WO2022105104A1 - 一种基于多新息递推贝叶斯算法的电池模型参数辨识方法 - Google Patents
一种基于多新息递推贝叶斯算法的电池模型参数辨识方法 Download PDFInfo
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- 229910001416 lithium ion Inorganic materials 0.000 claims abstract description 37
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- 239000011159 matrix material Substances 0.000 claims description 18
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- 238000005457 optimization Methods 0.000 description 4
- 238000004146 energy storage Methods 0.000 description 3
- 230000010355 oscillation Effects 0.000 description 3
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- 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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- the invention relates to the technical field of lithium ion batteries, in particular to a battery model parameter identification method based on a multi-innovation recursive Bayesian algorithm.
- Lithium-ion batteries have the characteristics of long life, low self-discharge effect and high energy density, and have become the main battery energy storage components.
- Lithium-ion battery is a non-linear time-varying electrochemical system, which is greatly affected by the working environment temperature and working conditions, and the battery management system (BMS) can only detect the battery terminal voltage and load current, which is a typical black box.
- BMS battery management system
- a high-precision battery model needs to be established. Accurate identification of battery parameters is a prerequisite for accurate BMS management.
- least squares algorithm and swarm intelligence algorithm have been widely studied due to their ability to identify online.
- Swarm intelligence algorithms such as particle swarm optimization and its improved algorithms, can be better applied to different working conditions, but there are also problems of large computational load and premature convergence.
- the purpose of the present invention is to provide a battery model parameter identification method based on the multi-innovation recursive Bayesian algorithm.
- the recursive Bayesian identification algorithm based on multiple innovations introduces the innovation length parameter, which can overcome the influence of bad data on parameter estimation, improve the accuracy of parameter estimation, and has strong robustness. In the battery system, it can Reduce the impact of current abrupt changes on the results.
- the present invention is realized by the following measures: a battery model parameter identification method based on the multi-innovation recursive Bayesian algorithm, which specifically includes the following steps:
- Step 1) Measure the terminal voltage and load current data of the lithium ion battery with a duration of 21211 seconds by the intermittent constant current discharge method. Determine the functional relationship of its OCV-SOC by polynomial fitting method;
- Step 2) Determine the dual-polarization equivalent circuit model of the lithium-ion battery, and establish a system equation representing the relationship between the battery parameter identification vector and the system output;
- Step 3 construct the identification process of the multi-innovation recursive Bayesian algorithm
- the step 2) specifically includes the following steps:
- Step 2-1) Establish a dual-polarization model of the lithium-ion battery, and establish the relationship between the electrical quantities of the lithium-ion battery according to the model:
- Q n is the rated capacity of the battery, and SOC is defined as the ratio of the remaining capacity to the nominal capacity, which can be expressed as:
- ⁇ t is the sampling period
- U oc and U correspond to the open-circuit voltage and terminal voltage of the battery
- the voltages at both ends of C 1 and C 2 are represented by U 1 and U 2 respectively
- Romc is Ohm internal resistance.
- R 1 and C 1 characterize the electrochemical polarization reaction, and the voltage changes rapidly;
- R 2 and C 2 characterize the concentration polarization reaction, and the voltage changes slowly and steadily.
- Step 2-2) Establish the battery parameter identification model of the dual polarization model:
- ⁇ 1 R 1 C 1
- ⁇ 2 R 2 C 2
- a R omc
- b ⁇ 1 ⁇ 2
- c ⁇ 1 + ⁇ 2
- d R omc +R 1 +R 2
- e R omc ( ⁇ 1 + ⁇ 2 )+R 1 ⁇ 1 +R 2 ⁇ 2 .
- Equation (9) is the identification expression in the system identification.
- the parameter ⁇ is identified by the parameter estimation method, and then the corresponding resistance and capacitance values are deduced by using the identified parameter values.
- the specific deduction process is as follows:
- the step 3) specifically includes the following steps:
- Step 3-1) Derive the recursive Bayesian identification algorithm:
- the core idea of the Bayesian identification algorithm is to regard the parameter to be estimated as a random variable, and obtain the parameter estimation by maximizing the posterior probability density function p( ⁇
- ⁇ is the parameter to be identified.
- the posterior probability density function for parameter ⁇ is expressed as:
- Step 3-2) called innovation
- the parameter estimate at the current moment is the product of the intermediate vector L(k) and the innovation e(k), the parameter estimation vector at the previous moment Make corrections.
- the resulting identification model is:
- the intermediate vector L(k) ⁇ Rn is expanded into ⁇ (p,k) ⁇ Rn ⁇ p (n is the dimension of the vector to be identified).
- step 3-1) establish a multi-innovation recursive Bayesian algorithm for lithium-ion batteries:
- Step 3-3) initialize parameter ⁇ to be identified, covariance matrix P, variance value ⁇ v and data length p;
- Step 3-4) obtain U oc (k) and SOC (k) according to the OCV-SOC relationship;
- Step 3-5 According to the collected terminal voltage and working current of the lithium ion battery, read the data of the terminal voltage and working current of the lithium ion battery at time k, and construct the output y(k) and the information vector
- Step 3-6 Construct innovation matrix E(p,k), output matrix Y(p,k) and information matrix ⁇ (p,k);
- Step 3-7) update the intermediate vector ⁇ (k) of the parameter to be identified
- Step 3-8) Update the parameters to be identified
- Step 3-9) update the covariance matrix P(k) of the parameter to be identified
- Step 3-11 According to the result of identifying the parameter ⁇ in step 3-10), combine the formulas (10) to (12) to obtain the battery Romc , R 1 , R 2 , C 1 , C 2 .
- the terminal is obtained.
- the voltage prediction value compared with the actual test value, can evaluate the validity and accuracy of the algorithm.
- the present invention establishes an ARX model for parameter identification of lithium-ion batteries, uses innovation correction technology to correct the results at the previous moment, and introduces innovation length parameters based on the multi-innovation identification method to overcome bad data for parameter estimation to improve the accuracy of parameter estimation.
- the multi-innovation recursive Bayesian algorithm can identify each model parameter well, and the parameter estimation value of this algorithm remains relatively stable when the input current has unstable oscillation. There is a certain error between the selection of the initial value of the parameter and the actual value, and the fluctuation is obvious in the initial stage of identification. With the continuous operation of the identification, the estimated value of the parameter gradually becomes stable.
- the multi-innovation recursive Bayesian algorithm has high identification accuracy, and the output estimated value is very close to the real value, which has engineering value.
- Fig. 1 is the bipolar model diagram of the lithium ion battery of the present invention
- Fig. 2 is the general flow chart of the multi-innovation recursive Bayesian algorithm of the present invention
- Fig. 3 is the overall structure block diagram of the present invention.
- Fig. 4 is the test voltage and current curve diagram of the present invention.
- Fig. 5 is the 9th fitting curve diagram of OCV-SOC in the embodiment of the present invention.
- FIG. 6 is an online identification curve diagram of parameters Romc , R 1 , R 2 , C 1 , C 2 obtained by the recursive Bayesian algorithm of the present invention
- Fig. 7 is the terminal voltage prediction curve obtained by the recursive Bayesian algorithm of the present invention.
- FIG. 8 is an online identification curve diagram of parameters Romc , R 1 , R 2 , C 1 , C 2 obtained by the multi-innovation recursive Bayesian algorithm of the present invention
- FIG. 9 is a graph of terminal voltage prediction obtained by the multi-innovation recursive Bayesian algorithm of the present invention.
- the research is carried out on the Panasonic lithium-ion battery NCR-18650B, the calibration voltage is 3.7V, and the battery capacity is 3400mAh.
- the battery is charged to the cut-off voltage by constant current charging (0.5C), and after standing for 1 hour, the battery is fully charged.
- the battery works in intermittent constant current discharge mode: discharge for 5min, stand for 30min, discharge current is 3400mA, and discharge rate is 1C. This process is repeated until the voltage drops to the discharge cut-off voltage.
- the test voltage curve and current curve are shown in Figure 4. Through this experiment, it is verified that the multi-innovation recursive Bayesian algorithm can identify each model parameter well. When the input current has unstable oscillation, the estimated parameter value remains relatively stable.
- the present invention provides a battery model parameter identification method based on the multi-innovation recursive Bayesian algorithm, comprising the following steps:
- Step 1) Measure the terminal voltage and load current data of the lithium ion battery within a certain period of time by the intermittent constant current discharge method.
- the sampling period is 1Hz, and a total of 21211 sets of data are collected.
- Step 2) Determine the dual-polarization equivalent circuit model of the lithium-ion battery, and establish a system equation representing the relationship between the battery parameter identification vector and the system output;
- Step 3 construct the identification process of the multi-innovation recursive Bayesian algorithm
- the step 2) specifically includes the following steps:
- Step 2-1) Establish a dual-polarization model of the lithium-ion battery, and establish the relationship between the electrical quantities of the lithium-ion battery according to the model:
- Q n is the rated capacity of the battery, and SOC is defined as the ratio of the remaining capacity to the nominal capacity, which can be expressed as:
- ⁇ t is the sampling period
- U oc and U correspond to the open-circuit voltage and terminal voltage of the battery
- the voltages at both ends of C 1 and C 2 are represented by U 1 and U 2 respectively
- Romc is Ohm internal resistance.
- R 1 and C 1 characterize the electrochemical polarization reaction, and the voltage changes rapidly;
- R 2 and C 2 characterize the concentration polarization reaction, and the voltage changes slowly and steadily.
- Step 2-2) Establish the battery parameter identification model of the dual polarization model:
- ⁇ 1 R 1 C 1
- ⁇ 2 R 2 C 2
- a R omc
- b ⁇ 1 ⁇ 2
- c ⁇ 1 + ⁇ 2
- d R omc +R 1 +R 2
- e R omc ( ⁇ 1 + ⁇ 2 )+R 1 ⁇ 1 +R 2 ⁇ 2 .
- Equation (9) is the identification expression in the system identification.
- the parameter ⁇ is identified by the parameter estimation method, and then the corresponding resistance and capacitance values are deduced by using the identified parameter values.
- the specific deduction process is as follows:
- the step 3) specifically includes the following steps:
- Step 3-1) Derive the recursive Bayesian identification algorithm:
- the core idea of the Bayesian identification algorithm is to regard the parameter to be estimated as a random variable, and obtain the parameter estimation by maximizing the posterior probability density function p( ⁇
- ⁇ is the parameter to be identified.
- the posterior probability density function for parameter ⁇ is expressed as:
- Step 3-2) called innovation
- the parameter estimate at the current moment is the product of the intermediate vector L(k) and the innovation e(k), the parameter estimation vector at the previous moment Make corrections.
- the resulting identification model is:
- the intermediate vector L(k) ⁇ Rn is expanded into ⁇ (p,k) ⁇ Rn ⁇ p (n is the dimension of the vector to be identified).
- step 3-1) establish a multi-innovation recursive Bayesian algorithm for lithium-ion batteries:
- Step 3-4) obtain U oc (k) and SOC (k) according to the OCV-SOC relationship;
- Step 3-5 According to the collected terminal voltage and working current of the lithium ion battery, read the data of the terminal voltage and working current of the lithium ion battery at time k, and construct the output y(k) and the information vector
- Step 3-6 Construct innovation matrix E(p,k), output matrix Y(p,k) and information matrix ⁇ (p,k);
- Step 3-7) update the intermediate vector ⁇ (k) of the parameter to be identified
- Step 3-8) Update the parameters to be identified
- Step 3-9) update the covariance matrix P(k) of the parameter to be identified
- Step 3-11 According to the result of identifying the parameter ⁇ in step 3-10), combine the formulas (10) to (12) to obtain the battery Romc , R 1 , R 2 , C 1 , C 2 .
- the terminal is obtained.
- the voltage prediction value compared with the actual test value, can evaluate the validity and accuracy of the algorithm.
- the OCV-SOC relationship curve used in this embodiment is shown in FIG. 5 , and the real-time online identification curves of parameters Romc , R 1 , R 2 , C 1 , and C 2 are shown in FIG. 8 .
- the terminal voltage of the dual-polarization model is predicted by the parameters identified at each moment and the operating current at the corresponding moment, and the results are shown in Figure 9.
- the accuracy of parameter identification is evaluated by comparing the predicted voltage values of the model parameters with the actual test values.
- the present invention provides a result graph of the recursive Bayesian algorithm, as shown in FIG. 6 and FIG. 7 .
- the multi-innovation recursive Bayesian algorithm can identify each model parameter well.
- the parameter estimates remain relatively stable. There is a certain error between the selection and the actual value, and the fluctuation is obvious in the initial stage of identification. With the continuous operation of the identification, the estimated parameter value gradually tends to be stable.
- the model terminal voltage predictions of the recursive Bayesian algorithm and the multi-innovation recursive Bayesian algorithm are relatively close to the actual test value, but when the current is abruptly changed from shelving to discharge or discharge to shelving, the multi-innovation recursive The Yess algorithm is relatively stable and the error is small.
Abstract
一种基于多新息递推贝叶斯算法的电池模型参数辨识方法,包括以下步骤:步骤1)通过间歇恒流放电法测取一定时间内的锂离子电池端电压、负载电流数据,通过多项式拟合法确定其OCV-SOC的函数关系;步骤2)确定锂离子电池的双极化等效电路模型,建立表示电池参数辨识向量和系统输出关系的系统方程;步骤3)构建多新息递推贝叶斯算法的辨识流程。该方法建立了锂离子电池参数辨识的ARX模型,利用新息修正技术对前一刻的结果进行修正,基于多新息的辨识方法引入了新息长度参量,克服坏数据对参数估计的影响,提高参数估计精度,由参数辨识结果可以看出,本方法辨识精度高,具有工程价值。
Description
本发明涉及锂离子电池技术领域,尤其涉及一种基于多新息递推贝叶斯算法的电池模型参数辨识方法。
随着交通运输业的发展,资源短缺、环境污染和安全问题日益严重,新能源产业兴起,新能源汽车受到越来越多的关注。相应地,储能系统由于其可灵活配置、响应速度快和易运行维护等优点已成为推动可再生能源消耗的革命性技术,电池储能在新能源接入领域具有广泛的应用前景。锂离子电池具有寿命长、低自放电效应和能量密度高等特性,已成为目前主要的电池储能元件。锂离子电池是非线性时变的电化学系统,受工作环境温度和工况影响较大,且电池管理系统(battery management system,BMS)只能检测到电池端电压以及负载电流,是一个典型的黑箱系统,为了对锂离子电池内部多种状态进行估计和预测,需要建立高精度的电池模型。对电池参数的准确辨识是实现BMS精确管理的先决条件。
目前在电池模型参数辨识算法方面,最小二乘算法和群智能算法等因具备在线辨识的能力而被广泛研究。最小二乘算法在线跟踪时变参数过程中存在随着数据量增大而出现数据饱和的问题。群智能算法,如粒子群优化及其改进算法可以较好地适用于不同工况,但也存在计算量大和过早收敛的问题。
如何解决上述技术问题为本发明面临的课题。
发明内容
本发明的目的在于提供一种基于多新息递推贝叶斯算法的电池模型参数辨识方法,该方法将锂离子电池模型参数辨识过程中的单新息修正加以推广,标量新息扩展成新息矩阵,基于多新息的递推贝叶斯辨识算法引入了新息长度参量,可以克服坏数据对参数估计的影响,提高参数估计精度,具有较强的鲁棒性,在电池系统,可以减小电流突变对结果的影响。
本发明是通过如下措施实现的:一种基于多新息递推贝叶斯算法的电池模型参数辨识方法,其中,具体包括以下步骤:
步骤1)通过间歇恒流放电法测取时长为21211秒的锂离子电池端电压、负载电流数据。通过多项式拟合法确定其OCV-SOC的函数关系;
步骤2)确定锂离子电池的双极化等效电路模型,建立表示电池参数辨识向量和系统输出关系的系统方程;
步骤3)构建多新息递推贝叶斯算法的辨识流程;
作为本发明提供的一种基于多新息递推贝叶斯算法的电池模型参数辨识方法进一步优化方案,所述步骤2)具体包括如下步骤:
步骤2-1)建立锂离子电池的双极化模型,根据模型建立锂离子电池电气量关系:
Q
n为电池的额定容量,SOC定义为剩余容量与标称容量之比,可以表示为:
以电流I为输入,端电压U为输出,[SOC,U
1,U
2]
T为状态变量建立双极化模型的离散化状态空间方程和输出方程如下:
式(3)和式(4)中,Δt为采样周期,U
oc、U对应的是电池开路电压与端电压,C
1、C
2两端的电压分别用U
1、U
2表示,R
omc是欧姆内阻。R
1、C
1表征电化学极化反应,电压快速变化过程;R
2、C
2表征浓差极化反应,电压缓慢稳定的变化过程。
步骤2-2)建立双极化模型的电池参数辨识模型:
采用双线性变化s=2(1-z
-1)/T(1+z
-1)(T为采样周期),将上式从s平面映射到z平面,可以得到:
其中,τ
1=R
1C
1,τ
2=R
2C
2,a=R
omc,b=τ
1τ
2,c=τ
1+τ
2,d=R
omc+R
1+R
2,e=R
omc(τ
1+τ
2)+R
1τ
1+R
2τ
2。
传递函数离散化后得到的差分方程为:
令y(t)=U(t)-U
oc(t),可以得到符合锂离子电池进行参数辨识的带外加输入的自回归(AutoRegressive with exogenous input,ARX)模型为:
因为b=τ
1τ
2,c=τ
1+τ
2,可以得到:
作为本发明提供的一种基于多新息递推贝叶斯算法的电池模型参数辨识方法进一步优化方案,所述步骤3)具体包括如下步骤:
步骤3-1)推导递推贝叶斯辨识算法:
贝叶斯辨识算法的核心思想是将要估计的参数视为随机变量,通过最大化参数的后验概率密度函数p(θ|D
k)得到参数的估计。θ为需要辨识的参数。使用贝叶斯理论,参数θ的后验概率密度函数表示为:
在上式中,基于参数θ和k-1时刻及以前的输入输出集合D
(k-1),系统的输出变量y(k)的先验概率密度函数记为p(y(k)|θ,D
(k-1))。p(θ|D
(k-1))是未知的,假设其遵循
与P(k-1)的正态分布:
其中,n是参数向量θ的维数,n=dimθ=5。
将公式(14)和(15)代入公式(13)中,那么,p(θ|D
(k-1))可以重新表示为
最大化后验概率函数,即
可以得到
其中,
引入中间变量L(k),得到的递推贝叶斯算法为:
考虑数据长度为p,定义输出向量Y(p,k),信息矩阵Φ(p,k),噪声向量V(p,k),
得到的辨识模型为:
Y(p,k)=Φ
T(p,k)θ+V(p,k) (20)
根据多新息理论将标量新息e(t)扩展成新息向量E(p,k):
中间向量L(k)∈R
n扩展成Γ(p,k)∈R
n×p(n为待辨识向量维数)。
根据步骤3-1)建立锂离子电池多新息递推贝叶斯算法:
步骤3-3)初始化待辨识参数θ,协方差矩阵P,方差值σ
v以及数据长度p;
步骤3-4)根据OCV-SOC关系得到U
oc(k)与SOC(k);
步骤3-6)构建新息矩阵E(p,k)、输出矩阵Y(p,k)和信息矩阵Φ(p,k);
步骤3-7)更新待辨识参数的中间向量Γ(k);
步骤3-9)更新待辨识参数的协方差矩阵P(k);
P(k)=[I-Γ(k)Φ
T(k)]P(k-1) (25)
步骤3-10)判断是否满足辨识终止时间,若满足,辨识结束输出辨识结果;否则,k=k+1,返回到步骤3-4);
步骤3-11)根据步骤3-10)辨识参数θ结果,结合式(10)至式(12)求得电池R
omc,R
1,R
2,C
1,C
2。
进一步地,根据参数辨识模型输出的锂离子电池参数R
omc,R
1,R
2,C
1,C
2以及工作电流值I,结合状态空间表达式(3)和式(4),求得端电压预测值,与实际测试值进行比较,可以评估算法的有效性及准确性。
与现有技术相比,本发明的有益效果为:
(1)、本发明建立了锂离子电池参数辨识的ARX模型,利用新息修正技术对前一刻的结果进行修正,基于多新息的辨识方法引入了新息长度参量,克服坏数据对参数估计的影响,提高参数估计精度。
(2)、相比于递推贝叶斯算法,多新息递推贝叶斯算法可以很好地辨识各个模型参数,该算法在输入电流存在不稳定振荡时参数估计值保持相对稳定,由于参数初始值的选取与实际值有一定误差,在辨识初期波动较为明显,随着辨识的持续运行,参数估计值逐渐趋于稳定。
(3)、递推贝叶斯算法与多新息递推贝叶斯算法的模型端电压预测都比较接近实际测试值,但在搁置到放电或者放电到搁置时,电流发生突变时,多新息递推贝叶斯算法比较稳定,误差较小。
(4)、多新息递推贝叶斯算法的辨识精度较高,输出的估计值与真实值非常接近,具有工程价值。
附图用来提供对本发明的进一步理解,并且构成说明书的一部分,与本发明的实施例一起用于解释本发明,并不构成对本发明的限制。
图1为本发明的锂离子电池双极化模型图;
图2为本发明的多新息递推贝叶斯算法的总体流程图;
图3为本发明的总体结构框图;
图4为本发明的测试电压电流曲线图;
图5为本发明实施例中的OCV-SOC的9次拟合曲线图;
图6为本发明的递推贝叶斯算法得到的参数R
omc,R
1,R
2,C
1,C
2在线辨识曲线图;
图7为本发明的递推贝叶斯算法得到的端电压预测曲线;
图8为本发明的多新息递推贝叶斯算法得到的参数R
omc,R
1,R
2,C
1,C
2在线辨识曲线图;
图9为本发明的多新息递推贝叶斯算法得到的端电压预测曲线图。
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。当然,此处所描述的具体实施例仅用以解释本发明,并不用于限定本发明。
实施例1
参见图1至图9,本实施例以松下锂离子电池NCR-18650B为对象展开研究,标定电压为3.7V,电池容量为3400mAh。电池以恒流充电方式(0.5C)充至截止电压,待静置1h后,电池为满电状态。电池以间歇恒流放电模式工作:放电5min,静置30min,放电电流为3400mA,放电倍率为1C。重复该过程直至电压降至放电截止电压。测试电压曲线与电流曲线如图4所示。通过该实验验证了多新息递推贝叶斯算法可以很好地辨识各个模型参数,该算法在输入电流存在不稳定振荡时参数估计值保持相对稳定,由于参数初始值的选取与实际值有出入,在辨识初期波动较为明显,随着辨识的持续运行,参数估计值逐渐趋于稳定。与递推贝叶斯算法进行比较,精确度高。
本发明提供一种基于多新息递推贝叶斯算法的电池模型参数辨识方法,包括下列步骤:
步骤1)通过间歇恒流放电法测取一定时间内的锂离子电池端电压、负载电流数据。采样周期为1Hz,一共采集到了21211组数据。通过时安法对SOC进行求解,在MATLAB中利用多项式拟合函数polyfit进行曲线拟合确定其OCV-SOC的函数关系;
U
oc=408.8953SOC
9-2086.5148SOC
8+4486.3357SOC
7-5290.2456SOC
6+3737.8499SOC
5-1630.8013SOC
4+440.5232SOC
3-72.3449SOC
2+7.3498SOC+3.1240
步骤2)确定锂离子电池的双极化等效电路模型,建立表示电池参数辨识向量和系统输出关系的系统方程;
步骤3)构建多新息递推贝叶斯算法的辨识流程;
作为本发明提供的一种基于多新息递推贝叶斯算法的电池模型参数辨识方法进一步优化方案,所述步骤2)具体包括如下步骤:
步骤2-1)建立锂离子电池的双极化模型,根据模型建立锂离子电池电气量关系:
Q
n为电池的额定容量,SOC定义为剩余容量与标称容量之比,可以表示为:
以电流I为输入,端电压U为输出,[SOC,U
1,U
2]
T为状态变量建立双极化模型的离散化状态空间方程和输出方程如下:
式(3)和式(4)中,Δt为采样周期,U
oc、U对应的是电池开路电压与端电压,C
1、C
2两端的电压分别用U
1、U
2表示,R
omc是欧姆内阻。R
1、C
1表征电化学极化反应,电压快速变化过程;R
2、C
2表征浓差极化反应,电压缓慢稳定的变化过程。
步骤2-2)建立双极化模型的电池参数辨识模型:
采用双线性变化s=2(1-z
-1)/T(1+z
-1)(T为采样周期,设置为1s),将上式从s平面映射到z平面,可以得到:
其中,τ
1=R
1C
1,τ
2=R
2C
2,a=R
omc,b=τ
1τ
2,c=τ
1+τ
2,d=R
omc+R
1+R
2,e=R
omc(τ
1+τ
2)+R
1τ
1+R
2τ
2。
传递函数离散化后得到的差分方程为:
令y(t)=U(t)-U
oc(t),可以得到符合锂离子电池进行参数辨识的带外加输入的自回归(AutoRegressive with exogenous input,ARX)模型为:
因为b=τ
1τ
2,c=τ
1+τ
2,可以得到:
具体地,所述步骤3)具体包括如下步骤:
步骤3-1)推导递推贝叶斯辨识算法:
贝叶斯辨识算法的核心思想是将要估计的参数视为随机变量,通过最大化参数的后验概率密度函数p(θ|D
k)得到参数的估计。θ为需要辨识的参数。使用贝叶斯理论,参数θ的后验概率密度函数表示为:
在上式中,基于参数θ和k-1时刻及以前的输入输出集合D
(k-1),系统的输出变量y(k)的先验概率密度函数记为p(y(k)|θ,D
(k-1))。p(θ|D
(k-1))是未知的,假设其遵循
与P(k-1)的正态分布:
其中,n是参数向量θ的维数,n=dimθ=5。
将公式(14)和(15)代入公式(13)中,那么,p(θ|D
(k-1))可以重新表示为
最大化后验概率函数,即
可以得到
其中,
引入中间变量L(k),得到的递推贝叶斯算法为:
考虑数据长度为p,定义输出向量Y(p,k),信息矩阵Φ(p,k),噪声向量V(p,k),
得到的辨识模型为:
Y(p,k)=Φ
T(p,k)θ+V(p,k) (20)
根据多新息理论将标量新息e(t)扩展成新息向量E(p,k):
中间向量L(k)∈R
n扩展成Γ(p,k)∈R
n×p(n为待辨识向量维数)。
根据步骤3-1)建立锂离子电池多新息递推贝叶斯算法:
步骤3-3)初始化待辨识参数θ,协方差矩阵P,方差值σ
v以及数据长度p,实施例中,方差值σ
v=0.1,数据长度p=5;
步骤3-4)根据OCV-SOC关系得到U
oc(k)与SOC(k);
步骤3-6)构建新息矩阵E(p,k)、输出矩阵Y(p,k)和信息矩阵Φ(p,k);
步骤3-7)更新待辨识参数的中间向量Γ(k);
步骤3-9)更新待辨识参数的协方差矩阵P(k);
P(k)=[I-Γ(k)Φ
T(k)]P(k-1) (25)
步骤3-10)判断是否满足辨识终止时间k
max=21211,所述终止条件为遍历所有时刻,即k=k
max,若满足,辨识结束输出辨识结果;否则,k=k+1,返回到步骤3-4);
步骤3-11)根据步骤3-10)辨识参数θ结果,结合式(10)至式(12)求得电池R
omc,R
1,R
2,C
1,C
2。
进一步地,根据参数辨识模型输出的锂离子电池参数R
omc,R
1,R
2,C
1,C
2以及工作电流值I,结合状态空间表达式(3)和式(4),求得端电压预测值,与实际测试值进行比较,可以评估算法的有效性及准确性。
本实施例所用的OCV-SOC关系曲线如图5所示,参数R
omc,R
1,R
2,C
1,C
2的实时在线辨识曲线如图8所示。通过对每一时刻所辨识出来的参数和对应时刻的工作电流对双极化模型的端电压进行预测,结果如图9所示。将模型参数预测电压值与实际测试值比较来评估参数辨识的准确性。为进行比较,本发明给出了递推贝叶斯算法的结果图,如图6和图7所示。
相比于递推贝叶斯算法,多新息递推贝叶斯算法可以很好地辨识各个模型参数,该算法在输入电流存在不稳定振荡时参数估计值保持相对稳定,由于参数初始值的选取与实际值有一定误差,在辨识初期波动较为明显,随着辨识的持续运行,参数估计值逐渐趋于稳定。
递推贝叶斯算法与多新息递推贝叶斯算法的模型端电压预测都比较接近实际测试值,但在搁置到放电或者放电到搁置时,电流发生突变时,多新息递推贝叶斯算法比较稳定,误差较小。
可以看出,多新息递推贝叶斯算法的辨识精度较高,输出的估计值与真实值非常接近,具有工程价值。
以上所述仅为本发明的较佳实施例,并不用以限制本发明,凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。
Claims (4)
- 一种基于多新息递推贝叶斯算法的电池模型参数辨识方法,其特征在于,包括以下步骤:步骤1)通过间歇恒流放电法测取时长为21211秒的锂离子电池端电压、负载电流数据,通过多项式拟合法确定其OCV-SOC的函数关系;步骤2)确定锂离子电池的双极化等效电路模型,建立表示电池参数辨识向量和系统输出关系的系统方程;步骤3)构建多新息递推贝叶斯算法的辨识流程。
- 根据权利要求1所述的基于多新息递推贝叶斯算法的电池模型参数辨识方法,其特征在于,所述步骤2)具体包括如下步骤:步骤2-1)建立锂离子电池的双极化模型,根据模型建立锂离子电池电气量关系:Q n为电池的额定容量,SOC定义为剩余容量与标称容量之比,可以表示为:以电流I为输入,端电压U为输出,[SOC,U 1,U 2] T为状态变量建立双极化模型的离散化状态空间方程和输出方程如下:式(3)和式(4)中,Δt为采样周期,U oc、U对应的是电池开路电压与端电压,C 1、C 2两端的电压分别用U 1、U 2表示,R omc是欧姆内阻,R 1、C 1表征电化学极化反应,电压快速变化过程;R 2、C 2表征浓差极化反应,电压缓慢稳定的变化过程;步骤2-2)建立双极化模型的电池参数辨识模型:采用双线性变化s=2(1-z -1)/T(1+z -1),T为采样周期,将上式从s平面映射到z平面,可 以得到:其中,τ 1=R 1C 1,τ 2=R 2C 2,a=R omc,b=τ 1τ 2,c=τ 1+τ 2,d=R omc+R 1+R 2,e=R omc(τ 1+τ 2)+R 1τ 1+R 2τ 2。传递函数离散化后得到的差分方程为:令y(t)=U(t)-U oc(t),可以得到符合锂离子电池进行参数辨识的带外加输入的自回归(AutoRegressive with exogenous input,ARX)模型为:因为b=τ 1τ 2,c=τ 1+τ 2,可以得到:
- 根据权利要求1所述的基于多新息递推贝叶斯算法的电池模型参数辨识方法,其特征在于,所述步骤3)具体包括如下步骤:步骤3-1)推导递推贝叶斯辨识算法:贝叶斯辨识算法是将要估计的参数视为随机变量,通过最大化参数的后验概率密度函数p(θ|D k)得到参数的估计,θ为需要辨识的参数,使用贝叶斯理论,参数θ的后验概率密度函数表示为:在上式中,基于参数θ和k-1时刻及以前的输入输出集合D (k-1),系统的输出变量y(k)的先验概率密度函数记为p(y(k)|θ,D (k-1)),p(θ|D (k-1))是未知的,假设其遵循 与P(k-1)的正态分布:其中,n是参数向量θ的维数,n=dimθ=5;将公式(14)和(15)代入公式(13)中,那么,p(θ|D (k-1))可以重新表示为最大化后验概率函数,即可以得到其中,引入中间变量L(k),得到的递推贝叶斯算法为:考虑数据长度为p,定义输出向量Y(p,k),信息矩阵Φ(p,k),噪声;向量V(p,k),得到的辨识模型为:Y(p,k)=Φ T(p,k)θ+V(p,k) (20)根据多新息理论将标量新息e(t)扩展成新息向量E(p,k):中间向量L(k)∈R n扩展成Γ(p,k)∈R n×p,n为待辨识向量维数;根据步骤3-1)建立锂离子电池多新息递推贝叶斯算法:步骤3-3)初始化待辨识参数θ,协方差矩阵P,方差值σ v以及数据长度p;步骤3-4)根据OCV-SOC关系得到U oc(k)与SOC(k);步骤3-6)构建新息矩阵E(p,k)、输出矩阵Y(p,k)和信息矩阵Φ(p,k);步骤3-7)更新待辨识参数的中间向量Γ(k);步骤3-9)更新待辨识参数的协方差矩阵P(k);P(k)=[I-Γ(k)Φ T(k)]P(k-1) (25)步骤3-10)判断是否满足辨识终止时间,若满足,辨识结束输出辨识结果;否则,k=k+1,返回到步骤3-4);步骤3-11)根据步骤3-10)辨识参数θ结果,结合式(10)至式(12)求得电池R omc,R 1,R 2,C 1,C 2。
- 根据权利要求1-3任一项所述的基于多新息递推贝叶斯算法的电池模型参数辨识方法,其特征在于,根据参数辨识模型输出的锂离子电池参数R omc,R 1,R 2,C 1,C 2以及工作电流值I,结合状态空间表达式(3)和式(4),求得端电压预测值,与实际测试值进行比较,可以评估算法的有效性及准确性。
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