Second-order equivalent circuit model suitable for super capacitor and parameter identification algorithm thereof

Abstract

The invention belongs to the technical field of supercapacitor equivalent circuit model design, and particularly relates to a second-order equivalent circuit model suitable for a supercapacitor and a parameter identification algorithm of the second-order equivalent circuit model. The parameter identification algorithm is simple and easy to implement, and errors generated in the simulation process of the second-order equivalent circuit model are effectively reduced by adopting variables to represent the dependency relationship of the capacitor on the voltage. The parameter identification algorithm of the second-order equivalent circuit model comprises the following steps of: 1, solving parameters of each structural unit in the second-order equivalent circuit model according to structural characteristics of the second-order equivalent circuit model; 2, deducing a relational expression between the charging current I and the terminal voltage U0 and a relational expression between the capacitor C1 and the terminal voltage U0; 3, fitting a function expression U0 (t) of the terminal voltage changing along with time; and 4, deriving to obtain a function expression k (t) of the terminal voltage variable parameter changing along with time.

Description

Technical Field

[0001] The present invention belongs to the technical field of supercapacitor equivalent circuit model design, and in particular relates to a second-order equivalent circuit model suitable for supercapacitors and a parameter identification algorithm thereof. Background Art

[0002] With the continuous development of new energy technology and various energy conversion application technologies, how to convert renewable energy into electrical energy for storage has become an urgent problem to be solved. Among them, energy distribution and optimization control of energy storage devices not only help to improve the energy conversion utilization rate, but also effectively improve the quality of electricity supply, thus becoming the core technical breakthrough point of sustainable energy storage technology.

[0003] As a new type of electrochemical energy storage device, supercapacitors have attracted extensive attention. Supercapacitors are also called electrochemical capacitors or double-layer capacitors. They have many advantages, such as long service life, high power density, high energy density, environmental friendliness, short charging and discharging time, high efficiency, and low environmental requirements. In order to accurately study the dynamic and static performance indicators of supercapacitors, it is necessary to establish a model for the supercapacitor and adopt appropriate parameter identification methods. Figure 1 As shown, Figure 1 A classic supercapacitor model of the prior art is provided. However, after further research, the inventors found that although the structure of the supercapacitor model is relatively simple, the accuracy of the model is not high, and the sensitive voltage of the main branch is too small, and there is actual time dependence and voltage dependence, which will eventually lead to an overestimation of the supercapacitor energy storage capacity in a short period of time, which is not conducive to the industrial application and promotion of supercapacitors. Summary of the invention

[0004] The present invention provides a second-order equivalent circuit model suitable for a supercapacitor and a parameter identification algorithm thereof. The second-order equivalent circuit model has higher simulation accuracy for the supercapacitor and can better reflect the dependency between the supercapacitor and the terminal voltage; the parameter identification algorithm is simple and easy to implement, and by using variables to characterize the dependency of the capacitor on the voltage, the error generated in the simulation process of the second-order equivalent circuit model is effectively reduced.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions: A second-order equivalent circuit model applicable to a supercapacitor, wherein the second-order equivalent circuit model is composed of an instantaneous branch, a voltage adjustment branch, and a self-discharge branch; The instantaneous branch is composed of a resistor R1, a capacitor C1, a controllable voltage source U and a hysteresis voltage U1 connected in sequence; the voltage adjustment branch is composed of a resistor R2 and a capacitor C2 connected in sequence; and the self-discharge branch is composed of a resistor R3; The resistor R1 and capacitor C1 in the instantaneous branch are used to simulate the steep rise and fall of the terminal voltage during constant current charging and discharging of the supercapacitor; the resistor R2 and capacitor C2 in the voltage adjustment branch are used to simulate the voltage self-recovery phenomenon after the supercapacitor is charged and discharged; the resistor R3 in the self-discharge branch is used to simulate the self-discharge phenomenon of the supercapacitor; the hysteresis voltage U1 in the instantaneous branch is used to reflect the voltage-dependent hysteresis characteristics between the capacitance increment of the capacitor C1 and the output voltage of the controllable voltage source U.

[0006] Further preferably, the method comprises the following steps: Step 1: According to the structural characteristics of the second-order equivalent circuit model, solve the parameters of each structural unit in the second-order equivalent circuit model; Step 2: Derive the relationship between the charging current I and the terminal voltage U0, and the relationship between the capacitance C1 and the terminal voltage U0; Step 3: Based on the measured data of the terminal voltage during the discharge process, fit the function expression U0(t) of the terminal voltage changing with time; Step 4: Derive the function expression k(t) of the terminal voltage variable parameter changing with time.

[0007] Further preferably, the process of solving the parameters of each structural unit in the second-order equivalent circuit model in step 1 specifically includes: Solve the parameters of each structural unit of the instantaneous branch; Solve the parameters of each structural unit of the voltage regulation branch; Solve the parameters of each structural unit of the self-discharge branch.

[0008] Further preferably, the resistance R1 in the instantaneous branch obtained by solving satisfies: R1=ΔU0 / I (1); Where I is the charging current, U0 is the terminal voltage, and ΔU0 is the mutation value of the terminal voltage U0; The capacitance C1 in the instantaneous branch obtained by solving the problem satisfies: The output voltage value U of the controllable voltage source in the instantaneous branch obtained by solving satisfies: U=U d kU0 / C1 (3); In formula (3), the relationship between U and C1 is considered linear, and the control parameter k is considered a constant; U d It is the charging voltage minus the internal resistance voltage divider.

[0009] Further preferably, the capacitor C2 in the voltage adjustment branch obtained by solving satisfies: Q=It=U f (C1+C2+kU f) (4); Among them, U f It is the terminal voltage of the supercapacitor after self-recovery and stabilization after charging according to a certain time constant; The resistor R2 in the voltage adjustment branch obtained by solving satisfies: R2=τ2 / C2 (5).

[0010] Further preferably, the resistor R3 in the self-discharge branch obtained by solving satisfies: R3=V n / I leak (6); Among them, V n is the rated voltage; I leak is the leakage current.

[0011] Further preferably, the relationship between the charging current I and the terminal voltage U0 derived in step 2 satisfies: Among them, since the shunting effect of the voltage adjustment branch is very small during the charging process, it is assumed that the voltage adjustment branch only distributes charge with the instantaneous branch after the charging is completed. Therefore, in formula (7), dU d =dU0; The relationship between the capacitance C1 and the terminal voltage U0 derived in step 2 satisfies: C1=C 10 +kU0(t)(8); Among them, C 10 is the initial value of capacitor C1, satisfying: Among them, U0(t) is the real-time voltage value of the terminal voltage. Further preferably, the functional expression k(t) of the terminal voltage variable parameter changing with time derived in step 4 satisfies: k(t)=a1u 3 +a2u 2 +a3u+a4 (10); Among them, coefficients a1, a2, a3, and a4 are all determined by the least squares method.

[0012] The present invention provides a second-order equivalent circuit model suitable for supercapacitors and a parameter identification algorithm thereof, wherein the second-order equivalent circuit model is composed of an instantaneous branch, a voltage adjustment branch and a self-discharge branch; the parameter identification algorithm of the second-order equivalent circuit model includes the following steps: Step 1: Solve the parameters of each structural unit in the second-order equivalent circuit model according to the structural characteristics of the second-order equivalent circuit model; Step 2: Derive the relationship between the charging current I and the terminal voltage U0, and the relationship between the capacitor C1 and the terminal voltage U0; Step 3: Fit the function expression U0(t) of the terminal voltage changing with time; Step 4: Derive the function expression k(t) of the terminal voltage variable parameter changing with time. The second-order equivalent circuit model having the above-mentioned structural characteristics and its parameter identification algorithm have at least the following technical advantages compared to the prior art: 1) The second-order equivalent circuit model provided by the present invention has high simulation accuracy and can better reflect the dependence between the supercapacitor and the terminal voltage; 2) The algorithm is simple and easy to use, and the derived fitting results are accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0014] Figure 1 A schematic diagram of the structure of a second-order equivalent circuit model applicable to a supercapacitor provided by the present invention; Figure 2 A schematic diagram of the parameter identification algorithm flow for the second-order equivalent circuit model of a supercapacitor provided by the present invention.

[0015] Figure 3 When k(t) takes a fixed value, the simulation circuit formed by fitting is shown in the figure; Figure 4 Schematic diagram of the simulation circuit formed by fitting when k(t) is a third-order polynomial. DETAILED DESCRIPTION

[0016] The present invention provides a second-order equivalent circuit model suitable for a supercapacitor and a parameter identification algorithm thereof. The second-order equivalent circuit model has higher simulation accuracy for the supercapacitor and can better reflect the dependency between the supercapacitor and the terminal voltage; the parameter identification algorithm is simple and easy to implement, and by using variables to characterize the dependency of the capacitor on the voltage, the error generated in the simulation process of the second-order equivalent circuit model is effectively reduced.

[0017] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Embodiment 1

[0018] The present invention provides a second-order equivalent circuit model suitable for supercapacitors, such as Figure 1 As shown, Figure 1 The second-order equivalent circuit model for supercapacitors is shown in FIG. 1 , wherein the second-order equivalent circuit model is specifically composed of an instantaneous branch, a voltage adjustment branch, and a self-discharge branch. The instantaneous branch is composed of a resistor R1, a capacitor C1, a controllable voltage source U, and a hysteresis voltage U1 connected in sequence; the voltage adjustment branch is composed of a resistor R2 and a capacitor C2 connected in sequence; and the self-discharge branch is composed of a resistor R3.

[0019] The resistor R1 and capacitor C1 in the instantaneous branch are used to simulate the steep rise and fall of the terminal voltage during constant current charging and discharging of the supercapacitor. The resistor R2 and capacitor C2 in the voltage adjustment branch are used to simulate the voltage self-recovery phenomenon after the supercapacitor is charged and discharged. Ideally, the shunt effect of the voltage adjustment branch during the charging process can be ignored, and the voltage self-recovery phenomenon is only simulated after the charging is completed, and the simulation effect of another branch will not be covered up during the charging process. The resistor R3 in the self-discharge branch is used to simulate the self-discharge phenomenon of the supercapacitor (the self-discharge phenomenon is relatively slow, so a large resistor R3 is used as the third parallel branch).

[0020] One point that needs to be supplemented is that, with the resistor R1, capacitor C1 and controllable voltage source U in the instantaneous branch connected in series, the technicians established the relationship between the capacitance increment and the output voltage of the controllable voltage source. At this time, the capacitance increment of the supercapacitor is equivalently expressed in the simulation model in the form of the output voltage U of the controllable voltage source. However, in the implementation process, there is a certain hysteresis in the voltage presentation, so the hysteresis voltage U1 in the instantaneous branch is used; specifically, the hysteresis voltage U1 in the instantaneous branch is used to reflect the voltage-dependent hysteresis characteristics between the capacitance increment of the capacitor C1 and the output voltage of the controllable voltage source U. Embodiment 2

[0021] The present invention also provides a parameter identification algorithm for a second-order equivalent circuit model of a supercapacitor, such as Figure 2 As shown, the following steps are included: Step 1: According to the structural characteristics of the second-order equivalent circuit model, solve the parameters of each structural unit in the second-order equivalent circuit model; Step 2: Derive the relationship between the charging current I and the terminal voltage U0, and the relationship between the capacitance C1 and the terminal voltage U0; Step 3: Based on the measured data of the terminal voltage during the discharge process, fit the function expression U0(t) of the terminal voltage changing with time; Step 4: Derive the function expression k(t) of the terminal voltage variable parameter changing with time.

[0022] In combination with the following specific implementation methods, a parameter identification algorithm for a second-order equivalent circuit model applicable to a supercapacitor provided by the present invention is described in detail as follows.

[0023] Specifically, as a preferred implementation, the process of solving the parameters of each structural unit in the second-order equivalent circuit model in step 1 specifically includes: Solve the parameters of each structural unit of the instantaneous branch; Solve the parameters of each structural unit of the voltage regulation branch; Solve the parameters of each structural unit of the self-discharge branch.

[0024] Among them, reference Figure 1 As shown in the schematic diagram of the second-order equivalent circuit model, when constant current charging (assuming constant current charging current is I) starts, the charge in the capacitor is zero, but due to the existence of internal resistance, its terminal voltage U0 will suddenly change, and the voltage will all act on the resistor R1. At this time, the resistor R1 in the instantaneous branch obtained by solving satisfies: R1=ΔU0 / I (1); Among them, I is the charging current, U0 is the terminal voltage, and ΔU0 is the mutation value of the terminal voltage U0.

[0025] The capacitance C1 in the instantaneous branch obtained by solving the problem satisfies: The output voltage value U of the controllable voltage source in the instantaneous branch obtained by solving satisfies: U=U d kU0 / C1 (3); In formula (3), the relationship between U and C1 is considered linear, and the control parameter k is considered a constant; U d It is the charging voltage minus the internal resistance voltage divider.

[0026] The capacitor C2 in the voltage adjustment branch obtained by solving satisfies: Q=It=U f (C1+C2+kU f ) (4); Among them, U f It is the terminal voltage of the supercapacitor after charging according to a certain time constant and self-recovery and stability are completed.

[0027] The resistor R2 in the voltage adjustment branch obtained by solving satisfies: R2=v2 / C2 (5). The resistance R3 in the self-discharge branch obtained by solving satisfies: R3=V n / I leak (6); Among them, V n is the rated voltage; I leak is the leakage current.

[0028] After solving the parameters of each structural unit in the above second-order equivalent circuit model, the relationship between the charging current I and the terminal voltage U0 and the relationship between the capacitor C1 and the terminal voltage U0 are further derived.

[0029] First, considering the characteristics of the supercapacitor charging process, since the shunting effect of the voltage adjustment branch is very small during the charging process, it is assumed that the voltage adjustment branch only distributes charge with the instantaneous branch after the charging is completed. As long as the terminal voltage of the supercapacitor model is close to the charging cut-off voltage at the moment of charging, then all instantaneous branches are equivalent, and the parameters of the voltage self-adjusting branch should also be the same. Therefore, The relationship between the charging current I and the terminal voltage U0 derived in step 2 satisfies: In formula (7), dU d =dU0.

[0030] As for the relationship between the capacitance C1 and the terminal voltage U0, the specific derivation is that the relationship between the capacitance C1 and the terminal voltage U0 satisfies: C1=C 10 +kU0(t)(8); Among them, C 10 is the initial value of capacitor C1, satisfying: Among them, U0(t) is the real-time voltage value of the terminal voltage.

[0031] It should be noted that, through the above derivation process, it can be determined that the determination of U0(t) and k(t) can ultimately determine the relationship between the terminal voltage and the size of the supercapacitor. Embodiment 3

[0032] Embodiment 3 includes all the technical features of Embodiment 2. Specifically, Embodiment 3 further explains Step 3 and Step 4 as follows.

[0033] Among them, the functional expression U0(t) of the terminal voltage changing with time can be directly fitted by the measured data of the terminal voltage during the discharge process. The functional expression k(t) of the terminal voltage variable parameter changing with time can be divided into the following two cases. First, within a certain time range, if k(t) does not change much, the terminal voltage variable parameter k function value within the range can be averaged and used as the value of k (that is, k(t) is a certain value). At this time, the specific structure of the simulation circuit is schematically evolved into the following figure. Figure 3 shown.

[0034] However, in a larger time range, the constant k(t) will inevitably fail to meet the requirements of high-precision simulation. At this time, considering that the capacitance increment is a single-valued function of the terminal voltage U0, combined with the correlation between the terminal voltage variable parameter k and the terminal voltage U0, it is further deduced that k(t) and U0(t) are also related by a single-valued function. Among them, the correlation between the terminal voltage variable parameter k and the terminal voltage U0 can be referred to as follows: At this time, the fitting calculation of k(t) can be realized by using a trial and error method or an optimization algorithm. Specifically, as a preferred embodiment of the present invention, after calculation, the error obtained by fitting with a third-order polynomial is relatively low. At this time, the simulation circuit designed is as shown in the attached figure. Figure 4 As shown. The function expression (t) of the terminal voltage variable parameter k changing with time is further derived to satisfy: k(t)=a1u 3 +a2u 2 +a3u+a4 (10); Among them, coefficients a1, a2, a3, and a4 are all determined by the least squares method.

[0035] The present invention provides a second-order equivalent circuit model suitable for supercapacitors and a parameter identification algorithm thereof, wherein the second-order equivalent circuit model is composed of an instantaneous branch, a voltage adjustment branch and a self-discharge branch; the parameter identification algorithm of the second-order equivalent circuit model includes the following steps: Step 1: Solve the parameters of each structural unit in the second-order equivalent circuit model according to the structural characteristics of the second-order equivalent circuit model; Step 2: Derive the relationship between the charging current I and the terminal voltage U0, and the relationship between the capacitor C1 and the terminal voltage U0; Step 3: Fit the function expression U0(t) of the terminal voltage changing with time; Step 4: Derive the function expression k(t) of the terminal voltage variable parameter changing with time. The second-order equivalent circuit model having the above-mentioned structural characteristics and its parameter identification algorithm have at least the following technical advantages compared to the prior art: 1) The second-order equivalent circuit model provided by the present invention has high simulation accuracy and can better reflect the dependence between the supercapacitor and the terminal voltage; 2) The algorithm is simple and easy to use, and the derived fitting results are accurate and reliable.

[0036] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A second-order equivalent circuit model applicable to supercapacitors, characterized in that: The second-order equivalent circuit model consists of an instantaneous branch, a voltage adjustment branch and a self-discharge branch; The instantaneous branch is composed of a resistor R1, a capacitor C1, a controllable voltage source U and a hysteresis voltage U1 connected in sequence; the voltage adjustment branch is composed of a resistor R2 and a capacitor C2 connected in sequence; and the self-discharge branch is composed of a resistor R3; The resistor R1 and capacitor C1 in the instantaneous branch are used to simulate the steep rise and fall of the terminal voltage during constant current charging and discharging of the supercapacitor; the resistor R2 and capacitor C2 in the voltage adjustment branch are used to simulate the voltage self-recovery phenomenon after the supercapacitor is charged and discharged; the resistor R3 in the self-discharge branch is used to simulate the self-discharge phenomenon of the supercapacitor; the hysteresis voltage U1 in the instantaneous branch is used to reflect the voltage-dependent hysteresis characteristics between the capacitance increment of the capacitor C1 and the output voltage of the controllable voltage source U.

2. A parameter identification algorithm for a second-order equivalent circuit model of a supercapacitor, characterized in that: The steps include: Step 1: According to the structural characteristics of the second-order equivalent circuit model, solve the parameters of each structural unit in the second-order equivalent circuit model; Step 2: Derive the relationship between the charging current I and the terminal voltage U0, and the relationship between the capacitance C1 and the terminal voltage U0; Step 3: Based on the measured data of the terminal voltage during the discharge process, fit the function expression U0(t) of the terminal voltage changing with time; Step 4: Derive the function expression k(t) of the terminal voltage variable parameter changing with time.

3. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 1, characterized in that: The process of solving the parameters of each structural unit in the second-order equivalent circuit model in step 1 specifically includes: Solve the parameters of each structural unit of the instantaneous branch; Solve the parameters of each structural unit of the voltage regulation branch; Solve the parameters of each structural unit of the self-discharge branch.

4. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 3, characterized in that: The resistance R1 in the instantaneous branch obtained by solving the problem satisfies: R1=ΔU0 / I (1); Where I is the charging current, U0 is the terminal voltage, and ΔU0 is the mutation value of the terminal voltage U0; The capacitance C1 in the instantaneous branch obtained by solving satisfies: The output voltage value U of the controllable voltage source in the instantaneous branch obtained by solving satisfies: U=U d kU0 / C1 (3); In formula (3), the relationship between U and C1 is considered linear, and the control parameter k is considered a constant: U d It is the charging voltage minus the internal resistance voltage divider.

5. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 3, characterized in that: The capacitor C2 in the voltage adjustment branch obtained by solving satisfies: Q=It=U f (C1+C2+kU f ) (4); Among them, U f It is the terminal voltage of the supercapacitor after self-recovery and stabilization after charging according to a certain time constant; The resistor R2 in the voltage adjustment branch obtained by solving satisfies: R2=τ2 / C2 (5).

6. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 3, characterized in that: The resistance R3 in the self-discharge branch obtained by solving satisfies: R3=V n / I leak (6); Among them, V n is the rated voltage; I leak is the leakage current.

7. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 2, characterized in that: The relationship between the charging current I and the terminal voltage U0 derived in step 2 satisfies: Among them, since the shunting effect of the voltage adjustment branch is very small during the charging process, it is assumed that the voltage adjustment branch only distributes charge with the instantaneous branch after the charging is completed. Therefore, in formula (7), dU d =dU0; The relationship between the capacitance C1 and the terminal voltage U0 derived in step 2 satisfies: C1=C 10 +kU0(t) (8); Among them, C 10 is the initial value of capacitor C1, satisfying: Among them, U0(t) is the real-time voltage value of the terminal voltage.

8. The parameter identification algorithm for the second-order equivalent circuit model of supercapacitor according to claim 2, characterized in that: The functional expression k(t) of the terminal voltage variable parameter changing with time derived in step 4 satisfies: k(t)=a1u 3 +a2u 2 +a3u+a4 (10); Among them, coefficients a1, a2, a3, and a4 are all determined by the least squares method.

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