be described in detail with reference to specific embodiments, which are illustrative of the invention and are not to be construed as limiting the invention.
The present invention will be described in further detail with reference to the accompanying drawings, which are provided for illustration and not for limiting the scope of the invention. For example: sampling period T in the example, iteration initial condition P0，
Figure BDA0002037104440000071
The specific values of the iteration end conditions and the like may be changed accordingly according to the present invention.
The following is an embodiment of the present invention:
as shown in FIG. 1, the equivalent circuit of the first-order RC network of the super capacitor with the controlled current source comprises an electrode-electrolyte equivalent resistance R1And an equivalent capacitance C1Controlled current source IchFromDischarge resistor R2(ii) a The equivalent capacitor C1Equivalent resistance R with electrode-electrolyte1Connected in series as a first-order RC branch, self-discharging resistor R2Is independently used as a self-discharge branch and is connected in parallel after a first-order RC branch, and a controlled current source IchAs a branch of the controlled current source, the anode is connected with an equivalent capacitor C1The anode and the cathode are connected with a self-discharge resistor R2The sliding end simulates compensation current corresponding to the internal residual charge effect when the super capacitor is in standing. R1For describing the electrode-electrolyte equivalent resistance, C, in supercapacitors1For describing the dynamic capacity of the supercapacitor.
Wherein, the equivalent capacitance C1＝C0+kV*U+kI*ΔC1Wherein, C0To constant capacity, kV*U+kI*ΔC1＝CV,IIs a variable related to the open-circuit voltage u and the charge/discharge current i of the super capacitor, and represents the dynamic change capacity of the super capacitor. Controlled current source branch IchThe expression is as follows:
Figure BDA0002037104440000072
where t represents the time elapsed in the rest phase after the end of charging, and τ ═ R (R)1+R2)C1Indicating the circuit time constant of the equivalent model circuit after the generation of the compensation current, η is the compensation coefficient, and the compensation current is obtained by dividing the self-discharge resistor R2And is obtained by experimental calculation, and delta Q is equal to C1Δ u, wherein Δ u represents the difference between the measured value of the super capacitor terminal voltage and the equivalent model terminal voltage before the controlled current source does not generate the compensation current at the end of the charging/discharging standing stage, and is divided into Δ u according to the difference of the charging/discharging standing stagecharge-restAnd Δ udischarge-restControlled current source IchThe internal residual charge effect is simulated only during the charge/discharge rest phase.
The parameter determination method of the supercapacitor first-order RC network equivalent circuit comprises the following steps:
the method comprises the following steps: testing the working voltage and the working current of the super capacitor under the conditions of constant current charging/discharging and standing to obtain the charging/discharging current and terminal voltage sampling values under the current conditions;
step two: determining parameters of the super-capacitor first-order RC network equivalent circuit by adopting a recursive least square method, and obtaining model parameters according to the result of parameter identification of the recursive least square method;
step three: computationally controlled current source Ich(t) circuit time constant τ ═ R1+R2)C1，ΔQ＝C1Δ u, where Δ u represents the maximum value of the difference between the model-calculated voltage value and the experimentally measured voltage value before the controlled current source generates the compensation current, the compensation factor η is determined by applying a self-discharge resistance R to the current2Carrying out segmentation, and comparing simulation with experimental curve calculation to obtain the result;
step four: computing
Figure BDA0002037104440000081
And the controlled current source simulates the effect generated by the residual charge in the equivalent circuit only in the standing stage after the charge/discharge is finished;
step five: and comparing and analyzing the voltage value obtained by model calculation with the voltage value measured by experiments, and verifying that the supercapacitor first-order RC network equivalent circuit containing the controlled current source can simulate the residual charge effect in the supercapacitor to improve the model precision.
Wherein, the super capacitor is a monomer electric double layer super capacitor (EDLC).
The charge/discharge current and terminal voltage sampling values can be acquired by a super-capacitor multi-channel tester or measured by other instruments, and the super-capacitor multi-channel tester is a new Wille 4000 series battery tester.
Or the current sampling value is acquired by a current sensor which is a Hall sensor, a shunt or an electromagnetic current transformer.
Or the voltage sampling value is acquired by a voltage sensor, and the real-time voltage sensor is a resistance voltage divider, a capacitance voltage divider, an electromagnetic voltage transformer, a capacitance voltage transformer or a Hall voltage sensor.
Open-loop voltage of super capacitor and its capacitance value existNon-linear relationship, equivalent capacitance C1Is shown in fig. 2. Obtaining the equivalent capacitance C by adopting a curve fitting method for the voltage and current data measured by the experiment1First order expression of (C)1＝C0+kV*U+kI*ΔC1Wherein, C0Denotes the fixed capacitance part, k, in the equivalent capacitanceV*U+kI*ΔC1＝CV,IThe variable capacitance representing the linear change in the equivalent capacitance is a dynamically changing capacity related to the open circuit voltage u and the charge/discharge current i of the super capacitor.
The equivalent capacitance C1In the expression of (2), the proportionality coefficient kVCalculated as follows:
Figure BDA0002037104440000091
wherein Δ t is t2-t1Denotes a charge/discharge time period, Δ V ═ V (t)2)-V(t1) Representing the charge/discharge phase voltage difference.
Constant current charging/discharging experiments are carried out under different current values to obtain the linear change rule of the super capacitor decline amount and the charging/discharging current, and the slope of the linear change rule is the proportionality coefficient kI，kI*ΔC1I.e. the capacitance degradation value of the super capacitor under the current charge/discharge current.
The transfer function of the laplace transform of the circuit of the supercapacitor first-order RC network equivalent circuit with the controlled current source used in this embodiment is:
Figure BDA0002037104440000092
wherein u(s) is terminal voltage as system output, i(s) is charge/discharge current as system input, and the structure of the whole system is shown in fig. 1.
Discretizing, i.e. substituting, the transfer function by means of a bilinear transformation
Figure BDA0002037104440000093
Where T denotes the sampling period of the system, in this example T is 1 second.
The discretization transfer function of the first-order RC equivalent circuit is as follows:
Figure BDA0002037104440000101
in the formula (I), the compound is shown in the specification,
Figure BDA0002037104440000102
the difference equation corresponding to the discretized transfer function is as follows:
U(z)＝-a1U(z-1)+b0I(z)+b1I(z-1)
the above equation can be written as:
Figure BDA0002037104440000103
in the formula, the parameter to be identified
Figure BDA0002037104440000104
System measurement value h (z) ═ U (z-1) I (z-1)]T。
Estimating the parameters of the formula by using a recursive least square method, wherein the recursive process comprises the following steps:
Figure BDA0002037104440000105
in the formula, k and k +1 respectively represent the values of each parameter in the k-th and k + 1-th iteration processes, and y (k) represents the k-th measured value of the terminal voltage of the system.
In the formula, PkAnd
Figure BDA0002037104440000106
an initial value of the iteration, in this case P, needs to be determined0＝225I，
Figure BDA0002037104440000107
The iteration termination condition is determined using the minimum Mean Square Error (MSE), which in this example is:
Figure BDA0002037104440000108
and after determining the identification parameters when the iteration is terminated, obtaining the equivalent circuit parameters by using the identification result.
Then according to IchThe expression (3) calculates the relevant parameters, and fig. 3 is a terminal voltage result calculated by a common first-order super capacitor equivalent model, namely a comparison graph of the equivalent model without using a controlled current source and the change curve of the terminal voltage obtained by an experiment. The charging/discharging standing phase of the delta u is divided into-delta ucharge-restAnd discharge rest stage-Deltaudischarge-restRespectively as controlled current sources IchThe calculated parameters of (1).
The operation principle of the controlled current source is shown in fig. 4, whether the charging/discharging current of the circuit is zero or not is used for judging the operation state of the super capacitor, if I (t) ≠ 0, the circuit is in the working state, and the controlled current source Ich0; if i (t) is 0, the circuit is in a static state, and the controlled current source simulates the effect of internal residual charge to generate compensation current after determining relevant parameters according to the method described herein.
The specific flow of the model parameter determination process is shown in fig. 5, the working voltage and the working current of the super capacitor are tested under the conditions of constant current charging/discharging and standing, the charging/discharging current and terminal voltage sampling values under the current conditions are obtained, the model parameters are obtained by using a recursive least square method, and finally, the voltage values obtained by model calculation and the voltage values obtained by experiment are compared, analyzed and verified.
FIG. 6 is a diagram of an equivalent circuit structure in the operating state of a controlled current source in a self-discharge resistor R2Sliding end of (3) pair R2Does not affect the circuit time constant tau of the equivalent model circuit, and the controlled current source compensation coefficient η is formed by the first resistor R after being divided21And a second resistor R22To determine R2＝R21+R22。
Fig. 7 is a graph showing the variation of the terminal voltage obtained by the equivalent circuit simulation and experimental measurement of the super capacitor first-order RC network with the controlled current source according to this embodiment. As can be seen from the figure, the calculation result of the equivalent circuit of the first-order RC network of the super capacitor with the controlled current source is consistent with the experimental result.
FIG. 8 shows a controlled current source I for compensation simulating the effect of residual chargechGraph of the change of the charge amount. As can be seen from the figure, the controlled current source simulates the charge redistribution process during the rest phase, compensating for the self-discharge performance of the supercapacitor during the rest phase.
The above-described embodiments are merely illustrative of implementations of the invention that enable persons skilled in the art to make or use the invention, and the description is not limiting. Therefore, the present invention should not be limited to the embodiments shown herein, and all additions and equivalents made to the technical features of the present invention are intended to fall within the scope of the present application.

Claims (9)

1. The first-order RC network equivalent circuit of the super capacitor is characterized by comprising an electrode-electrolyte equivalent resistor R1And an equivalent capacitance C1Controlled current source IchAnd a self-discharge resistor R2(ii) a Equivalent capacitance C1And equivalent resistance R1Connected in series to form a first-order RC branch; self-discharge resistor R2Independently used as a self-discharge branch and arranged behind the first-order RC branch in parallel; controlled current source IchAs a branch of a controlled current source, a controlled current source IchIs connected with an equivalent capacitor C1The anode and the cathode are connected with a self-discharge resistor R2The sliding end of (a).
2. The supercapacitor first order RC network equivalent circuit according to claim 1, wherein the equivalent capacitor C is1The capacitance value of (a) satisfies: c1＝C0+kV*U+kI*ΔC1Wherein, C0Is a constant representing the constant capacity portion of the supercapacitor; k is a radical ofV*U+kI*ΔC1＝CV,IIs a variable related to the open-circuit voltage u and the charge/discharge current i of the super capacitor, representing the dynamic change capacity, deltaC, of the super capacitor1The actual capacity of the supercapacitor changes due to changes in the charge/discharge current i.
3. The supercapacitor first-order RC network equivalent circuit according to claim 2, wherein the controlled current source IchIs expressed as
Figure FDA0002037104430000011
Wherein τ ═ (R)1+R2)C1The circuit time constant of the equivalent model circuit after the generation of the compensation current is shown, t represents the time elapsed in the standing phase after the end of charging, and η is a compensation coefficient.
4. The supercapacitor-first order RC network equivalent circuit according to claim 3, wherein the self-discharge resistor R is2Is divided into a first resistor R21And a second resistor R22Compensation coefficient η is self-discharge resistance R through sliding end pair2Is determined and the sliding end pair R2Does not affect the circuit time constant τ of the equivalent model circuit.
5. The supercapacitor first order RC network equivalent circuit according to claim 3, wherein Δ Q satisfies: Δ Q ═ C1And delta u, wherein the delta u is divided into a charging standing stage and a discharging standing stage and represents the difference between the measured value of the end voltage of the super capacitor at the end of the standing stage and the end voltage of the equivalent model before the compensation current is not generated by the controlled current source.
6. The method of claim 1, wherein the super capacitor is a single electric double layer super capacitor.
7. The method for determining the parameters of the equivalent circuit of the supercapacitor first-order RC network according to any one of claims 1 to 6, comprising the steps of:
the method comprises the following steps: testing the working voltage and the working current of the super capacitor under the conditions of constant current charging/discharging and standing to obtain the charging/discharging current and terminal voltage sampling values under the current conditions;
step two: according to the charging/discharging current and terminal voltage sampling values measured by experiments, parameter determination is carried out on the super capacitor first-order RC network equivalent circuit, and model parameters are further calculated and identified by adopting a recursive least square method;
step three: calculating the parameters of the controlled current source according to the data obtained by identification;
step four: after parameters of the model are determined according to a super-capacitor experiment and a recursive least square method, relevant parameters are substituted into the super-capacitor first-order RC network equivalent circuit, a voltage value obtained by model calculation and a voltage value measured by the experiment are compared and analyzed, and the parameters of the super-capacitor first-order RC network equivalent circuit containing the controlled current source are determined or corrected.
8. The method for determining the parameters of the supercapacitor first-order RC network equivalent circuit according to claim 7, wherein the step two of further calculating and identifying the model parameters by using a recursive least square method comprises the following specific steps:
the transfer function of the circuit Laplace transform of the super capacitor first-order RC network equivalent circuit comprising the controlled current source is as follows:
Figure FDA0002037104430000021
wherein U(s) is terminal voltage as system output, I(s) is charging/discharging current as system input;
discretizing, i.e. substituting, the transfer function by means of a bilinear transformation
Figure FDA0002037104430000031
Wherein T represents the sampling period of the system;
the discretization transfer function of the first-order RC equivalent circuit is as follows:
Figure FDA0002037104430000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002037104430000033
the difference equation corresponding to the discretized transfer function is as follows:
U(z)＝-a1U(z-1)+b0I(z)+b1I(z-1)
the above equation is written as:
Figure FDA0002037104430000034
in the formula, the parameter to be identified
Figure FDA0002037104430000035
System measurement value h (z) ═ U (z-1) I (z-1)]T；
Estimating the parameters of the formula by using a recursive least square method, wherein the recursive process comprises the following steps:
Figure FDA0002037104430000036
in the formula, k and k +1 respectively represent the values of each parameter in the kth iterative process and y (k) represents the kth measured value of the terminal voltage of the system;
in the formula, PkAnd
Figure FDA0002037104430000037
determining an iteration initial value;
determining an iteration termination condition by using the minimum mean square error;
and after determining the identification parameters when the iteration is terminated, obtaining the equivalent circuit parameters by using the identification result.
9. The method for determining the parameters of the supercapacitor first-order RC network equivalent circuit according to claim 7, wherein the third specific step is:
computationally controlled current source Ich(t) circuit time constant τ ═ R1+R2)C1，ΔQ＝C1Δ u, where Δ u represents the maximum value of the difference between the model-calculated voltage value and the experimentally measured voltage value before the controlled current source generates the compensation current, the compensation factor η is determined by applying a self-discharge resistance R to the current2Carrying out segmentation, and comparing simulation with experimental curve calculation to obtain the result;
computing
Figure FDA0002037104430000041
And the controlled current source simulates the effect of residual charge in an equivalent circuit only in the standing phase after the charge/discharge is finished, wherein tau (R) is ═ R1+R2)C1The circuit time constant of the equivalent model circuit after the generation of the compensation current is shown, t represents the time elapsed in the standing phase after the end of charging, and η is a compensation coefficient.
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