CN112580289A - Hybrid capacitor power state online estimation method and system - Google Patents

Abstract

The invention discloses an on-line estimation method and system for the power state of a hybrid capacitor, and belongs to the technical field of hybrid capacitor application. The method includes obtaining a state space equation according to an equivalent circuit model of a hybrid capacitor, and discretizing the state space equation; performing a working condition test on the hybrid capacitor, collecting the voltage value and current value of the hybrid capacitor, and using recursion with a forgetting factor The parameters of the discretized state space equation are identified online by the augmented least squares method; the instantaneous peak power and the continuous peak power of the hybrid capacitor are estimated by using the parameters obtained in real time. Compared with the offline power state estimation method, the online estimation method of the hybrid capacitor power state provided by the invention can realize the online update of the model parameters and improve the accuracy of the hybrid capacitor power state estimation.

Description

A method and system for online estimation of power state of hybrid capacitors

technical field

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

Background technique

Cheap and efficient electrochemical energy storage is a key technology for the efficient utilization of renewable energy and the development of smart grids. As a newly developed advanced energy storage device, hybrid capacitors have broad application prospects in smart grid, electric vehicles and other fields. One pole of the hybrid capacitor is to store and convert energy through the electrochemical reaction of traditional battery electrodes, and the other pole is to store energy through the adsorption/desorption mechanism of the electric double layer. The energy density of hybrid capacitors is 5-10 times higher than that of electric double-layer capacitors, and at the same time, its power density and cycle life are higher than those of batteries.

The power state can be used to characterize the peak power for charging and discharging the hybrid capacitor over a predetermined time interval. The real-time estimation of peak power has important theoretical significance and practical value for rational use of hybrid capacitors, avoiding overcharge and discharge phenomena and prolonging their cycle life. Therefore, it is crucial to achieve an accurate estimation of the power state of the hybrid capacitor. At present, the commonly used power state estimation method is an HPPC method based on the Rint model proposed by the National Engineering and Environmental Laboratory in Idaho, USA. This method ignores the dynamic characteristics of the hybrid capacitor, the calculated peak discharge current is too high, and the peak charging current is too conservative, so it is difficult to objectively reflect its real-time characteristics. Furthermore, this method is only for 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. This method improves the battery model with current as input and voltage as output to a model with voltage as input and current as output. For power state estimation, the known current-to-voltage model can simplify the calculation steps and reduce the amount of calculation. Patent CN111537894A discloses a method for lithium battery SOC and SOP. This method fits the relationship between temperature and battery discharge capacity, and corrects the available capacity of the battery, thereby improving the accuracy of the estimation results. However, the above method only involves instantaneous peak power estimation, and adopts the offline parameter identification method, the circuit model parameters cannot be updated in real time, and the estimation effect is not ideal in practical applications. In addition, the above methods are all based on lithium battery design and do not involve hybrid capacitors with significant differences in mechanism and performance.

Due to the above-mentioned defects and deficiencies, further improvements and improvements are urgently needed in this field. Aiming at the lack of power state estimation methods for hybrid capacitors and the unsatisfactory estimation effect of existing methods in practical applications, an effective online estimation method for hybrid capacitor power states is designed to meet the needs of practical applications and improve the reliability of the estimation results. .

SUMMARY OF THE INVENTION

In view of the defects of the prior art, the purpose of the present invention is to provide an effective method and system for online estimation of the power state of a hybrid capacitor in view of the fact that the actual application effect of the existing power state estimation method is not ideal and is not suitable for hybrid capacitors. , to meet the needs of practical applications and improve the reliability of the estimation results, thereby providing an important theoretical basis for the optimal matching of the dynamic performance of the hybrid capacitor and the optimization of the control strategy.

In order to achieve the above object, one aspect of the present invention provides an online estimation method for the power state of a hybrid capacitor. Based on the equivalent circuit model of the hybrid capacitor, the voltage and current during its operation are collected, the model parameters are updated in real time, and the real-time updated model is used. The parameters estimate the instantaneous peak power as well as the continuous peak power of the hybrid capacitor. The specific method is implemented according to the following steps:

S1. Obtain a state space equation according to the hybrid capacitor equivalent circuit model, and discretize the state space equation;

Preferably, the present invention adopts an equivalent circuit model fused with multiple models to characterize the external characteristics of the hybrid capacitor. The model includes variable capacitance, ohmic resistance, and multiple RC circuits in series. Among them, the variable capacitance C ₀ represents the dual electrochemical energy storage mechanism of the hybrid capacitor; the ohmic internal resistance R ₀ represents the electrode material, electrolyte, diaphragm resistance and contact resistance of various parts; RC circuit is a circuit structure formed by parallel resistance and capacitance , to characterize the polarization characteristics of hybrid capacitors.

According to Kirchhoff's law, the state space equation of the multi-model fusion equivalent circuit model is established:

表示其对时间的微分。Among them, C ₀ is the variable capacitor, R ₀ is the ohmic internal resistance, R _i is the resistance of the RC circuit, C _i is the capacitance of the RC circuit, i represents the i-th RC circuit, i=1, 2, 3, ..., n, I is the load current, U _t is the terminal voltage, U _C0 and U _RCi are the voltage of the variable capacitor C ₀ and the voltage of the i-th RC circuit, respectively,

represents its derivative with respect to time.

After discretizing the equation of state, we can get:

In the formula, Δt is the sampling period of the system. I _k is the load current at time k, and U _t,k is the terminal voltage of the hybrid capacitor at time k. U _C0,k is the voltage of the variable capacitor C ₀ at time k, and U _RCi,k is the voltage of the i-th RC circuit at time k.

S2. Test the working conditions of the hybrid capacitor, collect the voltage value and current value of the hybrid capacitor at time k, and use the recursive augmented least squares method with forgetting factor to identify the parameters of the online identification model through the collected voltage value and current value of the hybrid capacitor. ;

Under the zero initial condition, Z-transform and inverse Z-transform are performed on equation (2), and the existence of colored noise _ek in the model is considered.

Preferably, in the present invention, the colored noise e _k is obtained by calculating the moving average value of the white noise w _k , then the difference equation can be written as:

where θ _j is a variable about the model parameters, j=1, 2, 3, . . . , 2n+3. e _k is the colored noise of the system at time k, w _k is the white noise at time k, r is the order of the white noise moving average model, c _l is the coefficient of the model, l=1,2,3,...,r.

Further, formula (3) can be written as:

y _k =H _k θ _k +w _k (4)

In the formula, y _k is the terminal voltage of the hybrid capacitor at time k, H _k and θ _k are the measured data matrix and model parameter matrix of the hybrid capacitor at time k, namely:

Preferably, the present invention adopts the recursive augmented least squares method with forgetting factor λ to perform online parameter identification. Through real-time parameter correction and update, the accuracy of the model in the whole life cycle is guaranteed. The recursive process of the algorithm is as follows:

In the formula, λ is the forgetting factor, K _k is the gain matrix, P _k is the error covariance matrix of the parameter estimates, and I is the identity matrix.

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

S3. Use the parameters obtained in real time to estimate the instantaneous peak power and continuous peak power of the hybrid capacitor;

1) Instantaneous peak power estimation

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

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

Considering the voltage constraints: U _t,min ≤U _t ≤U _t,max , where U _t,min is the discharge cut-off voltage, and U _t,max is the charge cut-off voltage. Then the instantaneous peak current of charging and discharging is:

和

分别是k时刻基于电压限制的瞬时峰值放电电流和瞬时峰值充电电流。In the formula,

and

are the instantaneous peak discharge current and instantaneous peak charging current based on the voltage limit at time k, respectively.

其中

是最小脉冲充电电流，

是最大脉冲放电电流。In order to ensure the safe and stable operation of the hybrid capacitor, the instantaneous charging and discharging current should meet:

in

is the minimum pulse charge current,

is the maximum pulse discharge current.

Further, the multi-constrained instantaneous peak current is:

和

分别是k时刻满足电压和电流限制的瞬时峰值充电电流和瞬时峰值放电电流。In the formula,

and

are the instantaneous peak charging current and the instantaneous peak discharging current satisfying the voltage and current limits at time k, respectively.

Further, calculate the instantaneous peak power:

和

分别是k时刻瞬时峰值充电功率和瞬时峰值放电功率。In the formula,

and

are the instantaneous peak charging power and instantaneous peak discharging power at time k, respectively.

2) Continuous peak power estimation

Preferably, formula (1) can be rewritten as:

x _k+1 =A _k x _k +B _k u _k (12)

where x _k is the state vector of the model at time _k , uk is the control vector of the model at time k, A _k is the state matrix of the model at time k, and B _k is the input matrix of the model at time k. details as follows:

Preferably, since the model parameters change slowly, it is assumed that the model parameters in the time T×Δt are approximately unchanged.

Further, assuming that the input of the system is approximately equal in the time of T×Δt, that is, uk _+T = uk _+T-1 =...=u _k , then

Substituting Equation (14) into the output equation, the voltage at this time can be obtained as:

Then the approximate value of the working current in the time T×Δt can be calculated as:

Further, the peak current based on the voltage limit for the duration of T × Δt can be obtained:

和

分别是k时刻基于电压限制的持续峰值充电电流和持续峰值放电电流。In the formula,

and

are the continuous peak charging current and continuous peak discharging current based on the voltage limit at time k, respectively.

Preferably, T=1, Equation (17) is the same as Equation (9), that is, Equation (17) is a general formula for calculating instantaneous peak current and continuous peak current based on voltage limitation.

其中

是最小持续充电电流，

是最大持续放电电流。In order to ensure the safe and stable operation of the hybrid capacitor, the continuous charge and discharge current should meet:

in

is the minimum continuous charge current,

is the maximum continuous discharge current.

Further, the multi-constrained continuous peak current can be obtained as:

和

分别是k时刻满足电压和电流限制的持续峰值充电电流和持续峰值放电电流。In the formula,

and

are the continuous peak charging current and the continuous peak discharging current that satisfy the voltage and current limits at time k, respectively.

Further, to calculate the continuous peak power:

和

分别是k时刻持续峰值充电功率和持续峰值放电功率。In the formula,

and

are the continuous peak charging power and the continuous peak discharging power at time k, respectively.

S4. For the next sampling interval, repeat the steps of S2 to S3 above.

Another aspect of the present invention provides a hybrid capacitor power state online estimation system, comprising: a computer-readable storage medium and a processor;

the computer-readable storage medium for storing executable instructions;

The processor is configured to read the executable instructions stored in the computer-readable storage medium, and execute the above-mentioned method for online estimation of the power state of the hybrid capacitor.

Through the above technical solutions conceived by the present invention, compared with the prior art, the following beneficial effects can be achieved:

1. The method for online estimation of the power state of the hybrid capacitor provided by the present invention adopts the recursive augmented least squares method with forgetting factor, which can realize the real-time online update of the parameters of the hybrid capacitor multi-model fusion equivalent circuit model. Compared with the offline parameter identification method, this method can effectively track the parameter changes of the model under different charge and discharge rates and aging states, and improve the accuracy of the hybrid capacitor model in the whole life cycle, thus laying the foundation for accurate and reliable peak power.

2. Compared with the offline power state estimation method, the online estimation method of the hybrid capacitor power state provided by the present invention can realize the online update of the model parameters and improve the accuracy of the hybrid capacitor power state estimation. In practical applications, thanks to the real-time update of model parameters, this method can ensure the high accuracy of power state estimation under various operating conditions.

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

Description of drawings

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

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

Fig. 3 (a) is a hybrid capacitor operating condition-current curve diagram provided by the present invention;

Fig. 3(b) is a working condition-voltage curve diagram of the hybrid capacitor provided by the present invention;

Figure 4(a) is a schematic diagram of the real-time identification result of the variable capacitance C ₀ of the hybrid capacitor provided by the present invention under working conditions;

Fig. 4(b) is a schematic diagram of the real-time identification result of the polarized capacitance C ₁ of the hybrid capacitor provided by the present invention under the working condition;

Figure 4(c) is a schematic diagram of the real-time identification result of the ohmic internal resistance R ₀ of the hybrid capacitor provided by the present invention under working conditions;

Figure 4(d) is a schematic diagram of the real-time identification result of the polarization internal resistance R ₁ of the hybrid capacitor provided by the present invention under working conditions;

Figure 5(a) is a comparison diagram of the instantaneous peak discharge current estimation results of the hybrid capacitor provided by the present invention under working conditions;

Figure 5(b) is a comparison diagram of the instantaneous peak discharge power estimation results of the hybrid capacitor provided by the present invention under working conditions;

Figure 6(a) is a comparison diagram of the estimation results of the continuous peak discharge current of the hybrid capacitor provided by the present invention at different times under working conditions;

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

Figure 6(c) is a comparison diagram of the continuous peak discharge current estimation results online and offline of the hybrid capacitor provided by the present invention under working conditions;

Figure 6(d) is a comparison diagram of the continuous peak discharge power estimation results of the hybrid capacitor provided by the present invention online and offline under working conditions;

Figure 7(a) is a comparison diagram of the estimation results of the instantaneous peak discharge current of the hybrid capacitor provided by the present invention under working condition 2;

Figure 7(b) is a comparison diagram of the instantaneous peak discharge power estimation results of the hybrid capacitor provided by the present invention under working condition 2;

Figure 8(a) is a comparison diagram of the estimation results of the continuous peak discharge current of the hybrid capacitor provided by the present invention under working condition 2;

Figure 8(b) is a comparison diagram of the continuous peak discharge power estimation results of the hybrid capacitor provided by the present invention under working condition 2;

Figure 8(c) is a comparison diagram of the estimation results of the continuous peak discharge current of the hybrid capacitor provided by the present invention under working condition 2;

FIG. 8(d) is a comparison diagram of the estimation results of the continuous peak discharge power of the hybrid capacitor provided by the present invention under the second working condition.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

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

In an embodiment of the present invention, the hybrid capacitor cell tested is a lithium-ion capacitor with a rated capacity of 160mAh and a model of EVE SPC1550.

In an embodiment of the present invention, n=1 is selected, that is, 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 Figure 1, the model includes a variable capacitor C ₀ , an ohmic internal resistance R ₀ and an RC circuit. The variable capacitance C ₀ characterizes the dual electrochemical energy storage mechanism of the hybrid capacitor. The ohmic internal resistance R ₀ characterizes the electrode material, electrolyte, diaphragm resistance and contact resistance of various parts. An RC circuit is a circuit structure formed by a parallel connection of a resistor and a capacitor, which characterizes the polarization characteristics of the hybrid capacitor.

FIG. 2 is a flow chart of the method for online estimation of the power state of the hybrid capacitor provided by the present invention. Its main steps include:

S1. Obtain a state space equation according to the hybrid capacitor equivalent circuit model, and discretize the state space equation;

S2. Test the working condition of the hybrid capacitor, collect the voltage value and current value of the hybrid capacitor at time k, substitute the collected voltage value and current value into the model, and use the recursive augmented least squares method with forgetting factor to identify the model at time k online. parameter value;

S3. According to the model parameter value at time k, using the power state online estimation method provided by the present invention, first calculate the peak current of the hybrid capacitor, and then calculate the peak power of the hybrid capacitor.

S4. At time k+1, repeat the above steps S2-S3 until the whole working condition ends.

FIG. 3(a) and FIG. 3(b) are respectively a current curve diagram and a voltage curve diagram of the hybrid capacitor provided by the present invention under operating conditions.

Preferably, in an embodiment of the present invention, a dynamic stress test (DST) working condition is used, as shown in the figure, Fig. 3(a) is the voltage curve of the hybrid capacitor under DST working condition, and Fig. 3(b) is the DST condition Current curves of hybrid capacitors under operating conditions.

Fig. 4(a) - Fig. 4(d) are respectively the model parameters of the hybrid capacitor provided by the present invention under the working condition: variable capacitance C ₀ , polarization capacitance C ₁ , ohmic internal resistance R ₀ , and polarization internal resistance R ₁ . Schematic diagram of real-time identification results.

In an embodiment of the present invention, the forgetting factor λ is taken as 0.996.

Further, the first-order multi-model fusion equivalent circuit model parameters of the hybrid capacitor can be calculated in real time, that is,

As shown in the figure, using the online parameter identification method provided by the present 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 operating conditions and aging states, the model parameters updated in real time can effectively improve the accuracy of the hybrid capacitor equivalent circuit model in the whole life cycle, thereby improving the accuracy of model-based power state estimation.

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 FIG. 5(b) are respectively a comparison diagram of the estimation results of the instantaneous peak discharge current and peak discharge power of the hybrid capacitor provided by the present invention under working conditions.

As shown in the figure, in Figure 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 obviously exceeds the mid-test condition upper limit. Figure 5(b) shows the instantaneous peak power estimation results. The instantaneous peak power estimation results obtained by using the power state online estimation method provided by the present invention are all between the upper and lower limits, while the offline estimation method is out of bounds. It can be seen that, compared with the 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 present invention, continuous power state estimation is performed on the hybrid capacitor for 30s, 60s, 90s, and 120s, respectively.

As shown in Figure 6(a)-Figure 6(d), it can be seen that the continuous peak discharge capacity of the hybrid capacitor is related to the length of the continuous output time, that is, the continuous peak discharge capacity decreases with the increase of the continuous 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, indicating that the offline estimation method is adopted, that is, the power estimation results obtained under the condition that the model parameters are not updated in real time It is very unreliable, which also shows that the online estimation method of the power state provided by the present invention can improve the reliability of the power state estimation of the hybrid capacitor through real-time parameter update.

FIG. 7(a) and FIG. 7(b) are comparison diagrams of the estimation results of the instantaneous peak discharge current and peak discharge power of the hybrid capacitor provided by the present invention under working condition two.

FIG. 8(a)-FIG. 8(d) are comparison diagrams of continuous power state estimation results of the hybrid capacitor provided by the present invention under working condition two.

Preferably, in another embodiment of the present invention, the United States Federal Urban Operating System (FUDS) is employed. Under FUDS conditions, the instantaneous power state estimation results and continuous power state estimation results obtained by the hybrid capacitor power state online estimation method provided by the present invention are still accurate and reliable, while the estimation results obtained by the offline estimation method have greater deviations. It can be seen that the method for online estimation of the power state of the hybrid capacitor provided by the present invention has strong applicability, and can effectively improve the reliability and accuracy of the power state estimation of the hybrid capacitor in practical applications.

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (9)

1. a hybrid capacitor power state online estimation method, is characterized in that, comprises the following steps: S1. Obtain a state space equation according to the hybrid capacitor equivalent circuit model, and discretize the state space equation; S2. Test the working condition of the hybrid capacitor, collect the voltage value and current value of the hybrid capacitor at time k, and use the recursive augmented least squares method with forgetting factor to identify the parameters of the discretized state space equation online; S3. Use the parameters obtained in real time by S2 to estimate the instantaneous peak power and continuous peak power of the hybrid capacitor; S4. At time k+1, repeat the above steps S2-S3 until the whole working condition ends. 2. The method for online estimation of the power state of a hybrid capacitor according to claim 1, wherein the hybrid capacitor equivalent circuit model comprises a variable capacitor, an ohmic internal resistance and a plurality of RC circuits connected in series, and the state space equation is expressed as :

Among them, C ₀ is the variable capacitor, R ₀ is the ohmic internal resistance, R _i is the resistance of the ith RC circuit, C _i is the capacitance of the ith RC circuit, RC _i represents the ith RC circuit, i =1,2,3,...,n, I is the load current, U _t is the terminal voltage of the hybrid capacitor, U _C0 and U _RCi are the voltage of the variable capacitor C ₀ and the voltage of the i-th RC circuit, respectively,

Represents a differentiation with respect to time. 3. The hybrid capacitor power state online estimation method according to claim 2, wherein the discretized state space equation is expressed as:

Among them, Δt is the sampling period of the system, I _k is the load current at time k, U _t,k is the terminal voltage of the hybrid capacitor at time k, U _C0,k is the voltage of the variable capacitor C ₀ at time k, U _RCi,k is The voltage of the i-th RC circuit at time k. 4. The hybrid capacitor power state online estimation method as claimed in 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 =θ ₁ U _t,k-1 +…+θ _n+1 U _t,kn-1 +θ _n+2 I _k +…+θ _2n+3 I _kn-1 +w _k +c ₁ w _k-1 +c ₂ w _k-2 +…+c _r w _kr (3) Among them, θ _j is a variable about model parameters, j=1,2,3,...,2n+3, _wk is the white noise at time k, r is the order of the white noise moving average model, and c _l is the model Coefficients, l=1,2,3,...,r. 5. The hybrid capacitor power state online estimation method according to claim 4, wherein the output measurement value of the system at time k is expressed as: y _k =H _k θ _k +w _k (4)

Among them, y _k is the output measurement value of the system at time k, and H _k and θ _k are the data matrix and parameter matrix at time k, respectively. 6. The hybrid capacitor power state online estimation method according to claim 5, wherein the recursive process of the recursive augmented least squares method with forgetting factor is as follows:

Among them, λ is the forgetting factor, K _k is the gain matrix, P _k is the error covariance matrix of the parameter estimates, and I is the identity matrix. 7. The method for online estimation of the power state of a hybrid capacitor according to claim 1, wherein the estimation of the instantaneous peak power 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:

in,

and

are the instantaneous peak discharge current and instantaneous peak charging current based on the voltage limit at time k, respectively, U _t,min is the discharge cut-off voltage, U _t,max is the charge cut-off voltage, U _t,min ≤U _t ≤U _t,max ; The multi-constrained instantaneous peak current is:

In the formula,

and

are the instantaneous peak charging current and the instantaneous peak discharging current satisfying the voltage and current limits at time k, respectively,

is the minimum pulse charge current,

is the maximum pulse discharge current,

The instantaneous peak power is:

In the formula,

and

are the instantaneous peak charging power and instantaneous peak discharging power at time k, respectively. 8. The method for online estimation of the power state of a hybrid capacitor according to claim 1, wherein the continuous peak power estimation of the hybrid capacitor specifically comprises: x _k+1 =A _k x _k +B _k u _k (12) where x _k is the state vector of the model at time _k , uk is the control vector of the model at time k, A _k is the state matrix of the model at time k, and B _k is the input matrix of the model at time k, as follows:

In the time of T×Δt, the input of the system is equal, that is, u _k+T =u _k+T-1 =...=u _k , then

The voltage at this time is:

The working current in the time T×Δt is obtained as:

The peak current based on the voltage limit for the duration of T × Δt is:

In the formula,

and

are the continuous peak charging current and continuous peak discharging current based on the voltage limit at time k, respectively; The multi-constrained sustained peak current is:

In the formula,

and

are the continuous peak charging current and the continuous peak discharging current that satisfy the voltage and current limits at time k, respectively,

is the minimum continuous charge current,

is the maximum continuous discharge current,

The sustained peak power is:

In the formula,

and

are the continuous peak charging power and the continuous peak discharging power at time k, respectively. 9. A hybrid capacitor power state online estimation system, comprising: a computer-readable storage medium and a processor; the computer-readable storage medium for storing executable instructions; The processor is configured to read the executable instructions stored in the computer-readable storage medium, and execute the method for online estimation of the power state of a hybrid capacitor according to any one of claims 1 to 8.

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