Vehicle lithium ion power battery state-of-charge estimation method based on improved extended Kalman filtering algorithm

Abstract

The invention relates to a vehicle lithium ion power battery charge state estimation method based on an improved extended Kalman filtering algorithm, and belongs to the technical field of lithium ion batteries. The method comprises the following steps: firstly, establishing a second-order RC equivalent circuit model of the lithium ion battery, and carrying out linearization processing by utilizing Taylor expansion; and then, searching an optimal noise covariance matrix by adopting a sunflower optimization algorithm, and applying the optimal noise covariance matrix to charge state online estimation of an extended Kalman filtering algorithm. In order to ensure that the extended Kalman filter can be in contact with sufficient state parameter information, a proportional integral differential control method is introduced to correct a Kalman gain matrix, so that accurate and stable estimation of the state of charge of the lithium ion battery is realized. According to the method, a voltage accumulative error judgment and charge state initial correction method is adopted, so that the precision of charge state estimation is improved. Compared with a traditional ampere-hour integral method and an extended Kalman filtering algorithm based on sunflower optimization, the method has higher charge state estimation precision.

Description

Technical Field

[0001] The invention belongs to the technical field of lithium-ion batteries and relates to a method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm. Background Art

[0002] Lithium-ion batteries have become the best power source for electric vehicles because of their long cycle life, high energy, power density and efficiency, high nominal voltage and low self-discharge rate. In order to ensure the best performance, safe operation and ideal life of power batteries under various charging and discharging and environmental conditions, it is necessary to add a battery management system to the automotive electronic control system. State of charge (SoC) is a key parameter reflecting the energy level of lithium-ion batteries, and factors such as open circuit voltage and state parameters are closely related to the state of charge. Therefore, accurate estimation of the state of charge is an important prerequisite for the battery management system to perform related functions efficiently and accurately. According to different estimation principles, the state of charge estimation methods can be divided into: table lookup method based on the measurement value of the characterization parameter, ampere-hour integration method, model-based estimation method and data-driven estimation method. Although there is a relatively stable correspondence between the characterization parameter and the state of charge, it is difficult for new energy vehicles to ensure a long-term constant state during driving to complete the accurate measurement of the characterization parameter. The ampere-hour integration method is the most commonly used state of charge estimation method in battery management systems. However, its estimation accuracy is affected by the initial state of charge value and the accuracy of the current sensor, and the integral open-loop operation will cause errors that gradually accumulate over time. Data-driven estimation methods are highly sensitive to the quantity and quality of data, and the adjustment of hyperparameters is cumbersome and time-consuming. In addition, real vehicle applications cannot meet the requirements of high-performance hardware. Model-based state of charge estimation methods combine empirical models, physical models, filters, observers and other algorithms to achieve accurate state of charge estimation. Among them, the Kalman filter algorithm and its variants are the most promising estimation methods. Their filtering performance is closely related to the noise covariance matrix of the system. The noise covariance matrix is ​​often selected and tuned by the enumeration trial and error method. However, the enumeration trial and error method is not only a cumbersome and complex process with a long operation, but also cannot guarantee that the state of charge estimation results are completely converged. Therefore, it is necessary to use an optimization algorithm to appropriately adjust the noise covariance matrix, improve the extended Kalman filter estimation method suitable for battery nonlinear systems, and finally achieve the improvement of the extended Kalman filter performance and accurate estimation of lithium-ion battery state parameters. Summary of the invention

[0003] In view of this, the purpose of the present invention is to provide a method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm. Through the influence mechanism of different noise covariances on the state of charge estimation, the sunflower optimization algorithm is introduced to search for the optimal value of the noise covariance matrix, and the extended Kalman filter is improved by the proportional integral differential control method, so as to achieve accurate and stable estimation of the state of charge of the lithium-ion power battery for a vehicle.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm comprises the following steps:

[0006] Establish the second-order RC equivalent circuit model of lithium-ion battery;

[0007] The model is linearized using Taylor expansion to obtain the state space equation of the model;

[0008] The root mean square error of the state of charge estimation result of the extended Kalman filter algorithm is used as the fitness function;

[0009] The Sunflower Optimization Algorithm is used to search for the optimal noise covariance matrix;

[0010] The proportional-integral-derivative control method is introduced into the Kalman filter gain matrix to correct the a posteriori estimate of the system state variables;

[0011] The initial value of the state of charge is corrected according to the accumulated error of the battery voltage.

[0012] Further, the sunflower optimization algorithm includes:

[0013] Generate a random or uniform population of sunflowers;

[0014] Calculate the fitness function corresponding to each individual, and select the individual with the highest fitness as the sun;

[0015] Look toward the sun and take random steps in a certain direction for control;

[0016] Based on the voltage measurement results of the battery test and the voltage simulation results of the battery model, the fitness function corresponding to the current excitation is calculated to adjust the value of the noise covariance matrix;

[0017] Determine the optimal value of the noise covariance matrix within the allowed range.

[0018] Further, the proportional integral differential control method includes:

[0019] Introducing the proportional part, integral part and differential part into the Kalman gain matrix;

[0020] Correct the a posteriori estimates of the system state variables;

[0021] The initial value of the state of charge is corrected according to the accumulated error of the battery voltage.

[0022] Furthermore, the battery voltage cumulative error correction method includes:

[0023] The voltage cumulative error is updated using the moving window estimation method;

[0024] When the accumulated error reaches the voltage limit of the effective voltage accumulated error, the proportional and differential links related to the dynamic output response speed in the PID control algorithm are used to complete the correction of the initial value of the state of charge.

[0025] The beneficial effects of the present invention are:

[0026] (1) The present invention takes the state of charge of lithium iron phosphate batteries as the research object, and uses the enumeration trial and error method to enumerate the process and measurement noise covariance matrices in the state space equation of the battery second-order RC equivalent circuit model linearized by Taylor expansion, and analyzes the influence mechanism of different noise covariance matrices on the state of charge estimation results of lithium-ion batteries.

[0027] (2) The present invention improves the lithium-ion state of charge estimation method of the extended Kalman filter algorithm. The root mean square error of the state of charge estimation result of the extended Kalman filter algorithm is used as the fitness function, and the sunflower optimization algorithm is used to search for the optimal noise covariance matrix, which is applied to the online state of charge estimation of the extended Kalman filter algorithm by interpolation. In order to ensure that the extended Kalman filter can access sufficient state parameter information, the proportional integral differential control method is introduced into the Kalman filter gain matrix to correct the a posteriori estimate of the system state variables, and the initial value of the state of charge is corrected according to the accumulated error of the battery voltage, so as to improve the performance of the extended Kalman filter and accurately and smoothly estimate the state of charge of the lithium-ion battery.

[0028] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0030] Figure 1 A second-order RC equivalent circuit model of a lithium-ion battery used in one embodiment of the present invention;

[0031] Figure 2 A flow chart of a method for estimating the state of charge of a lithium-ion battery based on a model according to an embodiment of the present invention;

[0032] Figure 3 The influence of different noise covariance matrices provided in one embodiment of the present invention on the state of charge estimation result of a lithium-ion battery;

[0033] Figure 4 A flow chart of a method for estimating the state of charge of a lithium-ion battery based on an improved extended Kalman filter algorithm used in the present invention;

[0034] Figure 5 An embodiment of the present invention provides a lithium-ion battery state of charge estimation result under normal temperature conditions. DETAILED DESCRIPTION

[0035] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0036] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0037] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0038] The equivalent circuit model of lithium-ion battery simulates the dynamic and static external characteristics of the battery to varying degrees based on circuit principles such as Thevenin's theorem, combined with a circuit network composed of electrical components such as ideal voltage sources, resistors and capacitors. The dual-polarization model (second-order RC equivalent circuit model) is selected as the battery electrical characteristic model by comprehensively weighing the complexity and accuracy of the battery model. The root mean square error of the state of charge estimation result of the extended Kalman filter algorithm is used as the fitness function, and the sunflower optimization algorithm is used to explore the optimal noise covariance matrix in the model state space equation linearized by Taylor expansion, and interpolated in the online state of charge estimation of the extended Kalman filter algorithm. In order to ensure that the extended Kalman filter can access sufficient state parameter information, the proportional part and integral part of the proportional integral differential control method are introduced into the Kalman gain matrix to correct the a posteriori estimation of the system state variables. The stable and accurate estimation of the state of charge of the lithium-ion battery is achieved by improving the extended Kalman filter algorithm.

[0039] The specific working process of the present invention is as follows:

[0040] 1. Influence of noise covariance matrix on state of charge

[0041] The second-order RC equivalent circuit model is as follows Figure 1 As shown, R0 is the ohmic internal resistance of the battery, R p1 , R p2 is the polarization internal resistance, C p1 , C p2 is the polarization capacitance, U t is the terminal voltage of the battery, U ocv is the open circuit voltage of the battery in a completely balanced state, U p1 , U p2 , U p3 R p1 , R p2 , R p3 The polarization voltage at both ends, I is the current, which is positive during battery discharge and negative during charging. The state space equation of the second-order RC equivalent circuit model is:

[0042]

[0043] The filtering performance of EKF in the battery SoC estimation process is closely related to the process noise covariance matrix and measurement noise covariance matrix of the system. The state space equation of the model is obtained by Taylor expansion and linearization of the battery model as follows:

[0044]

[0045] In the formula, m is the current moment; x is the system state variable; u is the system input variable; w is the process noise; y is the system output variable; v is the measurement noise; A is the state transfer matrix; B is the input gain matrix; C is the observation matrix; and D is the compensation matrix.

[0046] The state variables, input variables and output variables of the system are as follows:

[0047]

[0048] like Figure 2 As shown in the figure, the Kalman filter series algorithm uses the battery charging and discharging current as the system input variable and the terminal voltage as the output variable. It updates the system state in real time according to the error between the terminal voltage and the state of charge estimation, and achieves the optimal state of charge estimation result with the minimum variance. The extended Kalman filter algorithm is often used to solve the state estimation problem in nonlinear systems. The nonlinear objective function of the system is expanded by Taylor, the high-order terms of the expansion terms are omitted, and the first-order terms are retained, thereby realizing the linear transformation of the nonlinear function. The update stage is described as follows:

[0049]

[0050] In the formula, is the prior estimate of the system state variables; is the a posteriori estimate of the system state variables; P - is the prior error covariance matrix of the system state variables, P+ is the updated error covariance matrix, Q is the covariance of the system process noise ω, R is the covariance of the system measurement noise υ, K is the Kalman filter gain matrix, and I is the identity matrix.

[0051] In order to avoid the reduction or divergence of the accuracy of the lithium-ion battery state of charge estimation results, the values ​​of the process noise covariance matrix and the measurement noise covariance matrix need to be reconciled between the estimation error and the convergence speed. Based on the enumeration selection method, twelve groups of different noise covariance combinations are listed, and simulations are performed under normal temperature DST conditions, such as Figure 3 As shown in Figure 2, with the increase of process noise covariance matrix, the state of charge estimation error has a significant trend of increasing and gradually converges smoothly. With the decrease of measurement noise covariance matrix, the state of charge estimation error has a trend of decreasing.

[0052] 2. Lithium-ion battery state of charge estimation based on improved Kalman filter algorithm

[0053] In order to ensure the optimality of the extended Kalman filter performance and the accuracy of the battery state of charge estimation, it is necessary to use an optimization algorithm to appropriately adjust the noise covariance matrix. The sunflower optimization algorithm is introduced to search for the optimal value of the noise covariance matrix, thereby optimizing the extended Kalman filter estimator and improving the dynamic performance of the battery.

[0054] The main idea of ​​the sunflower optimization algorithm is to search for the best sunflower movement to absorb solar radiation. In the morning, the sunflower wakes up and follows the sun, while in the evening, the sunflower will go in the opposite direction and wait for the sunrise the next morning. If the sunflower is closer to the sun, it will absorb more heat and be more inclined to stay at that position, while the sunflower farther away from the sun receives less heat and needs to spend more effort to get as close to the sun as possible. The amount of heat Q obtained by the i-th sunflower in the sunflower population i Defined as:

[0055]

[0056] Where P s is the power of solar heat; r i is the distance between the sun and the i-th sunflower.

[0057] Assume that each sunflower produces only a single pollen gamete, which can only be reproduced once. The direction of the sunflower facing the sun as follows:

[0058]

[0059] Among them, X * represents the optimal solution, X i is the current solution.

[0060] The step length of the sunflower in the direction of the sun is calculated as follows:

[0061] d i =λ i ·P i (||X i +X i+1 ||)·||X i +X i+1 ||

[0062] In the formula, λ i is the constant value defining the “inertial” displacement of the plant; P i (||X i +X i+1 ||) is the probability of pollination, that is, the i-th sunflower pollinates with its nearest i+1-th sunflower neighbor, thus creating a new individual at a random position. The new position varies according to the distance between sunflowers. Sunflower individuals closer to the sun will take fewer steps to pursue local optimization, while sunflower individuals farther from the sun will move regularly and normally. The new sunflower position is updated by the following formula.

[0063]

[0064] The sunflower optimization algorithm first generates a random or uniform sunflower population and calculates the fitness function corresponding to each individual, and selects the individual with the highest fitness as the sun. It faces the sun and takes random steps in a certain direction for control. Based on the voltage measurement results of the battery test and the voltage simulation results of the battery model, the fitness function corresponding to the current excitation is calculated to adjust the value of the noise covariance matrix, and the optimal value of the noise covariance matrix is ​​determined within the allowed range. The objective function of the sunflower optimization algorithm is set to the minimum root mean square error of the state of charge estimation result. When the battery is discharged, the voltage must be kept above the discharge cut-off voltage, and the SoC must be between 0 and 1. After meeting the maximum number of iterations or the stopping criterion, the optimal parameter value of the extended Kalman filter is obtained according to the sunflower optimization algorithm, and the online estimation of the state of charge is completed by interpolation.

[0065] In order to improve the computational performance of online estimation of battery management system, a state of charge estimation method based on improved extended Kalman filter is proposed. The proportional integral differential (PID) control tracking mechanism is used to correct the posterior estimation of system state variables in the sunflower optimized extended Kalman filter. The proportional part, integral part and differential part in the PID control algorithm are introduced into the Kalman gain matrix to ensure that the extended Kalman filter can access sufficient state parameter information, thereby improving the state of charge estimation accuracy and convergence speed of the extended Kalman filter. The calculation process is as follows: Figure 4 The correction process of the posterior estimate of the system state variable in the extended Kalman filter is as follows:

[0066]

[0067] In the formula, K p , K i , K d They are the proportional constant, integral constant and differential constant of the position PID control algorithm, which play the role of dynamic linear output, eliminating steady-state error and reducing overshoot respectively. Through repeated experiments, the values ​​of them are 0.12, 0.024 and 0.018 respectively.

[0068] In addition, considering the accuracy of the method for obtaining the initial value of the state of charge corresponding to the open-circuit voltage offline in engineering applications, the voltage cumulative error judgment and the initial correction method of the state of charge are used to improve the estimation method. Since the calculation process of the voltage cumulative error is prone to the problem of excessive interference of too much historical data, the moving window estimation method is used to update the voltage cumulative error. The update process is as follows:

[0069]

[0070] In the formula, Ecal is the accumulated error of system voltage, and M is the window length of the moving window method.

[0071] If the cumulative error reaches the voltage limit of the effective voltage cumulative error, the proportional and differential links related to the dynamic output response speed in the PID control algorithm are used to correct the initial value of the state of charge. The correction process is as follows:

[0072] S oC (m) = S oC (m-1)+K p e(m-1)++K d [e(m-1)-e(m-2)]

[0073] 3. Verification of the accuracy of state of charge estimation

[0074] The ampere-hour integration method is the most common and simple battery state of charge estimation method in engineering practices such as battery management system installation. It extends the basic definition of the state of charge for calculation. Its discrete form is:

[0075]

[0076] In the formula, S oC,Ah is the battery SoC estimation result based on the ampere-hour integration method; η is the battery charge and discharge coulomb efficiency, the charge state is 0.98, and the discharge state is 1; Q a Represents the available capacity of the battery in its current state.

[0077] A lithium iron phosphate battery with a rated capacity of 20Ah was selected as the research object. Under the DST of 25℃ ambient temperature, the SoC estimation accuracy of the classic ampere-hour integration method, the sunflower-optimized extended Kalman filter algorithm, and the improved extended Kalman filter algorithm (SFO-PID-EKF) were verified. The results are as follows: Figure 5 shown.

[0078] Through verification, it can be seen that the accuracy of the state of charge estimation based on the improved extended Kalman filter algorithm is higher than that of the ampere-hour integration method and the sunflower-optimized extended Kalman filter algorithm. The error of the state of charge estimation of the ampere-hour integration method is mainly caused by the offset noise brought by the vehicle sensor, and gradually accumulates with the advancement of the time step. Due to the existence of offset noise in the true value of the current and the linearization process during the expansion of the Taylor formula, the accuracy of the state of charge estimation result based on the sunflower-optimized extended Kalman filter algorithm is limited and it is difficult to converge well. The state of charge estimation result based on the improved extended Kalman filter algorithm is relatively stable, and the error is stable near zero. The maximum root mean square error of the state of charge estimation result under the DST condition of 25℃ ambient temperature is only 0.427%. The results show that the state of charge estimation method based on the improved extended Kalman filter algorithm has good state of charge estimation performance.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm, characterized in that: The method comprises the following steps: Establish the second-order RC equivalent circuit model of lithium-ion battery; The model is linearized using Taylor expansion to obtain the state space equation of the model; The root mean square error of the state of charge estimation result of the extended Kalman filter algorithm is used as the fitness function; The Sunflower Optimization Algorithm is used to search for the optimal noise covariance matrix; The proportional-integral-derivative control method is introduced into the Kalman filter gain matrix to correct the a posteriori estimate of the system state variables; The initial value of the state of charge is corrected according to the accumulated error of the battery voltage.

2. The method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm according to claim 1, characterized in that: The sunflower optimization algorithm includes: Generate a random or uniform population of sunflowers; Calculate the fitness function corresponding to each individual, and select the individual with the highest fitness as the sun; Look toward the sun and take random steps in a certain direction for control; Based on the voltage measurement results of the battery test and the voltage simulation results of the battery model, the fitness function corresponding to the current excitation is calculated to adjust the value of the noise covariance matrix; Determine the optimal value of the noise covariance matrix within the allowed range.

3. The method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm according to claim 1, characterized in that: The proportional integral derivative control method comprises: Introducing the proportional part, integral part and differential part into the Kalman gain matrix; Correct the a posteriori estimates of the system state variables; The initial value of the state of charge is corrected according to the accumulated error of the battery voltage.

4. The method for estimating the state of charge of a lithium-ion power battery for a vehicle based on an improved extended Kalman filter algorithm according to claim 1, characterized in that: The battery voltage cumulative error correction method comprises: The voltage cumulative error is updated using the moving window estimation method; When the accumulated error reaches the voltage limit of the effective voltage accumulated error, the proportional and differential links related to the dynamic output response speed in the PID control algorithm are used to complete the correction of the initial value of the state of charge.

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