Super capacitor SOC online estimation algorithm based on uncertain deviation compensation

Abstract

The invention discloses a super capacitor SOC online estimation algorithm based on uncertain deviation compensation, and belongs to the technical field of battery state-of-charge estimation. The method aims at solving the problem that the result of estimating the SOC of the super capacitor based on the Kalman filtering algorithm is unreliable under the condition that various deviations coexist. Comprising the following steps: establishing a state-space equation based on a super-capacitor three-branch RC equivalent circuit model; adding the one-dimensional uncertain deviation item as one of states into a super capacitor state-space equation to construct an expansion state equation; after the extended state equation is decomposed, an unbiased Kalman filter and an uncertain deviation estimator are constructed based on a KF algorithm; and adding estimation results of the two estimators through a deviation compensation matrix to obtain an optimal estimation result. The method is used for super capacitor SOC estimation.

Description

Technical Field

[0001] The present invention relates to a supercapacitor SOC online estimation algorithm based on uncertain deviation compensation, and belongs to the technical field of battery state of charge estimation. Background Art

[0002] Supercapacitors have been widely used in electric vehicles, new energy power generation systems, electromagnetic catapults and other fields due to their advantages such as high power density, low equivalent series resistance, high cycle efficiency, long service life and wide operating temperature range.

[0003] As one of the key indicators of a supercapacitor management system, the supercapacitor's state of charge (SOC) can indicate its remaining charge and can also be used as an input variable in optimizing the system's energy management strategy to ensure the safe and reliable operation of the supercapacitor energy management system. However, the supercapacitor SOC cannot be measured directly and must be calculated using certain methods.

[0004] Currently, supercapacitor SOC estimation methods primarily include ampere-hour integration, data-driven methods, and model-based state estimation. The ampere-hour integration method is the most widely used, while model-based methods, particularly those based on equivalent circuit models (ECMs), are the most widely studied. The ampere-hour integration method is a mathematical expression defining the SOC. This is an open-loop calculation method, and its accuracy depends on the initial value and the accuracy of the current sampling. ECM-based methods can be broadly categorized as the Luenberger observer, the sliding mode observer, and the Kalman filter (KF). State estimation algorithms based on the KF family have garnered particular attention. The accuracy of model-based KFs is affected by many factors, such as model accuracy, algorithm accuracy, sampling error, and system noise. Regarding algorithm accuracy, algorithms such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter, and H∞ filter have been proposed to estimate the real-time state of systems with varying degrees of nonlinearity. To adapt to environments with uncertain noise, algorithms such as the adaptive extended Kalman filter and the adaptive unscented Kalman filter have been proposed. Because supercapacitor state parameters change with aging, temperature, and operating conditions, state estimation algorithms based on offline and online parameter identification have been proposed to improve modeling accuracy. Offline parameter identification can obtain the supercapacitor terminal voltage through fixed operating condition testing, then obtain one or more sets of model parameters through curve fitting. Alternatively, optimization algorithms can be used to obtain optimized model parameters based on the voltage-current relationship. Offline parameter identification obtains model parameters under specific operating conditions. With increased usage, inaccurate model parameters can lead to inaccurate state estimation. Consequently, several combined online parameter identification and state estimation algorithms have been proposed to update model parameters in real time, thereby improving state estimation accuracy. These include the iterative least squares-EKF combined algorithm, the dual EKF algorithm, and the EKF-AUKF algorithm.

[0005] Currently, the impact of current and voltage sampling errors on supercapacitor SOC estimation has been rarely studied, with relevant research primarily focusing on state estimation methods for lithium batteries. In reality, model errors are unavoidable, whether using online or offline identification algorithms. Sensor errors are also unavoidable due to manufacturing process limitations. Multiple biases often coexist when estimating a supercapacitor's SOC, making it difficult to pinpoint specific biases and their impact. Summary of the Invention

[0006] To address the problem that the results of supercapacitor SOC estimation based on the Kalman filter algorithm are unreliable when multiple deviations coexist, the present invention provides a supercapacitor SOC online estimation algorithm based on uncertain deviation compensation.

[0007] The present invention provides an online supercapacitor SOC estimation algorithm based on uncertainty deviation compensation, comprising: Based on the three-branch RC equivalent circuit model of the supercapacitor, the discrete state space equation of each branch of the supercapacitor is constructed; Adding a one-dimensional uncertain deviation term to the discrete state space equation to construct an extended state equation; The one-dimensional uncertain bias term is assumed to be a constant term, and the extended state equation is decoupled into an unbiased Kalman filter and an uncertain bias estimator using a decoupling method; wherein the unbiased Kalman filter calculates the current moment state vector prior estimate and the current moment state vector prior error covariance estimate based on the previous moment state vector posterior estimate and the previous moment state vector posterior error covariance estimate, thereby obtaining an unbiased Kalman gain and an unbiased voltage residual, and obtaining the current moment state vector posterior estimate; the uncertain bias estimator calculates the current moment bias vector posterior estimate based on the previous moment bias vector posterior estimate, the previous moment bias vector posterior error covariance estimate and the previous moment bias calculation process matrix, in combination with the unbiased Kalman gain and the unbiased voltage residual; The current state vector posterior estimate value and the current deviation vector posterior estimate value are added together through the deviation compensation matrix to obtain the optimal estimate result of the current state vector of each branch of the supercapacitor; the charge state of the supercapacitor is calculated based on the current optimal estimate results of the three branches.

[0008] According to the supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation of the present invention, the three-branch RC equivalent circuit model includes the first branch fixed capacitor , the first branch internal resistance , the first branch variable capacitor , the second branch resistance , the second branch capacitor , the third branch resistor , the third branch capacitor and supercapacitor self-discharge resistor ; The first branch internal resistance and the first branch variable capacitor Forming the first branch; the second branch resistance and the second branch capacitor Forming the second branch; the third branch resistor and the third branch capacitor Forming the third branch; supercapacitor self-discharge resistor As the fourth branch; the four branches are connected in parallel at the supercapacitor terminal voltage Between the positive and negative electrodes; The first branch fixed capacitor With the first branch variable capacitor in parallel.

[0009] According to the supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation of the present invention, the input-output relationship of the three-branch RC equivalent circuit model is: (1), In the formula is the current of the j-th branch, is the capacitor voltage of the j-th branch, is the current in the fourth branch, is the time constant of the first branch, ; is the time constant of the second branch, ; is the time constant of the third branch, .

[0010] According to the supercapacitor SOC online estimation algorithm based on uncertainty bias compensation of the present invention, the discrete state space equation of the supercapacitor is: (2), In the formula is the state vector at time k, representing the capacitor voltage of the jth branch , is the state matrix at time k, is the input matrix at time k, is the input vector at time k, representing the current of the jth branch , is the process noise at time k; is the terminal voltage at time k, indicating the supercapacitor terminal voltage ; is the output matrix at time k, is the direct matrix at time k, is the measurement noise at time k; (3), In the formula is the identity matrix, is the continuous state matrix, is the sampling time, is the continuous state input matrix, is the continuous state output matrix, is a continuous state direct matrix; (4) In the formula , represents the parallel resistance of four resistors.

[0011] According to the supercapacitor SOC online estimation algorithm based on uncertainty bias compensation of the present invention, a one-dimensional uncertainty bias term is added to the discrete state space equation, and the obtained extended state equation is: (5), In the formula is the one-dimensional uncertain deviation term at time k, is the k-1 moment deviation conversion matrix, is the deviation output coefficient matrix at time k.

[0012] According to the supercapacitor SOC online estimation algorithm based on uncertain bias compensation of the present invention, the state initialization of the unbiased Kalman filter includes: (6), (7), In the formula is the initial estimate of the state vector, is the initial value of the state vector, Indicates the mean value, is the initial error covariance of the state vector; Initialization of the uncertainty bias estimator includes: (8), (9), In the formula is the initial estimate of the bias vector, is the initial value of the bias vector, is the initial error covariance of the bias vector.

[0013] According to the supercapacitor SOC online estimation algorithm based on uncertain bias compensation of the present invention, the time update of the unbiased Kalman filter includes: (10), (11), In the formula is the prior estimate of the state vector at time k, is the posterior estimate of the state vector at time k-1, is the prior error covariance estimate of the state vector at time k, is the estimated value of the posterior error covariance of the state vector at time k-1, is the noise covariance of the process at time k; The temporal update of the uncertainty bias estimator consists of: (12), (13), In the formula is the prior estimate of the deviation vector at time k, is the posterior estimate of the deviation vector at time k-1, is the prior error covariance estimate of the deviation vector at time k, is the estimated value of the posterior error covariance of the deviation vector at time k-1; (14), In the formula is the k-time deviation calculation process matrix, is the k-1 moment deviation compensation matrix, is the residual coefficient matrix at time k; (15), In the formula is the unbiased Kalman gain of the unbiased Kalman filter at time k.

[0014] According to the supercapacitor SOC online estimation algorithm based on uncertain bias compensation of the present invention, the measurement update of the unbiased Kalman filter includes: (16), In the formula is the unbiased voltage residual at time k; (17), In the formula is the measurement noise covariance at time k; (18); (19); The measurement update of the uncertainty bias estimator includes: (20), (twenty one), In the formula is the Kalman gain of the uncertain bias estimator at time k; (twenty two), In the formula is the deviation residual at time k; (twenty three).

[0015] According to the supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation of the present invention, the optimal estimation result of the state vector of each supercapacitor SOC branch at time k is expressed as : (twenty four).

[0016] According to the supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation of the present invention, the supercapacitor state of charge calculation method is: (25), In the formula is the current capacity of the supercapacitor; (26), In the formula is the maximum capacity of the supercapacitor, is the rated capacitance of the supercapacitor, is the maximum voltage of the supercapacitor; Supercapacitor state of charge for: (27).

[0017] Beneficial effects of the present invention: The method of the present invention fully considers the impact of uncertain deviations such as model error, voltage and current measurement error on the accuracy of the algorithm, and designs an uncertain deviation compensation algorithm to achieve accurate estimation of the supercapacitor SOC. It adds the one-dimensional uncertain deviation term as one of the states to the supercapacitor state space equation to construct an extended state equation; after decomposing the extended estimation algorithm, it constructs an unbiased Kalman filter and an uncertain deviation estimator based on the KF algorithm; the estimation results of the two estimators are added through the deviation compensation matrix to obtain the optimal estimation result. The method of the present invention can effectively improve the accuracy of supercapacitor SOC estimation in the presence of uncertain deviations, has strong robustness, and does not significantly increase the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of the supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to the present invention; Initial value of the deviation calculation process matrix; Figure 2 It is the three-branch RC equivalent circuit model of the supercapacitor; i in the figure represents the loop circuit. DETAILED DESCRIPTION

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0020] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0022] Combine Figure 1 and Figure 2 As shown, the present invention provides a supercapacitor SOC online estimation algorithm based on uncertain deviation compensation, including: Based on the three-branch RC equivalent circuit model of the supercapacitor, the discrete state space equation of each branch of the supercapacitor is constructed; Adding a one-dimensional uncertain deviation term as one of the states into the discrete state space equation to construct an extended state equation; The one-dimensional uncertain bias term is assumed to be a constant term, and the extended state equation is decoupled into an unbiased Kalman filter and an uncertain bias estimator using a decoupling method; wherein the unbiased Kalman filter calculates the current moment state vector prior estimate and the current moment state vector prior error covariance estimate based on the previous moment state vector posterior estimate and the previous moment state vector posterior error covariance estimate, thereby obtaining an unbiased Kalman gain and an unbiased voltage residual, and obtaining the current moment state vector posterior estimate; the uncertain bias estimator calculates the current moment bias vector posterior estimate based on the previous moment bias vector posterior estimate, the previous moment bias vector posterior error covariance estimate and the previous moment bias calculation process matrix, in combination with the unbiased Kalman gain and the unbiased voltage residual; The current state vector posterior estimate value and the current deviation vector posterior estimate value are added together through the deviation compensation matrix to obtain the optimal estimate result of the current state vector of each branch of the supercapacitor; the charge state of the supercapacitor is calculated based on the current optimal estimate results of the three branches.

[0023] When constructing the extended state equation, the deviation term is a voltage quantity, as all unknown deviations are converted into voltage deviations. To reflect the role of the deviation, the deviation term is added to the state equation and output equation of the state-space equation. The coefficient matrices of the deviation term in both the state equation and the output equation are both unit matrices.

[0024] After decomposing the extended state equation, an unbiased Kalman filter and an uncertain bias estimator are constructed based on the KF algorithm. Based on the changing characteristics of the uncertain bias and to facilitate decoupling of the extended estimation algorithm, the bias term is assumed to be a constant term. The extended state equation is then decoupled into an unbiased Kalman filter and an uncertain bias estimator using a decoupling method. The uncertain bias estimator calculates the bias using the Kalman gain of the unbiased Kalman filter and the output voltage residual to obtain an estimated value.

[0025] Combine Figure 2As shown, the three-branch RC equivalent circuit model includes the first branch fixed capacitor , the first branch internal resistance , the first branch variable capacitor , the second branch resistance , the second branch capacitor , the third branch resistance , the third branch capacitor and supercapacitor self-discharge resistor ; Internal resistance of the first branch and the first branch variable capacitor Forming the first branch; the second branch resistance and the second branch capacitor Forming the second branch; the third branch resistor and the third branch capacitor Forming the third branch; supercapacitor self-discharge resistor As the fourth branch; the four branches are connected in parallel at the supercapacitor terminal voltage Between the positive and negative electrodes; The first branch fixed capacitor With the first branch variable capacitor in parallel.

[0026] The input-output relationship of the three-branch RC equivalent circuit model is: (1), In the formula is the current of the j-th branch, is the capacitor voltage of the j-th branch, is the current in the fourth branch, is the time constant of the first branch, ; is the time constant of the second branch, ; is the time constant of the third branch, .

[0027] Figure 2 In [1], the equivalent circuit model of a supercapacitor includes a second-order resistor-capacitor equivalent circuit consisting of a voltage source, an ohmic internal resistance, a reaction polarization internal resistance, a reaction polarization capacitor, a concentration polarization internal resistance, and a concentration polarization capacitor. The reaction polarization internal resistance and reaction polarization capacitor are used to describe the reaction polarization phenomenon inside the battery, while the concentration polarization internal resistance and concentration polarization capacitor are used to describe the concentration polarization phenomenon inside the battery.

[0028] The discrete state space equation of the supercapacitor is: (2), In the formula is the state vector at time k, representing the capacitor voltage of the jth branch , is the state matrix at time k, is the input matrix at time k, is the input vector at time k, representing the current of the jth branch , is the process noise at time k; is the terminal voltage at time k, indicating the supercapacitor terminal voltage ; is the output matrix at time k, is the direct matrix at time k, is the measurement noise at time k; (3), In the formula is the identity matrix, is the continuous state matrix, is the sampling time, is the continuous state input matrix, is the continuous state output matrix, is a continuous state direct matrix; (4) In the formula , represents the parallel resistance of four resistors.

[0029] Furthermore, the one-dimensional uncertain deviation term is added to the discrete state space equation, and the obtained extended state equation is: (5), In the formula is the one-dimensional uncertain deviation term at time k, is the k-1 moment deviation conversion matrix, is the deviation output coefficient matrix at time k.

[0030] The state initialization of the unbiased Kalman filter includes: (6), (7), In the formula is the initial estimate of the state vector, is the initial value of the state vector, Indicates the mean value, is the initial error covariance of the state vector; Initialization of the uncertainty bias estimator includes: (8), (9), In the formula is the initial estimate of the bias vector, is the initial value of the bias vector, is the initial error covariance of the bias vector.

[0031] The time update of the unbiased Kalman filter includes: Prior estimates of state quantities: (10), Prior estimate of state error covariance: (11), In the formula is the prior estimate of the state vector at time k, is the posterior estimate of the state vector at time k-1, is the prior error covariance estimate of the state vector at time k, is the estimated value of the posterior error covariance of the state vector at time k-1, is the noise covariance of the process at time k; The temporal update of the uncertainty bias estimator consists of: A priori estimate of the bias: (12), A priori estimate of the covariance of the bias errors: (13), In the formula is the prior estimate of the deviation vector at time k, is the posterior estimate of the deviation vector at time k-1, is the prior error covariance estimate of the deviation vector at time k, is the estimated value of the posterior error covariance of the deviation vector at time k-1; (14), In the formula is the k-time deviation calculation process matrix, is the k-1 moment deviation compensation matrix, is the residual coefficient matrix at time k; (15), In the formula is the unbiased Kalman gain of the unbiased Kalman filter at time k.

[0032] The measurement update of the unbiased Kalman filter includes: Residual calculation: (16), In the formula is the unbiased voltage residual at time k; is the terminal voltage measurement value at time k; Kalman gain calculation: (17), In the formula is the measurement noise covariance at time k; Calculation of state posterior estimate: (18); Calculation of the posterior estimate of the state error covariance: (19); The measurement update of the uncertainty bias estimator includes: Biased posterior error covariance calculation: (20), Bias estimator Kalman gain calculation: (twenty one), In the formula is the Kalman gain of the uncertain bias estimator at time k; Residual calculation of the deviance: (twenty two), In the formula is the deviation residual at time k; The posterior estimate of the bias is calculated: (twenty three).

[0033] Furthermore, the optimal estimation result of the state vector of each branch of the supercapacitor SOC at time k is expressed as : (twenty four).

[0034] Finally, the supercapacitor state of charge is calculated as: (25), In the formula is the current capacity of the supercapacitor; (26), In the formula is the maximum capacity of the supercapacitor, is the rated capacitance of the supercapacitor, is the maximum voltage of the supercapacitor; Supercapacitor state of charge for: (27).

[0035] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer control program. When the processor processes the program stored in the memory, it can implement the supercapacitor SOC online estimation algorithm based on uncertain deviation compensation described in the present invention.

[0036] The present invention also provides a computer-readable storage medium for storing a computer control program, wherein the computer control program can implement the supercapacitor SOC online estimation algorithm based on uncertain deviation compensation according to the present invention.

[0037] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A supercapacitor SOC online estimation algorithm based on uncertainty bias compensation, characterized by: include: Based on the three-branch RC equivalent circuit model of the supercapacitor, the discrete state space equation of each branch of the supercapacitor is constructed; Adding a one-dimensional uncertain deviation term to the discrete state space equation to construct an extended state equation; The one-dimensional uncertain bias term is assumed to be a constant term, and the extended state equation is decoupled into an unbiased Kalman filter and an uncertain bias estimator using a decoupling method; wherein the unbiased Kalman filter calculates the current moment state vector prior estimate and the current moment state vector prior error covariance estimate based on the previous moment state vector posterior estimate and the previous moment state vector posterior error covariance estimate, thereby obtaining an unbiased Kalman gain and an unbiased voltage residual, and obtaining the current moment state vector posterior estimate; the uncertain bias estimator calculates the current moment bias vector posterior estimate based on the previous moment bias vector posterior estimate, the previous moment bias vector posterior error covariance estimate and the previous moment bias calculation process matrix, in combination with the unbiased Kalman gain and the unbiased voltage residual; The current state vector posterior estimate value and the current deviation vector posterior estimate value are added together through the deviation compensation matrix to obtain the optimal estimate result of the current state vector of each branch of the supercapacitor; the charge state of the supercapacitor is calculated based on the current optimal estimate results of the three branches.

2. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 1 is characterized in that: The three-branch RC equivalent circuit model includes the first branch fixed capacitor , the first branch internal resistance , the first branch variable capacitor , the second branch resistance , the second branch capacitor , the third branch resistor , the third branch capacitor and supercapacitor self-discharge resistor ; Internal resistance of the first branch and the first branch variable capacitor Forming the first branch; the second branch resistance and the second branch capacitor Forming the second branch; the third branch resistor and the third branch capacitor Forming the third branch; supercapacitor self-discharge resistor As the fourth branch; the four branches are connected in parallel at the supercapacitor terminal voltage Between the positive and negative electrodes; The first branch fixed capacitor With the first branch variable capacitor in parallel.

3. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 2 is characterized in that: The input-output relationship of the three-branch RC equivalent circuit model is: （1）， In the formula is the current of the j-th branch, is the capacitor voltage of the j-th branch, is the current in the fourth branch, is the time constant of the first branch, ; is the time constant of the second branch, ; is the time constant of the third branch, .

4. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 3 is characterized in that: The discrete state space equation of the supercapacitor is: （2）， In the formula is the state vector at time k, representing the capacitor voltage of the jth branch , is the state matrix at time k, is the input matrix at time k, is the input vector at time k, representing the current of the jth branch , is the process noise at time k; is the terminal voltage at time k, indicating the supercapacitor terminal voltage ; is the output matrix at time k, is the direct matrix at time k, is the measurement noise at time k; （3）， In the formula is the identity matrix, is the continuous state matrix, is the sampling time, is the continuous state input matrix, is the continuous state output matrix, is a continuous state direct matrix; （4） In the formula , represents the parallel resistance of four resistors.

5. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 4 is characterized in that: Adding the one-dimensional uncertainty deviation term to the discrete state space equation, the obtained extended state equation is: （5）， In the formula is the one-dimensional uncertain deviation term at time k, is the k-1 moment deviation conversion matrix, is the deviation output coefficient matrix at time k.

6. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 5 is characterized in that: The state initialization of the unbiased Kalman filter includes: （6）， （7）， In the formula is the initial estimate of the state vector, is the initial value of the state vector, Indicates the mean value, is the initial error covariance of the state vector; Initialization of the uncertainty bias estimator includes: （8）， （9）， In the formula is the initial estimate of the bias vector, is the initial value of the bias vector, is the initial error covariance of the bias vector.

7. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 6 is characterized in that: The time update of the unbiased Kalman filter includes: （10）， （11）， In the formula is the prior estimate of the state vector at time k, is the posterior estimate of the state vector at time k-1, is the prior error covariance estimate of the state vector at time k, is the estimated value of the posterior error covariance of the state vector at time k-1, is the noise covariance of the process at time k; The temporal update of the uncertainty bias estimator consists of: （12）， （13）， In the formula is the prior estimate of the deviation vector at time k, is the posterior estimate of the deviation vector at time k-1, is the prior error covariance estimate of the deviation vector at time k, is the estimated value of the posterior error covariance of the deviation vector at time k-1; （14）， In the formula is the k-time deviation calculation process matrix, is the k-1 moment deviation compensation matrix, is the residual coefficient matrix at time k; （15）， In the formula is the unbiased Kalman gain of the unbiased Kalman filter at time k.

8. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 7 is characterized in that: The measurement update of the unbiased Kalman filter includes: （16）， In the formula is the unbiased voltage residual at time k; （17）， In the formula is the measurement noise covariance at time k; （18）； （19）； The measurement update of the uncertainty bias estimator includes: （20）， （21）， In the formula is the Kalman gain of the uncertain bias estimator at time k; （22）， In the formula is the deviation residual at time k; （23）。 9. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 8 is characterized in that: The optimal estimation result of the state vector of each branch of the supercapacitor SOC at time k is expressed as : （24）。 10. The supercapacitor SOC online estimation algorithm based on uncertainty deviation compensation according to claim 9 is characterized in that: The state of charge of a supercapacitor is calculated as follows: （25）， In the formula is the current capacity of the supercapacitor; （26）， In the formula is the maximum capacity of the supercapacitor, is the rated capacitance of the supercapacitor, is the maximum voltage of the supercapacitor; Supercapacitor state of charge for: （27）。

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