阅读说明：本技术 一种混合电容器功率状态在线估计方法及系统 (Hybrid capacitor power state online estimation method and system ) 是由 王康丽 陈文欣 蒋凯 徐成 陈曼琳 于 2020-12-04 设计创作，主要内容包括：本发明公开了一种混合电容器功率状态在线估计方法及系统,属于混合电容器应用技术领域。方法包括根据混合电容器等效电路模型获取状态空间方程,并对所述状态空间方程进行离散化；对混合电容器进行工况测试,采集混合电容器的电压值和电流值,利用带遗忘因子的递推增广最小二乘法在线辨识离散化的状态空间方程的参数；利用实时获得的参数,对混合电容器的瞬时峰值功率估计与持续峰值功率进行估计。本发明提供的混合电容器功率状态在线估计方法,与离线功率状态估计方法相比,能够实现模型参数的在线更新,提高混合电容器功率状态估计的精度。(The invention discloses a hybrid capacitor power state online estimation method and system, and belongs to the technical field of hybrid capacitor application. The method comprises the steps of obtaining a state space equation according to a hybrid capacitor equivalent circuit model, and discretizing the state space equation; the method comprises the steps of carrying out working condition testing on a hybrid capacitor, collecting a voltage value and a current value of the hybrid capacitor, and identifying parameters of a discretized state space equation on line by using a recursive augmented least square method with forgetting factors; the instantaneous peak power estimate and the sustained peak power estimate of the hybrid capacitor are estimated using the parameters obtained in real time. Compared with an offline power state estimation method, the online estimation method for the power state of the hybrid capacitor provided by the invention can realize online update of model parameters and improve the accuracy of the power state estimation of the hybrid capacitor.)

1. A hybrid capacitor power state online estimation method is characterized by comprising the following steps:

s1, acquiring a state space equation according to a hybrid capacitor equivalent circuit model, and discretizing the state space equation;

s2, carrying out working condition testing on the hybrid capacitor, collecting a voltage value and a current value of the hybrid capacitor at the moment k, and identifying parameters of the discretized state space equation on line by using a recursive augmented least square method with forgetting factors;

s3, estimating instantaneous peak power estimation and continuous peak power of the hybrid capacitor by using the parameters obtained in real time in S2;

and S4, at the moment of k +1, repeating the steps S2-S3 until the whole working condition is finished.

2. The hybrid capacitor power state online estimation method of claim 1, wherein the hybrid capacitor equivalent circuit model comprises a variable capacitance, an ohmic internal resistance, and a plurality of series-connected RC circuits, and the state space equation is expressed as:

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

3. The hybrid capacitor power state online estimation method of claim 2, wherein the discretized state space equation is expressed as:

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

4. The hybrid capacitor power state online estimation method of claim 3, wherein the discretized state space equation is subjected to Z transformation and Z inverse transformation to obtain a differential equation with time delay:

U_t,k＝θ₁U_t,k-1+…+θ_n+1U_t,k-n-1+θ_n+2I_k+…+θ_2n+3I_k-n-1+w_k+c₁w_k-1+c₂w_k-2+…+c_rw_k-r (3)

wherein, theta_jIs a variable related to the model parameter, j ═ 1,2,3, …,2n +3, w_kWhite noise at time k, r is the order of the white noise moving average model, c_lIs the coefficient of the model, l ═ 1,2,3, …, r.

5. The hybrid capacitor power state online estimation method of claim 4, wherein the output measurement of the system at time k is represented as:

y_k＝H_kθ_k+w_k (4)

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

6. The hybrid capacitor power state online estimation method of claim 5, wherein the recursive process of the recursive augmented least squares with forgetting factor is as follows:

whereinλ is forgetting factor, K_kAs a gain matrix, P_kIs an error covariance matrix of the parameter estimation values, and I is an identity matrix.

7. The hybrid capacitor power state online estimation method of claim 1, wherein the instantaneous peak power estimation of the hybrid capacitor specifically comprises:

the output voltage equation of the hybrid capacitor equivalent circuit model is expressed as:

the current of the hybrid capacitor at time k is:

the instantaneous peak current of charging and discharging is:

wherein the content of the first and second substances,andinstantaneous peak discharge current and instantaneous peak charge current, U, based on voltage limits at time k, respectively_t,minIs discharge cut-off voltage, U_t,maxIs the charge cut-off voltage, U_t,min≤U_t≤U_t,max；

The multi-constraint instantaneous peak current is:

in the formula (I), the compound is shown in the specification,andrespectively the instantaneous peak charge current and the instantaneous peak discharge current at time k satisfying the voltage and current limits,is the minimum pulse charging current that is to be charged,is the maximum pulse of the discharge current of the discharge,

the instantaneous peak power is:

in the formula (I), the compound is shown in the specification,andrespectively, the instantaneous peak charging power and the instantaneous peak discharging power at time k.

8. The hybrid capacitor power state online estimation method of claim 1, wherein the continuous peak power estimation of the hybrid capacitor specifically comprises:

x_k+1＝A_kx_k+B_ku_k (12)

in the formula, x_kIs the state vector of the model at time k, u_kIs the control vector of the model at time k, A_kIs the state matrix of the model at time k, B_kThe input matrix of the k-time model is as follows:

the inputs to the system are equal during the time T x Δ T, i.e. u_k+T＝u_k+T-1＝…＝u_kThen, then

The voltages at this time are:

the working current within T multiplied by delta T time is obtained as follows:

the peak current based on the voltage limit for the duration of T Δ T is:

in the formula (I), the compound is shown in the specification,andrespectively at time kA sustained peak charging current and a sustained peak discharging current based on the voltage limit;

the multi-constraint sustained peak current is:

in the formula (I), the compound is shown in the specification,andrespectively sustained peak charging current and sustained peak discharging current satisfying voltage and current limits at time k,is the minimum continuous charging current that is to be charged,is the maximum sustained discharge current that is to be discharged,

the sustained peak power is:

in the formula (I), the compound is shown in the specification,andrespectively, the sustained peak charging power and the sustained peak discharging power at time k.

9. A hybrid capacitor power state online estimation system, comprising: a computer-readable storage medium and a processor;

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

the processor is configured to read executable instructions stored in the computer-readable storage medium and execute the hybrid capacitor power state online estimation method according to any one of claims 1 to 8.

Technical Field

The invention belongs to the technical field of hybrid capacitor application, and particularly relates to a hybrid capacitor power state online estimation method and system.

Background

Cheap and efficient electrochemical energy storage is a key technology for efficiently utilizing renewable energy and developing a smart grid. The hybrid capacitor is an advanced energy storage device developed recently, and has a wide application prospect in the fields of smart power grids, electric automobiles and the like. One pole of the hybrid capacitor stores and converts energy through electrochemical reaction of conventional battery electrodes, and the other pole stores energy through an absorption/desorption mechanism of an electric double layer. The energy density of the hybrid capacitor is 5-10 times higher than that of a double-electric-layer capacitor, and the power density and the cycle life of the hybrid capacitor are higher than those of a battery.

The power state may be used to characterize the peak power of the charge and discharge of the hybrid capacitor over a predetermined time interval. The real-time estimation of the peak power has important theoretical significance and practical value for reasonably using the hybrid capacitor, avoiding the over-charge and discharge phenomenon and prolonging the cycle life of the hybrid capacitor. Therefore, it is crucial to achieve an accurate estimation of the hybrid capacitor power state. Currently, a commonly used power state estimation method is an HPPC method based on a Rint model proposed by the national engineering and environmental laboratory of adadalton. The method neglects the dynamic characteristic of the hybrid capacitor, the calculated peak discharge current is too high, the peak charging current is too conservative, and the real-time characteristic of the hybrid capacitor is difficult to objectively reflect. Furthermore, the method is only directed to instantaneous peak power estimation, while in practical applications, continuous peak power estimation is more important.

Patent CN111060820A discloses a lithium battery SOC and SOP estimation method based on a second-order RC model. The method improves the original battery model which takes current as input and voltage as output into a model which takes voltage as input and current as output. For power state estimation, a model of the known current computation voltage can simplify the computation steps and reduce the computation amount. Patent CN111537894A discloses a method for lithium batteries SOC and SOP. The method fits the relationship between the temperature and the battery discharge capacity, and corrects the available capacity of the battery, thereby improving the accuracy of the estimation result. However, the above method only involves instantaneous peak power estimation, and the off-line parameter identification method is adopted, so that the circuit model parameters cannot be updated in real time, and the estimation effect in practical application is not ideal. Furthermore, the above methods are all based on lithium battery design and do not involve hybrid capacitors with significant differences in mechanism and performance.

In view of the above-mentioned deficiencies and inadequacies, further improvements and modifications are needed in the art. Aiming at the defects of the hybrid capacitor power state estimation method and the problem that the estimation effect of the existing method in practical application is not ideal, the effective hybrid capacitor power state on-line estimation method is designed, the requirements of practical application are met, and the reliability of the estimation result is improved.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide an effective hybrid capacitor power state online estimation method and system aiming at the defects that the existing power state estimation method has unsatisfactory practical application effect and is not suitable for a hybrid capacitor, so that the method and system are suitable for the requirements of practical application, the reliability of an estimation result is improved, and an important theoretical basis is provided for optimal matching of the power performance of the hybrid capacitor and optimization of a control strategy.

In order to achieve the above object, an aspect of the present invention provides an online estimation method for a power state of a hybrid capacitor, which collects voltage and current during operation of the hybrid capacitor based on an equivalent circuit model of the hybrid capacitor, updates model parameters in real time, and estimates instantaneous peak power and continuous peak power of the hybrid capacitor using the model parameters updated in real time. The specific method is realized according to the following steps:

s1, acquiring a state space equation according to a hybrid capacitor equivalent circuit model, and discretizing the state space equation;

preferably, the present invention employs a multi-model fused equivalent circuit model to characterize the external characteristics of the hybrid capacitor. The model includes a variable capacitance, an ohmic internal resistance, and a plurality of series connected RC circuits. Wherein, the variable capacitance C₀Characterizing a hybrid capacitor dual electrochemical energy storage mechanism; ohmic internal resistance R₀Characterization electrode material, electrolysisLiquid, diaphragm resistance and contact resistance of each part; the RC circuit is a circuit structure formed by connecting a resistor and a capacitor in parallel and represents the polarization characteristic of the hybrid capacitor.

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

wherein, C₀Is a variable capacitance, R₀Is ohmic internal resistance, R_iIs the resistance of an RC circuit, C_iI denotes the ith RC circuit, I is 1,2,3, …, n, I is the load current, U is the capacitance of the RC circuit_tIs terminal voltage, U_C0And U_RCiAre respectively a variable capacitance C₀And the voltage of the ith RC circuit,representing its differential over time.

Discretizing the state equation to obtain:

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

S2, carrying out working condition testing on the hybrid capacitor, collecting the voltage value and the current value of the hybrid capacitor at the moment k, and utilizing a recursive augmented least square method with forgetting factors to identify parameters of the model on line according to the collected voltage value and current value of the hybrid capacitor;

under the zero initial condition, Z transformation and Z inverse transformation are carried out on the formula (2), and colored noise e in the model is considered_k。

Preferably, in the present invention,colored noise e_kBy calculating white noise w_kIs obtained, the difference equation can be written as:

wherein, theta_jIs a variable for the model parameter, j ═ 1,2,3, …,2n + 3. e.g. of the type_kColored noise of the system at time k, w_kWhite noise at time k, r is the order of the white noise moving average model, c_lIs the coefficient of the model, l ═ 1,2,3, …, r.

Further, equation (3) can be written as:

y_k＝H_kθ_k+w_k (4)

in the formula, y_kIs the mixed capacitor terminal voltage at time k, H_kAnd theta_kThe measured data matrix and the model parameter matrix of the hybrid capacitor at time k are respectively, namely:

preferably, the online parameter identification is carried out by adopting a recursive augmented least square method with a forgetting factor lambda. And the precision of the model in the whole life cycle is ensured through real-time parameter correction and updating. The algorithm recursion process is as follows:

in the formula, λ is forgetting factor, K_kAs a gain matrix, P_kIs an error covariance matrix of the parameter estimation values, and I is an identity matrix.

Further, related circuit parameters in the hybrid capacitor multi-model fusion equivalent circuit model can be calculated in real time.

S3, estimating instantaneous peak power and continuous peak power of the hybrid capacitor by using the parameters obtained in real time;

1) instantaneous peak power estimation

The output voltage equation for the hybrid capacitor equivalent circuit model can be written as:

then the current of the hybrid capacitor at time k is:

considering the voltage limiting conditions: u shape_t,min≤U_t≤U_t,maxWherein U is_t,minIs discharge cut-off voltage, U_t,maxIs the charge cut-off voltage. The instantaneous peak current of charging and discharging is:

in the formula (I), the compound is shown in the specification,andrespectively, the instantaneous peak discharge current and the instantaneous peak charge current at time k based on the voltage limit.

In order to ensure the safe and stable operation of the hybrid capacitor, the instantaneous charge-discharge current should satisfy:whereinIs the minimum pulse charging current that is to be charged,is the maximum pulsed discharge current.

Further, the multi-constraint instantaneous peak current is:

in the formula (I), the compound is shown in the specification,andthe instantaneous peak charge current and the instantaneous peak discharge current, respectively, at time k, meet the voltage and current limits.

Further, the instantaneous peak power is calculated:

in the formula (I), the compound is shown in the specification,andrespectively, the instantaneous peak charging power and the instantaneous peak discharging power at time k.

2) Continuous peak power estimation

Preferably, formula (1) is rewritable:

x_k+1＝A_kx_k+B_ku_k (12)

in the formula, x_kIs the state vector of the model at time k, u_kIs the control vector of the model at time k, A_kIs the state matrix of the model at time k, B_kIs the input matrix for the model at time k. The method comprises the following specific steps:

preferably, the model parameters within the time T x Δ T are assumed to be approximately constant, since the model parameters change slowly.

Further, assume that the inputs to the system are approximately equal over time T Δ T, i.e., u_k+T＝u_k+T-1＝…＝u_kThen, then

Substituting equation (14) into the output equation, the voltage at this time can be found to be:

then an approximation of the operating current during time T x Δ T may be calculated as:

further, the peak current based on the voltage limit over the duration of T × Δ T can be found:

in the formula (I), the compound is shown in the specification,andrespectively, a sustained peak charging current and a sustained peak discharging current at time k based on the voltage limit.

Preferably, T is 1, and equation (17) is the same as equation (9), i.e., equation (17) is a general equation for the calculation of the instantaneous peak current and the continuous peak current based on the voltage limitation.

In order to ensure the safe and stable operation of the hybrid capacitor, the continuous charge and discharge current should meet the following requirements:whereinIs the minimum continuous charging current that is to be charged,is the maximum sustain discharge current.

Further, a multi-constraint sustained peak current can be obtained as:

in the formula (I), the compound is shown in the specification,andrespectively, a sustained peak charging current and a sustained peak discharging current that satisfy the voltage and current limits at time k.

Further, the sustained peak power is calculated:

in the formula (I), the compound is shown in the specification,andrespectively, the sustained peak charging power and the sustained peak discharging power at time k.

And S4, repeating the steps from S2 to S3 at the next sampling interval.

In another aspect, the present invention provides an online estimation system for power state of a hybrid capacitor, including: a computer-readable storage medium and a processor;

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

the processor is used for reading the executable instructions stored in the computer readable storage medium and executing the hybrid capacitor power state online estimation method.

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

1. the hybrid capacitor power state online estimation method provided by the invention adopts a recursive augmented least square method with forgetting factors, and can realize real-time online update of the model parameters of the hybrid capacitor multi-model fusion equivalent circuit. Compared with an offline parameter identification method, the method can effectively track the parameter change of the model under different charging and discharging multiplying powers and aging states, and improve the precision of the hybrid capacitor model in the whole life cycle, thereby laying a foundation for accurate and reliable peak power.

2. Compared with an offline power state estimation method, the online estimation method for the power state of the hybrid capacitor provided by the invention can realize online update of model parameters and improve the accuracy of the power state estimation of the hybrid capacitor. In practical application, the method can ensure high precision of power state estimation under various working conditions thanks to real-time updating of model parameters.

3. The hybrid capacitor power state online estimation method provided by the invention is suitable for instantaneous peak power estimation and continuous peak power estimation, fills the blank of power state estimation in the field of hybrid capacitors, and provides an important application basis for optimal matching of hybrid capacitor power performance and optimization of a control strategy.

Drawings

FIG. 1 is a schematic diagram of a hybrid capacitor first-order multi-model fusion equivalent circuit model provided by the present invention;

FIG. 2 is a flow chart of a hybrid capacitor power state online estimation method provided by the present invention;

FIG. 3(a) is a graph of a current curve for a hybrid capacitor according to the present invention;

FIG. 3(b) is a voltage-voltage diagram of the hybrid capacitor according to the present invention;

FIG. 4(a) shows the variable capacitance C of the hybrid capacitor provided by the present invention under a working condition₀A real-time recognition result diagram;

FIG. 4(b) shows the polarization capacitance C of the hybrid capacitor provided by the present invention under a working condition₁A real-time recognition result diagram;

FIG. 4(c) is the ohmic internal resistance R of the hybrid capacitor provided by the present invention under the working condition₀A real-time recognition result diagram;

FIG. 4(d) is the polarization internal resistance R of the hybrid capacitor provided by the present invention under the working condition₁A real-time recognition result diagram;

FIG. 5(a) is a comparison graph of the estimation results of the instantaneous peak discharge current of the hybrid capacitor provided by the present invention under operating conditions;

FIG. 5(b) is a comparison graph of the estimation results of the instantaneous peak discharge power of the hybrid capacitor provided by the present invention under operating conditions;

FIG. 6(a) is a comparison graph of the estimation results of the sustained peak discharge current of the hybrid capacitor provided by the present invention at different times under different working conditions;

FIG. 6(b) is a comparison graph of the continuous peak discharge power estimation results of the hybrid capacitor provided by the present invention at different times under working conditions;

FIG. 6(c) is a graph comparing the online and offline continuous peak discharge current estimates for a hybrid capacitor provided in accordance with the present invention under operating conditions;

FIG. 6(d) is a graph comparing the online and offline sustained peak discharge power estimates for a hybrid capacitor provided in accordance with the present invention under operating conditions;

fig. 7(a) is a comparison graph of the estimation result of the instantaneous peak discharge current of the hybrid capacitor under the second working condition;

FIG. 7(b) is a comparison graph of the estimation result of the instantaneous peak discharge power of the hybrid capacitor under the second working condition;

fig. 8(a) is a comparison graph of the continuous peak discharge current estimation result of the hybrid capacitor provided by the present invention under the second working condition;

FIG. 8(b) is a comparison graph of the continuous peak discharge power estimation results of the hybrid capacitor provided by the present invention under the second operating condition;

fig. 8(c) is a comparison graph of the continuous peak discharge current estimation result of the hybrid capacitor provided by the present invention under the second working condition;

fig. 8(d) is a comparison graph of the continuous peak discharge power estimation result of the hybrid capacitor provided by the present invention under the second operating condition.

Detailed Description

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

Fig. 1 is a schematic diagram of a hybrid capacitor first-order multi-model fusion equivalent circuit model provided by the invention.

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

In one embodiment of the present invention, n is 1, i.e., a first-order multi-model fusion equivalent circuit model is used to characterize the external characteristics of the tested lithium ion capacitor.

As shown in FIG. 1, the model includes 1 variable capacitor C₀1 ohm internal resistance R₀And 1 RC circuit. Wherein the variable capacitance C₀The hybrid capacitor dual electrochemical energy storage mechanism is characterized. Ohmic internal resistance R₀And characterizing electrode materials, electrolyte, diaphragm resistance and contact resistance of parts. The RC circuit is a circuit structure formed by connecting a resistor and a capacitor in parallel and represents the polarization characteristic of the hybrid capacitor.

Fig. 2 is a flow chart of a hybrid capacitor power state online estimation method provided by the invention. The method mainly comprises the following steps:

s1, acquiring a state space equation according to a hybrid capacitor equivalent circuit model, and discretizing the state space equation;

s2, carrying out working condition testing on the hybrid capacitor, collecting a voltage value and a current value of the hybrid capacitor at the moment k, substituting the collected voltage value and current value into a model, and identifying a parameter value of the model at the moment k on line by adopting a recursive augmented least square method with a forgetting factor;

s3, according to the model parameter value at the moment k, the peak current of the hybrid capacitor is calculated firstly by adopting the power state online estimation method provided by the invention, and then the peak power of the hybrid capacitor is calculated.

And S4, at the moment of k +1, repeating the steps S2-S3 until the whole working condition is finished.

Fig. 3(a) and 3(b) are a current curve and a voltage curve, respectively, for the working condition of the hybrid capacitor provided by the present invention.

Preferably, in one embodiment of the present invention, a Dynamic Stress Test (DST) condition is used, as shown, fig. 3(a) is a voltage curve of the hybrid capacitor under the DST condition, and fig. 3(b) is a current curve of the hybrid capacitor under the DST condition.

FIGS. 4(a) -4 (d) are respectively the model parameter variable capacitance C of the hybrid capacitor provided by the present invention under the working condition₀And a polarization capacitor C₁Ohmic internal resistance R₀Internal polarization resistance R₁The real-time recognition result is shown schematically.

In one embodiment of the invention, the forgetting factor λ is taken to be 0.996.

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

As shown in the figure, by adopting the online parameter identification method provided by the invention, the parameters of the equivalent circuit model are updated online in real time under the DST working condition. Under the influence of factors such as different working conditions, aging states and the like, the model parameters updated in real time can effectively improve the precision of the equivalent circuit model of the hybrid capacitor in the whole life cycle, and further improve the precision of the power state estimation based on the model.

Preferably, the rated parameters of the lithium ion capacitor EVE SPC1550 used in the embodiment of the present invention are as follows:

fig. 5(a) and 5(b) are graphs comparing the estimation results of the instantaneous peak discharge current and the peak discharge power of the hybrid capacitor provided by the present invention under the working condition, respectively.

As shown in fig. 5(a), the instantaneous peak current calculated by the online estimation method provided by the present invention is strictly between the upper limit and the lower limit, while the instantaneous peak current calculated by the offline estimation method significantly exceeds the upper limit in the middle of the test condition. Fig. 5(b) shows the instantaneous peak power estimation results, and the instantaneous peak power estimation results obtained by the online power state estimation method provided by the present invention are all between the upper and lower limits, while the offline estimation method is out of range. Therefore, compared with an offline estimation method, the online estimation method effectively improves the reliability and accuracy of the hybrid capacitor power state estimation.

In one embodiment of the invention, continuous power state estimation is performed for the hybrid capacitor for 30s, 60s, 90s, 120s, respectively.

As shown in fig. 6(a) -6 (d), it can be seen that the sustained peak discharge capability of the hybrid capacitor is related to the sustained output time length, i.e., the sustained peak discharge capability decreases with increasing sustained output time. However, the 120s continuous peak power obtained by the offline estimation method is higher than the 30s continuous peak power obtained by the online estimation method provided by the present invention, which means that the power estimation result obtained by the offline estimation method is very unreliable under the condition that the model parameters are not updated in real time, and thus the power state online estimation method provided by the present invention can improve the reliability of the power state estimation of the hybrid capacitor by updating the parameters in real time.

Fig. 7(a) and 7(b) are comparative graphs of the estimation results of the instantaneous peak discharge current and the peak discharge power of the hybrid capacitor provided by the invention under the second working condition.

Fig. 8(a) -8 (d) are comparative graphs of continuous power state estimation results of the hybrid capacitor provided by the invention under the second working condition.

Preferably, in another embodiment of the present invention, the U.S. federal city operating conditions (FUDS) are employed. Under the FUDS working condition, the instantaneous power state estimation result and the continuous power state estimation result obtained by the hybrid capacitor power state online estimation method provided by the invention are still accurate and reliable, and the estimation result obtained by the offline estimation method has larger deviation, so that the hybrid capacitor power state online estimation method provided by the invention has stronger applicability and can effectively improve the reliability and the accuracy of hybrid capacitor power state estimation in practical application.

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