CN106093517A

CN106093517A - Lithium ion battery open circuit voltage curve approximating method based on Hermite's interpolation method

Info

Publication number: CN106093517A
Application number: CN201610372817.0A
Authority: CN
Inventors: 陈琳; 潘海鸿; 陈孝杰
Original assignee: Guangxi University
Current assignee: Guangxi University
Priority date: 2016-05-30
Filing date: 2016-05-30
Publication date: 2016-11-09

Abstract

This patent discloses a method for fitting a lithium ion battery open circuit voltage curve based on a Hermitian interpolation method. In this method, when the open circuit voltage (OCV) and the state of charge (SOC) of the lithium-ion battery are obtained experimentally, the interpolation and fitting of the OCV versus SOC variation curve is performed to achieve an accurate mapping relationship between the OCV and the SOC variation. Specifically, this method first conducts an open-circuit voltage characteristic experiment on a fully charged lithium-ion battery using the interval discharge method to obtain part of the interpolation node values, and then uses the cubic Hermitian interpolation method to interpolate two adjacent nodes in turn to obtain Multiple open-circuit voltage interpolation functions with unknown derivative values, and finally by selecting boundary conditions, solve the derivative values in the interpolation functions to establish a complete open-circuit voltage curve. The invention can accurately describe the mapping relationship between OCV and SOC, and has important significance for the SOC estimation and capacity screening of lithium ion batteries.

Description

Lithium-ion battery open circuit voltage curve fitting method based on Hermitian interpolation method

技术领域technical field

本发明属于锂离子电池领域中的开路电压曲线拟合方法，特别是涉及一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法。The invention belongs to an open-circuit voltage curve fitting method in the field of lithium-ion batteries, in particular to a method for fitting a lithium-ion battery open-circuit voltage curve based on a Hermitian interpolation method.

背景技术Background technique

随着电动汽车和微电网技术的发展，大量动力电池储能装置得到了广泛应用。锂离子电池因具有高能量密度、长循环寿命、低成本价格、环保无污染等特点成为电网储能系统、电动汽车动力电池及便携式电子设备电池的最佳选择。在这些系统中锂离子电池工作状态的好坏直接关系到整个系统的运行可靠性。为了确保锂离子电池的性能良好，需对电池进行合理有效地管理和控制。With the development of electric vehicles and micro grid technology, a large number of power battery energy storage devices have been widely used. Lithium-ion batteries have become the best choice for power grid energy storage systems, electric vehicle power batteries, and portable electronic device batteries due to their high energy density, long cycle life, low cost, and environmental protection. In these systems, the working status of lithium-ion batteries is directly related to the operational reliability of the entire system. In order to ensure the good performance of lithium-ion batteries, it is necessary to manage and control the batteries reasonably and effectively.

开路电压曲线主要反映了电池开路电压与荷电状态(SOC)的关系，其对锂离子电池的安全使用、延长寿命及性能的充分发挥具有重要的意义。然而开路电压随SOC变化具有明显的非线性特征，所以无论采用哪种实验方式，都只能获取开路电压曲线上有限个测试点数据值。若直接使用由大量数据点构成的开路电压曲线数值表，需要大量的存储空间和查询时间。若出现某个SOC值恰好没有直接对应的开路电压时，通常只能使用就近点近似或简单插值办法计算，使计算精度不足。目前锂离子电池开路电压曲线拟合方法有两个：1、简单的电化学函数式模型(Simplified Electrochemical Function Model)；2、多项式模型。这两种方法通常使用最小二乘法求解待定系数，以均方根值最小为求解目标。受限于模型函数形式，往往无法保证各SOC测试点对应模型输出的开路电压估算值与实测值相等。最终模型拟合的开路电压曲线数值只能无限趋近于实测数值，无法保证曲线恰好经过所有的测试点。The open circuit voltage curve mainly reflects the relationship between the open circuit voltage of the battery and the state of charge (SOC), which is of great significance to the safe use, extended life and full performance of lithium-ion batteries. However, the change of the open circuit voltage with the SOC has obvious nonlinear characteristics, so no matter which experimental method is used, only a limited number of test point data values on the open circuit voltage curve can be obtained. If the open-circuit voltage curve numerical table composed of a large number of data points is directly used, a large amount of storage space and query time are required. If a certain SOC value does not happen to have a direct corresponding open circuit voltage, usually it can only be calculated by using the nearest point approximation or simple interpolation method, which makes the calculation accuracy insufficient. At present, there are two methods for fitting the open-circuit voltage curve of lithium-ion batteries: 1. Simple electrochemical function model (Simplified Electrochemical Function Model); 2. Polynomial model. These two methods usually use the least square method to solve the undetermined coefficients, and take the minimum root mean square value as the solution goal. Limited by the form of the model function, it is often impossible to guarantee that the estimated value of the open circuit voltage output by the model corresponding to each SOC test point is equal to the measured value. The value of the open-circuit voltage curve fitted by the final model can only be infinitely close to the measured value, and there is no guarantee that the curve will pass through all the test points.

发明内容Contents of the invention

本发明的目的在于，针对上述背景中锂离子电池开路电压曲线拟合方法中的不足之处，提出一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法。该方法拟合的开路电压曲线不仅能够保证各SOC测试点对应曲线求出的开路电压估算值与实测值相等，而且使获得的开路电压曲线可满足精确性、平滑性和鲁棒性的要求。The object of the present invention is to propose a method for fitting a lithium-ion battery open-circuit voltage curve based on the Hermitian interpolation method for the deficiencies in the method for fitting the open-circuit voltage of the lithium-ion battery in the above-mentioned background. The open circuit voltage curve fitted by this method can not only ensure that the estimated value of the open circuit voltage obtained from the corresponding curve of each SOC test point is equal to the measured value, but also make the obtained open circuit voltage curve meet the requirements of accuracy, smoothness and robustness.

为实现上述目标，本发明所采用的技术方案如下：In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

一种基于埃尔米特插值法的锂离子电池开路电压拟合方法，其特征在于，该方法包括以下步骤：A method for fitting the open circuit voltage of a lithium-ion battery based on Hermitian interpolation, characterized in that the method comprises the following steps:

(1)对满充状态(SOC＝1)的锂离子电池以设定的间隔放电模式放电(恒流放电电流大小分别为0.25C和0.1C，用户也可自行设定)，直到电池端电压达到设定放电截止电压2.750V，然后导出实验结果(SOC_i,OCV_i)，i＝0,1,...,n。(1) Discharge the lithium-ion battery in the fully charged state (SOC = 1) in the set interval discharge mode (the constant current discharge current is 0.25C and 0.1C, and the user can also set it yourself) until the battery terminal voltage The set discharge cut-off voltage of 2.750V is reached, and then the experimental results (SOC _i , OCV _i ) are derived, i=0,1,...,n.

(2)令SOC_i＝x_i，OCV_i＝y_i，i＝0,1,...,n，以i＝0为例，选取(x₀,y₀)作为第一个插值节点，(x₁,y₁)作为第二个插值节点，且x₁-x₀＝Δx，Δx取值为0％～10％的SOC(用户可自行设定)。利用三次埃尔米特插值公式可以写出小区间[x₀,x₁]上的插值函数S₁(x)的表达式：(2) Let SOC _i =x _i , OCV _i =y _i , i=0,1,...,n, take i=0 as an example, select (x ₀ ,y ₀ ) as the first interpolation node, (x ₁ , y ₁ ) is used as the second interpolation node, and x ₁ −x ₀ =Δx, and the value of Δx is 0% to 10% of SOC (users can set it themselves). The expression of the interpolation function S ₁ (x) on the small interval [x ₀ ,x ₁ ] can be written by using the cubic Hermitian interpolation formula:

S₁(x)＝h₀(x)y₀+h₁(x)y₁+H₀(x)m₀+H₁(x)m₁ (1)S ₁ (x)=h ₀ (x)y ₀ +h ₁ (x)y ₁ +H ₀ (x)m ₀ +H ₁ (x)m ₁ (1)

其中，x∈(x₀,x₁)， m₀和m₁分别为插值节点(x₀,y₀)和(x₁,y₁)处的微分值。完成上述之后，再取i＝1,2,...,n-1，分别完成在[x_i,x_i+1]区间内的插值计算，且有x_i+1-x_i＝Δx，最后得到含有未知数m₀,m₁,...,m_n的分段插值函数S₁(x),S₂(x),...,S_n(x)。where x∈(x ₀ ,x ₁ ), m ₀ and m ₁ are the differential values at the interpolation nodes (x ₀ , y ₀ ) and (x ₁ , y ₁ ) respectively. After completing the above, take i=1,2,...,n-1, respectively complete the interpolation calculation in the interval [ _xi , _xi+1 ], and have x _i+1 _-xi =Δx, Finally, the piecewise interpolation functions S ₁ (x), S ₂ (x),...,S _n (x) containing unknowns m ₀ , m ₁ ,...,m _n are obtained.

(3)选取S₁”(x₀)＝S_n”(x_n)＝0为边界条件，利用插值函数S₁(x),S₂(x),...,S_n(x)在内节点x_i(i＝1,2,...,n-1)上的二阶微商连续的性质，求解步骤(2)插值函数S₁(x),S₂(x),...,S_n(x)中的未知数m₀,m₁,...,m_n，将求得的m₀,m₁,...,m_n代入埃尔米特插值函数S₁(x),S₂(x),...,S_n(x)中，获得开路电压曲线方程S(x),最终建立[0,1]区间内完整的开路电压曲线。(3) Select S ₁ ”(x ₀ )=S _n ”(x _n )=0 as the boundary condition, use interpolation functions S ₁ (x), S ₂ (x),...,S _n (x) in The continuous nature of the second-order differential quotient on internal nodes x _i (i=1,2,...,n-1), solve step (2) interpolation functions S ₁ (x), S ₂ (x),... .,The unknowns m ₀ ,m ₁ ,...,m _n in S _n (x), substitute the obtained m ₀ ,m ₁ ,...,m _n into the Hermitian interpolation function S ₁ (x ), S ₂ (x),..., S _n (x), the open circuit voltage curve equation S(x) is obtained, and finally a complete open circuit voltage curve in the [0,1] interval is established.

所述步骤(3)中求解m₀,m₁,...,m_n的具体方法如下：The specific method for solving m ₀ , m ₁ ,...,m _n in the step (3) is as follows:

在小区间[x_i,x_i+1]上，利用三次埃尔米特插值法可得插值函数S(x)的表达式：On the small interval [x _i , _xi+1 ], the expression of the interpolation function S(x) can be obtained by using the cubic Hermitian interpolation method:

$\begin{matrix} S S ((x x)) = = ((11 + + 22 \frac{x x - - {x x}_{i i}}{{x x}_{i i + + 11} - - {x x}_{i i}})) {((\frac{x x - - {x x}_{i i + + 11}}{{x x}_{i i} - - {x x}_{i i + + 11}}))}^{22} {y the y}_{i i} + + ((11 + + 22 \frac{x x - - {x x}_{i i + + 11}}{{x x}_{i i} - - {x x}_{i i + + 11}})) {((\frac{x x - - {x x}_{i i}}{{x x}_{i i + + 11} - - {x x}_{i i}}))}^{22} {y the y}_{i i + + 11} \\ + + ((x x - - {x x}_{i i})) {((\frac{x x - - {x x}_{i i + + 11}}{{x x}_{i i} - - {x x}_{i i + + 11}}))}^{22} {m m}_{i i} + + ((x x - - {x x}_{i i + + 11})) {((\frac{x x - - {x x}_{i i}}{{x x}_{i i + + 11} - - {x x}_{i i}}))}^{22} {m m}_{i i + + 11} \end{matrix} - - - - - - ((22))$

令h_i＝x_i+1-x_i，i＝0,1,...,n，得到Let h _i =x _i+1 -x _i , i=0,1,...,n, get

$\begin{matrix} {S S}^{' '' '} ((x x)) = = ((\frac{66}{{h h}_{i i}^{22}} - - \frac{1212}{{h h}_{i i}^{33}} (({x x}_{i i + + 11} - - x x)))) {y the y}_{i i} + + ((\frac{66}{{h h}_{i i}^{22}} - - \frac{1212}{{h h}_{i i}^{33}} ((x x - - {x x}_{i i})))) {y the y}_{i i + + 11} + + ((\frac{22}{{h h}_{i i}} - - \frac{66}{{h h}_{i i}^{22}} (({x x}_{i i + + 11} - - x x)))) {m m}_{i i} \\ - - ((\frac{22}{{h h}_{i i}} - - \frac{66}{{h h}_{i i}^{22}} ((x x - - {x x}_{i i})))) {m m}_{i i + + 11} \end{matrix} - - - - - - ((33))$

由有Depend on Have

$\frac{66}{{h h}_{i i - - 11}^{22}} {y the y}_{i i - - 11} - - \frac{66}{{h h}_{i i - - 11}^{22}} {y the y}_{i i} + + \frac{22}{{h h}_{i i - - 11}} {m m}_{i i - - 11} + + \frac{44}{{h h}_{i i - - 11}} {m m}_{i i} = = - - \frac{66}{{h h}_{i i}^{22}} {y the y}_{i i} + + \frac{66}{{h h}_{i i}^{22}} {y the y}_{i i + + 11} - - \frac{44}{{h h}_{i i}} {m m}_{i i} - - \frac{22}{{h h}_{i i}} {m m}_{i i + + 11} - - - - - - ((44))$

再对每个内点建立方程，由公式(4)得到方程组：Then establish an equation for each interior point, and obtain the equation system by formula (4):

(1-α_i)m_i-1+2m_i+α_im_i+1＝β_i，i＝1,2,...,n-1 (5)(1-α _i )m _i-1 +2m _i +α _i m _i+1 =β _i, i=1,2,...,n-1 (5)

其中， in,

选取边界条件S₁”(x₀)＝S_n”(x_n)＝0，由公式(3)得Select the boundary condition S ₁ ”(x ₀ )=S _n ”(x _n )=0, from the formula (3)

$\{\begin{matrix} 22 {m m}_{00} + + {α α}_{00} {m m}_{11} = = {β β}_{00} \\ ((11 - - {α α}_{n no})) {m m}_{n no - - 11} + + 22 {m m}_{n no} = = {β β}_{n no} \end{matrix} - - - - - - ((66))$

联立方程组(5)和(6)得到m₀,m₁,...,m_n的计算公式：The calculation formulas of m ₀ ,m ₁ ,...,m _n are obtained by combining equations (5) and (6):

m_i＝A_im_i+1+B_i，i＝0,1,...,n-1(7)m _i =A _i m _i+ 1+B _i , i=0,1,...,n-1(7)

当i＝n时，When i=n,

${m m}_{n no} = = {B B}_{n no} = = \frac{{β β}_{n no} - - ((11 - - {α α}_{n no})) {B B}_{n no - - 11}}{22 + + ((11 - - {α α}_{n no})) {A A}_{n no - - 11}} - - - - - - ((88))$

其中， in,

${A A}_{i i} = = \frac{- - {α α}_{i i}}{22 + + ((11 - - {α α}_{i i})) {A A}_{i i - - 11}},, {B B}_{i i} = = \frac{{β β}_{i i} - - ((11 - - {α α}_{i i})) {B B}_{i i - - 11}}{22 + + ((11 - - {α α}_{i i})) {A A}_{i i - - 11}},, i i = = 11,, 22,, ... ...,, n no - - 11,,$

α₀＝1，α_n＝0， α ₀ =1, α _n =0,

本发明与现有锂离子电池开路电压曲线拟合方法相比具有以下优点：Compared with the existing lithium ion battery open circuit voltage curve fitting method, the present invention has the following advantages:

(1)保证各SOC测试点对应曲线求出的开路电压估算值与实测值相等。(1) Ensure that the estimated value of the open circuit voltage obtained from the corresponding curve of each SOC test point is equal to the actual measured value.

(2)插值函数S(x)在插值节点处具有一阶和二阶连续微商，使拟合的曲线较为光滑。(2) The interpolation function S(x) has the first-order and second-order continuous derivatives at the interpolation node, which makes the fitted curve smoother.

(3)埃尔米特插值法获得的开路电压曲线可满足精确性、平滑性和鲁棒性的要求。(3) The open circuit voltage curve obtained by the Hermitian interpolation method can meet the requirements of accuracy, smoothness and robustness.

附图说明Description of drawings

图1是本发明一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法的流程图；Fig. 1 is a kind of flow chart of the present invention based on the Li-ion battery open circuit voltage curve fitting method of Hermitian interpolation method;

图2是本发明一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法的开路电压曲线图。Fig. 2 is a graph of the open circuit voltage of a lithium ion battery open circuit voltage curve fitting method based on the Hermitian interpolation method of the present invention.

具体实施方法Specific implementation method

下面结合附图对本发明做进一步阐述。The present invention will be further elaborated below in conjunction with the accompanying drawings.

如图1所示，按照发明内容步骤(1)到步骤(3)实现一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法流程图。首先对满充状态(SOC＝1)的锂离子电池以设定的间隔放电模式放电(恒流放电电流大小分别为0.25C和0.1C，用户也可自行设定)，直到电池端电压达到设定放电截止电压2.750V，然后导出实验结果(SOC_i,OCV_i)，i＝0,1,...,n；其次在依次更新的小区间[x_i,x_i+1]，即[SOC_i,SOC_i+1]内利用三次埃尔米特插值法建立含有未知数m₀,m₁,...,m_n的分段插值函数开路电压曲线方程S₁(x),S₂(x),...,S_n(x)；最后选取边界条件，求解插值函数S₁(x),S₂(x),...,S_n(x)中的未知数m₀,m₁,...,m_n，用求得的m₀,m₁,...,m_n代入插值函数S₁(x),S₂(x),...,S_n(x)中，获得开路电压曲线方程S(x),最终建立[0,1]区间内完整的开路电压曲线。As shown in FIG. 1 , according to the steps (1) to (3) of the content of the invention, a flow chart of a method for fitting the open circuit voltage curve of a lithium-ion battery based on the Hermitian interpolation method is realized. First, discharge the lithium-ion battery in the fully charged state (SOC=1) in the set interval discharge mode (the constant current discharge current is 0.25C and 0.1C, and the user can also set it yourself), until the battery terminal voltage reaches the set value. Set the cut-off voltage of discharge to 2.750V, and then derive the experimental results (SOC _i , OCV _i ), i=0,1,...,n; secondly, [x _i , _xi+1 ] in the sequentially updated cells, that is, [ In SOC _i , SOC _i ₊₁ _] , the cubic Hermitian interpolation method is used to establish the open-circuit voltage curve equations S ₁ ( _x ), S ₂ ( _x ₎ ,...,S _n ₍ _x ₎ ,...,m _n , substitute the obtained m ₀ ,m ₁ ,...,m _n into the interpolation function S ₁ (x),S ₂ (x),...,S _n (x), Obtain the open circuit voltage curve equation S(x), and finally establish a complete open circuit voltage curve in the [0,1] interval.

如图2所示，是本发明一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法的开路电压曲线图。如步骤(1)所示，该方法采用间隔放电法的开路电压特性实验得到插值节点数值为：(0.000000000,2.750)、(0.000068966,3.004)、(0.020275862,3.341)、(0.040482759,3.422)、(0.060689655,3.442)、(0.080927917,3.445)、(0.0104457274,3.46)、(0.127989937,3.488)、(0.151521293,3.516)、(0.245727831,3.579)、(0.340009817,3.608)、(0.434303538,3.637)、(0.528601181,3.697)、(0.622904964,3.765)、(0.717182955,3.851)、(0.811430287,3.952)、(0.905703156,4.063)、(1.000000000,4.200)。As shown in FIG. 2 , it is a graph of the open circuit voltage of a lithium ion battery open circuit voltage curve fitting method based on the Hermitian interpolation method of the present invention. As shown in step (1), this method uses the open-circuit voltage characteristic experiment of the interval discharge method to obtain interpolation node values: (0.000000000, 2.750), (0.000068966, 3.004), (0.020275862, 3.341), (0.040482759, 3.422), ( 0.060689655,3.442)、(0.080927917,3.445)、(0.0104457274,3.46)、(0.127989937,3.488)、(0.151521293,3.516)、(0.245727831,3.579)、(0.340009817,3.608)、(0.434303538,3.637)、(0.528601181, 3.697), (0.622904964, 3.765), (0.717182955, 3.851), (0.811430287, 3.952), (0.905703156, 4.063), (1.000000000, 4.200).

如步骤(2)所示，该方法依次以上述相邻的两个插值节点进行三次埃尔米特插值计算，获得在[0,1]区间内含有未知数m₀,m₁,...,m_n的三次埃尔米特插值函数S₁(x),S₂(x),...,S_n(x)。As shown in step (2), this method uses the above two adjacent interpolation nodes to perform three-time Hermitian interpolation calculations in turn, and obtains unknown numbers m ₀ , m ₁ ,..., in the interval [0,1] Cubic Hermitian interpolation functions S ₁ (x), S ₂ (x),...,S _n (x) for m _n .

如步骤(3)所示，将上述插值节点数值代入公式(7)和公式(8)，求解出插值函数S₁(x),S₂(x),...,S_n(x)中的未知数m₀,m₁,...,m_n，将求得的m₀,m₁,...,m_n代入小区间[x_i,x_i+1]上的插值函数S₁(x),S₂(x),...,S_n(x)中，获得开路电压曲线方程S(x),最终建立[0,1]区间内完整的开路电压曲线如图2所示。As shown in step (3), substitute the above interpolation node values into formula (7) and formula (8) to solve the interpolation function S ₁ (x), S ₂ (x),...,S _n (x) unknowns m ₀ ,m ₁ ,...,m _n _, substitute the obtained m ₀ ,m ₁ ,...,m _n into the interpolation function S ₁ ₍ x), S ₂ (x),..., S _n (x), the open circuit voltage curve equation S(x) is obtained, and finally a complete open circuit voltage curve in the interval [0,1] is established as shown in Figure 2.

最后说明的是本发明的一种基于埃尔米特插值法的锂离子电池开路电压曲线拟合方法不局限于上述实施例，还可进行相应的修改和变形。因此，说明书和附图应该被认为是说明性的范例而不是限制性的。凡是依据埃尔米特插值法进行修改或等同变形的开路电压曲线拟合方法，而不脱离本发明的思想和范围，其均应涵盖在本发明的权利要求范围当中。Finally, it is explained that the Hermitian interpolation method-based open-circuit voltage curve fitting method of lithium-ion batteries of the present invention is not limited to the above-mentioned embodiments, and corresponding modifications and deformations can also be made. Accordingly, the specification and drawings should be regarded as illustrative examples and not restrictive. Any open-circuit voltage curve fitting method that is modified or equivalently deformed based on the Hermitian interpolation method without departing from the spirit and scope of the present invention should be covered by the claims of the present invention.

Claims

1. A lithium ion battery open circuit voltage curve fitting method based on an Hermite interpolation method is characterized by at least comprising the following three steps:

the method comprises the following steps: performing an open-circuit voltage characteristic experiment on the lithium ion battery in the full charge state by adopting an interval discharge method to obtain each interpolation node numerical value (SOC)_i,OCV_i),i＝0,1,...,n；

Step two: sequentially interpolating two adjacent interpolation nodes (SOC) by utilizing a cubic Hermite interpolation method_i,OCV_i) And (SOC)_i+1,OCV_i+1) Is inserted betweenObtaining a value m containing unknown differential quotient₀,m₁,...,m_nOpen circuit voltage interpolation function S_i+1(x),i＝0,1,...,n-1；

Step three: by selecting boundary conditions, an interpolation function S is solved_i+1(x) Micro quotient value m of₀,m₁,...,m_nAnd obtaining an open circuit voltage curve equation S (x), and finally establishing a complete open circuit voltage curve.

2. The lithium ion battery open circuit voltage curve fitting method based on the hermitian interpolation method according to claim 1, characterized in that: in the first step, an open-circuit voltage characteristic experiment is performed in a set intermittent discharge mode, and particularly, intermittent discharge is performed at a smaller multiplying factor when discharge of the open-circuit voltage characteristic experiment is finished, so that obtained interpolation nodes are distributed on the whole SOC interval reasonably.

3. The lithium ion battery open circuit voltage curve fitting method based on the hermitian interpolation method according to claim 1, characterized in that: in the third step, the second-order differential quotient continuity of the open-circuit voltage interpolation function at the inner point is utilized, and the second-order differential quotient value of the open-circuit voltage interpolation function at the end point is selected to be equal to zero as a boundary condition, so that the interpolation function S is solved_i+1(x) Micro quotient value m of₀,m₁,...,m_nAnd obtaining an open circuit voltage curve equation S (x), and finally establishing a complete open circuit voltage curve.