CN114217234B - IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method - Google Patents
IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method Download PDFInfo
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- 229910001416 lithium ion Inorganic materials 0.000 title claims abstract description 58
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention provides a lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF, which belongs to the technical field of lithium ion batteries and comprises the following technical scheme: the method comprises the following steps: step 1), determining an OCV-SOC relation through intermittent constant current discharging measurement of load current and terminal voltage data of a battery; step 2) establishing a second-order RC model of the lithium ion battery; step 3) constructing an identification flow of an IDE algorithm, and identifying parameters of a battery model; step 4) constructing an estimation flow of an ASRCKF algorithm; and 5) determining each parameter in the lithium battery model by utilizing an IDE algorithm, and estimating the battery SOC by utilizing ASRCKF. The beneficial effects of the invention are as follows: the invention improves the convergence speed and precision of the algorithm; and the SOC estimation is carried out by combining the parameter result obtained by identification with an ASRCKF algorithm, so that the accuracy is high, the robustness is good, and the effect is better than CKF.
Description
Technical Field
The invention relates to the technical field of lithium ion batteries, in particular to a lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF.
Background
The State Of Charge (SOC) Of the lithium ion battery is one Of the important parameters in the battery management system (Battery Management System, BMS), and provides a judgment basis for the control strategy Of the automobile battery pack. Under normal conditions, the terminal voltage, the load current and the ambient temperature of the lithium ion battery are monitored in real time to perform SOC estimation, so that the control of the battery pack is completed, and the safe and reliable operation of the battery system can be ensured by an accurate SOC estimation result.
Establishing an appropriate, accurate battery model is critical to SOC estimation effectiveness. According to the different parameter processing methods in the battery model, the lithium ion battery model can be divided into an electrochemical model, a neural network model and an equivalent circuit model, wherein the equivalent circuit model is a model which is widely researched. The model identification method is mainly divided into online identification and offline identification, the traditional online identification method can correct parameters according to the environment where the battery is located and the current battery state, but under certain conditions, the parameter error is larger, compared with the traditional online identification method, a large amount of data can be called by offline identification, the parameter accuracy is higher, and certain advantages are achieved. Various intelligent optimization algorithms in the field of off-line identification are widely applied, and how to ensure high algorithm precision and high convergence speed is an important subject of research.
On the basis of a high-precision battery model, the selection of the SOC estimation method is important, and the currently commonly used estimation method is divided into 2 types: firstly, an ampere-hour integration method is used for direct calculation, but the method excessively depends on an initial value of the SOC, and under the condition of larger initial value error, the estimation error is larger, and the actual requirement is not met; secondly, estimation is carried out based on a battery model and a state quantity prediction result, such as a support vector machine, a neural network and a Kalman filtering algorithm, the former two methods have larger requirements on data quantity and data quality, the application is limited, the Kalman filtering algorithm is relatively mature in research, the SOC estimation problem can be well solved, and the problems of low precision, poor robustness and the like are still faced.
How to solve the technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF, which adds an adaptive factor on the basis of an original differential evolution algorithm (DE), improves variation and crossover processes, provides an improved differential evolution algorithm (IDE), effectively solves the problems that the traditional heuristic identification algorithm is easy to fall into local optimum, has low convergence speed and the like, has high identification parameter precision, considers that the positive nature of an error covariance matrix of the traditional volume Kalman filtering (CKF) algorithm is difficult to ensure, introduces square root filtering, directly calculates square root factors of a state quantity error covariance predicted value and a state quantity error covariance estimated value, and avoids square root solving of the matrix; and simultaneously introducing a residual sequence and an adaptive factor, and adaptively updating the process noise and the measurement noise, thereby improving the accuracy of the process noise and the measurement noise. The two improvements are combined, an adaptive volume Kalman filter (ASRCKF) algorithm is provided and used for estimating the SOC of the lithium ion battery, the estimation result is accurate, and the algorithm robustness is high.
The invention is realized by the following measures: the lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF specifically comprises the following steps:
step 1), determining an OCV-SOC relation through intermittent constant current discharging measurement of load current and terminal voltage data of a battery;
step 2) establishing a second-order RC model of the lithium ion battery;
step 3) constructing an identification flow of an IDE algorithm, and identifying parameters of a battery model;
step 4) constructing an estimation flow of an ASRCKF algorithm;
step 5) determining each parameter in the lithium battery model by utilizing an IDE algorithm, and estimating the battery SOC by utilizing ASRCKF;
as a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 2) specifically comprises the following steps:
taking the dual polarization characteristic of the lithium ion battery into consideration, establishing a second-order RC model of the lithium ion battery:
U oc u corresponds to the open-circuit voltage and terminal voltage of the battery, and the capacitor C 1 、C 2 The voltages at both ends are respectively U 1 、U 2 R represents 0 Representing ohmic internal resistance. The lithium ion battery model has two RC parallel links which respectively represent two polarization effects existing in the battery: from R 1 、C 1 Expressed electrochemical polarization effect and R 2 、C 2 Concentration differential polarization effect represented;
SOC represents the state of charge of a lithium ion battery, which is expressed as:
wherein Q is n Is rated capacity, SOC (t 0 ) The SOC value at time t is shown.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 3) specifically comprises the following steps:
step 3-1) differential evolution algorithm:
the differential evolution algorithm is based on a genetic evolution algorithm and is used for solving an overall optimal solution in a multidimensional space, and the core steps of the differential evolution algorithm comprise mutation, crossover and selection;
the differential evolution algorithm comprises the following steps:
a. initialization of
Setting the population number as M, the dimension number of the individuals as N and the maximum iteration number G m And a crossover factor w, randomly generating population individuals:
wherein: rand of i,j (0, 1) represents [0, 1]]The random number in the random number is used as the random number,an upper and lower limit of a j-th dimension representing an i-th individual;
b. individual variation
Wherein:and->Three individuals selected randomly in the population, < ->The difference vector is the difference vector of two individuals, F is a variation factor, G is the current iteration number, and the individual variation is to sum with a third individual according to a rule after the vector difference of the two individuals is weighted, so as to generate a variation individual;
c. crossover operation
The cross operation can effectively increase the diversity of the population, and the variant individuals are compared with a certain predetermined target to obtain variant individuals, wherein the specific formula is as follows:
wherein: randl i,j Is [0, 1]]A random number of the small number in between,is a variant +.>Is j-th dimensional vector of->Is individual->Is the j-th dimensional vector of (2)The crossover factor ω can control the degree of participation of individual dimensions in crossover and the balance of global and local search capabilities, at [0,1]Between them;
d. selection operation
Judging the fitness value of the target individual and the test individual, and selecting the individual with good adaptability by using a greedy method:
step 3-1) improving the differential evolution algorithm:
the variation factor F and the crossover factor w in the basic DE algorithm determine the diversity of the population, so that the convergence of the algorithm is affected, an improved differential evolution algorithm is provided by improving the variation and crossover processes in the basic DE algorithm, the algorithm optimizing process is improved, and the convergence speed is accelerated; the method comprises the following specific steps:
a. adaptive mutation factor
The variation is used as a step in the DE algorithm, the diversity of the population is increased, the optimizing performance of the algorithm is realized, the variation factor in the original algorithm is a constant, the randomness is high in the variation process, the optimal value is difficult to determine, the variation factor is changed into a periodically-changing dynamic value by introducing the self-adaptive operator, the variation factor searching range is in a reasonable range, the variation factor is also searching for the optimal value along with the increase of the iteration times, the algorithm effectively approaches to the optimal solution, the diversity of the population is ensured, and the specific improvement strategy is as follows:
F＝F 0 ×2 α (8)
b. improved interleaving strategy
The method is characterized by improving the crossing factor in the original algorithm crossing operation based on the self-adaptive principle:
ω＝0.6×(1+rand()) (10)
the self-adaptive adjustment of the crossing factors balances the global and local searching capability of the algorithm to quickly obtain the optimal solution.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 4) specifically comprises the following steps:
on the basis of a volume Kalman filtering algorithm, square root filtering is introduced to ensure symmetry and positive quality of an error covariance matrix in an iterative process, and a square root factor of a state quantity error covariance predicted value and a state quantity error covariance estimated value is directly calculated to avoid square root calculation of the matrix; in order to improve the accuracy of two errors, a residual sequence is introduced and the iteration thought in a group intelligent algorithm is combined to adaptively update the covariance of the process and the measurement noise, so that an adaptive square root volume Kalman filtering algorithm is provided;
the state equation and the observation equation of the nonlinear system are:
x(k)＝f(x(k-1),u(k-1))+w(k-1) (11)
y(k)＝g(x(k),u(k))+v(k) (12)
wherein: x (k) is a system state variable at time k, u (k) is input data, y (k) is output data, g is a nonlinear function of an observation equation, f is a nonlinear function of a state equation, w (k) is input noise, and v (k) is observation noise;
the algorithm comprises the following steps:
step 4-1) parameter initialization:
initializing initial values of state variablesState error covariance P 0 Process noise Q and measurement noise R;
step 4-2) time update:
a. calculating volume points
The error covariance matrix is decomposed by Cholesky and the volume points are calculated:
P k-1 ＝S k-1 S k-1 T (13)
where i=1, 2,3, …,2n, n is the dimension of the state quantity, ζ i Is a set of volumetric points, as follows:
wherein [1] is an identity matrix;
b. propagation volume point
c. Estimating a state predictor at time k
d. Calculating square root of state error covariance prediction value at k moment
S in Q ＝Chol(Q k ) Tria (…) represents triangulating the matrix, matrix arrayThe definition is as follows:
step 4-3) measurement updating:
a. using state predictors at time kSum state error covariance square root predictor +.>Updating volume points
b. Calculating the observed quantity predicted value
Wherein:
c. calculating the square root of the innovation covariance matrixAnd square root of error covariance matrix->
Wherein:
S R ＝chol(R k-1 ) (25)
R k-1 measuring the noise covariance for the k-1 moment;
d. updating Kalman gain
e. Calculating system state quantity estimation value
f. Calculating square root of system state quantity error covariance matrix
S k ＝Tria([μ k -K k r k K k S R ]) (30)
g. Updating measurement noise covariance R k System noise covariance Q k
The approximation of the voltage residual covariance at time K is:
in the middle ofRepresenting the deviation between the measured value and the estimated value at the moment k; l is the length of the innovation, an adaptive operator alpha is introduced and a weight n is defined, e.gThe following is shown:
n＝n 0 ×2 α (33)
g is the total length of the data set, H is the current data position, and k moment measurement noise covariance R is established k System noise covariance Q k The expression is as follows:
R k ＝(1-n k )R k-1 +n k F k (34)
step 4-4) ASRCKF algorithm estimates SOC:
according to the formulas (11) and (12), the values [ SOC, U ] 1 ,U 2 ]As a system state quantity, a discrete state space expression of a second-order RC model of the lithium ion battery is established:
wherein the current I is input, the terminal voltage U is output, [ SOC, U 1 ,U 2 ]As state variable, Δt is system sampling time, 1s, in ASRCKF algorithm, set observed quantity y (k) =U (k), state quantity x k ＝[SOC(k),U 1 (k),U 2 (k)]The input u (k) =i (k), the lithium ion battery is used as a nonlinear system, and the state equation and the observation equation are as follows:
through iteration, the algorithm can estimate the SOC value of the lithium ion battery at each moment.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 5) specifically comprises the following steps:
step 5-1) parameter identification:
under the condition of different SOCs, the parameter identification results of the lithium ion battery have deviation, so the whole discharging process is identified by 10 sections, and the battery is subjected to standing, pulse discharging and standing again in each stage. The SOC before discharge was set to the initial SOC. And identifying each section of battery discharging process by utilizing an IDE algorithm, and then performing polynomial fitting on the result obtained by each section of identification and the corresponding initial SOC, so that a change curve of battery model parameters under different SOCs can be obtained.
Step 5-2) SOC estimation:
substituting the identified parameters into a state equation and an observation equation, and combining terminal voltage and current data obtained through experiments, and predicting and updating state variables of the lithium ion battery by using an ASRCKF algorithm to obtain an SOC estimation result.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, a second-order RC model of the lithium ion battery is established according to kirchhoff's law, a group of intermittent constant current discharge data is measured through experiments, and an OCV-SOC relation is fitted.
(2) The invention provides a self-adaptive improvement method based on the original differential evolution algorithm, improves the variation and crossing steps in the original algorithm, effectively solves the problems that the original algorithm is easy to fall into local optimum and has low convergence speed in the process of identifying the parameters of the battery model, and has better identification effect than the traditional heuristic algorithm.
(3) Compared with the traditional CKF algorithm, the method has a certain effect in the SOC estimation process, but in the algorithm iteration process, the symmetry and the forward nature of the covariance matrix are easily damaged, so that the algorithm is stopped. Meanwhile, in the CKF algorithm iteration process, process noise and measurement noise are constant by default, and in the actual condition, the process noise and measurement noise are continuously changed in the lithium ion battery charging and discharging process, so that a larger error occurs in an algorithm estimation result, and in order to improve the accuracy of the two errors, a covariance residual sequence is introduced, and the self-adaptive thought is combined, so that the process covariance and measurement noise covariance are adaptively updated, the error accuracy is effectively improved, and the algorithm estimation accuracy is improved.
(4) The accuracy of the SOC estimation result of the invention depends on the accuracy of the model parameters and the effectiveness of the estimation algorithm. The invention effectively utilizes the characteristics of high precision and rapid convergence of the IDE algorithm, combines ASRCKF, can accurately and rapidly estimate the SOC of the battery, and has strong algorithm robustness. The combination of the two algorithms has good engineering value and wide practical application prospect.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
Fig. 1 is a schematic diagram of a second order RC model of a lithium ion battery according to the present invention.
Fig. 2 is a voltage-current curve of an intermittent constant current discharge experiment of the present invention.
FIG. 3 is a graph of the OCV-SOC fit for intermittent constant current experiments of the present invention.
Fig. 4 is a plot of fitness function change in the iterative process of IDE algorithm, DE algorithm and PSO algorithm according to the present invention.
FIG. 5 is a fitted curve of the IDE algorithm parameter identification result of the present invention.
Fig. 6 is a graph showing the terminal voltage prediction curves of the IDE algorithm and the DE algorithm according to the present invention under the intermittent constant current discharge test.
Fig. 7 is a plot of the predicted error of the terminal voltage of the IDE algorithm and the DE algorithm of the present invention in intermittent constant current discharge test.
Fig. 8 is an SOC estimation curve and an SOC estimation error curve according to the present invention.
Fig. 9 is a graph of the SOC estimation curve and the SOC estimation error curve in the case where there is a deviation in the initial value of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
According to the invention, the NCR-18650B of the loose lithium ion battery is used as a research object, the rated voltage of the battery is 3.7V, and the capacity is 3400mAh. The battery is charged in a constant current charging mode (0.5C) until the cut-off voltage is reached, and the battery reaches a full-charge state after standing for a period of time.
Referring to fig. 1 to 9, the invention provides a lithium battery parameter identification and SOC estimation method based on suburban wolf optimization algorithm. Comprises the following steps:
step 1) carrying out intermittent constant current discharge experiment on the battery under the environment of constant temperature of 25 ℃, discharging for 5min, standing for 30min, setting current at 3400mA, setting discharge multiplying power at 1C, repeating for a plurality of times and recording related data. According to the 21211 group terminal voltage and current data obtained through experiments, the data change curve is shown in fig. 2. Calculating a battery SOC theoretical value by utilizing an ampere-hour integration method, selecting a plurality of groups of terminal voltages and data of corresponding SOCs, fitting by utilizing a polyfit function in MATLAB, and determining an OCV-SOC coefficient of the battery:
f(x)＝P 1 x 9 +P 2 x 8 +P 3 x 7 +P 4 x 6 +P 5 x 5 +P 6 x 4 +P 7 x 3 +P 8 x 2 +P 9 x 1 +P 10 x 0 (1)
the OCV-SOC fit curve is shown in FIG. 3.
Step 2) establishing a second-order RC model of the lithium ion battery;
step 3) constructing an identification flow of an IDE algorithm, and identifying parameters of a battery model;
step 4) constructing an estimation flow of an ASRCKF algorithm;
step 5) determining each parameter in the lithium battery model by utilizing an IDE algorithm, and estimating the battery SOC by utilizing ASRCKF;
as a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 2) specifically comprises the following steps:
taking the dual polarization characteristic of the lithium ion battery into consideration, establishing a second-order RC model of the lithium ion battery:
U oc u corresponds to the open-circuit voltage and terminal voltage of the battery, and the capacitor C 1 、C 2 The voltages at both ends are respectively U 1 、U 2 R represents 0 Representing ohmic internal resistance. The lithium ion battery model has two RC parallel links which respectively represent two polarization effects existing in the battery: from R 1 、C 1 Expressed electrochemical polarization effect and R 2 、C 2 Concentration differential polarization effect is shown.
SOC represents the state of charge of a lithium ion battery, which is expressed as:
wherein Q is n Is rated capacity, SOC (t 0 ) The SOC value at time t is shown.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 3) specifically comprises the following steps:
step 3-1) differential evolution algorithm:
the differential evolution algorithm is based on a genetic evolution algorithm and is used for solving an overall optimal solution in a multidimensional space, and the core steps of the differential evolution algorithm comprise mutation, crossover and selection;
the differential evolution algorithm comprises the following steps:
a. initialization of
Setting the population number as M, the dimension number of the individuals as N and the maximum iteration number G m And a crossover factor w, randomly generating population individuals:
wherein: rand of i,j (0, 1) represents [0, 1]]The random number in the random number is used as the random number,an upper and lower limit of a j-th dimension representing an i-th individual;
b. individual variation
Wherein:and->Three individuals selected randomly in the population, < ->The difference vector is the difference vector of two individuals, F is a variation factor, G is the current iteration number, and the individual variation is to sum with a third individual according to a rule after the vector difference of the two individuals is weighted, so as to generate a variation individual;
c. crossover operation
The cross operation can effectively increase the diversity of the population, and the variant individuals are compared with a certain predetermined target to obtain variant individuals, wherein the specific formula is as follows:
wherein: randl i,j Is [0, 1]]A random number of the small number in between,is a variant +.>Is j-th dimensional vector of->Is individual->The crossover factor ω can control the degree of participation of the individual dimensions in crossover and the balance of global and local search capabilities, at [0,1]Between them;
d. selection operation
Judging the fitness value of the target individual and the test individual, and selecting the individual with good adaptability by using a greedy method:
step 3-1) improving the differential evolution algorithm:
the variation factor F and the crossover factor w in the basic DE algorithm determine the diversity of the population, so that the convergence of the algorithm is affected, an improved differential evolution algorithm is provided by improving the variation and crossover processes in the basic DE algorithm, the algorithm optimizing process is improved, and the convergence speed is accelerated; the method comprises the following specific steps:
a. adaptive mutation factor
The variation is used as a step in the DE algorithm, the diversity of the population is increased, the optimizing performance of the algorithm is realized, the variation factor in the original algorithm is a constant, the randomness is high in the variation process, the optimal value is difficult to determine, the variation factor is changed into a periodically-changing dynamic value by introducing the self-adaptive operator, the variation factor searching range is in a reasonable range, the variation factor is also searching for the optimal value along with the increase of the iteration times, the algorithm effectively approaches to the optimal solution, the diversity of the population is ensured, and the specific improvement strategy is as follows:
F＝F 0 ×2 α (9)
b. improved interleaving strategy
The method is characterized by improving the crossing factor in the original algorithm crossing operation based on the self-adaptive principle:
ω＝0.6×(1+rand()) (11)
the self-adaptive adjustment of the crossing factors balances the global and local searching capability of the algorithm to quickly obtain the optimal solution.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 4) specifically comprises the following steps:
on the basis of a volume Kalman filtering algorithm, square root filtering is introduced to ensure symmetry and positive quality of an error covariance matrix in an iterative process, and a square root factor of a state quantity error covariance predicted value and a state quantity error covariance estimated value is directly calculated to avoid square root calculation of the matrix; in order to improve the accuracy of two errors, a residual sequence is introduced and the iteration thought in a group intelligent algorithm is combined to adaptively update the covariance of the process and the measurement noise, so that an adaptive square root volume Kalman filtering algorithm is provided;
the state equation and the observation equation of the nonlinear system are:
x(k)＝f(x(k-1),u(k-1))+w(k-1) (12)
y(k)＝g(x(k),u(k))+v(k) (13)
wherein: x (k) is a system state variable at time k, u (k) is input data, y (k) is output data, g is a nonlinear function of an observation equation, f is a nonlinear function of a state equation, w (k) is input noise, and v (k) is observation noise;
the algorithm comprises the following steps:
step 4-1) parameter initialization:
initializing initial values of state variablesState error covariance P 0 Process noise Q and measurement noise R;
step 4-2) time update:
a. calculating volume points
The error covariance matrix is decomposed by Cholesky and the volume points are calculated:
P k-1 ＝S k-1 S k-1 T (14)
where i=1, 2,3, …,2n, n is the dimension of the state quantity, ζ i Is a set of volumetric points, as follows:
wherein [1] is an identity matrix;
b. propagation volume point
c. Estimating a state predictor at time k
d. Calculating square root of state error covariance prediction value at k moment
S in Q ＝Chol(Q k ) Tria (…) represents triangulating the matrix, matrix arrayThe definition is as follows:
step 4-3) measurement updating:
a. using state predictors at time kSum state error covariance square root predictor +.>Updating volume points
b. Calculating the observed quantity predicted value
Wherein:
c. calculating the square root of the innovation covariance matrixAnd square root of error covariance matrix->
Wherein:
S R ＝chol(R k-1 ) (26)
R k-1 measuring the noise covariance for the k-1 moment;
d. updating Kalman gain
e. Calculating system state quantity estimation value
f. Calculating square root of system state quantity error covariance matrix
S k ＝Tria([μ k -K k r k K k S R ]) (31)
g. Updating measurement noise covariance R k System noise covariance Q k
The approximation of the voltage residual covariance at time K is:
in the middle ofRepresenting the deviation between the measured value and the estimated value at the moment k; l is the length of the innovation, an adaptive operator alpha is introduced and a weight n is defined as follows:
n＝n 0 ×2 α (34)
g is the total length of the data set, H is the current data position, and k moment measurement noise covariance R is established k System noise covariance Q k The expression is as follows:
R k ＝(1-n k )R k-1 +n k F k (35)
step 4-4) ASRCKF algorithm estimates SOC:
according to the formulas (11) and (12), the values [ SOC, U ] 1 ,U 2 ]As a system state quantity, a discrete state space expression of a second-order RC model of the lithium ion battery is established:
wherein the current I is input, the terminal voltage U is output, [ SOC, U 1 ,U 2 ]As state variable, Δt is system sampling time, 1s, in ASRCKF algorithm, set observed quantity y (k) =U (k), state quantity x k ＝[SOC(k),U 1 (k),U 2 (k)]The input u (k) =i (k), the lithium ion battery is used as a nonlinear system, and the state equation and the observation equation are as follows:
through iteration, the algorithm can estimate the SOC value of the lithium ion battery at each moment.
As a further optimization scheme of the IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method, the step 5) specifically comprises the following steps:
step 5-1) parameter identification:
under the condition of different SOCs, the parameter identification results of the lithium ion battery have deviation, so the whole discharging process is identified by 10 sections, and the battery is subjected to standing, pulse discharging and standing again in each stage. The SOC before discharge was set to the initial SOC. Establishing a fitness function:
wherein x= [ R ] 0 ,R 1 ,R 2 ,C 1 ,C 2 ]；Is the terminal voltage estimated value; u (k) is the actual value of the terminal voltage; k is the discrete time. The iteration times are set to 1000, the IDE, DE and Particle Swarm Optimization (PSO) algorithm is utilized to conduct parameter identification on the second-order RC model of the lithium ion battery, the change curve of the fitness function in the iteration process is shown as shown in figure 4, comparison shows that the IDE algorithm has certain advantages in the aspects of convergence speed and accuracy, and the algorithm can be effectively prevented from falling into local optimum and is higher in convergence speed by improving the intersection and mutation operation of the original algorithm. And identifying each section of battery discharging process by utilizing an IDE algorithm, wherein the identification result is shown in the following table:
and then, performing polynomial fitting on the result obtained by each section of identification and the corresponding initial SOC to obtain a change curve of the battery model parameters under different SOCs, as shown in FIG. 5. By using the obtained parameters, a predicted value of the battery terminal voltage can be calculated, and the accuracy of the identification algorithm can be evaluated by comparing the predicted value with the actual value, and the comparison result is shown in fig. 6 and 7. The result shows that the parameters obtained by the IDE algorithm are more accurate, and the error between the terminal voltage predicted value and the actual value is smaller.
Step 5-2) SOC estimation:
the high-precision model parameter identification result is beneficial to accurately estimating the SOC by ASRCKF. Substituting the identified parameters into a state equation and an observation equation, combining terminal voltage and current data obtained through experiments, and predicting and updating the state variables of the lithium ion battery by using an ASRCKF algorithm, so that an SOC estimation result can be obtained and compared with CKF. As shown in fig. 8, the results indicate that the ASRCKF has a faster tracking speed and the error is significantly smaller than CKF. Under the condition that the initial SOC is set to be 0.8 and 0.6, the ASRCKF is utilized for SOC estimation, and the result is shown in fig. 9, and under the condition that the initial error is 20% and 40%, the estimation result is still accurate, so that the algorithm has good robustness.
In sum, the improved differential evolution algorithm and the self-adaptive volume Kalman filtering algorithm have good effects when applied to lithium ion battery parameter identification and SOC estimation, and have accurate model parameter identification results, high SOC estimation accuracy and engineering value.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (1)
1. The lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF is characterized by comprising the following steps:
step 1), determining an OCV-SOC relation through intermittent constant current discharging measurement of load current and terminal voltage data of a battery;
step 2) establishing a second-order RC model of the lithium ion battery;
step 3) constructing an identification flow of an IDE algorithm, and identifying parameters of a battery model;
step 4) constructing an estimation flow of an ASRCKF algorithm;
step 5) determining each parameter in the lithium battery model by utilizing an IDE algorithm, and estimating the battery SOC by utilizing ASRCKF;
the step 2) specifically comprises the following steps:
taking the dual polarization characteristic of the lithium ion battery into consideration, establishing a second-order RC model of the lithium ion battery:
U oc u corresponds to the open-circuit voltage and terminal voltage of the battery, and the capacitor C 1 、C 2 The voltages at both ends are respectively U 1 、U 2 R represents 0 Lithium ion battery with ohmic internal resistanceThe model has two RC parallel links which respectively represent two polarization effects existing in the battery: from R 1 、C 1 Expressed electrochemical polarization effect and R 2 、C 2 Concentration differential polarization effect represented;
SOC represents the state of charge of a lithium ion battery, which is expressed as:
wherein Q is n Is rated capacity, SOC (t 0 ) Representing the SOC value at the time t;
the step 3) specifically comprises the following steps:
step 3-1) improving the differential evolution algorithm:
the variation factor F and the crossover factor w in the basic DE algorithm determine the diversity of the population, so that the convergence of the algorithm is affected, an improved differential evolution algorithm is provided by improving the variation and crossover processes in the basic DE algorithm, the algorithm optimizing process is improved, and the convergence speed is accelerated; the method comprises the following specific steps:
a. adaptive mutation factor
The variation is used as a step in the DE algorithm, the diversity of the population is increased, the optimizing performance of the algorithm is realized, the variation factor in the original algorithm is a constant, the randomness is high in the variation process, the optimal value is difficult to determine, the variation factor is changed into a periodically-changing dynamic value by introducing the self-adaptive operator, the variation factor searching range is in a reasonable range, the variation factor is also searching for the optimal value along with the increase of the iteration times, the algorithm effectively approaches to the optimal solution, the diversity of the population is ensured, and the specific improvement strategy is as follows:
F＝F 0 ×2 α (8)
b. improved interleaving strategy
The method is characterized by improving the crossing factor in the original algorithm crossing operation based on the self-adaptive principle:
ω＝0.6×(1+rand()) (10)
wherein: randl i,j Is [0, 1]]A random number of the small number in between,is a variant +.>Is j-th dimensional vector of->Is an individualThe crossover factor ω can control the degree of participation of the individual dimensions in crossover and the balance of global and local search capabilities, at [0,1]Between them;
the self-adaptive adjustment of the crossing factors balances the global and local searching capability of the algorithm to quickly obtain the optimal solution;
the step 4) specifically comprises the following steps:
on the basis of a volume Kalman filtering algorithm, square root filtering is introduced to ensure symmetry and positive quality of an error covariance matrix in an iterative process, and a square root factor of a state quantity error covariance predicted value and a state quantity error covariance estimated value is directly calculated to avoid square root calculation of the matrix; in order to improve the accuracy of two errors, a residual sequence is introduced and the iteration thought in a group intelligent algorithm is combined to adaptively update the covariance of the process and the measurement noise, so that an adaptive square root volume Kalman filtering algorithm is provided;
the state equation and the observation equation of the nonlinear system are:
x(k)＝f(x(k-1),u(k-1))+w(k-1) (11)
y(k)＝g(x(k),u(k))+v(k) (12)
wherein: x (k) is a system state variable at time k, u (k) is input data, y (k) is output data, g is a nonlinear function of an observation equation, f is a nonlinear function of a state equation, w (k) is input noise, and v (k) is observation noise;
the algorithm comprises the following steps:
step 4-1) parameter initialization:
initializing initial values of state variablesState error covariance P 0 Process noise Q and measurement noise R;
step 4-2) time update:
a. calculating volume points
The error covariance matrix is decomposed by Cholesky and the volume points are calculated:
P k-1 ＝S k-1 S k-1 T (13)
where i=1, 2,3, …,2n, n is the dimension of the state quantity, ζ i Is a set of volumetric points, as follows:
wherein [1] is an identity matrix;
b. propagation volume point
c. Estimating a state predictor at time k
d. Calculating square root of state error covariance prediction value at k moment
S in Q ＝Chol(Q k ) Tria (…) represents triangulating the matrix, matrix arrayThe definition is as follows:
step 4-3) measurement updating:
a. using state predictors at time kSum state error covariance square root predictor +.>Updating volume points
b. Calculating the observed quantity predicted value
Wherein:
c. calculating the square root of the innovation covariance matrixAnd square root of error covariance matrix->
Wherein:
S R ＝chol(R k-1 ) (25)
R k-1 measuring the noise covariance for the k-1 moment;
d. updating Kalman gain
e. Calculating system state quantity estimation value
f. Calculating square root of system state quantity error covariance matrix
S k ＝Tria([μ k -K k r k K k S R ]) (30)
g. Updating measurement noise covariance R k System noise covariance Q k
The approximation of the voltage residual covariance at time K is:
in the middle ofRepresenting the deviation between the measured value and the estimated value at the moment k; l is the length of the innovation, an adaptive operator beta is introduced and a weight n is defined as follows:
n＝n 0 ×2 β (33)
where P is the total length of the data set, H is the current data position, n 0 For the initial value of the weight, establishing k moment measurement noise covariance R k System noise covariance Q k The expression is as follows
R k ＝(1-n k )R k-1 +n k F k (34)
Step 4-4) ASRCKF algorithm estimates SOC:
according to the formulas (11) and (12), the values [ SOC, U ] 1 ,U 2 ]As a system state quantity, a discrete state space expression of a second-order RC model of the lithium ion battery is established:
wherein the current I is input, the terminal voltage U is output, [ SOC, U 1 ,U 2 ]As state variable, Δt is system sampling time, 1s, in ASRCKF algorithm, set observed quantity y (k) =U (k), state quantity x k ＝[SOC(k),U 1 (k),U 2 (k)]The input u (k) =i (k), the lithium ion battery is used as a nonlinear system, and the state equation and the observation equation are as follows:
through iteration, the algorithm can estimate the SOC value of the lithium ion battery at each moment;
the step 5) specifically comprises the following steps:
step 5-1) parameter identification:
under the condition of different SOCs, the parameter identification results of the lithium ion battery have deviation, so the whole discharging process is identified in 10 sections, the battery in each stage is subjected to standing, pulse discharging and standing again, the SOC before discharging is determined as an initial SOC, the discharging process of each section of battery is identified by utilizing an IDE algorithm, and then the obtained result of each section of identification is subjected to polynomial fitting with the corresponding initial SOC to obtain a change curve of the battery model parameters under different SOCs;
step 5-2) SOC estimation:
substituting the identified parameters into a state equation and an observation equation, and predicting and updating the state variables of the lithium ion battery by using an ASRCKF algorithm by combining terminal voltage and current data obtained through experiments to obtain an SOC estimation result.
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