CN116449219A - Lithium battery model parameter identification method for improving VFFRLS - Google Patents
Lithium battery model parameter identification method for improving VFFRLS Download PDFInfo
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 24
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 24
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- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 description 9
- 229910001416 lithium ion Inorganic materials 0.000 description 9
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a lithium battery model parameter identification method for improving VFFRLS, which comprises the following steps: step 1, battery modeling: the Thevenin model is adopted as a battery equivalent circuit model, a functional relation of the model is obtained by using the kirchhoff law, and three model parameters are obtained through operation; step 2, parameter identification: step 21, carrying out parameter identification on experimental data of main characteristics of the battery under the room temperature condition by using a recursive least square method with forgetting factors; step 22, providing a correction function, and inverting the hyperbola by adopting an improved form of a hyperbola tangent function; step 3, simulation analysis: and (5) performing simulation verification on the precision and convergence of the VFFRLS algorithm. The invention adopts the improved parameter identification method of the lithium battery model of the VFFRLS, changes the constant forgetting factor in the traditional FFRLS algorithm into a variable, and improves the dynamic tracking capability of the system on parameters while not affecting the accuracy of the algorithm.
Description
Technical Field
The invention relates to the technical field of battery model parameter identification, in particular to a lithium battery model parameter identification method for improving VFFRLS.
Background
In recent years, new energy electric vehicles are favored by people due to excellent cruising performance and environmental friendliness due to the exhaustion of petroleum resources and the increasingly serious environmental pollution caused by fossil fuels. The lithium ion battery is widely used as a power source in new energy automobiles due to the advantages of high energy density, long service life, environmental friendliness and the like. The performance of the lithium ion battery directly influences the service performance of the new energy electric automobile. BMS is a key part of battery applications, whose core function is to accurately estimate and predict battery operating states, depending on battery models and model parameters. At present, how to improve the accuracy of battery models and parameter identification methods is a key problem to be solved in battery management.
The selection of a proper battery model is a precondition for ensuring the accuracy of battery parameter identification. Currently, electrochemical models, equivalent circuit models and the like are included. In which a large number of chemical reactions inside the battery are involved in the electrochemical model, many complex equations exist in the whole modeling process, specialized chemical knowledge is required, and the requirements on a modeler are high. The equivalent circuit model describes the voltage-current change relation of the battery during operation by using a simple combination of circuit elements, has clear and simple functional relation, and is a modeling mode selected by most students. The equivalent circuit model parameter identification method is mainly divided into off-line parameter identification and on-line parameter identification. The model parameters of the off-line parameter identification are fixed, and under some complex battery working conditions, the parameter values obtained by the off-line identification cannot accurately reflect the battery change condition under the current working condition of the battery. The Recursive Least Squares (RLS) algorithm is an easy algorithm to implement, but as data increases, data saturation and the like occur, and cannot be well used for parameter identification. In order to weaken the influence of historical data on parameter identification and strengthen the influence of current data, a least squares algorithm (FFRLS) with forgetting factors is added with forgetting factors on the basis of the RLS algorithm so as to solve the problem of data saturation but make it difficult to balance the relation between the parameter identification capability and convergence and stability.
The performance of the power battery is a key factor affecting the comprehensive performance of the electric automobile, so that accurate identification of parameters of a lithium ion battery model is important for charge state estimation and health state prediction of a subsequent battery system. The Recursive Least Squares (RLS) algorithm is considered to be an accurate method of identifying parameters of a lithium ion battery. However, conventional RLS algorithms typically employ a fixed forgetting factor, and voltage error values deviate, resulting in reduced model accuracy.
Disclosure of Invention
The invention aims to provide a method for identifying parameters of a lithium battery model by improving VFFRLS, which solves the problems in the background technology.
In order to achieve the above purpose, the invention provides a lithium battery model parameter identification method for improving the VFFRLS, which comprises the following steps:
step 1, battery modeling: the Thevenin model is adopted as a battery equivalent circuit model, a functional relation of the model is obtained by using the kirchhoff law, and three model parameters are obtained through operation;
step 2, parameter identification:
step 21, carrying out parameter identification on experimental data of main characteristics of the battery under the room temperature condition by using a recursive least square method with forgetting factors;
step 22, providing a correction function, and inverting the hyperbola by adopting an improved form of a hyperbola tangent function;
step 3, simulation analysis: and (5) performing simulation verification on the precision and convergence of the VFFRLS algorithm.
Preferably, in the first step, a kirchhoff law is applied to obtain a functional relation of a battery equivalent circuit model loop:
in U p Representing the voltage of RC loop, R 0 Represents ohmic internal resistance, R p Represents internal resistance of polarization, C p Representing the polarized capacitance, U oc Indicating an open circuit voltage, and U and I indicate an operating voltage and an operating current of the battery;
converting the time domain into the frequency domain:
let τ=r p C p Obtaining
The model transfer function is written as follows:
by passing throughIs discretized with respect to the model transfer function:
order the
The discretized formula is written as:
after discretizationThe method comprises the following steps:
U(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))+k 2 I(k)+k 3 (k-1)
wherein k=1, 2,3 …
Definition y (k) =u (k), then U (k) is written as:
y(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))+k 2 I(k)+k 3 (k-1)
the mathematical recursive function of the model is shown as follows:
θ= [ U ] oc (k),k 1 ,k 2 ,k 3 ] T The method comprises the steps of performing iterative decomposition on input quantity serving as an online parameter identification algorithm, obtaining a result, and obtaining three model parameters by corresponding inverse calculation, wherein the three model parameters are represented by the following formula:
preferably, in step 21, the iterative formula of the recursive least squares method with forgetting factors is as follows:
θ(k)＝θ(k-1)+K(k)e(k)
in the middle ofAn input signal vector at time K, θ (K) represents a weight vector at time K, y (K) is a desired output signal at time K, e (K) is a priori error, K (K) is a Kalman gain vector, and P (K) is an input signal vector at time Kλ is a forgetting factor;
exponentially weighted RLS algorithm with forgetting factor, its cost function isλ is a forgetting factor and has 0 < λ.ltoreq.1, and the parameters are error estimated by a modified RLS algorithm (VFFRLS) with a variable forgetting factor, as follows:
λ(k)＝λ min +(1-λ min )*2 L(k)
L(k)＝-round(ρe 2 (k))
in the above formula, round (x) is a function of letting x be a close integer, ρ is a sensitivity factor, λ min Is the minimum value of forgetting factors.
Preferably, in step 22, based on the understanding of λ, the idea of correcting the function is proposed: the hyperbola is inverted by adopting an improved form of a hyperbola tangent function, and the formula is as follows:
in the above formula, -round (x) is deleted, and the maximum value of λ is represented by λ max Instead of the original 1 from lambda max And lambda (lambda) min And controlling the value range of the function, wherein M is the size of a window, and a and b control the convergence speed of the function and improve the shape of the top of the inverted curve.
Preferably, in step 3, in order to verify the accuracy of online identification of parameters of the lithium battery based on the VFFRLS, the present work adopts the DST working condition to test the battery to verify the feasibility of online parameter identification, and selects all data in the VFFRLS algorithm identification process under the DST working condition to calculate the absolute error of the simulation result and the experimental result.
Therefore, the method for identifying the parameters of the lithium battery model by adopting the improved VFFRLS has the following beneficial effects:
(1) The invention provides a recursive least square algorithm for correcting forgetting factors based on a Thevenin model, which changes the constant forgetting factors in the traditional FFRLS algorithm into variables, and improves the dynamic tracking capability of the system on parameters while not affecting the accuracy of the algorithm;
(2) Under the DST experimental working condition, the invention adopts the improved VFFRLS algorithm to successfully identify the parameters of the battery model without distortion, can quickly achieve convergence, obtain stable parameter values and verify the feasibility of the algorithm.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a schematic flow chart of a method for identifying parameters of a lithium battery model by improving the VFFRLS of the invention;
FIG. 2 is a schematic diagram of a battery test platform according to an embodiment of the invention;
FIG. 3 is a graph of voltage and current for lithium battery discharge experiments in incremental OCV experimental tests in accordance with an embodiment of the present invention;
FIG. 4 is a graph of voltage versus current for a DST operating mode according to an embodiment of the present invention;
FIG. 5 is a graph of OCV versus SOC for an embodiment of the invention;
FIG. 6 is a schematic diagram of a Thevenin model of the present invention;
FIG. 7 is a graph showing the comparison of the open circuit voltage identification result with the forgetting factor of the present invention at the maximum value and the actual voltage;
FIG. 8 is a diagram showing the parameter identification results under different forgetting factors according to the present invention;
FIG. 9 is a graph comparing the corrected forgetting factor with the basic variable forgetting factor of the present invention;
FIG. 10 is a diagram showing the result of parameter identification according to the present invention;
FIG. 11 is a graph of variable forgetting factor variation in accordance with the present invention;
FIG. 12 is a graph showing voltage error values versus the present invention.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. "upper", "lower", "left", "right", etc. are used merely to indicate relative positional relationships, which may also be changed when the absolute position of the object to be described is changed.
Examples
FIG. 1 is a schematic flow chart of a method for identifying parameters of a lithium battery model by improving the VFFRLS of the invention; FIG. 2 is a schematic diagram of a battery test platform according to an embodiment of the invention; FIG. 3 is a graph of voltage and current for lithium battery discharge experiments in incremental OCV experimental tests in accordance with an embodiment of the present invention; FIG. 4 is a graph of voltage versus current for a DST operating mode according to an embodiment of the present invention; FIG. 5 is a graph of OCV versus SOC for an embodiment of the invention; FIG. 6 is a schematic diagram of a Thevenin model of the present invention; FIG. 7 is a graph showing the comparison of the open circuit voltage identification result with the forgetting factor of the present invention at the maximum value and the actual voltage; FIG. 8 is a diagram showing the parameter identification results under different forgetting factors according to the present invention;
FIG. 9 is a graph comparing the corrected forgetting factor with the basic variable forgetting factor of the present invention; FIG. 10 is a diagram showing the result of parameter identification according to the present invention; FIG. 11 is a graph of variable forgetting factor variation in accordance with the present invention; FIG. 12 is a graph showing voltage error values versus the present invention.
The embodiment of the invention adopts laboratory data from university of maryland to simulate, and as shown in fig. 2, the experimental platform consists of a test sample, a hot chamber, an Arbin BT2000 battery test system and a PC with Arbin software, and is used for sending out test system commands (such as charging and discharging) and monitoring data information. The test sample was a 18650LiNiMnCoO 2/graphite lithium ion battery.
Test samples were placed in the chamber to control their ambient temperature, and all test data were measured and recorded at 1 second intervals. The specifications of the cells are shown in table 1.
Table 1 cell specification
| Battery parameters | Specification of specification |
| Type(s) | LiNMC |
| Rated capacity | 2 |
| Nominal voltage | 3.6 |
| Cut-off voltage for charging | 4.2 |
| Cut-off voltage of discharge | 2.5 |
Incremental OCV experimental test:
incremental OCV experimental tests consisted of a number of SOC intervals and rest periods, after which OCV data with corresponding SOCs were observed. The experimental procedure used in the dataset was as follows:
1. placing the battery in an incubator with the temperature constant at 25 ℃ for a long time until the internal temperature and the external temperature of the battery are stable and consistent with the external temperature and have no obvious change;
2. the battery is fully charged in a constant-current and constant-voltage charging mode, namely SOC=100%;
3. discharging the battery at 0.5C (1A) until the battery SOC decreases by 10%;
4. standing the battery for 2 hours after discharging is finished;
5. steps 3 and 4 are repeated until the battery soc=0 or the discharge cut-off voltage is reached, and the experiment is ended. The experimental results are shown in FIG. 3.
Before parameter identification, the open circuit voltage U of the battery needs to be obtained oc ，U oc The value has a strong function mapping relation with the SOC value of the battery, and accurate U is obtained oc Has great significance for accurately estimating the SOC subsequently. U (U) oc The test voltage after standing for 2h is taken as U of the battery according to the test result shown in FIG. 3, wherein the test voltage is defined as the voltage of the battery which is stable at both ends of the battery after the battery is fully stood after the battery is charged and discharged oc Corresponding U under different SOC moments can be obtained oc As shown in table 2:
TABLE 2U at different SOCs oc
DST cycle condition test:
the DST working condition test is a standard test method for checking the dynamic performance of the model, and can test the dynamic performance of the power battery and evaluate the applicability of the power battery under the corresponding working condition. In the test, the DST circulation working condition test is used for verifying a parameter identification algorithm, and the specific flow is as follows:
1. standing for 5min;
2. charging at constant current of 0.5C (15A) to 4.2V, and stopping charging after constant voltage charging to current of less than 0.05C (1.5A);
3. standing for 120min;
4. standing for 5min;
5. performing a cycle test according to the DST cycle condition until the voltage is less than or equal to 2.5V;
6. standing for 5min.
The current-voltage curve of the discharge process is shown in fig. 4.
The SOC and OCV of a lithium ion battery have a very strong relationship. The OCV value per 10% soc discharge point was obtained from the delta OCV test. Since this OCV-SOC relationship is used only to obtain a baseline for algorithm reference, a polynomial least squares curve fit is employed and calculated offline by MATLAB. For practical embedded applications, piecewise linear fitting or look-up tables may be used to replace such higher order polynomial curve fitting OCV-SOC relationships. The OCV-SOC relationship is described as:
U oc ＝a 1 SOC 6 +a 2 SOC 5 +a 3 SOC 4 +a 4 SOC 3 +a 5 SOC 2 +a 6 SOC+a 7
a by using LS algorithm i The parameters of (i=1, 2,3,4,5,6, 7) can be solved, and the OCV-SOC relationship of the battery is shown in fig. 5.
DST is used to verify the parameter identification algorithm. The actual OCV values in these tests are considered as references in the algorithm validation. The actual OCV value is obtained as follows:
1. the actual capacity of the battery is obtained, and the actual capacity of the battery used in the embodiment is 2Ah;
2. the actual SOC values in these tests are calculated. The method is as follows:
wherein z is c Representing the SOC calculated by the ampere-hour integration method; η (eta) i Is coulombic efficiency; c (C) a Is the maximum available capacity; l is the total sampling time; i t Is the current measured by the current sensor, Δt represents the sampling interval.
3. According to the above formula U oc ＝a 1 SOC 6 +a 2 SOC 5 +a 3 SOC 4 +a 4 SOC 3 +a 5 SOC 2 +a 6 SOC+a 7 The OCV-SOC relationship shown in (c) is used to obtain the actual OCV value.
As shown in fig. 1, the method for identifying the parameters of the lithium battery model for improving the VFFRLS comprises the following steps:
step 1, battery modeling: and using a Thevenin model as a battery equivalent circuit model, obtaining a functional relation of the model by using a kirchhoff law, and obtaining three model parameters through operation.
The davinan model is widely used for SOC estimation studies. By comparing twelve equivalent circuits in the prior literature, the invention concludes that the Thevenin model is more suitable for the lithium battery, comprehensively considers the model precision and the identification difficulty, adopts the Thevenin model as the battery equivalent circuit model, and utilizes the experimental data of the main characteristics of the battery under the room temperature condition to carry out parameter identification and model simulation. There are only 4 parameters in this battery model: ohmic internal resistance, polarization capacitance and OCV value, the structure is simple, as shown in FIG. 6. The terminal voltage and the battery current are regarded as observations.
And obtaining a functional relation of a battery equivalent circuit model loop by using kirchhoff's law:
in U p Representing the voltage of RC loop, R 0 Represents ohmic internal resistance, R p Represents internal resistance of polarization, C p Representing the polarized capacitance, U oc Indicating an open circuit voltage, and U and I indicate an operating voltage and an operating current of the battery;
converting the time domain into the frequency domain:
let τ=r p C p Obtaining
The model transfer function is written as follows:
by passing throughIs discretized with respect to the model transfer function:
order the
The discretized formula is written as:
after discretization
U(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))+k 2 I(k)+k 3 (k-1)
Wherein k=1, 2,3 …
Definition y (k) =u (k), then U (k) is written as:
y(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))+k 2 I(k)+k 3 (k-1)
the mathematical recursive function of the model is shown as follows:
θ= [ U ] oc (k),k 1 ,k 2 ,k 3 ] T The method comprises the steps of performing iterative decomposition on input quantity serving as an online parameter identification algorithm, obtaining a result, and obtaining three model parameters by corresponding inverse calculation, wherein the three model parameters are represented by the following formula:
step 2, parameter identification:
and step 21, carrying out parameter identification on experimental data of main characteristics of the battery under the room temperature condition by using a recursive least square method with forgetting factors.
In electric car battery management applications, the parameter identification method is typically implemented in a microcontroller with limited computing power. The battery is a highly nonlinear time-varying system in actual operation, and the off-line parameter identification method cannot solve the problem that the parameters of the battery are not matched with the actual conditions in operation. In order to improve the accuracy of the equivalent circuit model, an online parameter identification method is required to be introduced to solve the problem that the battery parameters change at the moment. The on-line identification is to acquire various data of the battery, such as current and voltage, in the actual work of the battery, analyze mathematical relation formulas of various parameters according to an equivalent circuit model, and finally solve the specific numerical value of the battery, which is the various parameters at the current moment, according to an algorithm. The method has the greatest advantages that each parameter changes along with the time change of the battery operation, so that the parameters of the battery at different moments can be reflected truly, and the accuracy of the model can be improved to a certain extent.
The basic principle of the recursive least square method as one of typical methods of system identification is that the recursive least square method with forgetting factors is obtained by correcting according to the input value of the current moment and the estimated value of the last moment, and the iterative formula of the recursive least square method with forgetting factors is as follows:
θ(k)＝θ(k-1)+K(k)e(k)
in the middle ofAn input signal vector at time K, θ (K) represents a weight vector at time K, y (K) is a desired output signal at time K, e (K) is a priori error, K (K) is a Kalman gain vector, and P (K) is an input signal vector at time Kλ is the forgetting factor.
Exponentially weighted RLS algorithm with forgetting factor, its cost function isLambda is a forgetting factor and is more than 0 and less than or equal to 1. The smaller the lambda is, the stronger the tracking capability of the time-varying parameter is, but the sensitivity to noise is high, and the steady-state error is large; the larger λ is, the weaker the tracking ability is, but the less sensitive to noise is, and the smaller the estimation error of the parameter at the time of convergence is. For this purpose an improved RLS algorithm (VFFRLS) with a variable forgetting factor is proposed. In 1991, j.d.park proposed a variable forgetting factor method in his paper where the forgetting factor of the RLS algorithm can be optimized according to the prediction error of the current data point. The recursive least square of the basic variable forgetting factor is as follows, with faster tracking capability and smaller parameter estimation errors. The formula is as follows:
λ(k)＝λ min +(1-λ min )*2 L(k)
L(k)＝-round(ρe 2 (k))
in the above formula, round (x) is a function of letting x be a close integer, ρ is a sensitivity factor, λ min Is the minimum value of forgetting factors.
When the error becomes smaller, lambda (k) approaches 1, so that the error of the parameter is reduced; conversely, when the error becomes larger, λ (k) becomes smaller to a minimum value, which enhances the tracking ability of the system.
However, the above method has a great disadvantage. First, the forgetting factor limits only the minimum value, and setting only the maximum value to 1 is inaccurate, so that an additional search for a suitable maximum value is required. As shown in fig. 7, when the forgetting factor takes the maximum value of 0.995, the accuracy of the parameter identification result is insufficient. As shown in fig. 8, in the identification result with the forgetting factor of 0.985, the identification result of each parameter is relatively stable due to the suitable value of the forgetting factor, and the identification result has strong fast tracking capability, so that the dynamic characteristics of the battery in the working process can be well reflected. In the identification result of 0.95, the value of the forgetting factor is smaller, and although the identified parameters have very strong tracking capability, the identification result of part of the parameters is violent in oscillation and has insufficient stability.
Second point, for L (k) = -round (ρe) 2 (k) For ρe), when ρe 2 (k) If the value is less than 0.5, L (k) can only be 0, so that the sensitivity of the algorithm is low, and improvement on the method is needed. Furthermore ρe 2 (k) The above method is not stable enough because the forgetting factor is only determined by one data point, but the working state of the battery can be reflected in a certain time. To solve this disadvantage, the present invention employs the data window theory. In this method, the original single value is replaced by the mean square value of all the data in a window that moves over time. It can reduce the interference of single data point and raise the stability of algorithm.
Step 22, providing a correction function, and inverting the hyperbola by adopting a modified form of the hyperbola tangent function.
Based on the understanding of λ, the idea of correcting the function is proposed: the hyperbola is inverted by adopting an improved form of a hyperbola tangent function, and the formula is as follows:
in the above formula, -round (x) is deleted, and the maximum value of λ is represented by λ max Instead of the original 1 from lambda max And lambda (lambda) min And controlling the value range of the function, wherein M is the size of a window, and a and b control the convergence speed of the function and improve the shape of the top of the inverted curve.
The corrected forgetting factor versus basic variable forgetting factor curve pair is shown in fig. 9. The variable forgetting factor in a general form is changed stepwise, so that lambda (k) cannot sensitively adjust the forgetting factor according to the change of errors, and the tracking speed is limited; and λ (k) suddenly changes between intervals, affecting the stability of the system. In contrast, the improved curve has a stronger tracking ability and stability.
Step 3, simulation analysis: and (5) performing simulation verification on the precision and convergence of the VFFRLS algorithm.
The VFFRLS algorithm is the key point of the invention, and the part carries out simulation verification on the precision and the convergence of the VFFRLS algorithm based on battery test data by comparing with the FFRLS algorithm.
In order to verify the accuracy of online identification of parameters of the lithium battery based on the VFFRLS, the battery is tested by adopting a DST working condition to verify the feasibility of online parameter identification. The experimental data are also laboratory data using the university of maryland, the initial SOC value of the data being 80%, a being set to 15, b being set to 20000, and the window size M being set to 18. When the FFRLS algorithm is used for identifying the parameters of the lithium ion power battery model, if the value of the forgetting factor is larger than 0.995, the accuracy of the parameter identification result becomes unstable, and therefore the maximum value of the forgetting factor is set to be 0.995. When the value of the forgetting factor is smaller than 0.95, the FFRLS algorithm is difficult to converge and cannot complete parameter identification, so that the minimum value of the forgetting factor is set to be 0.95. The FFRLS algorithm forgetting factor of the control group used the optimum value under this test of 0.985. The voltage and the current under the DST working condition are used as the input and the output of FFRLS and VFFRLS algorithms, and the parameters of each model of the equivalent circuit can be accurately identified through the FFRLS and the VFFRLS algorithms when the battery works. The identification result is shown in fig. 10, and fig. 11 is a graph of the variable forgetting factor change according to the present invention.
In order to more intuitively embody that the VFFRLS algorithm has higher identification precision, all data in the FFRLS and VFFRLS algorithm identification process under the DST working condition are selected, and absolute errors of simulation results and experimental results are calculated, wherein the results are shown in FIG. 12.
As can be seen from comparison of experimental results and simulation results, the initial values of the parameters are not accurately set at the beginning, and the errors are relatively large, but the errors are gradually reduced along with the progress of the algorithm. Table 3 shows the comparison of errors under different parameter identification algorithms. Under DST conditions, the root mean square error RMSE identified by FFRLS is 0.0240V, respectively, while the RMSE of VFFRLS is 0.0215V. Under the same initial condition, compared with FFRLS, the recognition accuracy of the VFFRLS algorithm is improved.
Table 3 error comparison of different parameter identification methods
In the embodiment, laboratory data from the university of maryland is adopted for simulation, a first-order RC equivalent circuit model of the lithium ion battery is established, and the FFRLS algorithm for correcting forgetting factors is adopted for online parameter identification by developing a state equation of parameters of the lithium ion battery aiming at the defect of online parameter identification of the FFRLS algorithm. And (3) carrying out online parameter identification under the DST experimental working condition, and comparing with an FFRLS algorithm to obtain the following conclusion.
(1) Under the DST experimental working condition, the improved VFFRLS algorithm can successfully identify model parameters and cannot generate distortion, can quickly achieve convergence, obtain stable parameter values, and verifies the feasibility of the algorithm.
(2) Compared with the FFRLS algorithm, the convergence speed of the VFFRLS algorithm is faster, the time-varying parameters of the system can be tracked more accurately, and the error of the VFFRLS algorithm is obviously smaller than that of the FFRLS algorithm after the algorithm reaches convergence. The model parameter identification result shows that compared with FFRLS parameter identification, the root mean square error of the VFFRLS algorithm is reduced by 0.0025V, the corresponding accuracy is improved by 10.42%, and the effectiveness of the algorithm is verified. The VFFRLS algorithm for correcting the forgetting factor lays a foundation for the accurate estimation research of the subsequent SOC.
Therefore, the method for identifying the parameters of the lithium battery model by improving the VFFRLS changes the constant forgetting factor in the traditional FFRLS algorithm into a variable, and improves the dynamic tracking capability of the system on the parameters while not affecting the accuracy of the algorithm.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (5)
1. A lithium battery model parameter identification method for improving VFFRLS is characterized in that: the method comprises the following steps:
step 1, battery modeling: the Thevenin model is adopted as a battery equivalent circuit model, a functional relation of the model is obtained by using the kirchhoff law, and three model parameters are obtained through operation;
step 2, parameter identification:
step 21, carrying out parameter identification on experimental data of main characteristics of the battery under the room temperature condition by using a recursive least square method with forgetting factors;
step 22, providing a correction function, and inverting the hyperbola by adopting an improved form of a hyperbola tangent function;
step 3, simulation analysis: and (5) performing simulation verification on the precision and convergence of the VFFRLS algorithm.
2. The method for identifying the parameters of the lithium battery model by improving the VFFRLS of claim 1, wherein the method comprises the following steps of: in the first step, a kirchhoff law is applied to obtain a functional relation of a battery equivalent circuit model loop:
in U p Representing the voltage of RC loop, R 0 Represents ohmic internal resistance, R p Represents internal resistance of polarization, C p Representing the polarized capacitance, U oc Indicating an open circuit voltage, and U and I indicate an operating voltage and an operating current of the battery;
converting the time domain into the frequency domain:
let τ=r p C p Obtaining
The model transfer function is written as follows:
by passing throughIs discretized with respect to the model transfer function:
order the
The discretized formula is written as:
after discretizationThe method comprises the following steps:
U(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))
+k 2 I(k)+k 3 (k-1)
wherein k=1, 2,3 …
Definition y (k) =u (k), then U (k) is written as:
y(k)＝U oc (k)+k 1 (U(k-1)-U oc (k-1))+k 2 I(k)+k 3 (k-1)
the mathematical recursive function of the model is shown as follows:
θ= [ U ] oc (k),k 1 ,k 2 ,k 3 ] T The method comprises the steps of performing iterative decomposition on input quantity serving as an online parameter identification algorithm, obtaining a result, and obtaining three model parameters by corresponding inverse calculation, wherein the three model parameters are represented by the following formula:
3. the method for identifying the parameters of the lithium battery model by improving the VFFRLS of claim 2, wherein the method comprises the following steps of: in step 21, the iterative formula of the recursive least squares method with forgetting factors is as follows:
θ(k)＝θ(k-1)+K(k)e(k)
in the middle ofAn input signal vector at time K, θ (K) represents a weight vector at time K, y (K) is a desired output signal at time K, e (K) is a priori error, K (K) is a Kalman gain vector, and P (K) is an input signal vector at time K->λ is a forgetting factor;
exponentially weighted RLS algorithm with forgetting factor, its cost function isλ is a forgetting factor and has 0 < λ.ltoreq.1, and the parameters are error estimated by a modified RLS algorithm (VFFRLS) with a variable forgetting factor, as follows:
λ(k)＝λ min +(1-λ min )*2 L(k)
L(k)＝-round(ρe 2 (k))
in the above formula, round (x) is a function of letting x be a close integer, ρ is a sensitivity factor, λ min Is the minimum value of forgetting factors.
4. The method for identifying the parameters of the improved lithium battery model of the VFFRLS of claim 3, wherein the method comprises the following steps: in step 22, based on the understanding of λ, the idea of correcting the function is proposed: the hyperbola is inverted by adopting an improved form of a hyperbola tangent function, and the formula is as follows:
in the above formula, -round (x) is deleted, and the maximum value of λ is represented by λ max Instead of the original 1 from lambda max And lambda (lambda) min And controlling the value range of the function, wherein M is the size of a window, and a and b control the convergence speed of the function and improve the shape of the top of the inverted curve.
5. The method for identifying the parameters of the improved VFFRLS lithium battery model according to claim 4, characterized in that: in step 3, in order to verify the accuracy of online identification of parameters of the lithium battery based on the VFFRLS, the online identification feasibility of the parameters of the lithium battery is verified by adopting a DST working condition to test the battery, all data in the identification process of the VFFRLS algorithm under the DST working condition are selected, and the absolute errors of the simulation result and the experimental result are calculated.
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