CN108872865B - Lithium battery SOC estimation method for preventing filtering divergence - Google Patents
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Abstract
The invention discloses a lithium battery SOC estimation method for preventing filtering divergence, which relates to the technical field of state estimation of lithium batteries of electric vehicles and mainly comprises the following steps: acquiring an initial value of the SOC of the lithium battery by an open-circuit voltage method; II, considering the influence of system noise and observation noise, and estimating a real-time SOC value by using an improved Sage-Husa adaptive extended Kalman filtering method; and III, performing filtering divergence judgment on the previous step by using a filtering divergence criterion, and constructing an index freezing factor in the Kalman gain matrix to prevent filtering divergence when the criterion condition is not met. According to the invention, a noise estimator is added on the basis of the extended Kalman filtering algorithm, so that the estimation precision of the SOC is ensured, and the stability of system estimation is improved for preventing filtering divergence under severe working conditions.
Description
Technical Field
The invention relates to the technical field of state estimation of lithium batteries of electric vehicles, in particular to a lithium battery SOC estimation method for preventing filtering divergence.
Background
The state of charge (SOC) of the power battery is a link between a driver and the pure electric vehicle, and the driver knows the remaining mileage of the driven electric vehicle and whether charging is needed or not through the parameter. The SOC value is an important parameter in a battery management system of the pure electric vehicle, and is mainly embodied in the following aspects: (1) as a source for visually judging the residual energy of the vehicle by the driver. The driver usually intuitively judges the remaining mileage of the electric vehicle through the SOC value and comprehensively judges the running control and the like of the whole vehicle. (2) And reference is made to the whole vehicle control strategy. The whole vehicle control strategy refers to the SOC value of the battery, and the driving strategy of the whole vehicle is controlled according to the SOC value. (3) And protecting the power battery.
According to the statistical data of the China automobile technical center on the road working conditions in the Taiyuan city, the vehicles need to frequently start, accelerate, decelerate and stop, and the driving working conditions are complex. Complicated and variable running conditions easily cause large system noise, and the change of the ambient temperature can cause the change of internal parameters of the battery, so that filtering divergence can occur. Therefore, improving the estimation accuracy of the SOC of the battery and preventing the filter divergence are important research subjects.
Research on the SOC estimation method is very common with high heat of new energy vehicles, and currently, an ampere-hour integration method, an open-circuit voltage method, various adaptive algorithms based on a kalman filter method, a neural network model method, and the like are widely used. Integration of ampere-hour at initial state of charge SOC0In the case of accuracy, it has a fairly good accuracy over a period of time; however, the major disadvantages of the ampere-hour integration method are: charge estimation accuracy initiated SOC0The influence is large; coulomb efficiency η1Is greatly influenced by the working state of the battery (such as the charge state, the temperature, the current magnitude and the like), eta1Difficult to measure accurately; the current measurement accuracy error can generate an accumulative effect, and the accumulative error can be gradually increased along with time. The open circuit voltage method has a small capability of distinguishing SOC variations caused by small voltage variations, and the voltage rebound after the battery is left for a certain period of time causes a large estimation error. The self-adaptive algorithm can continuously detect and judge by means of various set index parameters in the working process of the system, and changes operation steps or parameters according to the change of measured parameters, so that the system is in a good and stable working state. Therefore, the method has better application prospect. The neural network method has strong self-learning capability, and has better capability of processing highly nonlinear system problems due to the adoption of a parallel processing structure; the method has the disadvantages that a large amount of screening experiment measurement data is needed to be used as initial data for neural network training, the training time is long, and the method has no transportability to different types of batteries.
Disclosure of Invention
The embodiment of the invention provides a control method for improving the SOC estimation precision of a lithium battery and preventing filtering divergence. The method is based on the extended Kalman filtering algorithm, a system noise estimator is added, after estimation at the moment K is completed, whether the system noise estimator diverges or not is judged through a filtering divergence criterion, and if the system noise estimator diverges, adaptive adjustment is carried out, so that the stability of the system is improved.
The invention provides a lithium battery SOC estimation method for preventing filtering divergence, which is characterized by comprising the following steps of:
obtaining an initial SOC value by using an open-circuit voltage method;
establishing a state space expression of an equivalent second-order RC network model of the battery, performing discrete linearization on the expression, and establishing a state space equation of the battery according to an SOC initial value;
performing iterative computation on state variables in the state space equation, and extracting a real-time SOC value from an iterative computation result;
and (4) carrying out filtering divergence judgment on the iteration result obtained in the step (a), and if filtering divergence occurs, constructing an index freezing factor in the Kalman filtering gain matrix to prevent filtering divergence.
The invention provides a lithium battery SOC estimation method for preventing filtering divergence, which mainly comprises the following steps: acquiring an initial value of the SOC of the lithium battery by an open-circuit voltage method; II, considering the influence of system noise and observation noise, and estimating a real-time SOC value by using an improved Sage-Husa adaptive extended Kalman filtering method; and III, performing filtering divergence judgment on the previous step by using a filtering divergence criterion, and constructing an index freezing factor in the Kalman gain matrix to prevent filtering divergence when the criterion condition is not met. According to the invention, a noise estimator is added on the basis of the extended Kalman filtering algorithm, so that the estimation precision of the SOC is ensured, and the stability of system estimation is improved for preventing filtering divergence under severe working conditions.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic structural diagram of a battery equivalent second-order RC network.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a lithium battery SOC estimation method for preventing filtering divergence, which comprises the following steps:
firstly, an open-circuit voltage method is used or the SOC of the battery at the last time is read to obtain an initial SOC value, the open-circuit voltage method is used for charging the battery, large current is firstly used, then trickle charging is carried out, the battery stops when the battery reaches a cut-off charging voltage, then the lithium battery is placed for 90-120min, and after the internal balance of the lithium battery is achieved, discharging experiments are carried out by currents of 0.5C, 1C, 2C and 3C respectively.
Second, assume that the state variable at time k is Xk∈Rn×1The input vector is Uk∈Rp×1The output vector is Yk∈Rq×1Then, there are:
Xk+1＝f(Xk,Uk)+Wk
Yk＝g(Xk,Uk)+Vk
wherein, WkIs system noise, VkTo measure noise.
Combining a non-linear function f (X)k,Uk) And g (X)k,Uk) At the predicted value
And performing Taylor series expansion, and omitting terms above high order to obtain the following state space equation:
let a step shift matrix
M x n order measuring matrix at k time
Comprises the following steps:
and then ordering:
E[Wk]＝qk，E[Vk]＝rk，cov[Wk,Wi]＝Qk ki，cov[Vk,Vi]＝Rk ki
where E is the mean symbol, cov is the covariance number,kias a function of Kronecker, QkIs the system noise covariance, RkTo measure the noise covariance.
Finally, the following is obtained:
now, a state space expression of a battery equivalent second-order RC network model shown in FIG. 1 is established:
U0＝Uocv-IR0-Up1-Up2
according to the expression, a state space equation is established after discrete linearization is carried out:
the observation equation is: u shapeo,k＝Uocv,k-Up1,k-Up2,k-R0Ik
Wherein, UocvRepresenting the ideal open circuit voltage, U0Representing the actual operating voltage of the battery, I representing the operating current of the battery, R0Represents the internal resistance of the battery, Rp1、Cp1Respectively representing the short-time polarization resistance and polarization capacitance, Rp2、Cp2Respectively representing long-time polarization resistance and polarization capacitance, SOCkIs the state of charge of the battery at time k, Up1,kAnd Up2,kRespectively a capacitance C at time kp1And Cp2The voltage on, eta represents the coulombic efficiency, T is the system sampling time, CNIs the rated capacity of the battery, tau1＝Rp1Cp1，τ2＝Rp2Cp2Current ikFor system input at time k, Uo,kFor the output of the system at the time k,
namely, it is
Three, pair state estimation matrix
State estimation mean square error matrix PkEstimating a model noise matrix
Estimating model noise update matrix
Measure noise covariance matrix
Measured noise covariance update matrix
Giving an initial value, namely a value at the moment when k is 0, then respectively carrying out iterative calculation according to the following formula, and obtaining the value after the iterative calculation
According to
To obtain Xk+1Extracting matrix Xk+1Get SOC from the first data ink+1And summarizing to obtain the real-time SOC.
Wherein,
and
collectively referred to as a noise covariance estimator, dkIs a weighting coefficient, and dk＝(1-b)/(1-bk+1) B is a forgetting factor, and the value range is 0.95<b<1，vkIs an innovation matrix reflecting the degree of inconsistency between the predicted value and the actual value, an
Zk＝HkXk+Vk，HkIs a m x n order measurement matrix at time k, an
XkIs a state variable at time k, VkIn order to measure the noise, the noise is measured,
predict a matrix for the one-step state, an
Pk/k-1The mean square error matrix is predicted for one step, an
KkIs a Kalman filter gain matrix, an
In this embodiment, the initial value assignment condition is:
P0＝10000*eye(3)
fourthly, performing filtering divergence judgment on the SOC iteration result at the k moment obtained by calculation in the third step, wherein the criterion of the filtering divergence is as follows:
vkvk T＜γtr[E(vkvk T)]
wherein gamma is a reserve coefficient, the value is more than 1, tr represents the trace of the matrix, vkvk TThe covariance matrix E (v) is the sum of squares of an innovation matrix, which contains information of the actual estimation errorkvk T)＝HkPk/k-1Hk T+Rk。
When the reserve coefficient γ is 1, the most stringent convergence condition at this time is:
vkvk T＜tr[E(vkvk T)]
if the above formula is not satisfied, it indicates that the actual error exceeds the theoretical value, i.e. the filtering is divergent, and it can be used to determine whether the state variable estimation has an excessive deviation according to the special attribute of the innovation matrix.
For the specific case of error, the kalman gain needs to be adaptively changed:
if the error is within the required range, the k +1 moment calculation is continued without changing any calculated k moment iteration value;
the estimation error is continuously increased, but the estimation value is smaller than the actual value, and an exponential freezing factor is introduced into a Kalman filtering gain matrix
1＜λ1< 1.1, the Kalman filter gain matrix at this time is expressed as:
the estimation error is continuously increased, the estimation value is larger than the actual value, and an exponential freezing factor is introduced into a Kalman filtering gain matrix
0.9＜λ2< 1, the Kalman filter gain matrix at this time is represented as:
as will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (2)
1. A lithium battery SOC estimation method for preventing filtering divergence is characterized by comprising the following steps:
obtaining an initial SOC value by using an open-circuit voltage method;
establishing a state space expression of an equivalent second-order RC network model of the battery, performing discrete linearization on the expression, and establishing a state space equation of the battery according to an SOC initial value;
performing iterative computation on state variables in the state space equation, and extracting a real-time SOC value from an iterative computation result;
carrying out filtering divergence judgment on the iteration result obtained in the step, and if filtering divergence occurs, constructing an index freezing factor in a Kalman filtering gain matrix to prevent filtering divergence;
wherein, the established state space equation is as follows:
therein, SOCkIs the state of charge of the battery at time k, Up1,kAnd Up2,kRespectively a capacitance C at time kp1And Cp2Voltage of Rp1、Cp1Respectively representing the short-time polarization resistance and polarization capacitance, Rp2、Cp2Respectively representing long-time polarization resistance and polarization capacitance, eta represents coulombic efficiency, T is system sampling time, CNIs the rated capacity of the battery, tau1＝Rp1Cp1，τ2＝Rp2Cp2Current ikInputting a system at the moment k;
order to
The state space equation is therefore simplified to:
then according to
Obtaining the state variable X at the moment of k +1k+1Wherein W iskIs the system noise;
performing iterative computation on state variables in the state space equation, and extracting a real-time SOC value from an iterative computation result specifically comprises:
the iterative calculation is performed according to the following formula:
wherein, PkThe state estimation mean square error matrix is used,
in order to estimate the model noise update matrix,
for measuring the noise covariance matrix，
To estimate the model noise matrix, dkIs a weighting coefficient, and dk＝(1-b)/(1-bk+1) B is a forgetting factor, and the value range is 0.95<b<1，vkIs an innovation matrix reflecting the degree of inconsistency between the predicted value and the actual value, an
Zk＝HkXk+Vk，HkM X n order measurement matrix for time k, XkIs a state variable at time k, VkIn order to measure the noise, the noise is measured,
predict a matrix for the one-step state, an
Pk/k-1The mean square error matrix is predicted for one step, an
KkIs a Kalman filter gain matrix, an
According to
And the state variable X at the moment of k +1 is obtained by iterative calculation of the formulak+1Extracting Xk+1Obtaining the state of charge SOC of the battery at the moment k +1k+1Summarizing to obtain a real-time SOC value;
and (3) carrying out filtering divergence judgment according to the following formula:
vkvk T＜tr[E(vkvk T)]
where tr denotes the trace of the matrix, vkvk TThe covariance matrix E (v) is the sum of squares of an innovation matrix, which contains information of the actual estimation errorkvk T)＝HkPk/k-1Hk T+RkWherein R iskTo measure the noise covariance;
if the formula is not satisfied, the actual error exceeds the theoretical value, namely the filtering is divergent;
when filtering divergence occurs, the Kalman gain is adaptively changed according to the following conditions:
if the error is within the required range, the k +1 moment calculation is continued without changing any calculated k moment iteration value;
the estimation error is continuously increased, but the estimation value is smaller than the actual value, and an exponential freezing factor is introduced into a Kalman filtering gain matrix
1＜λ1< 1.1, the Kalman filter gain matrix at this time is expressed as:
the estimation error is continuously increased, the estimation value is larger than the actual value, and an exponential freezing factor is introduced into a Kalman filtering gain matrix
0.9＜λ2< 1, the Kalman filter gain matrix at this time is represented as:
2. the method for estimating the SOC of the lithium battery as claimed in claim 1, wherein the open-circuit voltage method comprises charging the battery, charging the battery with a large current and then charging the battery with a small current, stopping the charging until the battery reaches a cut-off charging voltage, standing the lithium battery for 90-120min, and performing a discharging experiment with currents of 0.5C, 1C, 2C and 3C after the internal balance of the lithium battery.
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