CN107895175A - A kind of method degenerated based on Nonhomogeneous Markov Chains model prediction capacity of lithium ion battery - Google Patents
A kind of method degenerated based on Nonhomogeneous Markov Chains model prediction capacity of lithium ion battery Download PDFInfo
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- CN107895175A CN107895175A CN201711111694.6A CN201711111694A CN107895175A CN 107895175 A CN107895175 A CN 107895175A CN 201711111694 A CN201711111694 A CN 201711111694A CN 107895175 A CN107895175 A CN 107895175A
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- G06F18/29—Graphical models, e.g. Bayesian networks
- G06F18/295—Markov models or related models, e.g. semi-Markov models; Markov random fields; Networks embedding Markov models
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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
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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]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
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- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/10—Energy storage using batteries
Abstract
The invention discloses a kind of method degenerated based on Nonhomogeneous Markov Chains model prediction capacity of lithium ion battery, comprise the following steps：S1, on-line measurement lithium ion battery to be measured capacity data；S2, measured capacity data is fitted using Nonhomogeneous Markov Chains model to obtain the parameter of model；S3, the degradation in capacity model of lithium ion battery to be measured will be obtained in the S2 parameters obtaineds substitution Nonhomogeneous Markov Chains model, and carry out capacity of lithium ion batteryization to be measured using the model and predict.The Nonhomogeneous Markov Chains model is the Nonhomogeneous Markov Chains model of the state of three-phase five.By the model, the degradation in capacity dynamic of the lithium ion battery of different anode materials can be identified, can also identify degradation in capacity dynamic of the lithium ion battery of same material under different working conditions.So as to be laid the foundation for further lithium ion battery life prediction.
Description
Technical Field
The invention relates to the technical field of lithium ion batteries, in particular to a method for predicting capacity degradation of a lithium ion battery based on a non-homogeneous Markov chain model.
Background
Lithium ion batteries have a high energy density and are therefore widely used in the fields of mobile devices, electric vehicles and the like. There have been many studies on lithium ion batteries, focusing on improving cycle life, reliability, and other performance characteristics of lithium ion batteries. However, no matter how good the performance of the lithium ion battery is, the capacity of the lithium ion battery is degraded with the number of charge and discharge cycles used.
In order to study the capacity degradation process of lithium ion batteries, researchers have proposed many models. For example: calculating a voltage curve of a known lithium ion battery electrode material based on a first principle, and predicting the voltage of an unknown electrode material; and designing an electrothermal finite element model for predicting the thermal performance of the nickel-metal hydride battery. These models are used to predict the performance of lithium ion batteries of different formulations, however, the battery performance calculated using these models is often different from the actual battery performance, taking into account the randomness of the electrochemical reactions within the battery and the differences in performance of different batteries of the same formulation. The reasons for the differences generally include two aspects: the first is that the selection of model parameters is not systematic enough; secondly, the sensitive parameters influenced by the outside are greatly changed.
The capacity degradation mechanism of the lithium ion battery in the cycle life test is very complex, and for decades, many researches for exploring the capacity cycle degradation rule of the lithium ion battery exist, and relevant models are provided. These models can be roughly classified into three categories: an electrochemical model, an equivalent circuit model, and an analytical model. Electrochemical and equivalent circuit models are capable of building accurate mathematical representations for complex physical and chemical processes, but these models are generally complex and difficult to estimate parameters and build usable models in an application, and some of these models rely on real-time impedance testing, which requires special expensive equipment. The analytical model is a series of mathematical models used to fit the capacity degradation curve of the lithium ion battery. For example: based on the Peukert methodThe model analyzes the non-linear relationship between battery life and discharge rate, however the method is too simple and only takes into account the average discharge current. Some researchers have studied the surface active material change of the electrode material of the lithium ion battery, and proposed an active material diffusion model, but when applying the model, it is necessary to measure the relevant parameters of the electrode surface, which requires additional experimental data. In the case of analytical models, a Markov chain-based model may link mathematical parameters to related material property parameters. The active battery model uses Markov chain to describe the change rule of the battery characteristic, but the model is too large, and when the charging time of the battery reaches a certain degree, the model can even generate 27 multiplied by 10 7 To 45X 10 7 A charging unit.
Although there are many models describing the capacity degradation process of the lithium ion battery, these models rarely describe the capacity degradation characteristics of different formulations of the battery, and also rarely describe the capacity degradation rule of the lithium ion battery under different working conditions.
Risse, S.Angioletti-Uberti, J.Dzubiilla, M.Balluff, capacity fading in lithium/sulfur batteries: A linear four-state model, J.Power Source 267 (2014) 648-654. However, in the case of a lithium ion battery, the solid electrolyte membrane of the lithium ion battery is mainly formed at the anode, the degradation mechanism thereof is different from that of a lithium sulfur battery, and the state transition probability of the lithium ion battery is related to different life states of the battery. The four-phase markov chain model describing lithium sulfur batteries is therefore not applicable to lithium ion batteries.
Disclosure of Invention
In order to solve at least one technical problem, the invention provides a method for predicting the capacity degradation of a lithium ion battery based on a heterogeneous Markov chain model. A three-phase five-state heterogeneous Markov chain model is designed, and parameters of the model can be associated with known physical and chemical processes and material characteristics, so that the capacity degradation dynamics of the lithium ion battery is identified. The model can describe the capacity degradation rule of lithium ion batteries made of different materials and can also describe the capacity degradation rule of the lithium ion batteries under different working conditions.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for predicting the capacity degradation of a lithium ion battery based on a non-homogeneous Markov chain model; the method comprises the following steps:
s1, measuring capacity data of a lithium ion battery to be measured on line;
s2, fitting the measured capacity data by using a non-homogeneous Markov chain model to obtain parameters of the model;
and S3, substituting the parameters obtained in the S2 into the inhomogeneous Markov chain model to obtain a service life degradation model of the lithium ion battery to be tested, and carrying out quantitative prediction on the capacity of the lithium ion battery to be tested by using the model.
Preferably, the nonhomogeneous markov chain model is a three-phase five-state nonhomogeneous markov chain model.
Preferably, the three-phase five-state heterogeneous markov chain model is:
wherein n represents the nth charge-discharge cycle; c (n) The maximum available discharge capacity of the lithium ion battery during the nth charge and discharge is shown;indicating the capacity represented by the active material in the storage state during the first charge-discharge cycle,indicating the capacity represented by the active material in a stable activated state during the first charge-discharge cycle,represents the capacity represented by the active material in an inherently unstable activated state during the first charge-discharge cycle;
k 13 ,k 25 ,k 45 are three dimensionless constants, and k 13 ,k 25 ,k 45 Satisfies the following conditions:
k 13 ＜0
k 25 ＜0
k 45 ＜0。
preferably, the parameter in S2 isk 13 ，k 25 And k 45 。
Preferably, the maximum available discharge capacity C during the nth charge and discharge can be obtained by substituting the charge and discharge times n into the capacity degradation model of the lithium ion battery to be tested (n) 。
The invention has the advantages of
The invention provides a method for predicting the capacity degradation of a lithium ion battery based on a heterogeneous Markov chain model, which is used for identifying the capacity degradation dynamic state of the lithium ion battery by designing the heterogeneous Markov chain model with three phases and five states, and the parameters of the heterogeneous Markov chain model can be associated with the known physical and chemical processes and material characteristics. Through the model, the capacity degradation dynamics of the lithium ion batteries with different anode materials can be identified, and the capacity degradation dynamics of the lithium ion batteries with the same material under different working conditions can also be identified. Thereby laying a foundation for further lithium ion battery life prediction.
Drawings
FIG. 1 is a schematic diagram of the three-phase five-state in the non-homogeneous Markov chain model of the present invention;
FIG. 2 (a) is a plot of a fit of the model proposed by Risse to the lithium ion battery capacity degradation dynamics for different operating conditions;
FIG. 2 (b) is a diagram of a lithium ion battery capacity degradation dynamic fitting to different working conditions by using the model provided by the invention;
FIG. 3 (a) is a plot of a fit to the capacity degradation dynamics of a group A lithium ion battery using the model proposed by Risse;
FIG. 3 (b) is a graph of a fit of the proposed model to the capacity degradation dynamics of a group A lithium ion battery;
FIG. 3 (c) is a plot of a fit to the capacity degradation dynamics of a group B lithium ion battery using the model proposed by Risse;
FIG. 3 (d) is a graph of the fit of the proposed model to the capacity degradation dynamics of a group B of lithium ion batteries;
FIG. 3 (e) is a plot of a fit of the model proposed by Risse to the capacity degradation dynamics of a group C lithium ion battery;
fig. 3 (f) is a graph of the fit of the model proposed by the present invention to the capacity degradation dynamics of a group C lithium ion battery.
Detailed Description
The present invention is described in detail below by way of examples, it should be noted that the examples are only for the purpose of further illustration, and are not to be construed as limiting the scope of the present invention, and that those skilled in the art can make insubstantial modifications and adaptations to the invention in light of the above teachings. The embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
1. Heterogeneous Markov chain model building process
The invention designs a heterogeneous Markov chain model comprising five states, wherein the state space of the model is expressed as { S 1 ,S 2 ,S 3 ,S 4 ,S 5 }. These five states belong to three different phases: a storage phase, an activation phase, and an absorption phase. The state changes of the active materials in lithium ion batteries can be classified into these three phases. Considering that the capacity degradation of lithium ion batteries is irreversible, i.e. the active material is in its life cycleThe change of (2) is irreversible, and the partial state transition of the Markov chain model designed by the invention is also irreversible, as shown in figure 1. Fig. 1 depicts the change of each state of the lithium ion battery in the nth charge-discharge cycle. The line segment with an arrow in FIG. 1 represents the probability of each state transition at the end of the nth life cycle, denoted as P (X) n+1 ＝S j |X n ＝S i ) (i, j ∈ {1,2,3,4,5 }). The state transition matrix of the Markov chain depends only on n, and for the sake of simple representation, P is used in the nth period (time parameter is n) (n) (S j |S i ) Represents P (n) (X n+1 ＝S j |X n ＝S i )。
The first part of FIG. 1 shows the storage phase, comprising only one storage state S 1 . An active material of a lithium ion battery in this state is indicative of a current state of inactivity, but remains transferred to the active state S 3 At the nth cycle, the transition probability is P (n) (S 3 |S 1 ). The second part is an activated phase, which comprises three activation states: stable activated state S 2 Intrinsic unstable activation state S 4 And a stable activated state S converted from the storage state 3 . The active phase may be considered as lithium ions or other active materials that participate in the charge-discharge process. The number of active states in an active material of a lithium ion battery represents the electrochemical capacity of the battery, and the number of active materials in the active states represents the maximum available discharge capacity of the lithium ion battery. Thus, the maximum available discharge capacity of a lithium ion battery is S 2 、S 3 And S 4 The sum of (a) and (b). The last part is an absorption phase, containing only one absorption state S 5 Representing irreversible loss of the active phase. Active materials in the absorption phase mean that these materials can no longer participate in the charging and discharging process of the lithium ion battery, i.e. that these active materials have decomposed or become other compounds. The transitions between these five states are represented by 9 conditional probabilities.
The irreversible loss of the active material occurring during the formation of the solid electrolyte membrane is represented as an activated state S 2 With probability P (S) 5 |S 2 ) Transfer to absorption state S 5 The process of (1). The solid electrolyte membrane is unstable and thus frequently varies, which results in continuous loss of lithium ions and electrolyte. Another active state S 4 Indicating a more stable activated state in which the active material can participate in the charge-discharge process for a long time. Active state S 3 Is generated by changing from a storage state with the increase of the number of charge-discharge cycles. At S 3 Is at an active material ion ratio of S 4 The active material ions of (a) are in an activated state for a short time and remain in the activated state for a longer time, but in a smaller amount than in S 4 Has few ions of active material. The state of active ions in the alloy storing lithium ions and the storage material storing other ions is represented as S 1 . An active material in the storage phase indicates that this portion of ions does not participate in the charge-discharge process, but can be converted to the active phase in the cycle life test. The irreversible loss process caused by the conversion of the active material into other compounds is represented as a process in which the active material is converted from an activated state into an absorbed state.
For the nth charge-discharge cycle (hereinafter referred to as cycle) of a lithium ion battery, the active material state of the lithium ion battery can be expressed as a column vector containing 5 elements:
in the nth cycle, P is used (n) (S i ) Indicates that the active material is in the state S i Probability of (P) (n) (S j |S i ) Indicates that the active material is in the state S i Is transited to the state S j Then each state S i Transition to State S j Is a probability of P (n) (S j |S i )×P (n) (S i ) The above description may be expressed as:
P (n) (S j |S i )＝P(X n+1 ＝S j |X n ＝S i )
i,j∈{1,2,3,4,5} (2)
in the nth cycle, the state transition matrix of the lithium ion battery is as follows:
wherein, T (n) And the state transition matrix of the lithium ion battery in the nth period is shown. The state vector for the next cycle is represented as:
T (n) S (n) ＝S (n+1) (4)
for an initial state S (1) And the state vector of the lithium ion battery in the nth cycle is expressed as follows:
in the proposed model of the present invention, the state transition probability per cycle is continuously varied, taking into account the change in the chemical environment inside the battery caused by each cycle. The variation law may be determined according to the actual situation, for example, using a conventional exponential model. Since the active material in the active state determines the overall law of degradation of lithium ion batteries, for the sake of simplicity, only P will be used (n) (S 5 |S 4 ) Set as a function of life test cycle number. When n is more than or equal to 2, in the nth period, each transition probability is expressed as:
wherein (k) 45 ,k 25 ,k 13 ) Are three dimensionless constants.
Because in the lithium ion battery, S 3 Is smaller and the active material in this state is more active than in S 4 The active material in the state is formed later and relatively more stable, so that P can be assumed (n) (S 5 |S 3 ) =0 andunder this assumption, the state transition matrix can be expressed as:
the active materials in the active phase within a lithium ion battery represent the maximum available discharge capacity, and the sum of all active materials in the active state represents the theoretical electrochemical capacity. The maximum available discharge capacity can therefore be expressed as
The mutual constraints between the parameters are expressed as:
k 13 ＜0
k 25 ＜0
k 45 ＜0 (9)
2. lithium ion battery capacity degradation identification case under different working conditions
This example uses published Data published by the NASA Ames Properties Center of Excellence, (B.Saha, K.Goebel, battery Data Set ", NASA Ames Properties Data Repository, NASA Ames Research Center, moffett Field, CA., (2007) http:// ti.arc. Na. Gov/project/magnetic-Data-Repository) capacity degradation Data for three lithium ion cells numbered B0005, B0007 and B0018. In the cycle life test, the three batteries were charged in the same manner, and the discharge cut-off voltages were different only during the discharge, and for B0005, B0007 and B0018, the discharge cut-off voltages were 2.7V, 2.2V and 2.5V, respectively.
The model proposed by the present invention was used to fit the capacity degradation curves of these 3 cells, and the obtained fitting parameters are shown in table 1
TABLE 1 lithium ion battery capacity degradation identification under different conditions
As shown in fig. 2 (b), for lithium ion batteries of the same type of material, under different working conditions, the model provided by the invention can accurately identify characteristics such as the overall trend, the nonlinear part and the fluctuation in the capacity degradation process of the lithium ion battery. In contrast, as shown in fig. 2 (a), the model proposed by Risse cannot accurately identify the nonlinear part in the process of capacity degradation of the lithium ion battery.
3. Lithium ion battery capacity degradation identification case with different anode materials
In this embodiment, the data of a laboratory is used to verify the effectiveness of the model provided by the present invention in identifying the capacity degradation of lithium ion batteries with different anode materials. Three sets of cells (set a, set B and set C) were prepared in the laboratory, each set of cells having the same material formulation and each set comprising two cells, and tested at 25 ℃ and 60 ℃ respectively. The anode materials are different among different groups of cells, and other materials and processes are the same. Each cell underwent four types of body in the test: charging, standing, discharging and standing. First, the charging process was first stopped with a constant current of 2A until the voltage reached 4.2V, followed by constant voltage until the current dropped to 100 mA. Second, after the charging process was completed, the battery was left to stand for 5 minutes. Third, the discharge process was first discharged using a constant current of 2A until the voltage was reduced to 2.8V, while measuring the discharge capacity. Fourth, after the discharge was completed, the cell was allowed to stand for 5 minutes. To this end, one charge-discharge cycle of the battery is completed. In the tests, the charge/discharge magnification was set to 1C. This charge-discharge cycle process was repeated until the discharge capacity of the battery reached 82% of the initial discharge capacity of the battery.
The model proposed by the present invention was used to fit the capacity degradation curves of these 6 cells, and the obtained fitting parameters are shown in table 2
TABLE 2 lithium ion battery capacity degradation identification of different anode materials
As figures 3 (b), 3 (d) and 3 (f) are fits using the model proposed by the present invention, and figures 3 (a), 3 (c) and 3 (e) are fits using the model proposed by Risse. As shown in fig. 3 (b), 3 (d) and 3 (f), for lithium ion batteries of different materials, under the same working condition, the model provided by the invention can accurately identify the characteristics such as the overall trend, the nonlinear part and the fluctuation in the capacity degradation process of the lithium ion battery. In contrast, as shown in fig. 3 (a), 3 (c) and 3 (e), the model proposed by Risse cannot accurately identify the nonlinear part in the lithium ion battery capacity degradation process.
It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the 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 scope of the present invention.
Claims (5)
1. A method for predicting the capacity degradation of a lithium ion battery based on a non-homogeneous Markov chain model is characterized by comprising the following steps:
s1, measuring capacity data of a lithium ion battery to be measured on line;
s2, fitting the measured capacity data by using a non-homogeneous Markov chain model to obtain parameters of the model;
and S3, substituting the parameters obtained in the S2 into the inhomogeneous Markov chain model to obtain a capacity degradation model of the lithium ion battery to be tested, and carrying out quantitative prediction on the capacity of the lithium ion battery to be tested by using the model.
2. The method of claim 1, wherein the heterogeneous Markov chain model is a three-phase five-state heterogeneous Markov chain model.
3. The method of claim 2, wherein the three-phase five-state heterogeneous Markov chain model is:
wherein n represents the nth charge-discharge cycle; c (n) The maximum available discharge capacity of the lithium ion battery during the nth charge and discharge is shown;indicating the capacity represented by the active material in the storage state during the first charge-discharge cycle,indicating the capacity represented by the active material in a stable activated state during the first charge-discharge cycle,represents the capacity represented by the active material in an inherently unstable activated state during the first charge-discharge cycle;
k 13 ,k 25 ,k 45 are three dimensionless constants, and k 13 ,k 25 ,k 45 Satisfies the following conditions:
k 13 <0
k 25 <0
k 45 <0。
4. the method of claim 1, wherein the parameter in S2 isk 13 ，k 25 And k 45 。
5. The method of claim 1, wherein when performing the prediction in S3, the maximum available discharge capacity C during the nth charge and discharge can be obtained by substituting the charge and discharge times n into the capacity degradation model of the lithium ion battery to be tested (n) 。
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| CN108803334A (en) * | 2018-06-21 | 2018-11-13 | 广东工业大学 | Direct current generator finite-time control method and system based on nonhomogeneous Markov model |
| CN108803334B (en) * | 2018-06-21 | 2020-08-07 | 广东工业大学 | DC motor finite time control method and system based on non-homogeneous Markov model |
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| CN112937369A (en) * | 2021-02-01 | 2021-06-11 | 合肥国轩高科动力能源有限公司 | Active equalization control method for power battery pack based on Mahalanobis process |
| CN115424443A (en) * | 2022-09-20 | 2022-12-02 | 安徽江淮汽车集团股份有限公司 | Vehicle abnormity monitoring method based on driving data |
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