CN108414947B - Space lithium ion battery state joint estimation method based on multiple time scales - Google Patents

Space lithium ion battery state joint estimation method based on multiple time scales Download PDF

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CN108414947B
CN108414947B CN201810575839.6A CN201810575839A CN108414947B CN 108414947 B CN108414947 B CN 108414947B CN 201810575839 A CN201810575839 A CN 201810575839A CN 108414947 B CN108414947 B CN 108414947B
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刘大同
彭宇
印学浩
刘旺
彭喜元
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Harbin Institute of Technology
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Abstract

A multi-time scale-based spatial lithium ion battery state joint estimation method relates to the field of lithium ion battery management and aims to solve the problem that the existing method cannot be applied to SOC long-term estimation of a battery under the SOH degradation condition. Establishing a battery equivalent circuit model; carrying out model parameter identification, and establishing model parameter interpolation tables under different SOH conditions, wherein one SOH condition corresponds to a group of model parameter interpolation tables; each group of model parameter interpolation tables meet the condition that the voltage response error is in an allowable range when a current excitation signal is applied to the circuit model respectively; establishing a multi-time scale state space equation; and estimating the SOC under the micro scale and the SOH under the macro scale by adopting the established multi-time scale state space equation based on the UPF algorithm, and updating a battery capacity and model parameter interpolation table for SOC estimation according to the degradation condition of the SOH. Suitable for estimating SOC.

Description

Space lithium ion battery state joint estimation method based on multiple time scales
Technical Field
The invention relates to the field of lithium ion battery management, in particular to a lithium ion battery state joint estimation method based on multiple time scales.
Background
The lithium ion battery has the advantages of high single output voltage, long cycle life, low self-discharge rate, high energy density, no environmental pollution and the like, is widely applied to the fields of consumer electronics, electric automobiles, communication energy storage base stations and the like, and is gradually expanded to the military fields of aviation, aerospace, navigation and the like. Particularly in the aspect of space satellite application, the lithium ion battery can greatly reduce the weight and the volume of load, has great advantages compared with the traditional nickel-hydrogen battery and nickel-chromium battery, and becomes a third-generation satellite energy storage battery. As the only energy source for the operation of the satellite in the earth shadow period, the safe and reliable operation of the lithium ion battery is the premise for ensuring the on-orbit operation of the space vehicles such as the satellite. Therefore, lithium ion battery management for space-oriented applications has become a hot spot of research.
The State of Charge (SOC) estimation is one of the core contents of lithium ion battery management, and the online real-time estimation can predict the running time of the system and formulate a reasonable battery Charge-discharge strategy, thereby having important significance for guaranteeing the safe running of the system. For space application, SOC estimation can provide important reference for energy distribution and optimal management of a lithium ion battery or a spacecraft power subsystem. The strong non-linear characteristics of the lithium ion battery itself add difficulty to the estimation of SOC. Meanwhile, the State of Health (SOH) of the lithium ion battery decreases during long-term use, which causes changes in battery capacity parameters and model parameters (hereinafter, both are collectively referred to as "system parameters"), and these may challenge long-term estimation of SOC.
The model method is a typical SOC estimation method, and requires establishing an equivalent model describing battery characteristics, such as an equivalent circuit model or an electrochemical model, and performing SOC Filtering estimation by combining with certain nonlinear Filtering algorithms, such as extended kalman Filtering, Unscented kalman Filtering, Particle Filtering, Unscented Particle Filtering (UPF), and the like. The method has good SOC estimation performance at the initial stage of battery use, but along with the aging of the battery in the long-term use process, namely the SOH degradation, the representation capability of the originally established battery equivalent model and the corresponding model parameter interpolation table is reduced, and simultaneously the capacity parameter of the battery is changed, which can cause the reduction and even the divergence of the SOC estimation performance. That is, this type of method still cannot effectively solve the long-term SOC estimation problem of the battery under the SOH degradation condition. Therefore, developing a long-term estimation method of SOC that can adapt to SOH degradation conditions is a technical difficulty of current battery management.
Disclosure of Invention
The invention aims to solve the problem that the existing method cannot be suitable for long-term SOC estimation of a battery under the SOH degradation condition, and provides a spatial lithium ion battery state joint estimation method based on multiple time scales.
The invention relates to a space lithium ion battery state joint estimation method based on multiple time scales, which comprises the following steps:
step one, establishing a battery equivalent circuit model;
identifying model parameters, and establishing model parameter interpolation tables under different SOH conditions, wherein one SOH condition corresponds to one group of model parameter interpolation tables;
step three, respectively applying current excitation signals to the circuit model for each group of model parameter interpolation tables identified in the step two, judging whether voltage response errors are all in an allowable range, if so, performing the step four, otherwise, returning to the step two;
establishing a multi-time scale state space equation, namely establishing a state space equation of the SOC estimation system under the microscale and a state space equation of the SOH estimation system under the macroscale;
and step five, estimating the SOC under the micro scale and the SOH under the macro scale by adopting the multi-time scale state space equation established in the step four based on the UPF algorithm, and updating the battery capacity and the model parameter interpolation table for SOC estimation according to the degradation condition of the SOH.
The method adopts micro-scale estimation for the SOC of the battery which changes rapidly along with time, and estimates the SOH of the battery which changes slowly under the macro scale, and fully considers the change of the SOH in the estimation process of the SOC of the battery, thereby improving the long-term estimation performance of the SOC.
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FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a battery equivalent circuit model;
FIG. 3 is a flow chart of estimation of SOC at the micro-scale and SOH at the macro-scale based on the UPF algorithm;
FIG. 4 is a graph of operating current under RW conditions;
FIG. 5 is a load voltage curve under RW conditions;
FIG. 6 is a diagram of the result of SOC estimation for RW conditions without regard to SOH degradation;
(a) is SOC estimated value curve, (b) is estimation error curve;
FIG. 7 is a diagram of the SOC estimation results for RW conditions obtained by the method of the present invention;
(a) is SOC estimated value curve, (b) is estimation error curve;
FIG. 8 is a comparison of model parameter interpolation tables before and after updating;
(a) is R0A curve of variation with SOC, wherein (b) is RpA curve of variation with SOC, (C) is CpA curve relating to the change in SOC, wherein (d) is EmAnd the change relation curve of the SOC.
Detailed Description
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, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
A space lithium ion battery state joint estimation method based on multiple time scales comprises the following steps:
step one, establishing a battery equivalent circuit model;
the battery equivalent circuit model in the step one is a first-order RC circuit model, and the model parameter comprises ohmic internal resistance R0Polarization resistance RpAnd a polarization capacitor CpAnd electromotive force E of power supplym(ii) a The polarized capacitor is connected with the polarized resistor in parallel to form a parallel RC branch, one end of the branch is connected with the load, the other end of the branch is connected with the high potential end of the power supply after being connected with the ohmic resistor in series, and the low potential end of the power supply is connected with the load.
And secondly, identifying model parameters, building a model parameter identification simulation environment in Matlab/Simulink, and building model parameter interpolation tables under different SOH conditions, wherein one SOH condition corresponds to one group of model parameter interpolation tables.
The test data for identifying the multiple groups of model parameters are HPPC working condition data under different SOH conditions, the SOH degradation interval is 0.05, and the default battery failure threshold value is SOH which is 0.8. Respectively taking the HPPC working condition current as the excitation input of the identification environment, and taking the voltage as the response output of the identification environment. And establishing model parameter interpolation tables under different SOH conditions according to the obtained multiple groups of model parameter identification results.
Step three, evaluating a plurality of groups of model parameters: for each group of model parameter interpolation tables identified in the step two, respectively applying current excitation signals to the circuit model, judging whether voltage response errors are all in an allowable range, if so, performing the step four, otherwise, returning to the step two;
the voltage response error is the residual between the response voltage and the reference voltage (true value).
Establishing a multi-time scale state space equation, namely establishing a state space equation of the SOC estimation system under the microscale and a state space equation of the SOH estimation system under the macroscale;
(1) the state space equation of the SOC estimation system is as follows:
xk＝Ak-1xk-1+Bk-1Uk-1+wk-1
yk＝Ckxk-DkUk+f(SOCk)+vk
wherein k is a time scale at the microscopic scale, xkIs the system state quantity at time k, xk＝[Up,k,SOCk]T，Up,kTerminal voltage, U, of parallel RC branch at time kk-1Is the system control quantity at the time k-1, wk-1Systematic process noise at time k-1, Ak-1And Bk-1Respectively corresponding state transition transformation matrixes of the system state quantity and the system control quantity at the moment of k-1; y iskSystem observations at time k, Em＝f(SOCk)，EmThe value is obtained by looking up according to the model parameter interpolation table, SOCkSOC at time k, vkMeasurement noise at time k, CkThe transformation moment between the state quantity and the observed quantity corresponding to the system state quantity at the time kArray, DkAnd the transformation matrix is a transformation matrix between the state quantity and the observed quantity corresponding to the system control quantity at the time k.
(2) The state space equation of the SOH estimation system is:
θl＝θl-1+ξl-1
Figure BDA0001686889750000041
wherein l is a time scale under a macroscopic scale, and the system state quantity theta at the moment ll＝[al,bl,cl,dl]T，al，bl，clAnd dlParameters of the dual-exponential degradation model, ξ, at time l, respectivelyl-1System process noise at time l-1; thetal,1，θl,2，θl,3And thetal,4The first dimension, the second dimension, the third dimension and the fourth dimension of the system state quantity, and the on-line health factor HI at the moment llAs an observed quantity of the system, mulFor noise measurement, the cycle is the current charge/discharge cycle number of the battery, g (SOH)l) Is a mapping relation function between the SOH and the online HI.
Step five, multi-time scale state joint estimation based on the UPF algorithm: the multi-time scale state joint estimation comprises two parts of SOC online estimation at a micro scale and SOH estimation at a macro scale. The micro-scale estimation is used for the battery state quantity SOC which changes faster with time, while the estimation is performed on the macro-scale for the battery state quantity SOH which changes very slowly. And when the time scale k under the microscale reaches a charge-discharge cycle period, the scale conversion condition is met, and the time scale k is switched to the macroscale l to carry out SOH estimation once. When the SOH estimation under the macro scale is completed once, the current SOH degradation condition needs to be judged in the micro SOC estimation to determine whether to update the battery capacity parameter and the model parameter interpolation table. Therefore, the change of the SOH is fully considered in the estimation process of the SOC of the battery, and the battery capacity parameter and the model parameter interpolation table for SOC estimation are updated according to the degradation condition of the SOH, so that the long-term estimation performance of the SOC is improved.
The estimation process of SOC at the microscopic scale is as follows:
i. initialization: the UPF algorithm particle number N, the initial value of state quantity, the noise variance and the like for SOC estimation under the micro scale are set, and the particle distribution and the covariance matrix thereof are initialized.
And ii, judging whether the time scale k under the micro scale reaches a charge-discharge cycle period, if so, carrying out SOH estimation, otherwise, judging the current SOH degradation condition according to the SOH estimation result under the macro scale to determine whether the system parameters need to be updated, if so, executing iii, otherwise, executing iv.
And iii, updating the battery capacity parameter and the model parameter interpolation table according to the SOH at the current moment.
Suggested particle distribution
1) The sigma point distribution of each particle is calculated:
Figure BDA0001686889750000051
Figure BDA0001686889750000052
Figure BDA0001686889750000053
wherein the content of the first and second substances,
Figure BDA0001686889750000054
in order to generate the sigma point matrix,
Figure BDA0001686889750000055
is an amplification matrix of the system state quantity and noise,
Figure BDA0001686889750000056
an augmented covariance matrix of state quantities and noise,
Figure BDA0001686889750000057
l is the dimension of the state quantity and λ is a constant. w and Q are the state noise matrix and variance, respectively, and v and R are the measurement noise matrix and variance.
2) And (3) time updating:
Figure BDA0001686889750000058
Figure BDA0001686889750000059
Figure BDA00016868897500000510
Figure BDA00016868897500000511
Figure BDA00016868897500000512
wherein the content of the first and second substances,
Figure BDA00016868897500000513
the value is updated for one step of the system state quantity,
Figure BDA00016868897500000514
is an estimated value of the state quantity at the moment k-1,
Figure BDA00016868897500000515
for state quantity process noise at time k-1, Ak-1And Bk-1For state transition transformation matrices, Uk-1A system control quantity;
Figure BDA00016868897500000520
is a state quantity of oneThe step prediction value is obtained by the step prediction method,
Figure BDA00016868897500000516
and
Figure BDA00016868897500000517
is a weight constant;
Figure BDA00016868897500000518
one-step prediction value for covariance;
Figure BDA00016868897500000519
updating the value of the observed quantity by one step, CkAnd DkF (-) represents SOC and electromotive force E as transformation matrix between state quantity and observed quantitymFunctional relationship between;
Figure BDA0001686889750000061
and predicting the one-step prediction value of the observed quantity.
3) Measurement updating:
Figure BDA0001686889750000062
Figure BDA0001686889750000063
Figure BDA0001686889750000064
Figure BDA0001686889750000065
Figure BDA0001686889750000066
wherein the content of the first and second substances,
Figure BDA0001686889750000067
measuring a variance matrix;
Figure BDA0001686889750000068
is the covariance matrix between the state quantities and the measurements; kkIs the Kalman filter gain;
Figure BDA0001686889750000069
is the estimated value of the system state at the moment k;
Figure BDA00016868897500000610
an updated covariance matrix.
v, weight calculation and normalization:
Figure BDA00016868897500000611
Figure BDA00016868897500000612
wherein q isiThe weight value of each particle is used as the weight value,
Figure BDA00016868897500000613
is a normalized particle weight value, ykIs the system observed quantity at time k.
Particle resampling:
Figure BDA00016868897500000614
wherein the content of the first and second substances,
Figure BDA00016868897500000615
and
Figure BDA00016868897500000616
the original particles and their covariance matrix,
Figure BDA00016868897500000617
and
Figure BDA00016868897500000618
the resulting particles and their covariance matrix are resampled,
Figure BDA00016868897500000619
is a random number between 0 and 1.
Soc estimation:
Figure BDA00016868897500000620
therein, SOCkAs a result of the SOC estimation at time k,
Figure BDA00016868897500000621
for each of the estimated values of SOC for each particle,
Figure BDA00016868897500000622
is the second dimension value of the state quantity.
Model parameter interpolation calculation: SOC according to estimated value of k timekAnd updating the parameter R by combining the model parameter difference table0，Rp，CpAnd Em。
And (5) repeatedly executing the ii to viii until the full life cycle of the battery is reached, and exiting the estimation cycle.
The SOH estimation process at the macro scale is as follows:
1. initialization: the UPF algorithm particle number M, the initial value of state quantity, the noise variance and the like for SOH estimation under the macro scale are set, and the particle distribution and the covariance matrix thereof are initialized.
2. Suggested distribution of particles
1) The sigma point distribution of each particle is calculated:
Figure BDA0001686889750000071
Figure BDA0001686889750000072
Figure BDA0001686889750000073
wherein the content of the first and second substances,
Figure BDA0001686889750000074
in order to generate the sigma point matrix,
Figure BDA0001686889750000075
is an amplification matrix of the system state quantity and noise,
Figure BDA0001686889750000076
an augmented covariance matrix of state quantities and noise,
Figure BDA0001686889750000077
l is the dimension of the state quantity and λ is a constant. ξ and Q are the state noise matrix and variance, respectively, and μ and R are the measurement noise matrix and variance.
2) And (3) time updating:
Figure BDA0001686889750000078
Figure BDA0001686889750000079
Figure BDA00016868897500000710
Figure BDA00016868897500000711
Figure BDA00016868897500000712
wherein the content of the first and second substances,
Figure BDA00016868897500000713
the value is updated for one step of the system state quantity,
Figure BDA00016868897500000714
is an estimated value of the state quantity at the moment l-1,
Figure BDA00016868897500000715
process noise of state quantity at the moment l-1;
Figure BDA00016868897500000716
in order to predict the value of the state quantity in one step,
Figure BDA00016868897500000717
and
Figure BDA00016868897500000718
is a weight constant;
Figure BDA00016868897500000719
one-step prediction value for covariance;
Figure BDA00016868897500000720
the value is updated for one step of the observed quantity,
Figure BDA00016868897500000721
and
Figure BDA00016868897500000722
respectively representing a first dimension, a second dimension, a third dimension and a fourth dimension of the state quantity, g (-) represents the mapping relation between the online HI and the SOH, and cycle is the current charge-discharge cycle number of the battery;
Figure BDA00016868897500000723
and predicting the one-step prediction value of the observed quantity.
3) Measurement updating:
Figure BDA0001686889750000081
Figure BDA0001686889750000082
Figure BDA0001686889750000083
Figure BDA0001686889750000084
Figure BDA0001686889750000085
wherein the content of the first and second substances,
Figure BDA0001686889750000086
measuring a variance matrix;
Figure BDA0001686889750000087
is the covariance matrix between the state quantities and the measurements; klIs the Kalman filter gain;
Figure BDA0001686889750000088
is the estimated value of the system state at the moment l;
Figure BDA0001686889750000089
an updated covariance matrix.
3. Weight calculation and normalization:
Figure BDA00016868897500000810
Figure BDA00016868897500000811
wherein q isjThe weight value of each particle is used as the weight value,
Figure BDA00016868897500000812
is normalized particle weight, HIlIs the system observation at time l,
Figure BDA00016868897500000813
and
Figure BDA00016868897500000814
the first dimension, the second dimension, the third dimension and the fourth dimension of the state quantities are represented respectively.
4. And (3) resampling particles:
Figure BDA00016868897500000815
wherein the content of the first and second substances,
Figure BDA00016868897500000816
and
Figure BDA00016868897500000817
the original particles and their covariance matrix,
Figure BDA00016868897500000818
and
Figure BDA00016868897500000819
resampling generated particles and their covariance matrix, rl jIs a random number between 0 and 1.
SOH estimation:
Figure BDA00016868897500000820
wherein, SOHlFor the SOH estimation result at time i,
Figure BDA00016868897500000821
the SOH estimate for each particle.
And (3) experimental verification:
a Random Walk (RW) test data set of the NASA PCoE battery sample B09 is selected to be subjected to experimental verification of a multi-time scale state joint estimation method. The battery operating current and voltage change under the working condition have strong randomness, and are very complex battery operating conditions, and the corresponding operating current and load voltage are respectively shown in fig. 4 and fig. 5. In the experiment, the SOH degradation of the battery is not considered, that is, it is assumed that the battery system parameters (capacity and model parameter interpolation table) are not changed, that is, the battery capacity is still the rated capacity of the new battery (2.0977Ah), the model parameter table is the interpolation table when the SOH is 100%, and the corresponding SOC estimation result is shown in fig. 6.
If a spatial lithium ion battery state joint estimation method based on multi-time scale is adopted, the SOH estimated value at the moment is 96.81% through macroscopic scale estimation. When the model parameter interpolation table used for the microscopic SOC estimation is updated based on the current SOH estimation result and the battery capacity is set to 2.0308Ah again, the SOC estimation result at this time is shown in fig. 7, and the index pair ratio is shown in table 1. In the experiment, the model parameter interpolation table at the current time is updated with the corresponding interpolation table when SOH is 95%, and the interpolation table pair before and after the update is shown in fig. 8.
TABLE 1 SOC estimation Performance comparison
Figure BDA0001686889750000091
From the experimental results it can be derived: for the RW operating mode in this experiment, if the SOH degradation condition of the battery is not considered, the maximum SOC estimation error is 0.2728, the average error is 0.0909, and the root mean square error is 0.1149 using the system parameters when the battery is new. If the space lithium ion battery state joint estimation method based on the multi-time scale is adopted, namely the degradation of the battery SOH is considered in the SOC long-term estimation, and the battery capacity parameter and the model parameter interpolation table are updated according to the estimation result of the SOH, the maximum error of the SOC estimation at the moment is 0.1114, the root mean square error is 0.0543, and the average error is also reduced to 0.0463, so that the SOC long-term estimation performance is greatly improved. In addition, the method provided by the invention still has good estimation precision and stability under the complicated RW working condition, and the average estimation error is within 5%.

Claims (3)

1. A space lithium ion battery state joint estimation method based on multiple time scales is characterized by comprising the following steps:
step one, establishing a battery equivalent circuit model;
identifying model parameters, and establishing model parameter interpolation tables under different SOH conditions, wherein one SOH condition corresponds to one group of model parameter interpolation tables;
the test data for identifying the multiple groups of model parameters are HPPC working condition data under different SOH conditions, the SOH degradation interval is 0.05, and the battery failure threshold value is 0.8; respectively taking the HPPC working condition current as an excitation input of an identification environment, and taking the voltage as a response output of the identification environment; establishing model parameter interpolation tables under different SOH conditions according to the obtained multiple groups of model parameter identification results;
step three, respectively applying current excitation signals to the circuit model for each group of model parameter interpolation tables identified in the step two, judging whether voltage response errors are all in an allowable range, if so, performing the step four, otherwise, returning to the step two;
the voltage response error is a residual error between a response voltage and a reference voltage, wherein the reference voltage is a real voltage;
establishing a state space equation of the SOC estimation system under the microscale and a state space equation of the SOH estimation system under the macroscale;
the state space equation of the SOC estimation system is as follows:
xk＝Ak-1xk-1+Bk-1Uk-1+wk-1
yk＝Ckxk-DkUk+f(SOCk)+vk
wherein k is a time scale at the microscopic scale, xkIs the system state quantity at time k, Uk-1Is the system control quantity at the time k-1, wk-1Systematic process noise at time k-1, Ak-1And Bk-1Respectively corresponding state transition transformation matrixes of the system state quantity and the system control quantity at the moment of k-1; y iskSystem observations at time k, Em＝f(SOCk)，EmThe value is obtained by looking up according to the model parameter interpolation table, SOCkSOC at time k, vkMeasurement noise at time k, CkA transformation matrix between the observed quantities and the state quantities corresponding to the system state quantities at time k, DkA transformation matrix between the state quantity and the observed quantity corresponding to the system control quantity at the time k; emIs the electromotive force of the power supply;
step five, adopting the multi-time scale state space equation established in the step four, estimating the SOC under the micro scale and the SOH under the macro scale based on the UPF algorithm, and determining whether to update the battery capacity parameter and the model parameter interpolation table for SOC estimation according to the degradation condition of the SOH;
the SOC of the battery state quantity which changes rapidly along with time is estimated in a micro scale, and the SOH of the battery state quantity which changes slowly is estimated in a macro scale; during SOC online estimation, when the time scale k under the microscale reaches a charge-discharge cycle period, the scale transformation condition is met, and one-time SOH estimation is carried out.
2. The method according to claim 1, wherein the battery equivalent circuit model in the first step is a first-order RC circuit model, and includes model parameters with ohmic internal resistance R0Polarization resistance RpAnd a polarization capacitor CpAnd electromotive force E of power supplym(ii) a Polarization capacitorThe resistance is connected with the polarization resistor in parallel to form a parallel RC branch circuit, one end of the branch circuit is connected with the load, the other end of the branch circuit is connected with the high potential end of the power supply after being connected with the ohmic resistance in series, and the low potential end of the power supply is connected with the load.
3. The method for jointly estimating the state of the spatial lithium ion battery based on the multiple time scales according to claim 1, wherein the state-space equation of the SOH estimation system established in the fourth step is as follows:
θl＝θl-1+ξl-1
Figure FDA0002998908680000021
wherein l is a time scale under a macroscopic scale, and the system state quantity theta at the moment ll＝[al,bl,cl,dl]T，al，bl，clAnd dlParameters of the dual-exponential degradation model, ξ, at time l, respectivelyl-1System process noise at time l-1; thetal,1，θl,2，θl,3And thetal,4The first dimension, the second dimension, the third dimension and the fourth dimension of the system state quantity, and the on-line health factor HI at the moment llAs an observed quantity of the system, mulFor noise measurement, the cycle is the current charge/discharge cycle number of the battery, g (SOH)l) Is a function of the mapping relationship between the SOH and the online health factor HI.
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