CN112881918B - Lead-acid battery SOC estimation method - Google Patents

Lead-acid battery SOC estimation method Download PDF

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CN112881918B
CN112881918B CN202110258248.8A CN202110258248A CN112881918B CN 112881918 B CN112881918 B CN 112881918B CN 202110258248 A CN202110258248 A CN 202110258248A CN 112881918 B CN112881918 B CN 112881918B
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doe
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state
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胡旭
樊霈
曹训训
朱歆州
李松
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Wuhan Institute of Marine Electric Propulsion China Shipbuilding Industry Corp No 712 Institute CSIC
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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
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
    • G01R31/379—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator for lead-acid batteries
    • 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]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC

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Abstract

The invention discloses a lead-acid battery SOC estimation method based on improved lossless Kalman filtering, which comprises the steps of firstly, obtaining relevant data of a state of charge and battery electrolyte density through a mixed pulse power performance test, and obtaining a relation curve of the SOC and the electrolyte density by utilizing least square fitting; then, establishing a state equation and an observation equation by adopting an ampere-hour integration method; and finally, estimating the state of charge of the lead-acid battery by using an improved lossless Kalman filtering algorithm. Compared with the standard UKF algorithm, the improved lossless Kalman filtering algorithm is an adaptive estimation process for the system process and the measurement noise covariance on the basis of the standard UKF algorithm, and the robustness is stronger.

Description

Lead-acid battery SOC estimation method
Technical Field
The invention belongs to the technical field of battery management, and particularly relates to a lead-acid battery SOC estimation method based on lossless Kalman filtering.
Background
Lead-acid batteries are still one of the most widely used chemical power sources at present due to the advantages of mature technology, high safety, low price and the like. The Battery Management System (BMS) has an irreplaceable core position in the aspects of guaranteeing the safety of the power battery and prolonging the service life of the battery, and in recent years, along with the rapid development of industries such as electric ships, electric automobiles and the like, higher requirements are correspondingly provided for the performance index and the reliability of the power battery management system, and accurate estimation of the state of charge (SOC) of the power battery is the key content of the battery management work.
The SOC of the battery is used for representing the remaining capacity of the battery, and cannot be directly measured, and the SOC can only be estimated through parameters such as terminal voltage, charge-discharge current and internal resistance of the battery, and the parameters are influenced by various uncertain factors such as battery aging and ambient temperature. The conventional SOC estimation method mainly comprises an open-circuit voltage method, an ampere-hour integral method, an internal resistance method, a Kalman filtering method, a neural network method and the like, but the conventional estimation method has the problems of low precision or incapability of on-line estimation and the like, Kalman filtering has high precision requirement on a battery model, a data driving method represented by a neural network and fuzzy logic can well process the nonlinear characteristic of a battery system, but the performance of the method depends on the quantity and quality of a training data set, so that the method is difficult to cope with various complex actual working conditions.
Because the density of the electrolyte of the storage battery is closely related to the residual capacity, the method of the invention obtains a self-adaptive SOC-DOE curve by giving an initial relation model between the electrolyte Density (DOE) and the state of charge (SOC) and continuously correcting by utilizing updated data, and then optimizes the output result by combining an ampere-hour integration method and introducing a lossless Kalman filter.
Compared with a Kalman filtering method or an extended Kalman filtering method, lossless Kalman filtering is based on deterministic sampling to obtain a group of Sigma points, and then mean value and covariance estimation of a system state are obtained through a nonlinear state updating equation and an observation correction equation, so that linearization errors are avoided, and the method is more accurate and stable.
Disclosure of Invention
Aiming at the technical problems in the technology, the invention provides a lead-acid battery SOC estimation method based on lossless Kalman filtering.
The technical scheme adopted by the invention for solving the technical problems is as follows: a lead-acid battery SOC estimation method comprises the following steps:
step S1, establishing a lead-acid battery electrolyte density DOE and a mathematical model of the state of charge SOC according to the test data;
step S2, establishing a battery parameter database, adding a temperature compensation and aging degree correction SOC-DOE curve:
the density value obtained in the sampling process is converted into the density at 25 ℃ (normal temperature density d)N) The conversion formula is as follows:
dN＝d-kT*(T-25)
wherein d is the actually measured electrolyte density value, kTThe temperature coefficient of the electrolyte density is shown, T is the electrolyte temperature, and the electrolyte density used below is the normal temperature density;
the self-adaptive SOC-DOE model updating method comprises the following steps:
establishing a database to store the electrolyte density and temperature value of the lead-acid battery in the charging and discharging process, and selecting the maximum value d of the electrolyte density in the last n' times of full chargingNmaxTaking an average value:
Figure GDA0003612897580000021
obtaining an updated SOC-DOE curve, wherein the model is as follows:
Figure GDA0003612897580000022
wherein d ismaxMaximum electrolyte density in initial SOC-DOE curve, SOC (DOE)0Is an initial SOC-DOE function;
step S3, establishing a state equation and an observation equation by taking the SOC as a state variable and the electrolyte density as an observation variable by adopting an ampere-hour integration method based on the relation curve of the SOC-DOE;
step S4: and estimating the SOC of the lead-acid battery by using an improved lossless Kalman filtering algorithm.
Further, in step S1, obtaining DOE values corresponding to the same time interval of SOC through a mixed pulse power performance test, and performing least square fitting to obtain an SOC-DOE curve, where the specific method is as follows: charging to cut-off voltage at 0.1C in a constant temperature environment of 25 ℃, discharging to cut-off density at 0.01C after standing for 1 hour, recording the electrolyte density corresponding to each 1% of SOC, and then obtaining an SOC-DOE curve at 25 ℃ by adopting six-order polynomial fitting, wherein the fitting model is as follows:
SOC(DOE)＝a1(DOE)6+a2(DOE)5+a3(DOE)4+a4(DOE)3+a5(DOE)2+a6(DOE)1+a7。
further, the state equation and the observation equation in step S3 are as follows:
Figure GDA0003612897580000031
in the formula xk＝SOCk，ykDenotes the 25 ℃ density, I, of the battery electrolyte measured by a density sensork-1Represents the bus current value at the k-1 moment, eta is the coulomb coefficient, CNIs the rated capacity, omega, of lead-acid batteryk-1Representing system noise, vkRepresenting the measurement noise.
Further, the step S4 specifically includes:
step S4.1, initializing system parameters:
Figure GDA0003612897580000032
in the formula SOC0Is an initial SOC value, P, determined from electrolyte density measurements and SOC-DOE curves0To estimate the variance, Q is the process noise ωkR is the measurement noise vkThe variance of (a);
step S4.2, obtaining 2n +1 Sigma points and weight thereof according to the system model:
Figure GDA0003612897580000041
wherein λ ═ α2(n + κ) -n represents the distance between the sample point and the mean at the time k-1, n represents the system dimension, κ is a scale parameter and (n + κ) ≠ 0, Pk-1The covariance matrix at the moment k-1;
Figure GDA0003612897580000042
in the formula, alpha epsilon (0, 1) determines the degree of scattering of Sigma points, and beta is used for describing distribution information of chi;
step S4.3, obtaining prediction and prediction covariance matrix of the state through UT conversion:
Xi,k|k-1＝f(Xk-1,ik)+ωk-1,i＝1,…,2n
Figure GDA0003612897580000043
Figure GDA0003612897580000044
Yi,k|k-1＝g(Xk-1,ik)+νk-1
Figure GDA0003612897580000045
Figure GDA0003612897580000046
s4.4, correcting the system state estimation;
step S4.5, the noise covariance is updated.
Further, the method for estimating the revised system state in step S4.4 is as follows:
the joint covariance of the state variables and output variables at time k is:
Figure GDA0003612897580000047
kalman filter gain: kk＝Pxy,k(Py,k)-1
And (3) state estimation correction:
Figure GDA0003612897580000048
and (3) state covariance correction:
Figure GDA0003612897580000049
further, the method for updating the noise covariance in step S4.5 is as follows:
Figure GDA0003612897580000051
in the formula diDenotes the electrolyte density at time k, H, of the cellkIs an approximation of the covariance of the electrolyte density at time k.
Compared with the prior art, the invention has the advantages that:
1, the adaptive SOC-DOE curve can be suitable for the whole life cycle of the battery;
2, the improved lossless Kalman filtering algorithm is a self-adaptive estimation process for a system process and measurement noise covariance on the basis of a standard UKF algorithm.
And 3, correcting the noise covariance by using the electrolyte density corresponding to the online measured battery electrolyte density and the state of charge estimated by the model, and substituting the noise covariance into a state space equation to correct the system state, so that the robustness is stronger.
Drawings
FIG. 1 is a flow chart of an estimation method of the present invention;
FIG. 2 is a diagram illustrating an estimation method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
Referring to fig. 1 and 2, the invention provides a lead-acid battery SOC estimation method based on lossless kalman filtering, which includes the following steps:
step S1, establishing a mathematical model of electrolyte density DOE and state of charge SOC of the lead-acid battery according to the test data: the electrolyte density of a lead-acid battery is an important parameter that directly reflects the remaining capacity of the battery. Through a mixed pulse power performance test, DOE values corresponding to the same time interval of SOC are obtained, and a least square fitting is carried out to obtain an SOC-DOE curve, wherein the specific method comprises the following steps:
charging to cut-off voltage at 0.1C in a constant temperature environment of 25 ℃, discharging to cut-off density at 0.01C after standing for 1 hour, recording the electrolyte density corresponding to each 1% of SOC, and then obtaining an SOC-DOE curve at 25 ℃ by adopting six-order polynomial fitting, wherein the fitting model is as follows:
SOC(DOE)＝a1(DOE)6+a2(DOE)5+a3(DOE)4+a4(DOE)3+a5(DOE)2+a6(DOE)1+a7。
and step S2, establishing a battery parameter database, and adding a temperature compensation and aging degree correction SOC-DOE curve.
The density value obtained in the sampling process is converted into the density at 25 ℃ (normal temperature density d)N) The conversion formula is as follows:
dN＝d-kT*(T-25)
wherein d is the actually measured electrolyte density value, kTThe temperature coefficient of the electrolyte density, T, is the electrolyte temperature, and the electrolyte densities used below are all normal temperature densities.
Establishing a database to store the electrolyte density and temperature value of the lead-acid battery in the charging and discharging process, and selecting the maximum value d of the electrolyte density in the last n' times of full chargingNmaxTaking an average value:
Figure GDA0003612897580000061
obtaining an updated SOC-DOE curve, wherein the model is as follows:
Figure GDA0003612897580000062
wherein d ismaxMaximum electrolyte density in the initial SOC-DOE curve, SOC (DOE)0Is the initial SOC-DOE function.
Step S3, based on the relation curve of SOC-DOE, adopting an ampere-hour integration method to establish a state equation and an observation equation by taking SOC as a state variable and electrolyte density as an observation variable:
Figure GDA0003612897580000063
in the formula, xk＝SOCk，ykRepresents the 25 ℃ density, I, of the battery electrolyte measured by a density sensork-1Represents the bus current value at the k-1 moment, eta is the coulomb coefficient, CNIs the rated capacity, omega, of lead-acid batteryk-1Representing system noise, vkRepresenting the measurement noise.
And step S4, estimating the lead-acid battery SOC by using an improved lossless Kalman filtering algorithm.
And step S4.1, initializing system parameters.
Figure GDA0003612897580000071
In the formula, SOC0Is an initial SOC value, P, determined from electrolyte density measurements and SOC-DOE curves0To estimate the variance, Q is the process noise ωkR is the measurement noise vkThe variance of (c).
And S4.2, obtaining 2n +1 Sigma points and weight values thereof according to the system model.
Figure GDA0003612897580000072
Wherein λ ═ α2(n + k) -n represents the distance between the sample point and the mean at time k-1, n represents the system dimension, Pk-1Is the covariance matrix at time k-1.
Figure GDA0003612897580000073
Wherein, the alpha epsilon (0, 1) determines the degree of scattering of Sigma points, and beta is used for describing the distribution information of chi.
And S4.3, obtaining a prediction and prediction covariance matrix of the state through UT conversion.
Xi,k|k-1＝f(Xk-1,ik)+ωk-1,i＝1,…,2n
Figure GDA0003612897580000074
Figure GDA0003612897580000075
Yi,k|k-1＝g(Xk-1,ik)+νk-1
Figure GDA0003612897580000076
Figure GDA0003612897580000077
And S4.4, correcting the system state estimation.
The joint covariance of the state variables and output variables at time k is:
Figure GDA0003612897580000081
kalman filter gain: kk＝Pxk,k(Py,k)-1
And (3) state estimation correction:
Figure GDA0003612897580000082
state covariance correctionPositive:
Figure GDA0003612897580000083
step S4.5, the noise covariance is updated.
Figure GDA0003612897580000084
In the formula diDenotes the electrolyte density at time k, H, of the cellkIs an approximation of the covariance of the electrolyte density at time k.
In conclusion, compared with the standard UKF algorithm, the improved lossless Kalman filtering algorithm is an adaptive estimation process for a system process and a measurement noise covariance on the basis of the standard UKF algorithm. And correcting the noise covariance by utilizing the electrolyte density corresponding to the on-line measured battery electrolyte density and the state of charge estimated by the model, and substituting the noise covariance into a state space equation to correct the system state.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Claims (6)

1. A lead-acid battery SOC estimation method is characterized in that: comprises the following steps
Step S1, establishing a lead-acid battery electrolyte density DOE and a mathematical model of the state of charge SOC according to the test data;
step S2, establishing a battery parameter database, adding a temperature compensation and aging degree correction SOC-DOE curve:
converting the density value obtained in the sampling process into the density at 25 ℃, wherein the conversion formula is as follows:
dN＝d-kT*(T-25)
wherein d is the actually measured electrolyte density value, kTAs an electrolyteThe temperature coefficient of density, T is the electrolyte temperature, and the electrolyte density used below is the normal temperature density;
establishing a database to store the electrolyte density and temperature value of the lead-acid battery in the charging and discharging process, and selecting the maximum value d of the electrolyte density in the last n' times of full chargingNmaxTaking an average value:
Figure FDA0003612897570000011
obtaining a mathematical model of the updated SOC-DOE curve:
Figure FDA0003612897570000012
wherein d ismaxMaximum electrolyte density in the initial SOC-DOE curve, SOC (DOE)0Is an initial SOC-DOE function;
step S3, establishing a state equation and an observation equation by taking the SOC as a state variable and the electrolyte density as an observation variable by adopting an ampere-hour integration method based on the SOC-DOE curve;
step S4: and estimating the SOC of the lead-acid battery by using an improved lossless Kalman filtering algorithm.
2. The method for estimating the SOC of the lead-acid battery according to claim 1, wherein in step S1, the DOE values corresponding to the same time interval of the SOC are obtained through the hybrid pulse power performance test and subjected to least squares fitting to obtain the SOC-DOE curve: charging to cut-off voltage at 0.1C in a constant temperature environment of 25 ℃, discharging to cut-off density at 0.01C after standing for 1 hour, recording the electrolyte density corresponding to each 1% of SOC, and then obtaining an SOC-DOE curve at 25 ℃ by adopting six-order polynomial fitting, wherein the fitting model is as follows:
SOC(DOE)＝a1(DOE)6+a2(DOE)5+a3(DOE)4+a4(DOE)3+a5(DOE)2+a6(DOE)1+a7。
3. the lead-acid battery SOC estimation method according to claim 1, wherein the state equation and observation equation in step S3 are as follows:
Figure FDA0003612897570000021
in the formula, xk＝SOCk，ykRepresents the 25 ℃ density, I, of the battery electrolyte measured by a density sensork-1Represents the bus current value at the k-1 moment, eta is the coulomb coefficient, CNIs the rated capacity, omega, of lead-acid batteryk-1Representing system noise, vkRepresenting the measurement noise.
4. The lead-acid battery SOC estimation method according to claim 1, wherein the step S4 specifically includes:
step S4.1, initializing system parameters:
Figure FDA0003612897570000022
in the formula SOC0Is an initial SOC value, P, determined from electrolyte density measurements and SOC-DOE curves0To estimate the variance, Q is the process noise ωkR is the measurement noise vkThe variance of (a);
step S4.2, obtaining 2n +1 Sigma points and weight thereof according to the system model:
Figure FDA0003612897570000031
wherein λ ═ α2(n + κ) -n represents the distance between the sample point and the mean at time k-1, n represents the system dimension, κ is a scale parameter and (n + κ) ≠ 0, Pk-1At time k-1A covariance matrix;
Figure FDA0003612897570000032
in the formula, alpha epsilon (0, 1) determines the degree of scattering of Sigma points, and beta is used for describing distribution information of chi;
step S4.3, obtaining prediction and prediction covariance matrix of the state through UT conversion:
Xi,k|k-1＝f(Xk-1,ik)+ωk-1,i＝1,…,2n
Figure FDA0003612897570000033
Figure FDA0003612897570000034
Yi,k|k-1＝g(Xk-1,ik)+νk-1
Figure FDA0003612897570000035
Figure FDA0003612897570000036
s4.4, correcting the system state estimation;
step S4.5, the noise covariance is updated.
5. The lead-acid battery SOC estimation method according to claim 4, characterized in that, the corrected system state estimation method in step S4.4 is as follows:
the joint covariance of the state variables and output variables at time k is:
Figure FDA0003612897570000041
kalman filter gain: kk＝Pxy,k(Py,k)-1
And (3) state estimation correction:
Figure FDA0003612897570000043
and (3) state covariance correction:
Figure FDA0003612897570000044
6. the method of claim 5, wherein the method of updating noise covariance in step S4.5 is as follows:
Figure FDA0003612897570000042
in the formula diDenotes the electrolyte density at time k, H, of the cellkIs an approximation of the covariance of the electrolyte density at time k.
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