CN111220920B - Retired lithium ion battery state of charge calculation method based on H-infinity unscented Kalman filtering algorithm - Google Patents
Retired lithium ion battery state of charge calculation method based on H-infinity unscented Kalman filtering algorithm Download PDFInfo
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Abstract
The invention relates to a retired lithium ion battery state of charge calculation method based on an H-infinity control theory. The invention ensures the semi-positive quality of the matrix by continuously updating and correcting the covariance matrix, improves the adaptability of the filter, and realizes the accurate estimation of the charge state of the retired battery.
Description
Technical Field
The disclosure relates to the technical field of batteries, in particular to a retired lithium ion battery state of charge calculation method based on an H-infinity unscented Kalman filtering algorithm.
Background
Lithium ion batteries are widely used in various electric vehicles due to their high specific energy, long cycle life, and relatively low manufacturing costs. When the capacity of the power battery for the vehicle is attenuated to about 70% of the initial capacity, the power battery for the vehicle is retired without meeting the requirements of the endurance mileage and the safety performance of the electric vehicle. The retired battery still has considerable value in the fields of energy storage systems, UPS and the like with low requirements on battery performance. Because of the aging phenomenon of the retired battery in power density, energy density, capacity and the like to a certain extent, an accurate battery management system must be established to judge the working state of the battery. The state of charge (SOC) of the battery characterizes the change of the remaining energy of the battery, and is an important basis for energy management and prediction of the battery operation state. Therefore, accurate estimation of the state of charge of the battery is of great significance to the echelon utilization of retired batteries and improvement of battery management techniques.
The invention patent with the patent application number of CN201310500406.1 discloses an automobile power lithium battery SOC estimation method, which comprises the following steps: a. starting; b. c, entering a step c, wherein the rest time is smaller than the set time T0; otherwise, enter step d; c. using the SOC value when the last lithium battery stops being used as the SOC value at the moment; d. acquiring a real-time power lithium battery SOC value by utilizing the relation between the open-circuit voltage and the SOC, and entering a step g; e. f, the lithium battery is dynamic, and the step f is carried out; otherwise, returning to the step b; f. estimating the SOC by adopting an Ah integration method, and carrying out preliminary correction; g. d, judging the difference value between the SOC value obtained in the step d and the SOC value estimated by the Ah integration method, and if the difference value is smaller than a set value |e|, entering the step i; otherwise, entering a step h; h. the obtained SOC value corrects the initial SOC value of the Ah integration method; i. and (5) ending. The invention corrects the SOC from multiple aspects, improves the error accumulation brought by the Ah integration method for a long time, and can improve the accuracy of the SOC.
However, this technique is only modified based on the existing Ah integration method, that is, the ampere-hour integration method, but there is a requirement that an accurate initial state of charge is necessary to be provided, and the open circuit voltage method needs to stand for a sufficient time to allow the battery to reach a stable state, which is obviously not suitable for dynamic conditions.
Disclosure of Invention
In order to overcome the defects of the prior art, the present disclosure relates to a method for calculating the state of charge of a retired lithium ion battery based on an H-infinity unscented Kalman filtering algorithm, which improves the accuracy of calculating the state of charge of the retired battery and reduces the detection steps required during calculation.
In order to achieve the above object, the present disclosure is achieved by the following technical solutions:
according to the retired lithium ion battery state of charge calculation method based on the H-infinity unscented Kalman filtering algorithm, firstly, a lithium ion equivalent circuit model is established, model verification is carried out after parameters are identified, the verified model is passed through a standard unscented Kalman filtering algorithm, an H-infinity filter is designed by introducing an adjustment factor based on the H-infinity control theory, and the H-infinity filter is used for correcting a disease state matrix encountered when covariance is calculated in the unscented Kalman filtering algorithm.
Preferably, the filter is:
wherein: x0 and p0|0 are the initial state vector and covariance matrix, respectively; gamma is a positive scalar parameter that limits uncertainty.
Preferably, the estimated error covariance matrix pk|k satisfies if and only if all the time instants K
In the time-course of which the first and second contact surfaces,
the H-infinity filter can exist, and the H-infinity unscented Kalman filter is as follows:
wherein: i is an identity matrix; hk is no longer a jacobian matrix, hk= (Pzz, k|k-1) T (pk|k-1) -1.
Since Pk|k is a positive definite matrix, combine simultaneously
The available parameter γ should satisfy:
wherein: max {. Cndot. } is the maximum function; eig {.cndot }, is a function of the eigenvalues of the matrix.
Preferably, the method for establishing the lithium ion equivalent circuit model comprises the following steps: establishing a first-order RC equivalent circuit:
wherein the state of charge is defined as:
wherein SOCt represents the state of charge at time t; η is coulombic efficiency; QN is the rated capacity of the battery;
the state of charge equation can be described as a discrete-time form:
according to the RC equivalent circuit model of the retired battery, the state of charge (SOC) and the polarization voltage (Us) of the battery are selected as system state variables, and finally, the state space equation of the battery is obtained as follows:
the observation equation is as follows: u (U) out (k)＝U ocv (SOC(k))-U s (k)-R 0 I t (k)
Wherein T is sampling time; k is a discrete time variable.
Preferably, the method for calculating the charge state of the retired lithium ion battery based on the H-infinity unscented Kalman filtering algorithm comprises the following steps of
Step 1: the state of the system is initialized and,
step 2: sigma point acquisition, firstly, for state quantity at k moment
Transforming and then calculating to obtain +.>
P k|k-1 。
Step 3 vs step 2
Carrying out unscented Kalman filtering transformation again, and carrying out measurement updating by combining an observation equation;
step 4P zz,k|k-1 And P xz,k|k-1 Substituting the H-infinity unscented Kalman filter to obtain a Kalman gain Kk at the moment k;
step 5, calculating an adjustment factor gamma;
step 6, performing state update and covariance update according to Kk at time k and the measured voltage value yk of the battery to obtain time k+1
And pk|k;
step 7: the state estimate is saved.
Preferably, the method for initializing the system state in the step 1 is as follows: let the initial state variable be x 0 The mean value of the state variables is
Initial covariance P 0 . Then there are:
preferably, the Sigma spot acquisition in step 2 is specifically:
calculating sigma point sampling points x (i) and corresponding weights omega:
wherein: x is the mean value; p is covariance. The corresponding weight is
Wherein: m is the mean weight; c is covariance weight; the parameter λ=α2 (n+ki) -n is a scaling factor used to reduce the total prediction error. In general, the alpha value is smaller, and is more than or equal to 0 and less than or equal to 1, so as to control the sigma point weight at the average value; beta=2, which is used to control the error of the state estimation, improving the estimation accuracy.
The invention also comprises a lithium battery experiment platform for detecting the retired lithium ion battery state of charge calculation method based on the H-infinity unscented Kalman filtering algorithm, which consists of an AC power supply, a computer host, a battery tester and a programmable room for placing batteries.
Preferably, the battery is subjected to charge and discharge experiments under the experimental platform by taking the urban road circulation working condition formulated in the United states as the experimental condition. The ambient temperature for the battery test was set at 23 ℃ and the initial value of battery SOC was set at 0.7.
By the present disclosure, a method is provided that utilizes H-infinity theory to improve robustness to outliers and non-Gaussian noise. The particle filtering algorithm is introduced into the unscented Kalman filter, and the estimated value and covariance of each particle are calculated through the unscented Kalman filter algorithm, so that the problem of noise interference of system sampling is solved. The singular value decomposition is used for replacing Cholesky decomposition of the standard unscented Kalman filtering, so that the calculation termination of a covariance matrix non-positive timing filtering algorithm is avoided, and the nonlinear error in the system sampling process is restrained. The correction covariance matrix is updated continuously, so that the semi-positive quality of the matrix is guaranteed, the adaptability of the filter is improved, and the accurate estimation of the charge state of the retired battery is realized.
Meanwhile, the invention also provides a lithium battery experimental platform for verifying the accuracy of the calculation result.
Drawings
In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present disclosure, and other drawings may be obtained according to these drawings without inventive effort to a person of ordinary skill in the art.
Fig. 1 is an equivalent circuit topology of a retired battery.
FIG. 2 is a specific flowchart of the H-infinity based unscented Kalman filtering algorithm of the present disclosure.
Fig. 3 is a schematic structural diagram of the experimental platform.
FIG. 4 is a state of charge estimation contrast curve based on H-infinity and unscented Kalman filtering algorithms.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present disclosure more apparent, the technical solutions of the embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure, and it is apparent that the described embodiments are some embodiments of the present disclosure, but not all embodiments. Based on the embodiments in this disclosure, all other embodiments that a person of ordinary skill in the art would obtain without making any inventive effort are within the scope of protection of this disclosure.
Common charge state estimation methods in the prior art comprise an ampere-hour integration method, an open-circuit voltage method, a neural network intelligent algorithm and an extended Kalman filtering algorithm. The problems with the ampere-hour integration method are mentioned in the background. The neural network intelligent algorithm requires a large amount of experimental data sets to train the neural network model, and the actual estimation effect is poor. The Kalman filtering method based on the battery state space equation has strong applicability and universality, and solves the problem that the initial value of the battery state of charge and a large number of experimental data points are required to be trained. Meanwhile, the filtering technology can remarkably reduce the influence of sampling noise. The extended kalman filter algorithm ignores the taylor expansion higher order term, and the strong nonlinear characteristic of the lithium ion battery inevitably brings large estimation error, so that the filter diverges. In recent years, the unscented kalman filter algorithm is active in the field of battery state of charge estimation, but in practical applications, the following problems exist: the influence of noise can be reduced to a certain extent, but abnormal measurement noise still has a larger influence on the filtering effect; sampling data outside of the normal range during one or more sampling periods will cause the state of charge estimation algorithm to be subject to errors and convergence speed to decrease due to external factors. The technical scheme disclosed by the invention has the advantages that the problems are completely overcome, firstly, a lithium ion equivalent circuit model is established, the model verification is carried out after parameters are identified, the verified model is subjected to a standard unscented Kalman filtering algorithm, and an H-infinity filter is designed by introducing an adjustment factor based on an H-infinity control theory and is used for correcting a disease state matrix encountered when covariance is calculated in the unscented Kalman filtering algorithm.
1. Establishing a lithium ion equivalent circuit model:
common battery models include electrochemical models, neural network models, and integrated parameter equivalent circuit models. Among the three models, the equivalent circuit model has simple structure, is easy to identify parameters, and can betterReflecting the dynamic and static characteristics of the battery is widely used. The lumped parameter equivalent circuit model comprises a Rint model, a first order RC model, a high order RC model, a PNGV model and the like. The invention selects a first-order RC equivalent circuit to establish a state space model of the retired battery. The circuit structure of the model is shown in figure 1, R 0 Is the ohmic resistance of the retired battery, wherein the resistance R 0,chg Represents the discharge ohmic resistance, resistance R 0,dischg Representing the charging ohmic resistance. R is R s And C s Respectively representing the polarization resistance and the polarization capacitance of the battery; i t Representing the end current of the battery; u (U) ocv An open circuit voltage (open circuit voltage, OCV) representative of the battery as a function of the battery SOC; u (U) out Representing the output voltage of the battery. State of charge
According to the circuit principle, the first-order RC equivalent circuit can be expressed as:
mathematically, a common definition of state of charge can be expressed as:
wherein SOC is t Representing the state of charge at time t; η is coulombic efficiency, and is related to discharge speed, temperature, etc.; q (Q) N Is the rated capacity of the battery.
The state of charge equation can be described as a discrete-time form:
selecting a battery charge state SOC and a polarization voltage U according to an RC equivalent circuit model of the retired battery s As a system state variable. The state space equation of the battery is:
U out (k)＝U ocv (SOC(k))-U s (k)-R 0 I t (k) (5)
wherein T is sampling time; k is a discrete time variable.
2. And (3) parameter identification:
the common parameter identification algorithm mainly comprises a least square method, a prediction error method, a maximum likelihood estimation method and the like. The least square method is a data optimization tool, and the best matching of functions is realized by taking the sum of squares of residual errors as a criterion. It is widely used in various numerical analysis scenarios. For strong nonlinear systems such as retired batteries, a least squares method may be employed to identify model parameters. HPPC is a test environment for testing battery charge-discharge characteristics, and also serves as a data source for battery parameter identification.
When the battery is loaded with current, the battery voltage drops due to the ohmic internal resistance. When the battery current is unloaded, the polarization capacitor discharges, so that the battery voltage is slowly raised. The process of performing the charge and discharge test on the battery is divided into 10 stages. And processing experimental data by utilizing MATLAB software, and identifying battery model parameters of each stage of the state of charge by a least square method.
The ohmic internal resistance of the battery can be calculated from the change of the instantaneous voltage of the current loading of the battery. If U is 1 ＝3.973V，U 2 =3.843v, i=1.2a, then R is obtained s =0.108Ω. Wherein U is 1 Represents the terminal voltage at 90% of the battery charge and at steady state. U (U) 2 The terminal voltage of the battery at the moment of pulse discharge current loading is shown, and the current I is a continuous constant current of 0.2C.
During discharge of the polarized capacitor of the battery, the voltage output equation is as follows:
u in the above ocv 、I t R s 、τ s Regarding as undetermined coefficients, coefficient substitution for the equation is available:
U out ＝f+ae -bt (7)
comparing the two formulas to obtain:
U ocv ＝f (8)
R s ＝a/I t (9)
C s ＝1/(R s b) (10)
equations (8) - (10) are calculation formulas for battery model parameter identification, and then the battery parameters for each state of charge stage are fitted by a nonlinear least square method.
Parameters such as resistance and capacitance in the model are affected by the change of the battery electric quantity. Equations (11) - (13) are functional relationships between the established SOC and model parameters.
Model verification:
equivalent circuit model verification of retired power battery adopts dynamic pressure test (dynamic stress test, DST) working condition, which is a specific current battery working test scheme based on real vehicle operation data, and dynamic and static performance of the battery can be checked.
According to the principle of a standard unscented Kalman filtering algorithm, according to the state at the current moment and the predicted value at the last moment, a battery state equation (4) and an observation equation (5) are combined to obtain the state estimated value at the current moment. The discrete state space equation for retired lithium ion batteries can be described as follows:
wherein: x is x k ，y k A state vector and an observation vector representing the time of the system k; f and h are a state function and an observation function of the system respectively; w (w) k Representing process noise caused by model parameter errors, covariance Q k ；v k Representing measurement noise caused by inaccurate sampling of a system sensor, with covariance R k 。
The unscented kalman filter algorithm is mainly composed of four parts: system variable initialization, sigma point acquisition, time update, and measurement update. Unscented Kalman filtering algorithm utilizes unscented transforms to process the prediction mean and error covariance of nonlinear functions [15] Instead of the approximate equivalent of the extended Kalman filtering algorithm, derivative calculation of the jacobian matrix is not needed, so that estimation accuracy and calculation speed are improved.
1. Initialization of
Let the initial state variable be x 0 The mean value of the state variables is
Initial covariance P 0 . Then there are:
2. sigma Point acquisition
Calculating sigma point sampling point x (i) And the corresponding weights ω:
wherein:
is the mean value; p is covariance. The corresponding weight is
Wherein: m is the mean weight; c is covariance weight; parameter λ=α 2 (n+ki) -n is a scaling factor used to reduce the total prediction error. In general, alpha has smaller value, and alpha is more than or equal to 0 and less than or equal to 1 and is used for controlling the sigma point weight at the average value. Beta=2, which is used to control the error of the state estimation, improving the estimation accuracy.
3. Time update
One-step prediction for computing sigma point sets
Calculating a predictive estimate
Calculating a predicted covariance
4. Measurement update
Nonlinear transformation sigma point
Calculating predicted measurements
Predicting innovation covariance
Prediction cross covariance matrix
Calculating Kalman gain
K k ＝P xz,k|k-1 P zz,k|k-1 -1 (26)
System status update
Updating error covariance
In engineering application, unscented Kalman filtering algorithm is easily affected by factors such as abnormal sampling, uncertain initial value, inability of Cholesky to decompose non-semi-positive definite matrix, and the like, resulting in system divergence. To overcome the ill-condition matrix encountered by the unscented Kalman filtering method in calculating covariance, H is calculated ∞ Theory is applied to extended kalman filtering to describe the impact of system uncertainty. The filter achieves a minimum estimation error for all possible disturbances with a bounded energy [18] . The designed filter satisfies the following conditions:
wherein: x is x 0 And P 0|0 The initial state vector and the covariance matrix thereof respectively; gamma is a positive scalar parameter that limits uncertainty.
At the same time andonly when all moments K are estimated error covariance matrix P k|k When the formula (30) is satisfied, H represented by the formula (29) is present ∞ Filter
H ∞ Unscented kalman filtering is as follows:
wherein: i is an identity matrix; h k Not being a jacobian matrix anymore, H k ＝(P zz,k|k-1 ) T (P k|k-1 ) -1 。
Due to P k|k Is a positive definite matrix, and the parameters y obtained in combination with formula (30) should satisfy:
wherein: max {. Cndot. } is the maximum function; eig {.cndot }, is a function of the eigenvalues of the matrix.
From the above, the principle and structure of the H-infinity based unscented Kalman filter is similar to that of the standard unscented Kalman filter. Updating and correcting diseases encountered when covariance is calculated in unscented Kalman filtering by introducing adjustment factor gamma based on H-infinity unscented Kalman filteringThe state matrix, thereby ensuring a non-negative qualification of the estimation error covariance matrix. The adjustment factor gamma is used to balance H ∞ Robust control and minimum mean square error performance. When gamma tends to infinity, the H-infinity based unscented Kalman filter is approximately equivalent to the standard unscented Kalman filter. This also illustrates H of standard unscented Kalman filtering ∞ The norms can be very large, resulting in poor stability of the uncertainty of the model parameters. The minimum estimation error of all possible interferences is realized based on H-infinity unscented Kalman filtering.
H-infinity-based unscented Kalman filtering algorithm specific flow
Substituting the battery state equation (4) and the observation equation (5) into the standard unscented Kalman filtering algorithm formula to obtain the battery state of charge and the polarization voltage U s Real-time predicted values of the parameters. As shown in fig. 2, the algorithm specifically includes the following steps:
Step 2 the state quantity at time k is first calculated according to equations (17) and (18)
Performing unscented transformation, and substituting the formula (19) - (21) with the state equation of formula (4) to obtain +.>
P k|k-1 。
Step 3 vs step 2
Performing unscented transformation again, and substituting the observation equation of formula (5) into formulas (22) - (25) to obtain +.>
P zz,k|k-1 And P xz,k|k-1 。
Step 4P zz,k|k-1 And P xz,k|k-1 Substituting formula (31) to obtain Kalman gain Kk at k time.
Step 5, calculating an adjustment factor gamma.
Step 6, performing state update and covariance update according to Kk at time k and the measured voltage value yk of the battery to obtain time k+1
And pk|k.
Step 7: the state of charge estimate is saved.
As shown in fig. 3, is composed of an AC power source, a computer host, a battery tester, and a programmable room for placing a battery. And (3) taking the working condition of urban road circulation (Urban Dynamometer Driving Schedule, UDDS) formulated in the United states as a test condition, and carrying out a charge and discharge experiment on the battery under the test platform. The ambient temperature for the battery test was set at 23 ℃ and the initial state of charge of the battery was set at 0.7. The state of charge estimation versus curves based on the H-infinity and unscented Kalman filtering algorithms are shown in FIG. 4. Under the condition of setting an initial value (0.5) of the state of charge error, the H-infinity-based unscented Kalman filtering algorithm provided by the invention has a higher convergence rate than the unscented Kalman filtering algorithm. The unscented Kalman filter algorithm based on H-infinity can converge to a stable phase at about 100s, whereas the unscented Kalman filter algorithm requires about 70 s. This is because the unscented kalman filter weights and the distribution of sampling points lead to a covariance losing positive after several updates, resulting in invalid filtering results. When the filtering effect is optimal, the gain matrix remains stable. As the system model changes, it is difficult for the gain matrix to quickly keep up with the needs of the steady state system, which prevents the system from quickly converging. The H-infinity-based unscented Kalman filtering algorithm guarantees the semi-positive qualityof the matrix by continuously updating the modified covariance matrix, which enables the filtering algorithm to continue. The state of charge setting value can be quickly close to the real state when a larger error exists between the state of charge setting value and the real value at the beginning stage of the algorithm, so that the tracking speed is higher.
In addition, the tracking performance of the unscented Kalman filtering algorithm based on the H-infinity is obviously better than that of the unscented Kalman filtering algorithm. On the one hand, the absolute error estimated based on the H-infinity unscented Kalman filtering algorithm is maintained within 0.05, while the absolute error of the unscented Kalman filtering algorithm is greater than 0.05; on the other hand, the unscented Kalman filtering algorithm has poor robustness to non-Gaussian noise and system outliers, curve fluctuation is large in a convergence stage, the change trend of the battery charge state cannot be effectively predicted, and the H-infinity unscented Kalman filtering algorithm has strong adaptability to severe environments.
In conclusion, the H-infinity-based unscented Kalman filter algorithm provided by the invention has a certain improvement on convergence speed, estimation accuracy and robustness compared with unscented Kalman filter, and the effectiveness of the improved algorithm is verified.
The H-infinity control theory is an effective tool for solving the robustness problem. The invention is applied to the charge state calculation of the retired power battery. The influence of the abnormal value and non-Gaussian noise of the system sampling is overcome, the filtering algorithm is guaranteed to be continued, and the stability of the estimation algorithm when the system state is suddenly changed is improved. Experimental results show that under the condition of severe current working condition change, the H-infinity-based unscented Kalman filtering algorithm can still maintain higher filtering precision and robustness than unscented Kalman filtering.
In the actual working process, the invention is applicable to a plurality of scenes such as:
scene 1: in a photovoltaic energy storage system, an energy storage battery is used as an energy storage device of the whole energy storage system and is a key part of the whole photovoltaic energy storage system. Power and voltage fluctuations can be smoothed out with an energy storage battery. The invention is quite important to the prediction research of the state of charge of the energy storage battery, and the rest capacity is a key factor for improving the stability and reliability of the whole energy storage system and the electric energy quality. The state of charge estimation algorithm provided by the invention is applied to the state of charge estimation of the battery of the energy storage power station, so that the problem of overcharge and overdischarge of the battery is avoided. Reasonable charge and discharge control strategies can be constructed according to the change of the environment, so that the energy storage battery is reasonably utilized.
Scene 2: the battery management system collects, processes and stores important information in the running process of the battery pack in real time, exchanges information with external equipment such as a whole vehicle controller, and solves key problems of safety, usability, service life and the like in the lithium battery system. The algorithm provided by the invention is applied to a battery management system, provides an important theoretical basis for the battery management system, and prolongs the service life of the battery. For batteries with the same capacity, the electric vehicle can have higher endurance mileage. The high-precision state of charge estimation can improve the battery management level and enable the battery pack to exert the maximum efficiency.
It is noted that in the present invention, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above embodiments are merely for illustrating the technical solution of the present disclosure, and are not limiting thereof; although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present disclosure.
Claims (6)
1. The method for calculating the charge state of the retired lithium ion battery based on the H-infinity unscented Kalman filtering algorithm is characterized in that a lithium ion equivalent circuit model is firstly established, model verification is carried out after parameters are identified, and the verified model is subjected to a standard unscented Kalman filtering algorithm, and the method is characterized in that: an adjusting factor based on an H-infinity control theory is introduced to design an H-infinity filter for correcting a disease state matrix encountered when covariance is calculated in an unscented Kalman filtering algorithm; the H-infinity filter is:
wherein: x is x 0 And P 0|0 The initial state vector and the covariance matrix thereof respectively; gamma is a positive scalar parameter that limits uncertainty; if and only if the estimated error covariance matrix P of all the moments K k|k Satisfy the following requirements
In the time-course of which the first and second contact surfaces,
the H-infinity filter can exist, and the H-infinity unscented Kalman filter is as follows:
wherein: i is an identity matrix; h k Not being a jacobian matrix anymore, H k ＝(P zz,k|k-1 ) T (P k|k-1 )-1；
Due to P k|k Is a positive definite matrix, combined simultaneously
The available parameter γ should satisfy:
wherein: max {. Cndot. } is the maximum function; eig {.cndot } is a function of solving a matrix eigenvalue; the lithium ion equivalent circuit model building method comprises the following steps: establishing a first-order RC equivalent circuit:
wherein the state of charge is defined as:
wherein SOC is t Representing the state of charge at time t; η is coulombic efficiency; q (Q) N Is the rated capacity of the battery;
the state of charge equation can be described as a discrete-time form:
according to the RC equivalent circuit model of the retired battery, the state of charge (SOC) and the polarization voltage (Us) of the battery are selected as system state variables, and finally, the state space equation of the battery is obtained as follows:
the observation equation is as follows: u (U) out (k)＝U ocv (SOC(k))-U s (k)-R 0 I t (k)
Wherein T is sampling time; k is a discrete time variable;
x k : a state vector representing the time of the system k;
ω k : representing process noise caused by model parameter errors, covariance Q k ；
Q k -1 : representing covariance Q k Is the reciprocal of (2);
v k : representing measurement noise caused by inaccurate sampling of a system sensor, with covariance R k ；
H k ：H k ＝(P zz,k|k-1 ) T (P k|k-1 ) -1 Representing the product of the two matrices;
K k : calculating Kalman gain;
P k|k-1 : calculating a prediction covariance;
P xz,k|k-1 : representing a predictive cross covariance matrix;
P zz,k|k-1 : predicting a innovation covariance;
y k : an observation vector representing the time of the system k;
I t : representing the end current of the battery;
R s : representing the polarization resistance of the battery;
C s : representing battery polarization capacitance;
U ocv : indicating the open circuit voltage of the battery;
R 0 : representing the ohmic resistance of the retired battery.
2. The method for calculating the charge state of the retired lithium ion battery based on the H-infinity unscented Kalman filtering algorithm according to claim 1, wherein the method comprises the following steps of: the method comprises the following steps:
step 1: the state of the system is initialized and,
step 2: sigma point acquisition, firstly, for state quantity at k moment
Transforming and then calculating to obtain +.>
P k|k-1 ；
Step 3: for step 2
Carrying out unscented Kalman filtering transformation again, and carrying out measurement updating by combining an observation equation;
step 4: handle P zz,k|k-1 And P xz,k|k-1 Substituting into H-infinity filter to obtain Kalman gain K at K moment k ；
Step 5: calculating a positive scalar parameter gamma that limits uncertainty;
step 6: according to K at time K k And the measured voltage value y of the battery k Performing state update and covariance update to obtain k+1 time
And P k|k ；
Step 7: the state estimate is saved.
3. The method for calculating the charge state of the retired lithium ion battery based on the H-infinity unscented Kalman filtering algorithm according to claim 2, wherein the method is characterized in that: the system state initialization method in the step 1 is as follows: let the initial state variable be x 0 The mean value of the state variables is
Initial covariance P 0 The method comprises the steps of carrying out a first treatment on the surface of the Then there are:
wherein: q (Q) 0 : initial value of covariance of system noise
R 0 : ohmic resistance of retired cells.
4. The method for calculating the charge state of the retired lithium ion battery based on the H-infinity unscented Kalman filtering algorithm according to claim 2, wherein the method is characterized in that: sigma spot acquisition in step 2 is specifically:
calculating sigma point sampling points x (i):
wherein:
is the mean value; p is covariance; the corresponding weight ω is:
wherein: c is covariance weight; 1 to n: the value range of the variable i is from 1 to n;
n+1 to 2n: the value range of the variable i is from n+1 to 2n; where n refers to the dimension of the state;
ωm is the mean weight and ωc is the covariance weight;
parameter λ=α 2 (n+ki) -n is a scaling factor used to reduce the total prediction error; alpha is more than or equal to 0 and less than or equal to 1 and is used for controlling sigma point weight at the average value; beta=2, for controlling the error of the state estimation,and the estimation accuracy is improved.
5. A lithium battery experiment platform is characterized in that: a method for detecting the state of charge calculation of the retired lithium ion battery based on the H-infinity-free kalman filter algorithm according to any one of claims 1-3, which consists of an AC power supply, a computer host, a battery tester and a programmable room for placing the battery.
6. The lithium battery experimental platform of claim 5, wherein: taking the urban road circulation working condition formulated in the United states as a test condition, and carrying out a charge-discharge experiment on the battery under the experiment platform; the ambient temperature for the battery test was set at 23 ℃ and the initial value of battery SOC was set at 0.7.
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| CN114167295B (en) * | 2021-11-30 | 2022-08-30 | 北京理工大学 | Lithium ion battery SOC estimation method and system based on multi-algorithm fusion |
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