CN116754959A - SOC estimation method based on improved GWO optimized forgetting factor on-line parameter identification - Google Patents
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- G—PHYSICS
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract
The invention relates to a battery state of charge (SOC) estimation method based on online parameter identification of improved gray wolf algorithm optimized forgetting factor. The method comprises the steps of establishing a second-order RC equivalent circuit model, obtaining an equal-voltage-drop discharge time sequence according to constant-current discharge for equal period of time on a lithium battery, further obtaining an OCV-SOC function, and providing an improved gray-wolf algorithm optimized forgetting factor recursive least square method for selecting an optimal forgetting factor and a variable forgetting factor least square method (VFFRLS) algorithm for identifying model parameters on line for more accurately identifying equivalent circuit model parameters. And finally, estimating the SOC by combining the identified model parameters with unscented Kalman filtering. The invention solves the problem that the accuracy of estimating the state of charge (SOC) is insufficient due to the fact that the forgetting factor is unchanged in the forgetting factor recursive least square method, and the optimal forgetting factor recursive least square method and unscented Kalman filtering are used for jointly estimating the state of charge (SOC) of the battery, so that the convergence speed is accelerated while the accuracy is improved.
Description
Technical Field
The invention belongs to the technical field of lithium batteries, and particularly relates to an SOC estimation method based on improved GWO optimized forgetting factor on-line parameter identification, which realizes effective real-time identification of battery model parameters and has higher estimation precision and stability in battery SOC estimation.
Background
The wolf optimization algorithm, inspiration comes from the predation behavior of the wolf population. The method has strong convergence performance, simple structure, few parameters needing to be regulated, easy realization and an adaptive adjustment convergence factor and information feedback mechanism, but the traditional gray wolf algorithm is easy to sink into local optimum, the convergence factor value is linearly reduced from 2 to 0 in the iterative process, and the linear reduction cannot well balance the relation between global search and local search. The improved gray wolf optimization algorithm convergence factor is nonlinear, global search and local search are well performed in the optimization process of the balance algorithm, and the accuracy and convergence speed of parameter identification are improved.
The SOC of the lithium battery reflects the residual electric quantity of the battery, accurate SOC estimation can prevent the battery from being overcharged and overdischarged, and can also predict the endurance mileage of the electric vehicle, so that a trip plan is made in advance. However, in the manufacturing process of the lithium battery, inconsistency is unavoidable due to the difference of production processes, and the inconsistency is larger and larger along with the service time of the battery, so that overcharge or overdischarge of the single battery is caused, the overall performance of the lithium battery is affected, and the service life of the battery is finally shortened. Current researchers find that constructing a battery equivalent model, identifying model parameters, and estimating the SOC has higher precision.
The current recursive least square method (Recursive Least Square, RLS) can well identify parameters, overcome uncertainty of a model caused by environmental change through continuous parameter updating and correction, and therefore achieve real-time capture of system characteristics. However, the traditional RLS can generate a data saturation phenomenon along with the increase of the iteration times, and a variable forgetting factor is introduced into RFF (Recursive forgetting factor), so that the influence of old data can be continuously reduced, and the effect of new data is enhanced.
Therefore, the invention provides an SOC estimation method for optimizing forgetting factor on-line parameter identification based on improvement GWO, which realizes effective real-time identification of battery model parameters.
Disclosure of Invention
The embodiment of the invention aims to provide an SOC estimation method for optimizing forgetting factor on-line parameter identification based on improvement GWO, which can solve the problem that the forgetting factor of a forgetting factor recursive least square method is unchanged, can well identify equivalent model parameters of a battery at the current moment along with time and environmental changes, and further improves the accuracy of estimating the state of charge (SOC).
In order to achieve the above purpose, the technical scheme adopted by the invention is characterized by comprising the following steps:
the second-order equivalent circuit model is established as follows:
step 101: according to kirchhoff's law, a second-order RC loop model function relation and an SOC calculation formula deduced by an ampere-hour integration method at a moment t:
wherein Q is the rated capacity of the battery, SOC 0 Is the initial value SOC of the battery. After solving the differential equation in equation 1, a battery model equation of the continuous system can be established as follows:
wherein τ 1 ＝R 1 C 1 Represented as R in the model 1 C 1 The time response constant of the loop; τ 2 ＝R 2 C 2 Representing R in a model 2 C 2 The time response constant of the loop.
Step 102: and carrying out Laplace transformation on the formula 3, and finishing to obtain:
in the case of using bilinear transformation, letObtaining
θ＝[α 1 α 2 α 3 α 4 α 5 ] (6)
Wherein alpha is 1 、α 2 、α 3 、α 4 、α 5 And the coefficient of each sub term of the numerator denominator, and theta is a parameter matrix.
Step 103: let y=u oc (s) -U(s), the equivalent circuit model discretization expression is obtained after the transformation of the formula 5:
wherein, the input value of the I (k) system, y (k) is the output value of the system, let
The method comprises the following steps:
step 104: order theSubstituting into formula 5 to obtain:
comparison of equation 5 and equation 9
Standing and discharging the battery in the same period of time, collecting data such as voltage and current, obtaining a plurality of groups of data, and finally fitting an OCV-SOC curve, wherein the steps are as follows:
step S201: and (3) keeping the ambient temperature at 25 ℃, charging the lithium battery at constant current and constant voltage to enable the SOC to be 100%, standing and discharging for a period of time, and repeating the cycle until the battery is completely discharged. And acquiring relevant data such as voltage, current and the like through multiple discharge experiments on the lithium battery.
Step S202: and performing fitting processing on the obtained data through MATLAB to obtain the OCV-SOC functional relation.
The steps of the improved wolf algorithm are as follows:
step S301: initializing the number of wolves, the maximum iteration number and the random population position.
Step S302: and calculating the fitness value of the individual according to the corresponding fitness function, sequencing the fitness values according to the size, and selecting the optimal alpha, beta and delta wolf.
Step S303: the location of each individual wolf in the population is updated.
Step S304: the improved nonlinear convergence factors alpha, a and C are updated.
Step S305: and calculating the moderate values of all the wolves, and selecting the position of alpha wolves.
Step S306: judging whether the algorithm meets the termination condition, if so, using the optimal alpha wolf position as a forgetting factor recursion least square method optimal forgetting factor parameter, and ending the algorithm; otherwise, step S303 to step S305 are repeatedly performed.
The optimized forgetting factor recursive least square method comprises the following steps:
step S401: and (5) introducing a discretization expression of the equivalent circuit model of the formula 7, and initializing a parameter equation and a covariance matrix.
Step S402: the voltage and current sampled values are input.
Step S403: an error covariance matrix P (K) of the gain matrix K (K) and the state estimation value is calculated.
Step S404: a parameter matrix is calculated.
Step S405: the iteration times are reached, the parameters of the battery model are calculated, and the algorithm is ended; otherwise, step S402 to step S404 are performed.
The step of estimating the SOC by combining the identified model parameters with unscented Kalman filtering is as follows:
step S501: initializing system state variables x 0 Mean of (2)Sum covariance P 0 ：
Step S502: calculating Sigma points and corresponding weights:
wherein omega m ωc is the weight of the mean and variance respectively; n is the dimension of the state vector; β is a non-negative weight coefficient, and the motion differences in higher-order terms can be combined, and when Sigma points are gaussian distributed, β=2 is usually taken; alpha is a scale parameter, and the value range is 1e 4 Alpha is more than or equal to 1; as a scale factor, it can be expressed as:
μ＝α 2 (n+κ)-n (14)
where κ is an adjustable parameter, typically 0 or 3-n.
Step S503: state variable and measured variable predictions.
Step S504: calculating a gain matrix K k 。
Step S505: and updating the estimated value of the state variable at the k moment and the error covariance matrix, and separating the SOC estimated value at the k moment from the estimated value.
The invention has the following beneficial effects:
(1) The improved wolf algorithm is adopted, and in the initial iteration stage, as the iteration times are increased, the speed of reducing the convergence factor alpha is slow, so that the wolf clusters can be searched in a larger range, and the speed of reducing the convergence factor alpha is accelerated from the middle and later iteration stages, so that the target in the wolf clusters can be caused, and the optimizing effectiveness is promoted.
(2) After the improved gray wolf algorithm is introduced, the method has an accurate iteration initial value compared with a forgetting factor recursive least square method, and does not need to rely on human experience assignment, so that an equivalent model of a parameter identification result truly reflects the battery state at the current moment, and the accuracy of estimating the SOC is improved.
Drawings
FIG. 1 is a second order RC equivalent circuit model of the present invention
FIG. 2 is a flow chart of the improved gray wolf algorithm of the present invention
FIG. 3 is a flow chart of the optimized forgetting factor recursive least square method of the present invention
FIG. 4 is a flow chart of unscented Kalman filtering in accordance with the invention
FIG. 5 is a graph of SOC estimation and true SOC of the present invention
FIG. 6 is a graph of the SOC estimation and the true SOC error of the present invention
FIG. 7 is a flowchart of the improved GWO FFRLS and unscented Kalman filter joint estimation SOC of the present invention
Detailed Description
The invention is further described with reference to the accompanying drawings and specific embodiments, and the technical scheme of the invention is specifically described, and provides an SOC estimation method for optimizing forgetting factor on-line parameter identification based on improvement GWO, which comprises the following steps:
s1, referring to FIG. 1, is a second order RC equivalent circuit model, U is the battery terminal voltage, U oc R is the open circuit voltage of the battery 0 For ohmic internal resistance of battery R 1 、C 1 For electrochemically polarizing resistance and polarizing capacitance, R 2 、C 2 Is a concentration difference polarization resistance and a polarization capacitance. In the circuit, R 0 As the ohmic internal resistance of the battery, the abrupt change characteristic of the battery terminal voltage can be reflected, the second-order RC parallel network can reflect the gradual change characteristic of the battery terminal voltage, and the voltage source U oc The relationship between the battery electromotive force and the SOC can be reflected.
According to kirchhoff's law, a second-order RC loop model function relation and an SOC calculation formula deduced by an ampere-hour integration method at a moment t:
wherein Q is the rated capacity of the battery, SOC 0 Is the initial value SOC of the battery. After solving the differential equation in equation 1, a battery model equation of the continuous system can be established as follows:
wherein τ 1 ＝R 1 C 1 Represented as R in the model 1 C 1 The time response constant of the loop; τ 2 ＝R 2 C 2 Representing R in a model 2 C 2 The time response constant of the loop.
And carrying out Laplace transformation on the formula 3, and finishing to obtain:
the transfer function is:
wherein τ 1 ＝R 1 C 1 ，τ 2 ＝R 2 C 2 Adopts bilinear transformation to makeObtaining
Wherein the method comprises the steps ofα 1 、α 2 、α 3 、α 4 、α 5 The specific expression is as follows for each sub-term coefficient of the molecular denominator:
let y=u oc (s) -U(s), the differential equation obtained after the transformation of the formula 6 is the discretization expression of the equivalent circuit model:
wherein, the input value of the I (k) system, y (k) is the output value of the system, let
The method comprises the following steps:
order theSubstituting into formula 7:
comparison of equation 6 and equation 11
The theta matrix can be obtained through online identification, and finally R is reversely deduced according to a formula 0 ，R 1 ，R 2 ，C 1 ，C 2 。
S2, keeping the ambient temperature at 25 ℃, charging the lithium battery at constant current and constant voltage to enable the SOC to be 100%, standing for 2 hours to enable the internal chemical reaction to be stable, discharging at 1C for 3min, standing for 2h, discharging at 1C for 3min, and repeating circularly until the battery is completely discharged. Multiple sets of OCV-SOC data can be obtained by performing multiple experiments.
Fitting the obtained data by MATLAB to obtain an OCV-SOC functional relation:
U 0c ＝564.6SOC 8 -201.2SOC 7 -190.6SOC 6 -18.7SOC 5 -70.566SOC 4 +60.656SOC 3 -32.646SOC 2 +6.64SOC 1 +3.065 (13)
s3, FIG. 2 is a flow chart of the improved wolf algorithm, which comprises the following specific steps:
initializing each parameter, population scale N and maximum iteration number t max And a, A and C
Calculating the gray wolf fitness value: calculating the fitness value of the initial gray wolf according to the position of the initial gray wolf
Updating the wolf group position: the gray wolf population has a strict population system, the wolves are classified into alpha, beta, delta and omega 4 grades, alpha is a leader, beta assists alpha management, delta listens to alpha and beta commands, and commands the bottommost wolves omega and omega are responsible for balancing the internal relationship of the population and completing the task of alpha, beta and delta wolves copulation.
The behavior of the wolf hunting is defined as:
wherein X is p (t) is the position of the prey, X (t) is the position of the t th generation of the wolf individual; a and C are coefficient vectors, and the formulas of A and C are as follows:
wherein r is 1 And r 2 Is located at [0-1 ]]Is a random vector of (a); alpha is an improved nonlinear convergence factor.
In the initial stage of iteration, as the number of iterations increases, the convergence factor α The decreasing speed is slow, so that the wolf clusters can be searched in a larger range, the decreasing speed of the convergence factor alpha is increased in the middle and later stages of iteration, and the target in the wolf clusters can be caused to promote the optimizing effectiveness.
The mathematical description of the gray wolf updated individual position is as follows:
the distance between wolf and prey; />Position vector of wolf at time t; />The position vector of the delta wolf at the moment alpha, beta, delta wolf. Finally, the positions of all wolves are averaged to obtain an update:
calculating the moderate values of all the gray wolves, and updating the moderate values and positions of alpha, beta and delta;
judging whether the algorithm meets the termination condition, if so, ending the algorithm by taking the optimal alpha wolf position as an optimal solution; otherwise, the gray wolf moderate value is recalculated.
S4, FIG. 3 is a forgetting factor recursive least square method flow chart, and the steps are as follows:
and (5) introducing an equivalent circuit model discretization expression, and initializing a parameter equation and a covariance matrix.
The voltage and current sampled values are input.
Calculating a gain matrix K (K) and an error covariance matrix P (K) of the state estimation values:
k (K) is the gain of the algorithm, P (K) is the error covariance matrix of the state estimation value, h (K) is the system data variable, lambda is the forgetting factor after optimization, and E is the unit matrix.
Calculating a parameter matrix
Y (k) is the system output observations at time k,and->LS estimates obtained from the top k and top k-1 samples, respectively.
The iteration times are reached, the parameters of the battery model are calculated, and the algorithm is ended; otherwise, recalculating K (K), P (K) and the parameter matrix.
S5, further, the identified circuit model parameters are combined with an unscented Kalman filtering algorithm to estimate the SOC, as shown in FIG. 4.
The Unscented Kalman Filtering (UKF) algorithm adopts a nonlinear Unscented Transformation (UT) iterative technique to directly approximate the determined discrete sampling points to the posterior distribution of the state. And simultaneously updating the state covariance and the measurement covariance of the nonlinear model in the iterative process. After adding the system process noise and the measurement noise, the state equation and the measurement equation of the nonlinear battery dynamic system model can be expressed as:
wherein y is k U is an observed variable of the system k Is an input variable of the system; f is the state function of the system, g is the systemAn observation function of the system; omega k V (k) is the measurement noise of the system, which is the process noise of the system.
The unscented Kalman filtering algorithm steps are as follows:
initializing system state variables x 0 Mean of (2)Sum covariance P0
Calculating Sigma points and corresponding weights
Wherein omega m ，ω c Weights of mean and variance, respectively; n is the dimension of the state vector; β is a non-negative weight coefficient, and the motion differences in higher-order terms can be combined, and when Sigma points are gaussian distributed, β=2 is usually taken; alpha is a scale parameter, and the value range is 1e 4 Alpha is more than or equal to 1; as a scale factor, it can be expressed as:
μμ＝α 2 (n+κ)-n (26)
where κ is an adjustable parameter, typically 0 or 3-n.
And calculating to obtain the predicted value of the mean and covariance of the state variable at the k moment and the predicted value of the observed variable.
Wherein q k-1 Is the mean value of the noise of the system process;representing the state value based on the k-1 time, for the k timePredicting a state value; r is (r) k-1 The mean value of the noise is measured for the system.
Calculating a gain matrix K k 。
K k ＝P xy，k ·(P y，k ) -1 (28)
Wherein, the liquid crystal display device comprises a liquid crystal display device,
and updating the estimated value of the state variable at the moment k and an error covariance matrix.
After the state variable estimated value at the moment k is updated, the method can be used forAnd separating the SOC estimation value at the k moment.
The improved gray-wolf algorithm optimizes the forgetting factor of the recursive least square method and the unscented Kalman filtering is combined to estimate the state of charge (SOC) of the battery, the improved gray-wolf algorithm optimizes the forgetting factor of the recursive least square method, the identified model parameters basically accord with the actual battery condition, the accuracy is high, the identified model parameters are combined with the unscented Kalman filtering to estimate the SOC, the estimated SOC and the SOC are shown in a graph 5, the estimated error is shown in a graph 6, and the estimated accuracy is high and the error is below 0.4%.
The foregoing examples illustrate only a few embodiments of the invention and are described in detail herein without thereby limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
The foregoing is illustrative of the present invention and is not to be construed as limiting thereof, but rather as various modifications, equivalent arrangements, improvements, etc., which fall within the spirit and principles of the present invention.
Claims (1)
1. An SOC estimation method for optimizing forgetting factor on-line parameter identification based on improvement GWO is characterized in that: the method comprises the following steps:
s1, establishing a 2-order RC equivalent circuit model, deducing a model function, and carrying out Laplace transformation and bilinear transformation on the model function to obtain an equivalent circuit model discretization expression:
y(k)＝U OC (k)-U(k)
＝a 1 y(k-1)+a 2 y(k-2)+a 3 I(k)+a 4 I(k-1)+a 5 I(k-2) (1)
wherein I (k) is an input value of the system, and y (k) is an output value of the system;
and (3) making:
the system may be expressed as:
the second-order battery model is converted into a form suitable for identification;
s2, charging the lithium battery at constant current and constant voltage to enable the SOC to reach 100%, then discharging at constant current in an equal period of time until discharging is finished, and obtaining multiple groups of data through multiple experiments. Finally, obtaining an OCV-SOC curve through MABTLAB fitting;
s3, adopting an improved gray wolf algorithm to select an optimal forgetting factor, and firstly determining the maximum iteration times t max Initializing a wolf group; calculating the fitness value of each wolf, and selecting the head wolf; updating the current position of the gray wolf; updating the convergence factor; calculating the fitness value of all the gray wolves; recording the current wolf crowd fitThe individual gray wolves with highest stress degree are head wolves; judging whether the termination condition is met, if not, updating the position of the gray wolf again, otherwise, outputting the optimal forgetting factor lambda;
s4, aiming at an equivalent circuit model, adopting a forgetting factor selected by an improved gray wolf optimization algorithm to solve the problem of parameter and model matching, and introducing continuous parameter updating and correction of a recursive least square method to overcome the uncertainty of the model caused by environmental change;
obtaining an RFF recurrence formula according to formula (3):
where K (K) is the gain of the algorithm; p (k) is an error covariance matrix of the state estimation value; λ is a selected forgetting factor;is a system data variable;
obtaining second-order RC equivalent model parameters through system identification;
s5, combining the identified model parameters with unscented Kalman filtering to estimate the SOC. Initializing a system state variable; calculating Sigma points and corresponding weights; each Sigma point is transmitted through a state function, and a mean value of a state variable at the moment k, a predicted value of covariance and a predicted value of an observation variable are obtained through calculation; calculating a gain matrix K k The method comprises the steps of carrying out a first treatment on the surface of the And updating the estimated value of the state variable at the k moment and the error covariance matrix, and separating the SOC estimated value at the k moment from the estimated value.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117452234A (en) * | 2023-12-22 | 2024-01-26 | 齐鲁工业大学(山东省科学院) | SOC estimation method and system for improving fusion of parameter identification and infinite algorithm |
| CN117591796A (en) * | 2024-01-19 | 2024-02-23 | 四川帝威能源技术有限公司 | Online identification method for parameters of double-layer forgetting factor recursive least square battery model |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117452234A (en) * | 2023-12-22 | 2024-01-26 | 齐鲁工业大学(山东省科学院) | SOC estimation method and system for improving fusion of parameter identification and infinite algorithm |
| CN117591796A (en) * | 2024-01-19 | 2024-02-23 | 四川帝威能源技术有限公司 | Online identification method for parameters of double-layer forgetting factor recursive least square battery model |
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