CN115015781A - Lithium battery SOC estimation method based on dynamic adaptive square root unscented Kalman filter - Google Patents

Lithium battery SOC estimation method based on dynamic adaptive square root unscented Kalman filter Download PDF

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CN115015781A
CN115015781A CN202210705903.4A CN202210705903A CN115015781A CN 115015781 A CN115015781 A CN 115015781A CN 202210705903 A CN202210705903 A CN 202210705903A CN 115015781 A CN115015781 A CN 115015781A
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邓丹
刘胜永
黄俊华
罗文广
吴明慧
孔德昊
陆云祺
李柏青
王国盛
陈俊霖
王笠力
官柳龙
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Liuzhou Teltel New Energy Co ltd
Guangxi University of Science and Technology
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Abstract

The invention discloses a dynamic self-adaptive SOC estimation method of square root unscented Kalman filtering, aiming at the accurate estimation target of the SOC value of a lithium ion battery pack, the method is combined with a high-order Thevenin equivalent model to realize the effective iterative calculation of the SOC value of the lithium ion battery pack by Kalman filtering; the nonlinear transfer problem of the mean value and the covariance is processed by utilizing a square root algorithm, so that a large error generated by the re-decomposition in the calculation process is avoided; aiming at the problems of uncertain statistical characteristics and filtering divergence of measured noise, an improved method of adding noise adaptive covariance matching is adopted, and meanwhile, the size of a windowing window is dynamically determined by utilizing a threshold value adjusting factor, so that the transient characteristics of a system are accurately reflected, and the real-time correction of a noise matrix is realized; and the establishment of an SOC estimation model of the lithium ion battery pack and the reliable operation of a mathematical iterative operation algorithm of the SOC value are realized.

Description

Lithium battery SOC estimation method based on dynamic adaptive square root unscented Kalman filter
Technical Field
The invention relates to a lithium ion battery SOC estimation method based on dynamic self-adaptive square root unscented Kalman filtering, and belongs to the field of new energy measurement and control.
Background
Energy safety is a strategic problem of the development of the national economic society, and under the great trend of the vigorous development of new energy, the new energy industry is highlighted by the continuously deepened energy crisis and the increasingly enhanced environmental awareness; the power lithium battery is used as a bridge for energy transfer of the new energy automobile, and the core technology of the power lithium battery is battery equivalent model construction and accurate estimation of different states; in order to avoid the safety problem caused by overcharge and discharge, it is necessary to establish a Battery Management System (BMS) that can continuously monitor the state of the lithium ion Battery; the State of Charge (SOC) of the lithium battery is an important parameter for reflecting the remaining service time of the lithium battery, and is a key factor for ensuring the safe and stable operation of the lithium battery pack; the accurate SOC estimation of the lithium ion battery can effectively prevent the overcharge and the overdischarge of the battery, prolong the service life of the battery and play a crucial role in a BMS; the lithium ion battery model is a bridge connecting the external characteristic and the internal state of the lithium ion battery model, and the accurate equivalent battery model lays a foundation for the SOC estimation of the battery; therefore, establishing a proper equivalent model to analyze the dynamic working characteristics inside the lithium ion battery has important significance for controlling and monitoring the performance of the lithium ion battery.
For the SOC estimation of the lithium ion battery pack, related researchers have made a lot of research in the field in recent years; some colleges and scientific research units at home and abroad are dedicated to the research on the battery management system, and related achievements are published in journals at home and abroad, such as Energy, Journal of Cleaner Production, Energy Science and Engineering, Journal of Power Sources, Applied Energy, Power technology, Power source Journal and the like; research institutions such as the national academy of labor in Massachusetts, the university of Ritz in England, the State university of Bingzhou, the Laiden energy resource in America, Germany, the English-flying-technology Limited company and the like carry out deep analysis on the grouping application of the lithium batteries and provide a series of balancing strategies; the battery working characteristics of Qinghua university, Harbin industry university, China science and technology university and the like in China are tested, influence factors of battery performance are analyzed, and further research and improvement are carried out on model construction and SOC estimation methods; as described in Ge, etc., the methods of ampere-hour integration, open-circuit voltage, kalman and its extended algorithm, particle filtering, neural network, etc. have been gradually applied in SOC estimation of lithium batteries; according to different establishment mechanisms, battery models can be divided into types such as a simple electrochemical model, an intelligent mathematical model, an equivalent circuit model and the like; because of the influence of various factors such as different charge and discharge multiplying power, temperature, battery self-discharge and the like on the estimation result, the requirement on battery experimental test equipment in practical application is continuously increased, the performance change of the lithium ion battery has obvious influence on the SOC estimation precision, and a universal method is not available for realizing the accurate estimation of the SOC value; in addition, the lithium ion battery pack still lacks an effective SOC estimation method due to the influence of consistency among the monomers in the grouping working process; at present, the practical application is usually realized by adopting a basic ampere-hour integration method, but the open-circuit voltage of the battery changes very slowly in a platform period, the SOC estimation error is likely to be large due to extremely small voltage measurement error, and the accumulated error is obvious under the influence of external factors and noise; aiming at the SOC estimation research of the lithium ion battery pack, the related research provides thought reference; on the basis, an SOC estimation method under a complex working condition environment is explored, and effective iterative estimation of the SOC of the lithium ion battery pack is achieved; meanwhile, for the grouping application of the lithium ion batteries, the SOC estimation needs to be carried out by considering the balance state among all battery monomers in the group, and then the BMS is utilized to carry out effective energy management; improving the SOC estimation precision, comprehensively considering the Lu wave effect and the calculated amount, seeking the optimal balance point between the two, continuously optimizing and improving the estimation method, and improving the SOC estimation precision.
In the conventional lithium ion battery pack BMS application, an SOC estimation method based on ampere-hour integration and open-circuit voltage cannot accurately represent accumulated errors existing in SOC estimation and cannot correct parameters by combining the current state; through analysis of the existing SOC estimation method, based on dynamic self-adaptive square root unscented Kalman filtering algorithm research, closed-circuit voltage and current are used as real-time input parameters, and working condition information of a lithium ion battery pack is considered in the SOC estimation process, so that errors caused by the linearization process of the traditional unscented Kalman filtering algorithm are overcome, and the robustness of the system is enhanced; aiming at the problems that the estimation accuracy is insufficient and the tracking effect is weakened due to the accuracy deviation and the state covariance negativity of the constructed model, the semipositive and the digital calculation stability are ensured by utilizing a square root algorithm; meanwhile, an improved method of noise adaptive covariance matching is introduced, so that extremely strong uncertainty of an estimation process caused by time-varying noise variance is eliminated; aiming at the SOC estimation problem of the lithium ion battery pack, a dynamic self-adaptive square root unscented Kalman algorithm is provided and the iterative calculation method is researched by combining the advantage analysis of the iterative calculation process of Kalman filtering, so that the effective construction of an equivalent model and the accurate estimation of the SOC are realized.
Disclosure of Invention
The invention aims to overcome the defects of the traditional lithium ion battery pack SOC estimation method, provides a lithium ion battery pack SOC estimation method based on dynamic self-adaptive square root unscented Kalman filtering, and solves the problem of accurate estimation of an SOC value in the grouping application of lithium ion batteries.
In order to solve the problems, the invention is mainly realized by the following technical scheme:
a lithium ion battery SOC estimation method of dynamic square root unscented Kalman filtering provides a dynamic self-adaptive square root unscented Kalman filtering algorithm, and effective iterative computation of the SOC value of a lithium ion battery pack by Kalman filtering is realized by combining with a high-order Thevenin equivalent model. Aiming at the problems of numerical instability and filtering divergence in the estimation process, an improved method of adding noise adaptive covariance matching is adopted, and meanwhile, the size of a windowing window is dynamically determined by utilizing a threshold value adjusting factor, so that the real-time correction of a noise matrix is realized.
Further, by carrying out iterative computation on the covariance matrix in the form of square root, the re-solution of the computation process is avoided; the noise covariance matrix is automatically and circularly updated and transmitted, so that the effective iterative calculation of the SOC value of the lithium ion battery pack is realized, and the limitation error of external measurable parameter signal detection and the accumulated error of discretization digital sampling and iterative calculation noise are overcome.
Furthermore, aiming at the situation that the statistical property of the measurement noise is not clear, the transient property of the system is accurately reflected by self-defining the size of the window of the self-adaptive window function, and the filtering divergence caused by the unclear statistical property of the measurement noise is prevented.
Further, a time-varying noise correction method of square root unscented Kalman filtering is fully considered on the basis of grouping work of the lithium ion batteries, an iterative computation process based on the square root unscented Kalman filtering is improved on the basis of a high-order Thevenin equivalent model circuit, and establishment of an SOC estimation model of the lithium ion battery pack and reliable operation of a mathematical iterative operation algorithm of an SOC value are achieved.
Further, the estimation method specifically includes the following steps:
1): given an initial quantity of states, assume
Figure BDA0003705283250000045
Is the initial value of the state variable and P 0 Initial value of covariance, covariance P, representing estimation error 0 Cholesky decomposition factor S 0 The concrete conditions are as follows:
Figure BDA0003705283250000041
constructing a sigma point set according to the UT transformation in formula (1):
Figure BDA0003705283250000042
2): carrying out iterative computation on the above formula to obtain a sigma point set, and carrying out nonlinear processing on the point set by using a state equation; due to different values of alpha and k, covariance weight omega may be caused 0 c Negative nature of (1), in order to overcome omega 0 c The influence on the matrix ensures semi-positive nature, and the system state quantity and the square root of the error covariance at the moment k are calculated to carry out one-step prediction as shown in a formula (3)
Figure BDA0003705283250000043
3): in the measurement update phase of the algorithm, the Sigma points are resampled:
Figure BDA0003705283250000044
4): combining the resampling of the sigma point of the formula with a system observation equation, and calculating to obtain a step of prediction of the k-time observation system
The measured value and the observation vector are as shown in equation (5):
Figure BDA0003705283250000051
5): calculating a one-step predicted value of the observation variable and the square root of the error covariance matrix at the moment k according to the one-step predicted value of the system state quantity obtained by the formula (5); carrying out posterior estimation based on data at the moment k, namely correcting prior estimation so as to obtain a more accurate estimated value; as shown in formula (6):
Figure BDA0003705283250000052
in the formula: k k Is the Kalman filter gain; p xkyk The method is characterized in that a cross covariance function of a sigma point set state equation and an observation equation of a system directly influences the Kalman filtering gain; y is k+1 Is the observed quantity measured by the instrument at the time k +1, and
Figure BDA0003705283250000055
then the observed quantity obtained by prior estimation is the optimal estimation of the current moment;
6): system state update and square root update of a posteriori covariance matrix:
Figure BDA0003705283250000053
7): systematic errors are a determining factor for innovation, e k Innovative definitions, H, referring to observed variables k An innovation covariance approximation value at the time k is shown, and the current time error can be clearly reflected, as shown in equation (8):
Figure BDA0003705283250000054
in the above formula, M is used to represent the dynamic windowing size of covariance matching, in general, M is taken to be 3 to perform innovation calculation, however, the value still cannot well reflect the good filtering and tracking effects of the algorithm, so d is defined as a dynamic adaptive window adjustment factor, and the windowing size is selected to reach an optimal value;
Figure BDA0003705283250000061
8): the optimum windowing window size of d, λ, is selected min ＝0，λ max 1 is a judgment threshold value; the convergence rate of the windowing size M is mu; the judgment formula is shown as the formula (10):
Figure BDA0003705283250000062
obviously, the convergence rate of the windowing size M is an important technical index for measuring the quality of the adaptive filtering algorithm, and the convergence interval is more than or equal to 1 and less than or equal to k; when P is present ykyk When the value d is large enough or small enough, the value d is less than 0 or more than 1, the windowing window is greatly changed, the system calculation amount is increased, and the tracking effect is good; when 0 is present<d<1 hour, the windowing window M is k × μ d-λmin Due to the existence of proper values, a good tracking effect is ensured, and the system has small calculation amount;
9): the process of updating the statistical characteristics of the estimation process noise and the observation noise is shown as follows:
Figure BDA0003705283250000063
the invention has the beneficial effects that:
the method is mainly used for solving the SOC estimation of the lithium ion battery pack, ensures the semipositive nature of the state covariance by utilizing a square root algorithm in an unscented Kalman filtering algorithm, improves the stability of digital calculation, introduces a noise adaptive covariance matching algorithm in consideration of the influence of system time-varying noise on an SOC value, defines a threshold value adjusting factor to dynamically adjust the windowing size for real-time filtering, enables the SOC estimation value to be more stable and accurate under the environment with inaccurate noise statistical characteristics, and realizes the updating and correction of the time-varying noise.
The SOC estimation method of the lithium ion battery pack based on the dynamic adaptive square root unscented Kalman filter algorithm is based on the experimental analysis of the power application requirement and the working characteristic of the lithium ion battery pack, combines the research idea of the modern control theory, and has strong applicability; aiming at the accurate estimation target of the SOC value of the lithium ion battery pack, the recursive calculation process is optimized by using the covariance square root to replace covariance in the iterative process of a filter, so that negative determination of an error covariance matrix is solved; noise variance matrixes are estimated on line through a self-adaptive algorithm, and dynamic threshold adjustment factors are added, so that mathematical description of grouped SOC estimation is realized, and the calculation reliability is improved; the method can provide method reference for the establishment of the SOC estimation model of the lithium ion battery pack and the calculation of the SOC value under different application scenes, and has the advantages of simplicity in calculation, good adaptability and high precision.
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FIG. 1 is a schematic diagram of an iterative process for estimating SOC values.
Detailed Description
The method for estimating the SOC of the lithium ion battery pack based on the dynamic adaptive square root unscented kalman filter according to the present invention will be described in further detail with reference to the accompanying drawings; the invention provides a lithium ion battery pack SOC estimation method based on dynamic adaptive square root unscented Kalman filtering, which aims at the SOC estimation problem when the lithium ion batteries are applied in groups, and realizes the effective representation of the SOC estimation of the lithium ion battery groups through the iterative calculation process based on online accurate model parameter identification and real-time correction algorithm; on the basis of accurate modeling, the lithium ion battery pack SOC estimation method based on the dynamic adaptive square root unscented Kalman filtering obtains the functional relation between each parameter in the model and the SOC value through the rectangular window least square method on-line identification; on the basis of accurate modeling and identification, the lithium ion battery pack SOC estimation method based on dynamic adaptive square root unscented Kalman filtering utilizes the square root of a covariance matrix to replace the covariance of an unscented Kalman algorithm to participate in iterative computation, thereby effectively avoiding negative determination of the covariance matrix, improving the filtering stability and reducing the calculated amount; considering the influence of the SOC value on the internal parameters of the model, calculating to obtain the functional relation between the SOC and each parameter and applying the functional relation to the algorithm; the method fully considers the time-varying noise correction method of square root unscented Kalman filtering on the basis of the grouping work of lithium ion batteries, realizes the accurate online identification of parameters of an SOC estimation model of the lithium ion battery pack based on a high-order Thevenin equivalent model circuit, and constructs an SOC estimation scheme of the lithium ion battery pack based on dynamic self-adaptive square root unscented Kalman filtering; in order to better embody the present invention, the lithium ion battery pack is only exemplified in the present embodiment, but it should be well known to those skilled in the art that various lithium ion battery pack SOC estimation based on the dynamic adaptive square root unscented kalman filter can be realized according to the technical idea of the present invention; the implementation steps of the lithium ion battery pack SOC estimation method based on the dynamic adaptive square root unscented kalman filter are described in detail below.
Aiming at the goal of improving the SOC estimation precision, the circuit model of the lithium ion battery pack is subjected to online parameter identification based on a rectangular window least square method, so that the precision of a simulation model is ensured, and a foundation is laid for SOC estimation by using a Kalman filtering algorithm; combining a state space model of the lithium ion battery pack, and accurately estimating the mean value and covariance of a system equation by utilizing unscented transformation to enable the estimated value to reach second-order accuracy; defining a self-adaptive window factor to dynamically determine the size of a window, and effectively avoiding filtering divergence under the condition of uncertain measurement noise statistical characteristics; and based on the iterative computation of the dynamic self-adaptive square root unscented Kalman, the accurate estimation of the SOC value is realized.
In fig. 1, when the estimation is started, an initial value of the state is given first, and the principle of the unscented kalman filter algorithm knows that the value is given arbitrarily, and whether the initial value truly reflects the state of charge of the lithium ion battery pack is unimportant. Then the loop processing procedure of the algorithm is entered. Firstly carrying out sigma transformation on the SOC value at the moment k to obtain a sampling point at the moment k, and then calculating the state quantity of a system at the moment k and the square root of the error covariance; the square root unscented Kalman algorithm utilizes a sampling method of covariance square root to replace the original covariance, so that resampling is needed again; combining resampling with a system observation equation, and calculating to obtain a one-step predicted value and an observation vector of the observation system at the k moment; carrying out posterior estimation based on data at the moment k, namely correcting prior estimation so as to obtain a more accurate estimated value; updating the state vector and the variance thereof by using Kalman gain according to the difference between the estimated value and the true value of the observation vector; introducing innovation covariance to clearly reflect the current system error, dynamically selecting the size of a self-adaptive windowing window, and realizing real-time updating of statistical properties of estimation process noise and observation noise; and inputting the online parameters into a dynamic self-adaptive square root unscented Kalman filtering algorithm, and establishing a joint estimation algorithm for SOC estimation. The method comprises the following specific steps:
1): given an initial quantity of states, assume
Figure BDA0003705283250000095
Is the initial value of the state variable and P 0 Initial value of covariance, covariance P, representing estimation error 0 Cholesky decomposition factor S 0 The concrete conditions are as follows:
Figure BDA0003705283250000091
constructing a sigma point set according to the UT transformation in formula (1):
Figure BDA0003705283250000092
2): and carrying out iterative calculation on the above formula to obtain a sigma point set, and carrying out nonlinear processing on the point set by using a state equation. Due to different values of alpha and k, covariance weight omega may be caused 0 c Negative nature of (1), in order to overcome omega 0 c Influence on the matrix, semi-positive nature is ensured, and the state quantity of the system at the moment k and the square root of the error covariance are calculated to carry out one-step prediction as shown in a formula (3)
Figure BDA0003705283250000093
3): in the measurement update phase of the algorithm, the Sigma points are resampled:
Figure BDA0003705283250000094
4): combining the resampling of the sigma point of the formula with a system observation equation, and calculating to obtain a step of prediction of the k-time observation system
The measured value and the observation vector are shown in formula (5):
Figure BDA0003705283250000101
5): calculating observation variable and error covariance matrix average at the k moment according to the one-step predicted value of the system state quantity obtained by the formula (5)
And (5) predicting the one-step root prediction value. And performing posterior estimation based on the data at the time k, namely correcting the prior estimation so as to obtain a more accurate estimation value. As shown in formula (6):
Figure BDA0003705283250000102
in the formula: k k Is the Kalman filter gain; p xkyk The cross covariance function of the state equation and the observation equation of the sigma point set of the system directly influences the Kalman filtering gain. y is k+1 Is the observed quantity measured by the instrument at the time k +1, and
Figure BDA0003705283250000103
the observed quantity obtained by prior estimation is the optimal estimation of the current moment.
6): system state update and square root update of a posteriori covariance matrix:
Figure BDA0003705283250000104
7): systematic errors are a determining factor for innovation, e k Innovative definitions, H, referring to observed variables k Denotes that the innovation covariance at time k is closeLike the value, can clearly reflect the error at present moment, as shown in equation (8):
Figure BDA0003705283250000105
in the above equation, M is used to represent the dynamic windowing size of covariance matching, and in general, M is taken to be 3 to perform innovation calculation, however, the value still cannot well reflect the good filtering and tracking effects of the algorithm, so d is defined as a dynamic adaptive window adjustment factor, and is selected for the windowing size to reach an optimal value.
Figure BDA0003705283250000111
8): the optimum windowing window size of d, λ, is selected min ＝0，λ max 1 is a judgment threshold value; the convergence rate of the window size M is μ. The judgment formula is shown as the formula (10):
Figure BDA0003705283250000112
obviously, the convergence rate of the windowing size M is an important technical index for measuring the quality of the adaptive filtering algorithm, and the convergence interval is more than or equal to 1 and less than or equal to k. When P is present ykyk When the value d is large enough or small enough, the value d is less than 0 or more than 1, the windowing window is greatly changed, the system calculation amount is increased, and the tracking effect is good. When 0 is present<d<1, the windowing window M is k × μ d-λmin Due to the existence of proper values, a good tracking effect is ensured, and the system has small calculation amount.
9): the updating process of the statistical characteristics of the estimation process noise and the observation noise is shown as the formula.
Figure BDA0003705283250000113
In the SOC estimation process of the lithium ion battery pack, iterative computation is carried out based on a dynamic self-adaptive square root unscented Kalman filtering algorithm, the schematic diagram of the iterative process of estimating the SOC value is shown in FIG. 1, the nonlinear transfer problem of mean value and covariance is processed by a sampling method of two times of unscented transformation, and the noise is automatically and circularly updated and transferred by using a self-adaptive covariance matching algorithm of noise, so that the noise of discretization digital sampling and iterative computation processing is effectively reduced; dynamically selecting a windowing window of a window function based on the innovation sequence sample to obtain an optimal estimation SOC value of a system state variable; the method is based on a dynamic self-adaptive square root unscented Kalman algorithm framework to realize an iterative computation process, and the SOC estimation model of the lithium ion battery pack is constructed through the iterative process. The traditional square root unscented Kalman filtering algorithm ignores a system process noise variance matrix or an observation noise variance matrix, and can only estimate through experience generally, so that filtering divergence is caused; the dynamic adaptive covariance matching principle provided by the algorithm is greatly improved in the aspect, and the accuracy of the SOC estimated value is effectively improved.
In summary, the invention provides a lithium ion battery pack SOC estimation method based on dynamic adaptive square root unscented Kalman filtering aiming at the accurate SOC estimation target of the lithium ion battery pack, comprehensively considering the estimation precision, the calculation complexity and the stability of the algorithm, realizes iterative computation of the SOC estimation of the lithium ion battery pack by combining the establishment of an SOC estimation model on the basis of fully considering the grouping work of the lithium ion batteries, and provides a basis for the SOC estimation and the real-time monitoring of the working state of the lithium ion battery pack.
The above embodiments of the present invention have been described for the lithium ion battery pack SOC estimation based on the dynamic adaptive square root unscented kalman, but it is understood that any changes and variations can be made by those skilled in the art without departing from the spirit and scope of the present invention.

Claims (5)

1. A lithium ion battery SOC estimation method based on dynamic adaptive square root unscented Kalman filtering is characterized in that a dynamic adaptive square root unscented Kalman filtering algorithm is provided, and effective iterative computation of Kalman filtering on a lithium ion battery pack SOC value is realized by combining with a high-order Thevenin equivalent model; aiming at the problems of numerical instability and filtering divergence in the estimation process, an improved method of adding noise adaptive covariance matching is adopted, and meanwhile, the size of a windowing window is dynamically determined by utilizing a threshold value adjusting factor, so that the real-time correction of a noise matrix is realized.
2. The SOC estimation method based on the dynamic adaptive square root unscented Kalman filter of claim 1, characterized in that the re-solution of the calculation process is avoided by performing iterative computation of covariance matrix in square root form; the noise covariance matrix is automatically and circularly updated and transmitted, so that the effective iterative calculation of the SOC value of the lithium ion battery pack is realized, and the limitation error of external measurable parameter signal detection and the accumulated error of discretization digital sampling and iterative calculation noise are overcome.
3. The SOC estimation method based on the adaptive square root unscented Kalman filter of claim 1, wherein for the case of ambiguous measurement noise statistical characteristics, the transient characteristics of the system are accurately reflected by self-defining the size of the adaptive window function window, and the occurrence of filtering divergence caused by the ambiguous measurement noise statistical characteristics is prevented.
4. The SOC estimation method based on the dynamic adaptive square root unscented Kalman filter of claim 1, characterized in that the time-varying noise correction method of the square root unscented Kalman filter is fully considered on the basis of the grouping work of the lithium ion batteries, and the iterative computation process based on the square root unscented Kalman filter is improved based on a high-order Thevenin equivalent model circuit, so as to realize the establishment of the SOC estimation model of the lithium ion battery pack and the reliable operation of the mathematical iterative operation algorithm of the SOC value.
5. The SOC estimation method based on the dynamic adaptive square root unscented Kalman filter of claim 1, characterized in that the estimation method specifically comprises the following steps:
1): given an initial quantity of states, assume
Figure FDA0003705283240000011
Is the initial value of the state variable and P 0 Initial value of covariance, covariance P, representing estimation error 0 Cholesky decomposition factor S 0 The concrete conditions are as follows:
Figure FDA0003705283240000012
constructing a sigma point set according to the UT transformation in formula (1):
Figure FDA0003705283240000021
2): carrying out iterative computation on the above formula to obtain a sigma point set, and carrying out nonlinear processing on the point set by using a state equation; due to different values of alpha and k, covariance weight omega may be caused 0 c Negative nature of (1), in order to overcome omega 0 c The influence on the matrix ensures semi-positive nature, and the system state quantity and the square root of the error covariance at the moment k are calculated to carry out one-step prediction as shown in a formula (3)
Figure FDA0003705283240000022
3): in the measurement updating stage of the algorithm, the sigma points are resampled:
Figure FDA0003705283240000023
4): the resampling of the sigma point of the formula is combined with a system observation equation, and the one-step prediction of the k-time observation system is obtained through calculation
The measured value and the observation vector are shown in formula (5):
Figure FDA0003705283240000024
5): calculating a one-step predicted value of the observation variable and the square root of the error covariance matrix at the moment k according to the one-step predicted value of the system state quantity obtained by the formula (5); carrying out posterior estimation based on data at the moment k, namely correcting prior estimation so as to obtain a more accurate estimated value; as shown in formula (6):
Figure FDA0003705283240000031
in the formula: k k Is the Kalman filter gain; p xkyk The method is characterized in that a cross covariance function of a sigma point set state equation and an observation equation of a system directly influences the Kalman filtering gain; y is k+1 Is the observed quantity measured by the instrument at the time k +1, and
Figure FDA0003705283240000032
then, according to observed quantity obtained by prior estimation, the optimal estimation of the current moment is carried out;
6): system state update and square root update of a posteriori covariance matrix:
Figure FDA0003705283240000033
7): systematic errors are a determining factor for innovation, e k Innovative definitions, H, referring to observed variables k An innovation covariance approximation value at the time k is shown, and the current time error can be clearly reflected, as shown in equation (8):
Figure FDA0003705283240000034
in the above formula, M is used to represent the dynamic windowing size of covariance matching, in general, M is taken to be 3 to perform innovation calculation, however, the value still cannot well reflect the good filtering and tracking effects of the algorithm, so d is defined as a dynamic adaptive window adjustment factor, and the windowing size is selected to reach an optimal value;
Figure FDA0003705283240000035
8): the optimal window size of d, λ, is selected min ＝0，λ max 1 is a decision threshold; the convergence rate of the windowing size M is mu; the judgment formula is shown as the formula (10):
Figure FDA0003705283240000036
obviously, the convergence rate of the windowing size M is an important technical index for measuring the quality of the adaptive filtering algorithm, and the convergence interval is more than or equal to 1 and less than or equal to k; when P is present ykyk When the value d is large enough or small enough, the value d is less than 0 or more than 1, the windowing window is greatly changed, the system calculation amount is increased, and the tracking effect is good; when 0 is present<d<1, the windowing window M is k × μ d-λmin Due to the existence of proper values, a good tracking effect is ensured, and the system has small calculation amount;
9): the process of updating the statistical characteristics of the estimation process noise and the observation noise is shown as follows:
Figure FDA0003705283240000041
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CN117277520B (en) * 2023-11-22 2024-02-02 深圳清瑞博源智能科技有限公司 SOC-SOH combined calculation method and device for new energy storage power station

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