CN111198326B - Battery monomer short-circuit resistance online detection method with anti-disturbance characteristic - Google Patents

Battery monomer short-circuit resistance online detection method with anti-disturbance characteristic Download PDF

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CN111198326B
CN111198326B CN202010103235.9A CN202010103235A CN111198326B CN 111198326 B CN111198326 B CN 111198326B CN 202010103235 A CN202010103235 A CN 202010103235A CN 111198326 B CN111198326 B CN 111198326B
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魏中宝
胡鉴
何洪文
阮浩凯
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Beijing Institute of Technology BIT
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    • 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]
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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]
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Abstract

The invention discloses an on-line detection method for a single battery short-circuit resistor with an anti-disturbance characteristic, which comprises the following steps: s1, establishing a battery fractional order model and a state space equation thereof, and determining parameters of the model to be identified; s2, performing an intermittent discharge-standing experiment and an Electrochemical Impedance Spectroscopy (EIS) experiment, further determining a functional relation between a state of charge (SOC) and an open-circuit voltage (OCV), and identifying model parameters according to EIS experiment data; s3, measuring the load current and terminal voltage of the battery in real time; s4, estimating the SOC of the battery on line by adopting a closed-loop observer; and S5, calculating the SOC increment difference, and identifying the battery short-circuit resistance on line by adopting a recursive total least square method (RTLS). The invention adopts a fractional order model with higher precision, better ensures the battery characteristic simulation precision and the SOC estimation precision, has stronger anti-interference capability, can effectively overcome the current and voltage measurement interference and the uncertainty introduced in the calculation process, and improves the robustness and precision of short-circuit resistance identification.

Description

Battery monomer short-circuit resistance online detection method with anti-disturbance characteristic
Technical Field
The invention relates to battery fault detection, in particular to an on-line detection method for a single battery short-circuit resistor with an anti-disturbance characteristic.
Background
The lithium ion battery is the most commonly used power supply of the electric automobile at present, and has the advantages of high specific energy and specific power, long cycle life and the like. However, the safe and efficient use of the lithium ion battery needs to be established on the basis of high-precision and high-robustness fault real-time detection. The short-circuit resistance is one of the most important fault characterization parameters of lithium ions and is directly related to dangerous internal short-circuit and external short-circuit faults. Accurate online short-circuit resistance detection is particularly important for improving the safety of single lithium ion batteries and grouping.
The existing on-line detection method for the short-circuit resistance of the lithium ion battery is extremely limited. The pole piece impedance test based on the electrochemical workstation can realize direct and accurate short-circuit resistance measurement, but the battery needs to be disassembled and tested off-line, and the on-line application is difficult. The short-circuit resistance detection method based on the equivalent circuit model can identify early slight short circuit, is easy to be applied on line, and is representative like short-circuit resistance detection based on an average-difference equivalent model. However, the method needs a lot of monomer information, and the average and monomer difference model has a simple structure, so that the estimation accuracy of the state of charge (SOC) and the short-circuit resistance is limited; in addition, in practical application, the load current and terminal voltage measurement values contain a large amount of interference, and noise information is also introduced in the calculation process, so that the noise resistance of the existing method is to be further enhanced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides the on-line detection method of the battery single short-circuit resistance with the anti-disturbance characteristic, ensures the simulation precision and the SOC estimation precision of the battery characteristic, has strong anti-interference capability, can effectively overcome the current and voltage measurement interference and the uncertainty introduced in the calculation process, and further improves the robustness and the precision of the short-circuit resistance identification.
The purpose of the invention is realized by the following technical scheme: a battery cell short-circuit resistance online detection method with disturbance-resistant characteristics comprises the following steps:
s1, establishing a battery fractional order model and a state space equation thereof, and determining parameters of the model to be identified;
s2, performing intermittent discharge-standing test, and determining a functional relation between SOC and Open Circuit Voltage (OCV); performing Electrochemical Impedance Spectroscopy (EIS) test, and identifying model parameters according to test data;
s3, measuring the load current and terminal voltage of the battery in real time;
s4, estimating the SOC of the battery on line by adopting a closed-loop observer;
and S5, calculating the SOC increment difference, and identifying the battery short-circuit resistance on line by adopting a recursive total least square method (RTLS).
The invention has the beneficial effects that: the invention adopts a fractional order model with higher precision to describe the dynamic characteristics of the lithium ion battery, and can realize the on-line identification of the battery short-circuit resistance only according to the load current and terminal voltage measured values of the single battery; the method has the characteristics of wide detection range, high precision and strong anti-interference performance. Compared with the prior method, the method has the advantages of three aspects: firstly, a fractional order model with higher precision is adopted, so that the battery characteristic simulation precision and the SOC estimation precision are better ensured; secondly, the on-line identification of the short-circuit resistor can be realized only through the terminal voltage of the battery monomer and the load current which are collected in real time without depending on other monomers in the battery pack; and thirdly, the method has strong anti-interference capability, can effectively overcome current and voltage measurement interference and uncertainty introduced in a calculation process, and improves the robustness and precision of short-circuit resistance identification.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of an equivalent circuit of the fractional order model in the embodiment;
FIG. 3 is a flow chart of parameter identification for a fractional order model;
FIG. 4 is a schematic diagram of a closed-loop observer;
FIG. 5 shows the fitting result of the SOC-OCV function;
FIG. 6 is a flow chart of an adaptive extended Kalman filter algorithm.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, an on-line detection method for a battery cell short-circuit resistance with disturbance rejection characteristics includes the following steps:
s1, establishing a battery fractional order model and a state space equation thereof, and determining parameters of the model to be identified;
s101, establishing a battery fractional order equivalent circuit model:
on the basis of a first-order equivalent circuit model, a capacitance element is replaced by a constant phase angle element (CPE), then modeling is carried out by utilizing Grunnwald-Letnikov (G-L) definition in fractional calculus to obtain a fractional order model, and a circuit schematic diagram of the fractional order equivalent circuit model is shown in FIG. 2.
The mathematical expression for the impedance of the CPE is:
Figure BDA0002387571450000021
wherein C ispA constant representing a capacitive effect, n represents a fractional order, and-1<n<1, w represents the angular frequency of the alternating current signal; the fractional order mathematical model of the battery is:
Figure BDA0002387571450000022
Ul(t)＝Uoc(t)+IL(t)R0+Up(t)
Figure BDA0002387571450000023
wherein t is time, ILIs the load current (during discharge I)LIs negative, when charging ILIs a positive number), corresponding toL(t) is the load current at time t, UpTo polarize the voltage, UlIs terminal voltage, where UocLet OCV, η be the coulombic efficiency of the battery, z be SOC, and the parameters to be identified in the model are: battery capacity Q0d.C. resistance R0Polarization resistance RpConstant of capacitance effect Cp。
S102, establishing a discrete state space expression of the fractional order model:
discretizing the fractional order mathematical model according to the G-L definition of the fractional order calculus to obtain the following state space expression:
Figure BDA0002387571450000031
in the formula
Figure BDA0002387571450000032
Is the state variable at time k, y (k) ═ Ul(k) For the system output at time k, the remaining correlation matrices are defined as:
Figure BDA0002387571450000033
Figure BDA0002387571450000034
where Δ t is the sampling period and L is a finite length variable, taking values greater than 64.
S2, performing an intermittent discharge-standing experiment and an EIS experiment, further determining a functional relation between SOC and OCV, and identifying model parameters according to EIS experiment data;
s201, testing the battery capacity, and fully charging the battery by adopting a constant current-constant voltage method under the constant temperature condition, wherein the constant current charging current, the end voltage and the end current adopted in the embodiment are respectively 0.5C, 4.2V and 0.05C. The discharge is then carried out using a nominal current to a discharge cutoff voltage, and the cell capacity is expressed as:
Figure BDA0002387571450000035
in the formula, t0To the discharge start time, t1Is the discharge termination time.
S202, charging the lithium ion battery until the SOC reaches 100%, performing an intermittent discharge-standing experiment, and fitting to determine that the SOC-OCV relational expression is as follows:
Figure BDA0002387571450000036
wherein n ispTo fit the polynomial order, ciAre fitting parameters.
The intermittent discharge-standing experiment means that in the discharge process, the SOC is reduced by 10% every time, the battery is placed for two hours to eliminate the polarization phenomenon of the battery, and then the OCV of the battery is measured to improve the measurement accuracy. OCV corresponding to different SOC can be obtained through experiments, and a functional relation between SOC and OCV can be obtained through fitting. Specifically, the fitting result of the SOC-OCV function relationship in this embodiment is shown in fig. 5.
S203, performing EIS experiments on the target battery, identifying battery model parameters in an off-line mode according to EIS experimental data, wherein the available off-line identification methods comprise a batch least square method, a genetic algorithm, a particle swarm algorithm and the like, but are not limited to the methods; fractional order model parametersThe number identification process is shown in FIG. 3; specifically, in this embodiment, the batch least square method is used to identify the dc internal resistance R of the battery model offline0Internal polarization resistance RpAnd a polarization capacitor Cp。
The EIS experimental method comprises the steps of loading sine wave current signals with specific frequency and small enough amplitude at two ends of a stable battery system, enabling electrode potentials of the battery to generate sine wave response voltage signals with the same frequency, recording the current and voltage signals by using high-precision measuring equipment, enabling a frequency response function of the battery to be electrochemical impedance, measuring a group of frequency response function values under a series of different frequencies to obtain an electrochemical impedance spectrum of the battery, and then carrying out off-line identification on model parameters according to an impedance spectrum characteristic curve.
Specifically, a nonlinear batch least square optimization algorithm is adopted to optimize a target vector to obtain characteristic parameters of a fractional order model, and a target function of the method is as follows:
Figure BDA0002387571450000041
Figure BDA0002387571450000042
Figure BDA0002387571450000043
wherein N is the number of data points obtained by EIS test, wiAngular frequency, Z, corresponding to the ith data pointiIs a frequency wiImpedance of fractional order equivalent Circuit model of'iIs ZiReal part of, Z "iIs ZiImaginary part of, Z'i side testReal part of the impedance, Z', obtained for EIS testing "i side testThe imaginary part of the resulting impedance is tested for EIS.
S3, measuring load current I of battery in real timeL(k) And terminal voltage Ul(k)。
S4, estimating the SOC of the battery in real time by adopting a common closed-loop observer:
and (3) estimating the SOC in real time by adopting a state observer based on error feedback correction based on a discrete state space equation of the fractional order model. The closed-loop observer that can be used includes closed-loop observers including a variety of commonly used state estimation methods, such as a Luneberg observer, extended Kalman filter, unscented Kalman filter, particle filter, synovial observer, H∞Observers, etc., but are not limited to the above; the schematic diagram of the closed loop observer is shown in fig. 4; specifically, the embodiment adopts an Adaptive Extended Kalman Filter (AEKF) algorithm to estimate the SOC in real time, the AEKF algorithm is an improved form based on the Extended Kalman Filter (EKF) algorithm, the EKF algorithm assumes that the input and output noises of the system are all white gaussian noises, and the vehicle-mounted environment actually has various noises, so the AEKF algorithm corrects the process noise and the measurement noise when updating the measurement data of each step in order to cope with the influence of noise uncertainty on the estimation result, and the uncertainty of the estimation result caused by unknown noise to the system is reduced. The flow of the AEKF algorithm is as follows:
discretizing the state space equation of the linear system as:
xk+1＝f(xk,uk)+ek
yk＝g(xk,uk)+vk
defining:
Figure BDA0002387571450000051
wherein xkIs the state vector at time k, ykIs the system output at time k, ukFor the input of the system at time k, ekRandom process noise reflects some unmeasured interference inputs that affect the system state; v. ofkFor measuring noise, reflecting the system output ykThe measurement error of (2).
Initializing AEKF filtering:
Figure BDA0002387571450000052
E[·]period representing random variableInspection is performed.
Iterative calculations are performed at each measurement interval:
and (3) AEKF filtering prior estimation, namely updating the state parameter value and the error covariance matrix at the k moment in real time by the state parameter value and the error covariance matrix at the k-1 moment:
state prior estimation:
Figure BDA0002387571450000053
error covariance matrix prior estimation:
Figure BDA0002387571450000054
wherein
Figure BDA0002387571450000055
And
Figure BDA0002387571450000056
and respectively representing the state parameter value and the prior estimated value of the state error covariance at the moment k, wherein Q is a covariance matrix of input measurement noise.
The kalman gain matrix is:
Figure BDA0002387571450000057
wherein
Figure BDA0002387571450000058
A covariance matrix of the noise is measured for the output.
Estimation of AEKF filtered posterior parameters, i.e. using measured output values at time K and the above Kalman gain matrix KkAnd updating the state parameters and the error covariance matrix at the moment k in real time to obtain a more accurate estimation result:
updating an estimation error:
Figure BDA0002387571450000059
updating the state posterior:
Figure BDA00023875714500000510
updating the error covariance matrix posteriori:
Figure BDA00023875714500000511
wherein I is an identity matrix;
Figure BDA0002387571450000061
the update of (1) is:
process noise variance update:
Figure BDA0002387571450000062
and (3) updating the measurement noise variance:
Figure BDA0002387571450000063
in the formula dk＝(1-ρ)/(1-ρk+1) ρ is a forgetting factor, and is generally a decimal between 0.9 and 1.
The AEKF can estimate the noise variance in real time on line
Figure BDA0002387571450000064
And
Figure BDA0002387571450000065
the estimation result is more accurate, and the alternating cycle updating of the state parameter value and the noise characteristic is realized.
According to the state space equation established in S102, the system state, input, and output are respectively defined as:
Figure BDA0002387571450000066
u(k)＝IL(k)，y(k)＝Ul(k)，
correspondingly, the correlation matrix in the adaptive extended kalman filter algorithm is:
Figure BDA0002387571450000067
D＝R0。
estimating the SOC of the battery on line according to the algorithm flow of the AEKF, and recording the optimal estimated value of the SOC of the battery at the k moment as Ze(k)。
S5, calculating the difference of SOC increment, and identifying the short-circuit resistance of the battery on line by adopting a recursive total least square method (RTLS);
s501, calculating SOC increment difference
And calculating the SOC increment from the k-1 moment to the k moment by using the load current value at the k-1 moment:
Figure BDA0002387571450000068
then the difference between the SOC increment zo (k) directly calculated by using the load current measurement value and the SOC increment estimated by using the AEKF algorithm between the time k-1 and the time k is:
ΔZ(k)＝ZO(k)-[Ze(k)-Ze(k-1)]
s502, establishing a regression equation:
the theoretical function relationship of the terminal voltage, the SOC increment difference and the short-circuit resistance is as follows:
Figure BDA0002387571450000069
order to
Figure BDA00023875714500000610
And establishing a regression equation according to a theoretical functional relation:
Ul(k)＝ω(k)·θ(k)
terminal voltage measurement U in regression equationl(k) As an output, ω (k) related to the difference of the SOC increment is used as an input, and θ (k) is a parameter R to be identifiedISC。
S503, short-circuit resistance is identified on line by adopting recursive overall least square algorithm
Exist for solving both input and outputRegression of interference, the embodiment of the invention adopts a recursive total least square method to carry out short-circuit resistance RISCAnd performing online identification.
Referring to the regression description method, the recursive least squares algorithm flow is as follows:
firstly, algorithm parameters are initialized according to existing information and experience, specifically, the following initialization parameters are adopted in the embodiment: g (0) ═ 0, pi (0) ═ 0, λ0(0)＝0，θ(0)＝0，φ(0)＝0，β＝0.5，μ＝0.998；
Iterative calculations are performed at each predetermined calculation point:
g(k)＝μg(k-1)+ω(k-1)ω(k)
π(k)＝μπ(k-1)+ω2(k)
Figure BDA0002387571450000071
λ0(k)＝μλ(k-1)(β+θ2(k-1))+(θ(k-1)ω(k)-Ul(k))2
φ(k)＝μφ(k-1)+ω(k)Ul(k)
a(k)＝ω3(k)φ(k)
Figure BDA0002387571450000072
Figure BDA0002387571450000073
Figure BDA0002387571450000074
θ(k)＝θ(k-1)+α(k)ω(k)
Figure BDA0002387571450000075
wherein theta (k) represents the parameter to be identified at the moment kRISCThe estimated value of (1), mu, is a forgetting factor, and other intermediate variables can be obtained according to initialization and iterative calculation.
In conclusion, the invention establishes a state space equation according to the established fractional order equivalent circuit model of the battery, calculates the SOC increment difference of the battery by using the load current and the terminal voltage measurement value of the battery through the ampere-hour accumulation characteristic and a closed-loop SOC observer with error feedback correction, and identifies the short-circuit resistance of the battery on line by adopting a recursive total least square method. Compared with the traditional short-circuit resistance detection method based on a simple equivalent circuit model, the method is independent of other monomers in the battery pack, and has wider application range; the adopted fractional order equivalent circuit model has higher precision and can better simulate the nonlinear dynamic characteristics of the battery; the recursive total least square method used by the invention has stronger resistance to input and output interference, can effectively overcome uncertainty caused by measurement noise and calculation errors, and improves the robustness and precision of short circuit resistance estimation.
Finally, it is to be understood that the foregoing is illustrative of the preferred embodiments of the present invention and is not to be construed as limited to the forms disclosed herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein and other features and advantages disclosed herein as well as those skilled in the relevant art and equivalents thereof. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (7)

1. A battery monomer short circuit resistance on-line detection method with disturbance-resistant characteristic is characterized in that: the method comprises the following steps:
s1, establishing a battery fractional order equivalent circuit model and a state space equation thereof, and determining parameters of the model to be identified;
s2, performing intermittent discharge-standing test, and determining a functional relation between the SOC and the OCV; performing electrochemical impedance spectrum test, and identifying model parameters according to test data;
s3, measuring the load current and terminal voltage of the battery in real time;
s4, estimating the SOC of the battery on line by adopting a closed-loop state observer;
s5, calculating SOC increment difference, and identifying the battery short-circuit resistance on line by adopting a recursive total least square algorithm; the SOC increment difference is a difference value between an SOC increment which is directly calculated by adopting a load current measurement value from the moment k-1 to the moment k and an SOC increment which is estimated by adopting a closed-loop observer, wherein the SOC increment is a variation of the SOC from the moment k-1 to the moment k.
2. The on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 1, wherein: the step S1 includes the following sub-steps:
s101, establishing a battery fractional order equivalent circuit model:
on the basis of a first-order equivalent circuit model, replacing a capacitance element with a constant phase angle element, and modeling by utilizing a G-L definition in fractional order calculus to obtain a fractional order equivalent circuit model;
the mathematical expression for the impedance of the constant phase angle element CPE is:
Figure FDA0002956720540000011
wherein, CpRepresents a constant of a capacitive effect, n represents a fractional order, and-1<n<1, w represents the angular frequency of the alternating current signal;
the mathematical description of the fractional order equivalent circuit model of the battery is:
Figure FDA0002956720540000012
Ul(t)＝Uoc(t)+IL(t)R0+Up(t)
Figure FDA0002956720540000013
wherein t is time, ILFor load current, during discharge ILIs negative, when charging ILIs a positive number, corresponding toL(t) is the load current at time t, UpTo polarize the voltage, UlIs terminal voltage, UocIs OCV, η is the coulombic efficiency of the battery, and z is SOC; the parameters to be identified in the model are: battery capacity Q0d.C. resistance R0Polarization resistance RpConstant of capacitance effect Cp；
S102, establishing a discrete state space equation of the fractional order equivalent circuit model:
according to the G-L definition of the fractional calculus, discretizing the mathematical description of the fractional equivalent circuit model to obtain the following state space equation:
Figure FDA0002956720540000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002956720540000022
is the state variable at time k, y (k) ═ Ul(k) For the system output at time k,. DELTA.t is the sampling period, L is a finite length variable, A, B are coefficient matrices and:
Figure FDA0002956720540000023
Figure FDA0002956720540000024
3. the on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 2, wherein: the step S2 includes the following sub-steps:
s201, testing the battery capacity, fully charging the battery by adopting a constant current-constant voltage method under a constant temperature condition, and then discharging to a discharge cut-off voltage under a nominal current, wherein the battery capacity is expressed as follows:
Figure FDA0002956720540000025
in the formula, t0To the discharge start time, t1Is the discharge termination time;
s202, carrying out intermittent discharge-standing test, and fitting to determine an SOC-OCV relational expression as follows:
Figure FDA0002956720540000026
wherein n ispTo fit the polynomial order, ciIs a fitting coefficient;
s203, performing electrochemical impedance spectrum test on the battery, and performing R on a battery model according to the data obtained by the test0、RpAnd CpAnd performing off-line identification.
4. The on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 3, wherein: the method for the off-line identification includes but is not limited to one of a batch least square method, a genetic algorithm and a particle swarm algorithm.
5. The on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 3, wherein: when the closed loop observer is used to estimate the SOC of the battery in real time in step S4, the estimation result of the SOC at the time k is recorded as Ze(k)。
6. The on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 5, wherein: the closed-loop observer includes, but is not limited to, a Lorber observer, extended Kalman Filter, NoTrace Kalman filter, particle filter, synovial observer and H∞One of the observers.
7. The on-line detection method for the short-circuit resistance of the battery cell with the disturbance rejection characteristic as claimed in claim 5, wherein: the step S5 includes the following sub-steps:
s501, calculating SOC increment difference
And calculating the SOC increment from the k-1 moment to the k moment by using the load current measured value at the k-1 moment:
Figure FDA0002956720540000031
the difference between the SOC increment zo (k) directly calculated from the load current measurement value from time k-1 to time k and the SOC increment estimated by the closed-loop observer is:
ΔZ(k)＝ZO(k)-[Ze(k)-Ze(k-1)]；
s502, establishing a regression equation:
the theoretical function relationship of the terminal voltage, the SOC increment difference and the short-circuit resistance is as follows:
Ul(k)＝ω(k)·θ(k)
wherein ω (k) is Q0Δ Z (k)/[ delta ] t, θ (k) is the parameter R to be identified at the time kISC，RISCThe resistance value of the battery short-circuit resistor;
s503, performing online identification on the short-circuit resistance by adopting a recursive overall least square algorithm:
for parameters g, pi, lambda0θ, β, φ, initializing;
iterative calculations are performed at each predetermined calculation point:
g(k)＝μg(k-1)+ω(k-1)ω(k)
π(k)＝μπ(k-1)+ω2(k)
Figure FDA0002956720540000032
λ0(k)＝μλ(k-1)(β+θ2(k-1))+(θ(k-1)ω(k)-Ul(k))2
φ(k)＝μφ(k-1)+ω(k)Ul(k)
a(k)＝ω3(k)φ(k)
Figure FDA0002956720540000033
Figure FDA0002956720540000034
Figure FDA0002956720540000041
θ(k)＝θ(k-1)+α(k)ω(k)
Figure FDA0002956720540000042
wherein mu is a forgetting factor, and the contained intermediate variables are obtained according to initialization and iterative calculation.
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