CN112364471A - Research on lithium battery SOC estimation method based on Thevenin model and unscented Kalman filter - Google Patents
Research on lithium battery SOC estimation method based on Thevenin model and unscented Kalman filter Download PDFInfo
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Abstract
The invention relates to an unscented Kalman SOC estimation method which is characterized in that unscented transformation is utilized on the basis of a Kalman filtering algorithm to enable Kalman filtering to be applied to SOC estimation of a lithium ion battery pack with an obvious nonlinear relation, so that effective iterative computation of an SOC value of the lithium ion battery pack is realized, and accumulated errors existing in SOC initial value errors and ampere-hour integration are overcome; aiming at the fact that high-order terms are ignored by Kalman, the method ensures low estimation precision and poor stability, and unscented Kalman does not ignore the high-order terms and has higher precision; the Thevenin equivalent circuit model is established, so that the defect that the internal resistance model cannot represent the dynamic characteristics of the lithium battery is overcome to a certain extent, and the RC is added to represent the polarization effect in the battery, so that the battery has a better representation effect; the method improves the iterative computation process based on Kalman on the basis of an equivalent model circuit on the basis of fully considering the grouping work of the lithium ion batteries, and realizes the establishment of an SOC estimation model of the lithium ion battery pack and the reliable operation of a mathematical iterative computation algorithm of an SOC value.
Description
Technical Field
The invention relates to a lithium ion battery SOC estimation method of unscented Kalman, this method is directed against the accurate estimation goal of the SOC value of the lithium ion battery pack, have proposed a unscented Kalman filtering method, through confirming the sampling point near estimating the point with the unscented change on the basis of Kalman filtering algorithm, the probability density function of approximate state of Gaussian density expressed with these sample points, use the unscented transformation to process the nonlinear transfer problem of mean value and covariance, can apply to the SOC estimation of the lithium ion battery pack with obvious nonlinear relation, have realized the effective iterative computation of the SOC value of the lithium ion battery pack, overcome the accumulative error that SOC initial value error and ampere hour integral exist; aiming at the fact that high-order terms are ignored by Kalman, the method ensures low estimation precision and poor stability, and unscented Kalman does not ignore the high-order terms and has higher precision; the Thevenin equivalent circuit model is established to make up for the defect that the internal resistance model cannot represent the dynamic characteristics of the lithium battery to a certain extent, and the RC is added to represent the polarization effect inside the battery, so that the battery has a better representation effect. Establishing an SOC estimation model of the lithium ion battery pack and performing mathematical iterative operation on an SOC value by using an unscented Kalman algorithm on the basis of a battery equivalent circuit model; the method is a state estimation method of a lithium ion battery pack based on a modern control theory, and belongs to the field of new energy measurement and control.
Background
In the whole life cycle of the lithium ion Battery pack, the monitoring and the adjustment of a Battery Management System (BMS) on a core parameter SOC will affect the effect and the safety of emergency power output; therefore, it is very necessary to monitor the change of the parameter in real time and ensure the working performance of the lithium ion battery pack based on the change; because the grouped SOC estimation technology in the BMS is not mature, potential safety hazards existing in the use process seriously restrict the development of the lithium ion battery pack; for lithium ion battery packs, reliable BMS management relies on accurate SOC values; under the condition that the value is known, not only is reliable energy management and safety control carried out on the lithium ion battery pack, but also the lithium ion battery pack is prevented from being damaged in advance, and the service life of the lithium ion battery pack is prolonged; therefore, the SOC value is accurately estimated, and the method is vital to guarantee the working performance, energy and safety management of the lithium ion battery pack; the construction and accurate estimation values of an SOC estimation model of the lithium ion battery pack are obtained, and the core problem of energy and safety management of the lithium ion battery pack is solved; the lithium ion battery pack is formed by combining lithium cobaltate battery monomers with high energy density and closed circuit voltage, and the safety of the lithium ion battery pack is influenced by the working state of the lithium cobaltate battery; the SOC represents the residual capacity of the lithium ion battery pack and is a key parameter which is the most basic and the most important of a battery management system; in addition, the charge and discharge process of the lithium ion battery pack comprises complicated links of electric energy, chemical energy, heat energy conversion and the like, safety accidents are easily caused by overcharge and overdischarge phenomena, and accurate SOC estimation plays an important role in preventing overcharge and overdischarge; in the application of lithium ion battery pack, the safety of the lithium ion battery pack is still the most concerned problem, and the SOC estimation is the basis and precondition for the safe use of the lithium ion battery pack; the lithium ion battery pack adopts a battery monomer cascade structure, and meets the capacity and voltage requirements in the energy supply process of the auxiliary power; however, due to unavoidable material and process differences, the phenomenon of inconsistency between monomers is objective and unavoidable; moreover, the phenomenon becomes more and more obvious along with the increase of the cycle number, so that the expression and correction of the inconsistency among the monomers become an important component of the estimation of the SOC group, and meanwhile, great challenges are brought to the accurate estimation of the SOC group.
With respect to the necessity and urgent need of SOC estimation, a great deal of research and intensive research has been conducted on SOC estimation in relevant research institutes and universities, such as the massachusetts institute of technology, state university of bingzhou, southern card university of usa, litz university of uk, robert university of uk, national renewable energy house of usa, leideng energy company, germany english-flying-technologies company, qinghua university, beijing aerospace university, beijing university of rationale, beijing university of transportation, chongqing university, china university of scientific technology, and harbin university of industry; many periodicals at home and abroad, such as Journal of Power Sources, Applied Energy, IEEE Transactions on Power Systems, Power technology and the like, establish highly targeted columns for relevant research result display; aiming at the problem of SOC estimation of the lithium ion battery, relevant research workers at home and abroad make great research progress at present; as described in Hu et al, there are currently mainly an Ampere-hour integration method (Ah), an Open Circuit Voltage method (OCV), kalman Filter and its extended algorithm, a Particle Filter method (PF), a Neural Network method (NN), and the like; due to the influence of various factors such as charging and discharging current, temperature, internal resistance, self-discharge, aging and the like, the performance change of the lithium ion battery can obviously influence the SOC estimation precision, and a universal method for realizing the accurate estimation of the SOC value is not available; in addition, the consistency among the single batteries in the grouping working process is influenced, and the lithium ion battery pack still lacks an effective SOC estimation method; at present, SOC estimation in practical application is realized by a basic ampere-hour integration method, but the estimation error is large, and the accumulation effect is obvious under the influence of a plurality of factors; 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 an aviation working condition is explored, and effective SOC estimation of the lithium ion battery pack is achieved; meanwhile, aiming at aviation grouping application, the SOC estimation needs to be carried out by considering the balance state of each battery monomer in the group, and then the BMS is utilized to carry out effective energy management; an SOC estimation model with parameter correction and regulation capabilities is built, a parameter estimation theory based on an equivalent circuit model is applied, the trend of SOC estimation development is formed, an optimal balance point is found between the improvement of precision and the reduction of calculated quantity, and an estimation method is continuously optimized and improved.
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 be combined with the current state for parameter correction; through analysis of the existing SOC estimation method, based on unscented Kalman algorithm research, closed-circuit voltage and current are used as real-time input parameters, and working condition information of the lithium ion battery pack is considered in the SOC estimation process, so that the defects of large error, gradual accumulation and the like caused by insufficient real-time correction of the traditional SOC estimation method are overcome; meanwhile, high-order terms are ignored by Kalman, so that the estimation precision is low, the stability is poor, the unscented Kalman does not ignore the high-order terms, and the accuracy is higher; aiming at the SOC estimation problem of the lithium ion battery pack, the improved Kalman algorithm is provided and the iterative calculation method is researched by combining the advantage analysis of the actual single chip microcomputer processing method and the iterative calculation process, so that the construction and experimental verification of an SOC estimation model are realized.
Disclosure of Invention
The invention aims to overcome the defects of the traditional lithium ion battery pack SOC estimation method, provides the lithium ion battery pack SOC estimation method based on unscented Kalman, and solves the problem of accurate estimation of an SOC value in the grouping application of lithium ion batteries.
The method is mainly used for solving the SOC estimation of the lithium ion battery pack, and the non-linear function relation, namely the non-linear transfer problem of the mean value and the covariance, is processed by utilizing the unscented change in the Kalman filtering algorithm, so that the effective iterative computation of the SOC value of the lithium ion battery pack is realized, and the estimation precision and the stability are improved.
The SOC estimation method of the lithium ion battery pack is based on the power application requirement and the working characteristic experimental analysis of the lithium ion battery pack, combines the research idea of the modern control theory, is based on the unscented Kalman algorithm, and has strong applicability; aiming at the accurate estimation target of the SOC value of the lithium ion battery pack, the Thevenin equivalent circuit model is established to make up for the defect that the internal resistance model cannot represent the dynamic characteristics of the lithium battery to a certain extent, and the RC is added to represent the polarization effect in the battery, so that the battery has better representation effect. Aiming at the fact that high-order terms are ignored by Kalman, the estimation precision is low, the stability is poor, and unscented Kalman does not ignore the high-order terms, 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.
Drawings
FIG. 1 is a schematic diagram of a lithium ion battery pack SOC estimation model structure according to the present invention.
FIG. 2 is a schematic diagram of the present invention implemented using unscented Kalman.
Detailed Description
The unscented kalman based lithium ion battery pack SOC estimation method of 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 unscented Kalman aiming at the SOC estimation problem when the lithium ion batteries are applied in groups, and the method realizes the effective representation of the SOC estimation of the lithium ion battery groups through the intermittent aging degree measurement and the real-time calibration calculation processing; on the basis of capacity normalization representation, the lithium ion battery pack SOC estimation method based on unscented Kalman obtains mathematical expression of the influence of an aging state on electric quantity through calculation of influence coefficients of the aging state on the electric quantity; on the basis of regular measurement and calibration, the lithium ion battery pack SOC estimation method based on unscented Kalman obtains and corrects a function relation of correction of the superimposed cycle times through synchronous acquisition and correction of a rated capacity and a cycle time correlation value; the method for estimating the SOC of the lithium ion battery pack based on unscented Kalman combines the superposition calculation processing of the influence of two factors on the basis of the correction calculation of the aging influence coefficient and the cycle number to obtain a calculation method for correcting the influence of the aging process on the rated capacity; the method is based on fully considering the grouping work of the lithium ion batteries, combines the establishment of SOC estimation, realizes the mathematical expression of the aging process characteristics of the lithium ion battery pack, and constructs the SOC estimation scheme of the lithium ion battery pack based on unscented Kalman; 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 unscented kalman based estimation of the SOC of the lithium ion battery pack can be realized according to the technical idea of the present invention; the following describes in detail the implementation steps of the unscented kalman based lithium ion battery pack SOC estimation method.
Aiming at the goal of improving the SOC estimation precision, the non-linear transfer problem of the mean value and the covariance is processed by using unscented transformation so as to conveniently carry out SOC estimation by using a Kalman filtering algorithm; combining a state space model of the lithium ion battery pack, and realizing iterative calculation of an SOC value based on unscented Kalman iterative calculation, wherein when the method is used for tracking the output voltage of the lithium ion battery pack, the average estimation error is 0.005V, and the maximum estimation error is 0.01V; the SOC is used as a variable in a state equation of the SOC, and closed-circuit voltage is output to be used as a variable of an observation equation, so that the state equation and an observation equation expression are constructed;SOC(k) As a state variable, iskOf time of daySOCA value;U L (k) Outputting an observation variable for the working voltage; coefficients of equation of stateAIn order to be a matrix of the system,Binputting a matrix for control;Hto observe the matrix, initiallyA value of [ 001](ii) a System noise parameterw(k)And observing the noise parameterv(k) Are white Gaussian noise, and the covariance is respectivelyQAndR；U L (k) To take into account measurement errorsv(k)An affected voltage signal output; by iterative calculation, from the last state valueSOC(k-1) input signalI(k) And measuring the signalU L (k) Calculating an estimate of the Kalman modelSOC(k) (ii) a Using unscented transformation instead of state variable statistical property linearized transformation for different momentskValue of white Gaussian noisew (k)Random vector ofSOCAnd has Gaussian white noisev(k) Is observed variable ofU L (k) Forming a discrete time nonlinear system; constructing a lithium ion battery pack SOC estimation model by applying the estimation framework in the estimation process as shown in FIG. 1; the battery state space model is as follows.
For different time instantskThe SOC estimation process includes fusing white Gaussian noisew(k) Random state variable ofSOCAnd white Gaussian noise is blended inv(k) Is observed for a random variableU L (k)；f(*) Is a nonlinear state equation used for describing the SOC state of the lithium ion battery pack;g(*) Is a nonlinear observation equation used for describing the characteristics of the output closed circuit voltage; noise matrixw(k) Variance usage ofQDescribing, the noise matrixv(k) Variance usage ofRThe description is carried out; under the influence of random noise, the target is accurately estimated aiming at the SOC of the lithium ion battery pack at different momentskThe estimation of (b) is achieved by the following steps.
In fig. 1, the stage S1 represents the calculation process of the state equation, and the stage S2 represents the calculation process of the observation equation; to provide better stability and higher accuracy of the estimation process, an unscented transformation is introduced into the SOC estimationEquation of state, without having to function on a nonlinear equation of statefFunctions of equation of origin and observationgAnd (9) performing Jacobian matrix calculation and linearization processing.
1): using unscented transformation to find out sampling points, setting the dimension of a state variable x as n,
and P are their mean and covariance matrices, respectively, and y is the observed variable. Assuming in a non-linear system
2n +1 sampling points are obtained as shown in the following formula.
The corresponding weight is shown as the following formula.
Wherein beta is more than or equal to 0, and is generally 2. Alpha is more than or equal to 0 and less than or equal to 1, kappa is an auxiliary scale factor, and lambda is a scaling parameter. The following relationship is generally satisfied: k =3-n, and (c) is,
. The sampling point is used to transmit the original state backwards as shown in the following formula.
2): the expected values of the system state variables at time k +1 are as follows.
Sample points obtained using an unscented transformation, where i =1,2,3 … 2n + 1. Where uk is the input variable. And (4) carrying out one-step prediction on the sampling point by combining the upper formula.
The error variance matrix at time k +1 is also predicted as follows.
Substituting the state quantity predicted value point set at the moment k +1 into an observation equation, obtaining an observation predicted value at the moment k +1 by using the observation equation, and carrying out state transmission once in the observation equation; and then weighting to obtain the average value of the measured quantity at the k +1 moment.
The variance matrix of the measurements at time k +1 is calculated.
The covariance of the state quantity and the measured quantity at the time k +1 is calculated.
3): and calculating Kalman filtering gain.
Updating the value of the system state variable:
and updating the error variance matrix.
In the estimation process of the lithium ion battery pack SOC, the iteration process is as shown in FIG. 2, and the optimal estimation SOC value of the system state variable is obtained by iteration through the above series of formulas. The method is based on a Kalman algorithm framework to realize an iterative computation process; solving the problem of nonlinear conversion of the mean and variance of SOC estimation by using the unscented transformation in the one-step prediction calculation process of SOC estimation; through the iterative computation process and based on the unscented Kalman algorithm, the construction of the SOC estimation model of the lithium ion battery pack is realized.
In summary, the invention provides an unscented kalman-based lithium ion battery pack SOC estimation method 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, and combining the establishment of an SOC estimation model on the basis of fully considering the grouping work of the lithium ion batteries to realize the iterative calculation of the SOC estimation of the lithium ion battery pack and provide a basis for the real-time monitoring of the SOC estimation and the working state of the lithium ion battery pack.
The above embodiments of the present invention have been described only with respect to the lithium ion battery pack as an example, but it is to be understood that those skilled in the art may make any changes and variations thereto without departing from the spirit and scope of the present invention.
Claims (4)
1. A lithium ion battery SOC estimation method based on a Thevenin equivalent circuit model and unscented Kalman is characterized in that an unscented Kalman method is provided, effective iterative computation of an unscented Kalman filter algorithm on a lithium ion battery pack SOC value is achieved through the Thevenin equivalent model, and the problem of function nonlinear function is solved through unscented transformation.
2. The SOC estimation method based on Thevenin equivalent circuit model and unscented Kalman according to claim 1, characterized in that by approximating the probability density distribution of the nonlinear function in unscented Kalman filtering algorithm, the derivation of Jacobian matrix is not required, reducing the computational complexity; high-order terms are not ignored, the calculation precision of nonlinear distribution is higher, the effective iterative calculation of the SOC value of the lithium ion battery pack is realized, and the accumulated errors existing in the initial value error and ampere-hour integral of the SOC are overcome.
3. The Thevenin equivalent circuit model and unscented Kalman SOC estimation method according to claim 1, characterized in that the Thevenin equivalent circuit model makes up for the disadvantage that the internal resistance model cannot represent the dynamic characteristics of the lithium battery to a certain extent, and adds RC return to represent the polarization effect inside the battery, thereby having better representation effect on the battery.
4. The square root extended Kalman SOC estimation method of claim 1, characterized in that the method is based on Thevenin equivalent model circuit and unscented Kalman based iterative computation process on the basis of fully considering the grouping work of lithium ion batteries, to realize the establishment of SOC estimation model of lithium ion battery pack and the reliable operation of SOC value mathematical iterative algorithm.
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