CN113203955A - Lithium iron phosphate battery SOC estimation method based on dynamic optimal forgetting factor recursive least square online identification - Google Patents

Lithium iron phosphate battery SOC estimation method based on dynamic optimal forgetting factor recursive least square online identification Download PDF

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CN113203955A
CN113203955A CN202110477371.9A CN202110477371A CN113203955A CN 113203955 A CN113203955 A CN 113203955A CN 202110477371 A CN202110477371 A CN 202110477371A CN 113203955 A CN113203955 A CN 113203955A
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forgetting factor
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葛才安
郑燕萍
王浩
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Nanjing Forestry University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/005—Testing of electric installations on transport means
    • G01R31/006—Testing of electric installations on transport means on road vehicles, e.g. automobiles or trucks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/3644—Constructional arrangements
    • G01R31/3648—Constructional arrangements comprising digital calculation means, e.g. for performing an algorithm
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements

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Abstract

The invention provides a lithium iron phosphate battery state of charge (SOC) estimation method based on dynamic optimization forgetting factor recursive least square online identification. The forgetting factor selected in real time can enable the terminal voltage following error to be extremely small, so that the accuracy of parameter online identification is guaranteed, the optimized forgetting factor recursive least square and extended Kalman filtering are combined to estimate the SOC of the lithium iron phosphate battery, the combined estimation precision is high, and the dynamic requirements of combined estimation on the forgetting factor value under different batteries and different battery use environments can be self-adapted.

Description

Lithium iron phosphate battery SOC estimation method based on dynamic optimal forgetting factor recursive least square online identification
Technical Field
The invention relates to a power battery state of charge (SOC) estimation method, and provides a lithium iron phosphate battery SOC estimation method based on dynamic preferred forgetting factor recursive least square online identification, which aims to improve the online identification precision of battery model parameters and further improve the battery SOC estimation precision.
Background
In recent years, electric vehicles are developed increasingly rapidly, and a power battery is taken as a power source of the electric vehicles, so that the function of the power battery is self-evident. The SOC is used as an important parameter of the power battery, and researchers hope to estimate the SOC more accurately to provide energy management and safety service for the whole vehicle.
The equivalent circuit model observation method is the mainstream battery SOC estimation method at present. And based on the circuit model, the SOC of the battery is estimated by utilizing the charge and discharge data identification parameters and combining with a filtering algorithm. The model parameters influence the model precision and further influence the estimation accuracy of the SOC of the battery. Parameter identification can be divided into off-line and on-line. The off-line identification has a simpler least square fitting method, but generally needs appropriate initial parameters, but the internal parameters of the battery inevitably change along with the change of the battery use environment and the cycle number, and the parameter condition under the current environment is only obtained when the accuracy of the off-line identification is higher. Therefore, with the online identification concept, online identification is to update the equivalent circuit model parameters in real time to ensure the model accuracy and further improve the SOC estimation accuracy.
Disclosure of Invention
The invention provides a lithium iron phosphate battery SOC estimation method based on dynamic preferred forgetting factor recursive least square online identification, and aims to improve the online identification precision of battery model parameters and further improve the battery SOC estimation precision.
The technical scheme of the invention is as follows:
and establishing a second-order RC equivalent circuit model as shown in figure 1. In the figure, Uoc(t) is open circuit voltage; r0(t) ohmic internal resistance; i (t) is working current, and discharge is positive; r1(t)、R2(t) electrochemical polarization internal resistance and concentration polarization internal resistance, C1(t)、C2(t) electrochemical polarization capacitance and concentration polarization capacitance, respectively[11]；U1(t) is the voltage at the end of the electrochemical polarization ring; u shape2(t) is the voltage at the end of the concentration polarization ring; u shapet(t) is the battery terminal voltage.
Further, an electrical relation of the equivalent circuit model obtained according to kirchhoff's voltage law and kirchhoff's current law is as follows:
Figure BSA0000240928160000011
further, after the OCV (open circuit voltage) and SOC corresponding points are obtained by the segmental equidistant discharge standing test, an open circuit voltage model is established as follows:
UOC＝-23.7SOC6+86.9SOC5-122.9SOC484.5a4SOC3-29.2SOC2+4.9a6SOC+2.9 (2)
an open-circuit voltage model curve (discharge SOC-OCV curve relationship) is shown in fig. 2.
Further, terminal voltage error is used as a fitness function, a particle swarm optimization is adopted to optimize a real-time optimal forgetting factor:
the fitness function is:
Figure BSA0000240928160000012
in the formula of Ut(k) Is a recorded measured value of the terminal voltage; u (k) is the estimated terminal voltage value; u shapeoc(k-1) is obtained from the SOC estimated at the time k-1 and the SOC-OCV curve.
Lambda is an optimization variable, lambda changes to influence a gain K (k) and covariance P (k), and iterative optimization is carried out by taking J minimization as a target so as to make optimal estimation on parameters.
Further, in combination with a real-time preferred forgetting factor, before parameter identification is performed based on the FFRLS (forgetting factor recursive least square), a second-order equivalent circuit model is subjected to discrete recursion to be converted into a least square basic form. And (3) performing Laplace transform on the formula (1) to convert the formula (1) into a frequency domain expression (4), mapping the formula (4) from an s domain to a z domain by using a bilinear transformation formula (5) to obtain a transfer function of the system on the z domain, and mathematically simplifying the transfer function to obtain a form of a formula (6).
Figure BSA0000240928160000013
Figure BSA0000240928160000021
Figure BSA0000240928160000022
Taking y (k) ═ Ut(k)-Uoc(k) Discretizing the formula (6) to obtain a formula (7).
y(k)＝θ1，ky(k-1)+θ2，ky(k-2)+θ3，kI(k)+θ4，kI(k-1)+θ5，kI(k-2) (7)
The least square parameter vector is theta (k) ═ theta1，k，θ2，k，θ3，k，θ4，k，θ5，k]TThe data vector is
Figure BSA0000240928160000023
U1(k) And I (k) are respectively a terminal voltage measured value and a current measured value of the test record, and theta (k) is estimated in real time by recursive least squares so as to obtain a real-time parameter value of the model.
Further, an online identification algorithm is combined with the extended kalman filter, and model parameters and SOC are estimated in real time, and the combined algorithm is shown in fig. 3.
The invention has the technical effects that:
the forgetting factor recursive least square online identification needs to select a better forgetting factor for different batteries and different use environments to identify parameters, and compared with a traditional forgetting factor determining algorithm needing to select the better forgetting factor, the SOC estimation algorithm based on the particle swarm optimization dynamic forgetting factor recursive least square online identification can realize real-time self-screening of the best forgetting factor, meet dynamic requirements for the forgetting factor under different batteries or different use environments, adopt real-time optimal forgetting factor online estimation parameters, and improve model precision to a certain extent and further improve SOC estimation accuracy.
Drawings
FIG. 1 second order equivalent circuit model;
FIG. 26 is a polynomial fit SOOC-OCV curve of order 26;
FIG. 3 is a joint algorithm flow diagram;
Detailed Description
Establishing a second-order equivalent circuit model:
see FIG. 1, Uoc(t) is open circuit voltage; r0(t) ohmic internal resistance; i (t) is working current, and discharge is positive; r1(t)、R2(t) electrochemical polarization internal resistance and concentration polarization internal resistance, C1(t)、C2(t) electrochemical polarization capacitance and concentration polarization capacitance, respectively[11]；U1(t) is the voltage at the end of the electrochemical polarization ring; u shape2(t) is the voltage at the end of the concentration polarization ring; u shapet(t) is the battery terminal voltage. The electrical relation of the equivalent circuit model obtained according to kirchhoff voltage law and kirchhoff current law is as follows:
Figure BSA0000240928160000024
further, an open circuit voltage model is established:
aiming at the characteristics that the open-circuit voltage at the SOC middle value position of the lithium iron phosphate battery is relatively flat and the two ends of the lithium iron phosphate battery are changed violently, a sectional equal SOC interval test method is designed to obtain a representative SOC-OCV point as far as possible, and the test scheme is as follows:
controlling the test environment temperature by a temperature control box to be 25 ℃, carrying out constant current charging at a rate of c/3 until the cut-off voltage is 3.65V, carrying out constant voltage charging until the current is less than 4A, and standing for 1 h;
starting from 100% SOC, releasing 1.25% of capacity at c/3 multiplying power each time, standing for 1h, and repeating for 4 times to 95% SOC;
starting from the 95% SOC, releasing 5% of capacity to 90% SOC at c/3 multiplying power, and standing for 1 h;
starting from 90% SOC, releasing 10% of capacity at c/3 multiplying power each time, standing for 1h, and repeating for 8 times to 10% SOC;
starting from the 10% SOC, discharging 5% of capacity to 5% SOC at c/3 multiplying power, and standing for 1 h;
starting at 5% SOC, 1.25% capacity was discharged at c/3 rate each time, left for 1h, and repeated 4 times to 0% SOC.
And (3) recording data after the test is kept still for 1h, comprehensively considering the influence of over-fitting and under-fitting, and finally adopting a 6-order polynomial fitting data point to obtain a discharge SOC-OCV curve relation as shown in figure 2, wherein the fitting formula is as shown in formula (2).
UOC＝-23.7SOC6+86.9SOC5-122.9SOC484.5a4SOC3-29.2SOC2+4.9a6SOC+2.9 (2)
Further, a particle swarm algorithm is adopted to optimize a forgetting factor in real time:
the particle swarm optimization is used as an evolutionary intelligent optimization algorithm and is widely applied in the optimization field, the particle swarm optimization is introduced to a forgetting factor recursion least square algorithm, the minimum terminal voltage error is taken as an optimization target, the selection of the forgetting factor is optimized in real time, and therefore the accuracy of parameter online identification is improved.
The fitness function is:
Figure BSA0000240928160000031
in the formula of Ut(k) Is a recorded measured value of the terminal voltage; u (k) is the estimated terminal voltage value; u shapeoc(k-1) is obtained from the SOC estimated at the time k-1 and the SOC-OCV curve.
Lambda is an optimization variable, lambda changes to influence a gain K (k) and covariance P (k), and iterative optimization is carried out by taking J minimization as a target so as to make optimal estimation on parameters.
The particle swarm optimization algorithm process is as follows:
at time k;
setting a population scale i, an iteration number it, a self-learning factor c1, a population learning factor c2 and an inertia factor omega 1;
initializing a population position: lambda [ alpha ]1，λ2......λi；
Initializing a population speed: v (lambda)1)，V(λ2)......V(λi)；
Calculating the initial fitness function value of each particle of the population as the respective individual optimal solution;
comparing the fitness function values of all particles, and taking the minimum node as a global optimal solution;
starting iteration;
according to the learning factors c1, c2 and omega 1, updating the speed of each particle;
updating the position of each particle;
calculating the fitness function value of each particle in the population and comparing the fitness function value with the optimal solution of each individual to update the optimal solution of the particle;
comparing the self optimal solution of all the particles with the global optimal solution, and updating a global optimal solution lambda;
and the iteration is carried out for it times, and then the optimal lambda at the current moment is output.
Further, transmitting the real-time optimized forgetting factor to a forgetting factor recursive least square online identification algorithm to complete parameter real-time estimation:
before parameter identification, a second-order equivalent circuit model is converted into a least square basic form in a discrete recursion mode. And (3) performing Laplace transform on the formula (1) to convert the formula (1) into a frequency domain expression (4), mapping the formula (4) from an s domain to a z domain by using a bilinear transformation formula (5) to obtain a transfer function of the system on the z domain, and mathematically simplifying the transfer function to obtain a form of a formula (6).
Figure BSA0000240928160000032
Figure BSA0000240928160000033
Figure BSA0000240928160000034
In the formula, T is a sampling period; theta1，k、θ2，k、θ3，k、θ4，k、θ5，kTo simplify the representative coefficient, a specific expression is as follows.
Figure BSA0000240928160000041
Wherein a ═ R1；b＝τ1τ2；c＝τ1+τ2；d＝R0+R1+R2；e＝R0(τ1+τ2)+R1τ2+R2τ1；τ1＝R1C1；τ2＝R2C2。
Taking y (k) ═ Ut(k)-Uoc(k) Discretizing the formula (6) to obtain a formula (8).
Figure BSA0000240928160000042
The least squares parameter vector is then θ (k) — θ1，k，θ2，k，θ3，k，θ4，k，θ5，k]TThe data vector is
Figure BSA0000240928160000043
Ut(k) And I (k) are the voltage and current measured values recorded in the test.
θ (k) is estimated in real time by recursive least squares, and then can be solved back by equation (7):
Figure BSA0000240928160000044
the expression of a, b, c, d, e in the formula (7) is combined, and then:
Figure BSA0000240928160000045
Figure BSA0000240928160000046
the forgetting factor recurs the least square and introduces the forgetting factor lambda to adjust the weight of new and old data, the value of lambda is close to 1, and the value of lambda is generally more than or equal to 0.95 and less than or equal to 1. The gain coefficient is K (k), the parameter estimation value is theta (k), the covariance matrix P (k), and the forgetting factor recursive least square recursive equation is as follows:
Figure BSA0000240928160000051
parameters of the equivalent circuit model can be estimated in real time by recursion so as to provide real-time and accurate estimation service for the SOC.
Further, estimating the SOC by combining the parameter online identification algorithm and the extended Kalman filtering algorithm.
Referring to fig. 3, at time k, initializing a forgetting factor population by taking a terminal voltage error as a fitness function, iteratively optimizing an optimal forgetting factor at the current time to perform online identification by using a recursive least square method, estimating a current time SOC by combining a parameter identification result with extended kalman filtering, obtaining a corresponding current open-circuit voltage value according to an SOC-OCV (open-circuit voltage) curve relationship, and transmitting the current open-circuit voltage value to a forgetting factor recursive least square online identification algorithm at the next time, so as to circularly recur real-time model online parameters and real-time estimation of the SOC.
The extended kalman filter recursion principle is as follows:
(1) the original nonlinear state equation of the system is set to be in a form of a formula (13), x is a system state variable, u is a system input quantity, z is a system output quantity, omega is state noise, and v is observation noise.
Figure BSA0000240928160000052
(2) Combining the formula (1), linearizing the nonlinear functions f and g at the estimation point by first-order taylor expansion to obtain the formula (14), wherein the system state quantity x is [ U ]1，U2，SOC]TThe system input u is equal to I,system output z ═ UtThen the system discrete state space is:
Figure BSA0000240928160000053
the expressions A (k), B (k) are as follows, wherein eta is the charge-discharge efficiency, CNFor battery capacity, T is the sampling period:
Figure BSA0000240928160000054
(3) a Kalman recursion process, where Q is a state noise covariance matrix and R is an observation noise covariance matrix.
Initializing the state variable and error covariance matrix:
Figure BSA0000240928160000055
updating state estimation time:
Figure BSA0000240928160000056
error covariance matrix time update:
Figure BSA0000240928160000057
updating a gain matrix:
Figure BSA0000240928160000061
updating the state estimation measurement;
Figure BSA0000240928160000062
error covariance matrix measurement update:
Pe(k|k)＝[I(k)-Ke(k)C(k)]Pe(k|k-1) (21)。

Claims (3)

1. the lithium iron phosphate battery SOC estimation method based on dynamic preferred forgetting factor recursive least square online identification is applied to power battery state of charge (SOC) estimation and is characterized in that:
obtaining a corresponding relation point of an Open Circuit Voltage (OCV) and an SOC through a subsection equal interval discharge standing test, and fitting a relation curve of the OCV and the SOC by utilizing a polynomial;
and dynamically and preferably selecting a forgetting factor with a forgetting factor recurrence minimum method suitable at the current moment by adopting a particle swarm optimization algorithm to identify the battery model parameters, and combining the online identification parameters with the SOC-OCV curve and the extended Kalman filtering to estimate the SOC value in real time.
2. The lithium iron phosphate battery SOC estimation method based on dynamic optimization forgetting factor recursion least square online identification as claimed in claim 1, wherein the fitness function of the particle swarm optimization algorithm is the absolute value of the difference between the actually measured terminal voltage and the terminal voltage estimated by the online identification algorithm, the minimum absolute value of the terminal voltage error is taken as a target, iteration is continuously carried out in the selectable range of the forgetting factor until a set termination condition is reached, and the forgetting factor found when the iteration is terminated is the forgetting factor value which is more suitable for parameter online identification of the battery system at the current time and under the current environment.
3. The lithium iron phosphate battery SOC estimation method based on the dynamic optimization forgetting factor recursive least square online identification as claimed in claim 1, characterized in that a forgetting factor population is initialized by taking a terminal voltage error as a fitness function, a forgetting factor more suitable at the current moment is iteratively optimized to be subjected to online identification by a recursive least square method, a parameter identification result is combined with an extended Kalman filtering to estimate the SOC value at the current moment, a corresponding current open-circuit voltage value is obtained from an SOC-OCV curve relationship, the open-circuit voltage value at the current moment is transmitted to a forgetting factor recursive least square online identification algorithm at the next moment, and the real-time estimation of model parameters and SOC is realized by the loop recursive method.
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CN117269801A (en) * 2023-11-22 2023-12-22 潍柴新能源动力科技有限公司 Battery charge state determining method and device and electronic equipment
CN117269801B (en) * 2023-11-22 2024-03-01 潍柴新能源动力科技有限公司 Battery charge state determining method and device and electronic equipment
CN117538760A (en) * 2024-01-10 2024-02-09 广东电网有限责任公司茂名供电局 Lead-acid storage battery parameter identification method and related device
CN117538760B (en) * 2024-01-10 2024-04-23 广东电网有限责任公司茂名供电局 Lead-acid storage battery parameter identification method and related device

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Application publication date: 20210803