阅读说明：本技术 一种基于双e指数模型的随机充放电电池容量衰减预测方法 (Random charge-discharge battery capacity attenuation prediction method based on double e index model ) 是由 钱诚 徐炳辉 任羿 孙博 冯强 杨德真 王自力 于 2019-10-16 设计创作，主要内容包括：本发明公开了一种能够适用于随机充放电条件的基于双e指数模型的锂电池容量预测方法,包括以下步骤：步骤1)、对电池连续充放电过程中的端电压、电流和容量进行数据采集和降噪处理；步骤2)、根据采集到的电压、电流数据计算电池和设备之间的等效累积转移能量,绘制电池容量随等效累积转移能量的退化曲线；步骤3)、利用双e指数模型对电池容量随等效累积转移能量退化曲线进行拟合,采用极大似然估计方法得到双e指数模型参数；步骤4)、基于步骤3拟合得到的双e指数模型,将等效累积转移能量值代入模型,对未来电池容量进行预测。本发明可适用于随机充放电条件下的锂电池容量衰减预测,简单易行,预测精度高,具有很高的实际应用价值。(The invention discloses a lithium battery capacity prediction method based on a dual-e index model and applicable to random charge and discharge conditions, which comprises the following steps: step 1), carrying out data acquisition and noise reduction processing on terminal voltage, current and capacity in the continuous charging and discharging process of a battery; step 2), calculating equivalent accumulated transfer energy between the battery and the equipment according to the acquired voltage and current data, and drawing a degradation curve of the battery capacity along with the equivalent accumulated transfer energy; step 3), fitting a battery capacity degradation curve along with equivalent accumulated transfer energy by using a dual-e index model, and obtaining dual-e index model parameters by using a maximum likelihood estimation method; and 4) substituting the equivalent accumulated transfer energy value into the model based on the double-e exponential model obtained by fitting in the step 3, and predicting the future battery capacity. The method can be suitable for predicting the lithium battery capacity attenuation under the random charging and discharging condition, is simple and easy to implement, has high prediction precision and has high practical application value.)

1. A random charge-discharge battery capacity fading prediction method based on a dual e-index model is characterized by comprising the following steps:

step 1: carrying out data acquisition and noise reduction processing on terminal voltage, current and capacity in the continuous charging and discharging process of the battery;

step 2: calculating equivalent accumulated transfer energy between the battery and the equipment according to the acquired voltage and current data, and drawing a degradation curve of the battery capacity along with the equivalent accumulated transfer energy;

and step 3: fitting a battery capacity degradation curve along with equivalent accumulated transfer energy by using a dual-e index model, and obtaining parameters of the dual-e index model by using a maximum likelihood estimation method;

and 4, step 4: and (3) substituting the equivalent accumulated transfer energy value into the model based on the double e index model obtained by fitting in the step (3) to predict the future battery capacity.

2. The battery capacity prediction method of claim 1, wherein: the step 1 further comprises the following steps:

step 11: acquiring terminal voltage, current and corresponding time stamp in the continuous charging and discharging process of the battery;

step 12: calculating the battery capacity from the current data and the time stamp of the standard charge or discharge cycle, the calculation of the capacity satisfying the following formula:

wherein: c is the battery capacity (Ah); t is t₀Is the time at which a standard charge or discharge cycle begins; t is t₁Is the time (h) at which the standard charge or discharge cycle ends; i (τ) is the battery current (A) at time τ;

step 13: the capacity data of the battery is denoised by adopting a moving average method, and the method meets the following formula:

wherein: c_lThe first battery capacity data; t is the length of the mobile window, and the value of T in the method is 5.

3. The battery capacity prediction method of claim 1, wherein: the equivalent accumulated transfer energy between the battery and the device in the step 2 satisfies the following formula:

wherein: e_equ(t) is the equivalent cumulative transfer energy (kw) between the battery and the device from time 0 to time t; u (τ) is the battery terminal voltage (V) at time τ; i (τ) is the battery current (A) at time τ.

4. The battery capacity prediction method of claim 1, wherein: the step 3 further comprises the following steps:

step 31: initializing parameters and sigma of a dual-e exponential model;

step 32: calculating the error between the model fitting result and the actual capacity value under the given parameter;

step 33: assuming that the error in step 32 follows a normal distribution N (0, σ), calculating a likelihood function L of the error;

step 34: and (3) with-L as an optimization target, searching and obtaining an unconstrained optimization minimum solution which minimizes-L by utilizing a Nelder-Mead method, and correspondingly taking the unconstrained optimization minimum solution as the values of the parameters and sigma of the dual-e exponential model obtained by fitting.

5. The battery capacity prediction method of claim 4, wherein: the dual e-exponential model satisfies the following formula:

C(E_equ)＝a₁·exp(b₁·E_equ)+a₂·exp(b₂·E_equ)

wherein: c (E)_equ) To correspond to E_equ(ii) a battery capacity of; a is₁，b₁，a₂，b₂Is the undetermined parameter of the dual e-exponential model.

Technical Field

The invention relates to a random charge-discharge battery capacity attenuation prediction method based on a dual-e exponential model.

Background

In terms of battery capacity prediction, the methods can be roughly classified into a physical model method, an empirical model method, and a data-driven method.

Physical modeling studies the cell degradation mechanism, and the growth of a solid electrolyte interface film is widely considered as a major cause of active material loss and deterioration of health. Empirical modeling characterizes the dynamic behavior of the cell with an equivalent plant model, while various observers are used to estimate the equivalent plant model parameters. The data-driven approach focuses on studying experimental data to explore the relationship between the internal state of the battery and the operating or environmental conditions, and estimates battery capacity using a variety of predictive methods, including support vector machines, gaussian process regression, and the like.

However, these methods are mostly based on charge and discharge experiments for cycling the battery under the same load, which is not in accordance with the actual situation. In the actual use process, the charge and discharge of the lithium battery have strong randomness. Therefore, the models and methods proposed by these battery experiments based on cycling the same load are very limited in practical application, and some of them are not even applicable.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention provides a lithium battery capacity prediction method based on a dual-e index model, which can be suitable for random charge and discharge conditions. The method unifies random use conditions and laboratory strict experiment conditions for circulating the same load, is simple and easy to implement, has high prediction precision, and has great practical application value.

A random charge and discharge battery capacity prediction method based on a dual e index model comprises the following steps:

step 1: carrying out data acquisition and noise reduction processing on terminal voltage, current and capacity in the continuous charging and discharging process of the battery;

step 2: calculating equivalent accumulated transfer energy between the battery and the equipment according to the acquired voltage and current data, and drawing a degradation curve of the battery capacity along with the equivalent accumulated transfer energy;

and step 3: fitting a battery capacity degradation curve along with equivalent accumulated transfer energy by using a dual-e index model, and obtaining parameters of the dual-e index model by using a maximum likelihood estimation method;

and 4, step 4: and (3) substituting the equivalent accumulated transfer energy value into the model based on the double e index model obtained by fitting in the step (3) to predict the future battery capacity.

The step 1 further comprises the following steps:

step 11: acquiring terminal voltage, current and corresponding time stamp in the continuous charging and discharging process of the battery;

step 12: calculating the battery capacity from the current data and the time stamp of the standard charge or discharge cycle, the calculation of the capacity satisfying the following formula:

wherein: c is the battery capacity (Ah); t is t₀Is the time at which a standard charge or discharge cycle begins; t is t₁Is the time (h) at which the standard charge or discharge cycle ends; i (τ) is the battery current (A) at time τ;

step 13: the capacity data of the battery is denoised by adopting a moving average method, and the method meets the following formula:

wherein: c_lThe first battery capacity data; t is the length of the mobile window, and the value of T in the method is 5.

The equivalent accumulated transfer energy between the battery and the device in the step 2 satisfies the following formula:

E_equ＝∫₀ ^tu(τ)|i(t)|dt

wherein: e_equ(t) is the equivalent cumulative transfer energy (kw) between the battery and the device from time 0 to time t; u (τ) is the battery terminal voltage (V) at time τ;i (τ) is the battery current (A) at time τ;

the step 3 further comprises the following steps:

step 31: initializing parameters and sigma of a dual-e exponential model;

step 32: calculating the error between the model fitting result and the actual capacity value under the given parameter;

step 33: assuming that the error in step 32 follows a normal distribution N (0, σ), calculating a likelihood function L of the error;

step 34: and (3) with-L as an optimization target, searching and obtaining an unconstrained optimization minimum solution which minimizes-L by utilizing a Nelder-Mead method, and correspondingly taking the unconstrained optimization minimum solution as the values of the parameters and sigma of the dual-e exponential model obtained by fitting.

The dual e-exponential model in step 32 satisfies the following equation:

C(E_equ)＝a₁·exp(b₁·E_equ)+a₂·exp(b₂·E_equ)

wherein: c (E)_equ) To correspond to E_equ(ii) a battery capacity of; a is₁，b₁，a₂，b₂Is the undetermined parameter of the dual e-exponential model.

Drawings

Fig. 1 is a flowchart illustrating steps of a method for predicting a capacity of a randomly charged and discharged battery based on a dual-e-index model according to an embodiment of the present invention.

Fig. 2 is a graph of the degradation of battery capacity with equivalent accumulated transferred energy for an embodiment of the present invention.

Detailed Description

The invention is further described by the following description and specific implementation method in combination with the accompanying drawings.

As shown in fig. 1, a method for predicting the capacity of a random charge and discharge battery based on a dual-e index model includes the following steps:

s1, acquiring terminal voltage and current data in the random charging and discharging process of the battery, calculating the capacity of the battery and performing noise reduction processing. In this example, random charge and discharge data of lithium ferrous phosphate cell RW3, supplied by the american national institute of astronavigation (NASA Ames Research Center), was used as a data source, and in this experiment, the cell was continuously operated at room temperature by repeatedly charging to 4.2V and then discharging to 3.2V using a random discharge current sequence between 0.5A and 4A as a random discharge cycle, and the cell voltage and current data were collected every 10 seconds, and standard charge and discharge was performed every 50 random discharge cycles to measure the capacity. The volume degradation data obtained by processing the collected data are shown in table 1.

And S2, obtaining equivalent accumulated transfer energy data between the battery and the equipment according to the acquired voltage and current data as shown in the table 1. In this embodiment, the first 18 groups of measured capacity and equivalent accumulated transfer energy data are taken as historical data to fit the dual-e index model, and the last 4 groups of measured capacity and equivalent accumulated transfer energy data are used to compare and verify the validity and accuracy of the model.

TABLE 1 Battery Capacity and equivalent cumulative transfer energy data

Equivalent cumulative transfer energy (kw)	Capacity (Ah)
		0	2.00896
0.58757	1.94339
		1.12896	1.86323
1.64168	1.80122
		2.11328	1.75395
2.55923	1.70397
		2.99715	1.67401
3.41359	1.63951
		3.81516	1.58843
4.04536	1.62892
		4.43561	1.55579
4.79013	1.52118
		5.11939	1.48561
5.43067	1.44246
		5.70158	1.37363
5.95392	1.32775
		6.13919	1.33471
6.34576	1.29237
		6.50389	1.23346
6.68428	1.20278
		6.85249	1.09308
6.97106	1.05967

S3, fitting a battery capacity degradation curve along with equivalent accumulated transfer energy by using a dual-e index model, and obtaining dual-e index model parameters by using a maximum likelihood estimation method, wherein the dual-e index model satisfies the following formula:

C(E_equ)＝a₁·exp(b₁·E_equ)+a₂·exp(b₂·E_equ)

giving an initial parameter of a dual-e exponential model and a normal distribution parameter sigma:

calculating a likelihood function corresponding to the given parameter:

wherein the content of the first and second substances,

the battery capacity is calculated according to the collected current data;

is and

corresponding equivalent accumulated transfer energy;

is to be

Substituting the double e index model into a model output result; f (x; mu, sigma) is a probability density function of normal distribution.

And (3) searching and obtaining an unconstrained optimization minimum solution which enables-L to be minimum by utilizing a Nelder-Mead method, namely the unconstrained optimization minimum solution is the corresponding value of the parameter and sigma of the dual-e exponential model:

and S4, substituting the estimated future equivalent accumulated transfer energy value into the model based on the fitted dual-e exponential model, predicting the future battery capacity, and obtaining a capacity predicted value and an actual measured value as shown in figure 2.

TABLE 2 comparison of predicted and measured values of capacity

Measured value of capacity (Ah)	Capacity prediction value (Ah)	Relative error (%)
			1.23346	1.22609	-0.422
1.20278	1.16475	-0.980
			1.09308	1.09482	-2.118
1.05967	1.03624	-2.211

The relative error values of the actual capacity measurement result and the prediction result are shown in table 2, and it can be seen that the relative errors of the predicted capacity value and the measured value are very small and are within ± 2.5%, which shows that the prediction result is good, and the feasibility and the effectiveness of the method in the battery capacity prediction are proved.