CN103439668B

CN103439668B - The charge state evaluation method of power lithium-ion battery and system

Info

Publication number: CN103439668B
Application number: CN201310400509.0A
Authority: CN
Inventors: 党选举; 伍锡如; 姜辉; 杨青; 张向文; 许勇; 刘振丙; 赵龙阳; 许凯; 莫妍; 陈波
Original assignee: Guilin University of Electronic Technology
Current assignee: Guilin University of Electronic Technology
Priority date: 2013-09-05
Filing date: 2013-09-05
Publication date: 2015-08-26
Anticipated expiration: 2033-09-05
Also published as: CN103439668A

Abstract

The present invention is charge state evaluation method and the system of power lithium-ion battery, this method first step sets up the circuit model of battery eliminator, discharge and recharge is carried out to battery and obtains volt-time curve, by formula identification model parameter, the nonlinear relationship obtaining open-circuit voltage OCV and SoC with standing experiment, timing sampling; Second step, based on Kalman Algorithm, with status predication, predicated error variance, filter gain, state estimation and estimation error variance equal matrix, obtain SoC maximum likelihood estimate.Native system analog to digital converter, program storage, programmable storage, timer and display are connected with microprocessor respectively, and electric current, voltage sensor are connected in the circuit that mesuring battary is connected with load respectively, export and access analog to digital converter.Programmable storage stores the battery model parameter of experiment gained, and program storage stores the estimation program of this method.SoC estimation precision of the present invention can reach 1%, and more stable; System provides SoC estimated value in real time.

Description

State of charge estimation method and system for power lithium-ion battery

技术领域technical field

本发明涉及汽车动力锂电池的电荷状态估算技术领域，具体为一种采用多状态分解卡尔曼滤波的动力锂离子电池的电荷状态(SoC)估算方法及系统。The invention relates to the technical field of state of charge estimation of automotive power lithium batteries, in particular to a method and system for estimating the state of charge (SoC) of power lithium ion batteries using multi-state decomposition Kalman filtering.

背景技术Background technique

动力电池是新能源汽车发展的关键，在电动汽车领域，多采用锂离子电池作为动力源。锂离子电池具有高能量、长循环寿命、无记忆效应、安全无公害、快速充电放电及工作温度范围宽等优点。Power batteries are the key to the development of new energy vehicles. In the field of electric vehicles, lithium-ion batteries are mostly used as power sources. Lithium-ion batteries have the advantages of high energy, long cycle life, no memory effect, safety and pollution-free, fast charging and discharging, and wide operating temperature range.

电池的电荷状态SoC(State of Charge)是动力电池管理系统BMS(Battery Management System)中的重要参数，它是保证电池安全寿命运行重要参数。但是SoC估算是较难解决的问题，由于电池工作状况的不确定性及电流、温度、自放电、老化等因素的影响，特别是电池在使用过程中表现出的高度非线性，使电池SoC估算的难度加大。目前电池SoC估算方法有电量累积法、开路电压法阻抗法、卡尔曼滤波法、神经网络法等。这些方法均是将电动汽车所用的电池组可看作是由输入和输出组成的动态系统，建立系统的状态方程，利用电池的输出的信息，获得对系统包括荷电状态等无法直接测量的内部状态的估算。The state of charge (SoC) of the battery is an important parameter in the power battery management system BMS (Battery Management System), and it is an important parameter to ensure the safe life of the battery. However, SoC estimation is a difficult problem to solve. Due to the uncertainty of battery working conditions and the influence of current, temperature, self-discharge, aging and other factors, especially the highly nonlinear performance of the battery during use, battery SoC estimation increased difficulty. At present, battery SoC estimation methods include power accumulation method, open circuit voltage method, impedance method, Kalman filter method, neural network method, etc. These methods regard the battery pack used in electric vehicles as a dynamic system composed of input and output, establish the state equation of the system, and use the output information of the battery to obtain internal information about the system that cannot be directly measured, including the state of charge. Estimation of state.

经典的卡尔曼(Kalman)滤波法只适用于线性系统。由于电池内部的化学特性是复杂的非线性过程，所以不能直接用于估算电池的SoC。扩展卡尔曼滤波法EKF(Extended Kalman Filter)适用于非线性系统，对SoC的初始值偏差有很强的修正作用，是目前动力电池SoC中较好的方法。但随实际工况条件剧烈波动，使噪声统计特性的变化，会导致估算误差变大，甚至出现滤波估算过程发散。因此要准确估算电池的SoC，有效提高估算精度，现有的EKF仍需要改进。The classic Kalman filter method is only suitable for linear systems. Since the chemical characteristics inside the battery are complex nonlinear processes, they cannot be directly used to estimate the SoC of the battery. The extended Kalman filter method EKF (Extended Kalman Filter) is suitable for nonlinear systems and has a strong correction effect on the initial value deviation of SoC. It is a better method in power battery SoC at present. However, as the actual working conditions fluctuate sharply, the statistical characteristics of the noise will change, which will lead to larger estimation errors and even divergence in the filtering estimation process. Therefore, in order to accurately estimate the SoC of the battery and effectively improve the estimation accuracy, the existing EKF still needs to be improved.

发明内容Contents of the invention

本发明的目的是设计一种动力锂离子电池的电荷状态估算方法，第一步建立一个三阶RC等效电路模型，通过充电和恒流放电实验辨识模型参数，得到电池开路电压OCV(Open Circuit Voltage)与SoC的非线性关系；第二步采用卡尔曼滤波，对多状态变量分开独立估算电池的开路电压，结合电池开路电压与SoC的非线性关系，最终得到SoC估算值。The purpose of the present invention is to design a method for estimating the state of charge of a power lithium-ion battery. The first step is to establish a third-order RC equivalent circuit model, and to identify the model parameters through charging and constant current discharge experiments to obtain the battery open circuit voltage OCV (Open Circuit Voltage) and the nonlinear relationship between SoC; in the second step, Kalman filtering is used to independently estimate the open circuit voltage of the battery for multiple state variables, and combined with the nonlinear relationship between the open circuit voltage of the battery and SoC, the estimated value of SoC is finally obtained.

本发明的另一目的是设计一种采用上述动力锂离子电池的电荷状态估算方法设计基于计算机信号处理系统的动力锂离子电池的电荷状态估算系统，实现实时显示在线估算的动力电池电荷状态。Another object of the present invention is to design a state-of-charge estimation system for a power lithium-ion battery based on a computer signal processing system by using the method for estimating the state of charge of the above-mentioned power lithium-ion battery, so as to realize real-time display of the state-of-charge of the power battery estimated online.

本发明设计的动力锂离子电池的电荷状态估算方法分为两步，The charge state estimation method of the power lithium-ion battery designed by the present invention is divided into two steps,

第一步、建立模型，实验和公式辨识模型参数The first step, model building, experiment and formula identification model parameters

I、建立模型I. Build a model

建立一个等效动力锂离子电池的三阶RC等效电路模型，该模型的组成如下：极化电阻R₁、R₂和R₃分别和电容C₁、C₂和C₃构成三个RC电路，串联的三个RC电路再串联动力锂离子电池的开路电压OCV(Open Circuit Voltage)和欧姆内阻R₀₀，该等效电路模型的端电压为动力锂离子电池的输出端电压Y_L。Establish a third-order RC equivalent circuit model of an equivalent power lithium-ion battery. The composition of the model is as follows: Polarization resistors R ₁ , R ₂ and R ₃ and capacitors C ₁ , C ₂ and C ₃ respectively form three RC circuits , and three RC circuits connected in series to the open circuit voltage OCV (Open Circuit Voltage) of the power lithium-ion battery and the ohmic internal resistance R ₀₀ , the terminal voltage of this equivalent circuit model is the output terminal voltage Y _L of the power lithium-ion battery.

其对应的数学模型如下：The corresponding mathematical model is as follows:

$\begin{matrix} \frac{{dU U}^{11}}{dt dt} = = - - \frac{{U u}^{11}}{{R R}_{11} {C C}_{11}} + + \frac{I I}{{C C}_{11}} \\ \frac{{dU U}^{22}}{dt dt} = = - - \frac{{U u}^{22}}{{R R}_{22} {C C}_{22}} + + \frac{I I}{{C C}_{22}} \\ \frac{{dU U}^{33}}{dt dt} = = - - \frac{{U u}^{33}}{{R R}_{33} {C C}_{33}} + + \frac{I I}{{C C}_{33}} \\ {Y Y}_{L L} = = OCV OCV ((SoC SoC)) - - {IR IR}_{0000} - - {U u}^{11} - - {U u}^{22} - - {U u}^{33} \end{matrix}\} - - - - - - ((11))$

其中Y_L是动力锂离子电池的输出端电压，R₀₀是欧姆内阻，U¹、U²、U³、分别表示电容C₁、C₂、C₃、的端电压；R₁、R₂、R₃为极化内阻，I为等效电路模型中的电流值。Among them, Y _L is the output terminal voltage of the power lithium-ion battery, R ₀₀ is the internal resistance in ohms, U ¹ , U ² , and U ³ represent the terminal voltages of capacitors C ₁ , C ₂ , and C ₃ , respectively; R ₁ , R ₂ , R ₃ is the polarization internal resistance, and I is the current value in the equivalent circuit model.

动力锂离子电池的电荷状态SoC数学模型的定义为：The definition of the state-of-charge SoC mathematical model of a power lithium-ion battery is:

$SoC SoC = = So so {C C}_{initial initial} + + \frac{11}{{C C}_{n no}} &Integral; &Integral; ηIdt ηIdt$

SoC_initial为SoC初始值，η为库仑效率，C_n为动力锂离子电池的额定容量。SoC _initial is the initial value of SoC, η is the Coulombic efficiency, and C _n is the rated capacity of the power lithium-ion battery.

上述电池三阶RC等效电路模型，需要辨识的参数分别为：欧姆内阻R₀₀，电容C₁、C₂、C₃，极化内阻R₁、R₂、R₃，其参数是通过实验和多元非线性回归方法辨识得到。The above three-order RC equivalent circuit model of the battery, the parameters to be identified are: ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , polarization internal resistance R ₁ , R ₂ , R ₃ , and the parameters are determined by It was identified experimentally and by multiple nonlinear regression methods.

II、动力锂离子电池充电、恒流放电和静置实验II. Power lithium-ion battery charging, constant current discharge and static experiment

辨识模型参数的实验包括动力锂离子电池充电、恒流放电和静置过程，在实验过程中，高精度测量动力锂离子电池连接负载后电路的电流和输出端电压，并按一定采样频率对电池输出端电压采样，采样频率为0.5～2秒，得到实验过程的电压和时间的曲线。The experiment of identifying model parameters includes the process of power lithium-ion battery charging, constant current discharge and standing. During the experiment, the current and output terminal voltage of the circuit after the power lithium-ion battery is connected to the load are measured with high precision, and the battery is tested at a certain sampling frequency. The voltage at the output terminal is sampled, and the sampling frequency is 0.5 to 2 seconds, and the curve of voltage and time during the experiment is obtained.

II-1、充电II-1. Charging

动力锂离子电池恒流恒压充电，输出端电压达到电池输出端额定电压U₀；The power lithium-ion battery is charged with constant current and constant voltage, and the output terminal voltage reaches the rated voltage U ₀ of the battery output terminal;

II-2、恒流放电II-2. Constant current discharge

常温下恒流放电，设电池额定容量为M安时，放电电流值取18～22％M，也就是放电率为0.18～0.22，动力锂离子电池输出端电压Y_Lx迅速下降，持续放电500s～2000s，停止恒流放电，此时对应电池输出端电压为U_B；Constant current discharge at room temperature, assuming that the rated capacity of the battery is M ampere hours, the discharge current value is 18-22% M, that is, the discharge rate is 0.18-0.22, the output voltage Y _Lx of the power lithium-ion battery drops rapidly, and the continuous discharge is 500s～ 2000s, stop constant current discharge, at this time the corresponding battery output voltage is _UB ;

II-3、在停止恒流放电的瞬间，电池输出端电压跳变上升为U_B，其突变电压与恒流的比为欧姆内阻R₀₀参数值；II-3. At the moment when the constant current discharge is stopped, the voltage at the output terminal of the battery jumps up to U _B, and the ratio of the sudden change voltage to the constant current is the parameter value of the ohm internal resistance R ₀₀ ;

即 $R_{00} = \frac{U_{B^{'}} - U_{B}}{I}$ Right now $R_{00} = \frac{u_{B^{'}} - u_{B}}{I}$

II-4、静置II-4. Stand still

停止恒流放电之后静置，动力锂离子电池输出端电压Y_Ls缓慢上升，电压前后两次采样的电压差值在此处电压值的5％以内，即进入稳态，稳态电压为U_C，U_C是开路电压OCV；Stand still after stopping the constant current discharge, the output voltage Y _Ls of the power lithium-ion battery rises slowly, and the voltage difference between the two samples before and after the voltage is within 5% of the voltage value here, that is, it enters a steady state, and the steady state voltage is U _C , U _C is the open circuit voltage OCV;

III、获得开路电压OCV与SoC的非线性关系III. Obtain the nonlinear relationship between open circuit voltage OCV and SoC

III-1、在步骤II-4动力锂离子电池输出端电压上升段，3个阻容电路电压特性为零输入响应的电压输出值，故III-1. In step II-4, the output terminal voltage of the power lithium-ion battery rises, the voltage characteristics of the three resistance-capacitance circuits are zero input response voltage output values, so

${Y Y}_{Ls ls} = = {b b}_{00} - - {b b}_{11} ex ex p p ((- - \frac{{t t}_{11}}{{τ τ}_{11}})))) - - {b b}_{22} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{22}})) - - {b b}_{33} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{33}})) - - - - - - ((22))$

其中：Y_Is是电池上升段电压输出值，τ₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃。(2)式中t₁为从结束放电时刻到进入电压稳态静置结束时刻的时间区间内的任意时刻，结束放电时刻t₁＝0。Wherein: Y _Is is the voltage output value of the rising stage of the battery, τ ₁ =R ₁ C ₁ , τ ₂ =R ₂ C ₂ , τ ₃ =R ₃ C ₃ . In the formula (2), t ₁ is any time in the time interval from the end of the discharge time to the end time of entering the voltage steady-state static state, and the end of the discharge time t ₁ =0.

根据步骤II-4所得的时间电压实验数据，采用最小二乘法，求得待定系数b₀、b₁、b₂、b₃、τ₁、τ₂、τ₃。According to the time-voltage experimental data obtained in step II-4, use the least square method to obtain the undetermined coefficients b ₀ , b ₁ , b ₂ , b ₃ , τ ₁ , τ ₂ , τ ₃ .

III-2、在步骤II动力锂离子电池输出端电压下降段电压输出III-2. Voltage output during step II power lithium-ion battery output terminal voltage drop stage

${Y Y}_{Lx Lx} = = {U u}_{00} - - {IR IR}_{11} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{11}})))) - - {IR IR}_{22} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{22}})))) - - {IR IR}_{33} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{33}})))) - - - - - - ((33))$

其中，Y_LX是电池下降段电压输出值，U₀是步骤I充电完成后的动力锂离子电池输出端电压，将式(2)求得的参数τ₁、τ₂、τ₂代入式(3)，根据步骤II所得的时间电压实验数据，采用最小二乘法，得到极化电阻R₁、R₂、R₃。(3)式中t₂是从开始放电时刻到停止放电时刻的时间区间内的任意时刻，开始放电时刻t₂＝0。Among them, Y _LX is the voltage output value of the falling section of the battery, U ₀ is the output voltage of the power lithium-ion battery after the charging in step I is completed, and the parameters τ ₁ , τ ₂ , τ ₂ obtained in formula (2) are substituted into formula (3 ), according to the time-voltage experimental data obtained in step II, use the least square method to obtain polarization resistances R ₁ , R ₂ , and R ₃ . (3) In the formula, t ₂ is any time in the time interval from the discharge start time to the discharge stop time, and the discharge start time t ₂ =0.

以上步骤II的实验重复3～5次，每次实验后按III-1和III-2计算所得各参数，各次实验所得的参数分别取平均值，作为对应参数值。The experiment of the above step II was repeated 3 to 5 times, and each parameter was calculated according to III-1 and III-2 after each experiment, and the parameters obtained in each experiment were respectively averaged as corresponding parameter values.

III-3、在不同恒流值充放电过程中，高精度测量动力锂离子电池连接负载后的电路的电流和对应开路电压U_C，同时根据SoC的定义得到与开路电压对应的SoC值，根据实验得到欧姆内阻R₀₀，电容C₁、C₂、C₃，极化内阻R₁、R₂、R₃的参数值，即可由上述电池三阶RC等效电路数学模型方程组(1)获得开路电压OCV与SoC的非线性关系OCV(SoC_k-1)，如下：III-3. In the process of charging and discharging with different constant current values, measure the current and the corresponding open circuit voltage U _C of the circuit after the power lithium-ion battery is connected to the load with high precision, and obtain the SoC value corresponding to the open circuit voltage according to the definition of SoC. The parameter values of ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , and polarization internal resistance R ₁ , R ₂ , R ₃ are obtained from the experiment, which can be obtained from the mathematical model equations of the above-mentioned third-order RC equivalent circuit of the battery (1 ) to obtain the nonlinear relationship OCV(SoC _k-1) between open circuit voltage OCV and SoC, as follows:

$OCV OCV (({SoC SoC}_{k k - - 11})) = = {k k}_{11} So so {C C}_{k k - - 11}^{88} + + {k k}_{22} So so {C C}_{k k - - 11}^{77} + + {k k}_{33} So so {C C}_{k k - - 11}^{66} + + {k k}_{44} {SoC SoC}_{k k - - 11}^{55} + + {k k}_{55} {SoC SoC}_{k k - - 11}^{44}$

$+ + {k k}_{66} {SoC SoC}_{k k - - 11}^{33} + + {k k}_{77} So so {C C}_{k k - - 11}^{22} + + {k k}_{88} So so {C C}_{k k - - 11} + + {k k}_{99} . . - - - - - - ((44))$

(4)式中SoC_k为当前采样时刻、k时刻的SoC，SoC_k-1是前一采样时刻，k-1时刻的SoC。(4) where SoC _k is the SoC at the current sampling time at time k, and SoC _k-1 is the SoC at the previous sampling time at time k-1.

采用最小二乘法求出OCV与SoC的非线性关系模型参数k₁～k₉。The nonlinear relationship model parameters k ₁ -k ₉ of OCV and SoC are calculated by the least square method.

第二步、基于卡尔曼滤波的SoC估算The second step, SoC estimation based on Kalman filter

采用卡尔曼滤波法，对多状态变量分开独立估算电池的开路电压，结合第一步所得的动力锂离子电池开路电压与SoC的非线性关系，估算SoC当前值。Using the Kalman filter method, the open-circuit voltage of the battery is independently estimated for multiple state variables, and the current value of the SoC is estimated by combining the nonlinear relationship between the open-circuit voltage of the power lithium-ion battery and SoC obtained in the first step.

针对非线性系统的扩展的卡尔曼(Kalman)算法(EKF)，结合第一步所建立的电池三阶RC等效电路数学模型，选取SoC及电容C₁、C₂、C₃的端电压为状态变量，即：The extended Kalman algorithm (EKF) for nonlinear systems, combined with the mathematical model of the third-order RC equivalent circuit of the battery established in the first step, selects the terminal voltage of SoC and capacitors C ₁ , C ₂ , and C ₃ as State variables, namely:

${X x}_{k k} = = {[\begin{matrix} X x 11 & X x 22 & X x 33 & X x 44 \end{matrix}]}^{T T}$

$= = {[\begin{matrix} {SoC SoC}_{k k} & {U u}_{k k}^{11} & {U u}_{k k}^{22} & {U u}_{k k}^{33} \end{matrix}]}^{T T} - - - - - - ((55))$

其中，SoC_k是k时刻SoC；是k时刻电容C₁端电压；是k时刻电容C₂端电压；是k时刻电容C₃端电压，T为对向量转置的数学符号。Among them, SoC _k is the SoC at time k; is the terminal voltage of capacitor _C1 at time k; is the terminal voltage of capacitor C ₂ at time k; is the terminal voltage of capacitor C ₃ at time k, and T is the mathematical symbol of vector transposition.

根据上式(5)将第一步的方程组(1)离散化，并考虑到系统噪声，得其状态方程(6)和测量方程(7)，分别如下：According to the above formula (5), the equation group (1) in the first step is discretized, and considering the system noise, the state equation (6) and measurement equation (7) are obtained, respectively as follows:

${X x}_{k k} = = (\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - Δt Δt / / {τ τ}_{11}} & 00 & 00 \\ 00 & 00 & {e e}^{- - Δt Δt / / {τ τ}_{22}} & 00 \\ 00 & 00 & 00 & {e e}^{- - Δt Δt / / {τ τ}_{33}} \end{matrix}) {X x}_{k k - - 11} + + (\begin{matrix} - - \frac{{η η}_{i i} Δt Δt}{{C C}_{n no}} \\ {R R}_{11} ((11 - - {e e}^{- - Δt Δt / / {τ τ}_{11}})) \\ {R R}_{22} ((11 - - {e e}^{- - Δt Δt / / {τ τ}_{22}})) \\ {R R}_{33} ((11 - - {e e}^{- - Δt Δt / / {τ τ}_{33}})) \end{matrix}) {I I}_{k k - - 11} + + {w w}_{k k - - 11} - - - - - - ((66))$

${Y Y}_{k k} = = OCV OCV ((So so {C C}_{k k - - 11})) - - {I I}_{k k} {R R}_{0000} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} {- - U u}_{k k}^{33} {+ + v v}_{k k} - - - - - - ((77))$

其中：Y_k是k时刻电池输出端电压；Δt为采样时间；I_k为k时刻电池回路电流，即系统控制输入量；η_i为库仑效率；OCV(SoC_k-1)表示通过实验数据拟合所得的电池开路电压OCV与SOC前一时刻SoC_k-1之间的非线性函数关系；τ₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃；w_k和v_k分别为过程噪声和测量噪声。Among them: Y _k is the battery output terminal voltage at time k; Δt is the sampling time; I _k is the battery loop current at time _k , that is, the system control input; η _i is the Coulomb efficiency; The nonlinear functional relationship between the battery open-circuit voltage OCV and the SoC _k-1 at the previous moment of SOC; τ ₁ = R ₁ C ₁ , τ ₂ = R ₂ C ₂ , τ ₃ = R ₃ C ₃ ; w _k and v _k are process noise and measurement noise, respectively.

动力电池的内部特性本身表现出复杂的非线性，在实际混和动力汽车工况条件剧烈变化时存在噪声，用EKF算法直接估算电池的SoC，估算结果误差偏大，甚至出现滤波估算发散。The internal characteristics of the power battery itself show complex nonlinearity, and there is noise when the actual operating conditions of the hybrid electric vehicle change drastically. Using the EKF algorithm to directly estimate the SoC of the battery, the error of the estimation result is too large, and even the filtering estimation diverges.

本方法为一种能准确估算电池的SoC及其它参数的、基于EKF的新型SOC估算方法。从第一步所建立的电池三阶RC等效电路模型可知，系统的状态变量不止一个，在实际对SoC估算时，需要同时估算多个状态变量。估算的过程中，由于多个状态变量之间存在关联、耦合与影响，状态变量越多，相互之间的关系越复杂，状态估算的运算量愈大。特别是系统噪声干扰很大时，容易导致滤波估算发散。从测量方程式(7)可知，电池输出端电压Y_k是OCV(SoC_k-1)、i_kR₀₀的线性组合，将Y_k看成是OCV(SoC_k-1)、I_kR₀₀、线性叠加，测量方程可分解为四个独立的测量方程子系统，每个子系统独立观测相应的状态变量，各状态变量的估算互不影响，有效消除状态变量估算时相互之间的耦合关系，提高估算精度。具体方法如下：The method is a new EKF-based SOC estimation method that can accurately estimate the SoC and other parameters of the battery. From the third-order RC equivalent circuit model of the battery established in the first step, it can be seen that there are more than one state variables in the system. When actually estimating the SoC, multiple state variables need to be estimated at the same time. During the estimation process, due to the correlation, coupling and influence among multiple state variables, the more state variables there are, the more complex the relationship between them is, and the greater the computational load of state estimation is. Especially when the system noise interference is very large, it is easy to cause the filter estimation to diverge. From the measurement equation (7), it can be seen that the battery output terminal voltage Y _k is OCV(SoC _k-1 ), The linear combination of i _k R ₀₀ , regard Y _k as OCV(SoC _k-1 ), I _k R ₀₀ , Linear superposition, the measurement equation can be decomposed into four independent measurement equation subsystems, each subsystem independently observes the corresponding state variable, the estimation of each state variable does not affect each other, effectively eliminates the coupling relationship between each other when estimating the state variable, and improves Estimation accuracy. The specific method is as follows:

将测量方程式(7)进行分解如下：The measurement equation (7) is decomposed as follows:

$\begin{matrix} {Y Y}_{k k,, x x 11} = = OCV OCV (({SoC SoC}_{k k - - 11})) - - {I I}_{k k} {R R}_{k k} \\ {Y Y}_{k k,, x x 22} {= = - - U u}_{k k}^{{R R}_{11} {C C}_{11}} \\ {Y Y}_{k k,, x x 33} = = {- - U u}_{k k}^{{R R}_{11} {C C}_{22}} \\ {Y Y}_{k k,, x x 44} = = {- - U u}_{k k}^{{R R}_{33} {C C}_{33}} \end{matrix}\} - - - - - - ((88))$

结合式(6)和式(8)，并运用EKF算法对状态变量X1＝SoC_k进行估算，其EKF算法递归过程的状态预测如下：Combining formula (6) and formula (8), and using the EKF algorithm to estimate the state variable X1=SoC _k , the state prediction of the recursive process of the EKF algorithm is as follows:

i、状态预测矩阵i. State prediction matrix

${\overset{^^}{X x}}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {\overset{^^}{X x}}_{k k - - 11 | | k k - - 11} + + {Γ Γ}_{k k - - 11} {I I}_{k k - - 11} - - - - - - ((99))$

其中，I_K-1是k-1时刻的电池连接负载后的电路中的回路电流，状态转移矩阵：Among them, I _K-1 is the loop current in the circuit after the battery is connected to the load at time k-1, and the state transition matrix is:

${ψ ψ}_{k k | | k k - - 11} = = (\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} & 00 & 00 \\ 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} & 00 \\ 00 & 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} \end{matrix}) - - - - - - ((1010))$

系统控制输入矩阵：System control input matrix:

${Γ Γ}_{k k - - 11} = = {[\begin{matrix} - - \frac{ηΔt ηΔt}{{C C}_{n no}} & {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) & {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) & {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) \end{matrix}]}^{T T} - - - - - - ((1111))$

ii、预测误差方差矩阵ii. Forecast error variance matrix

${P P}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {P P}_{k k - - 11 | | k k - - 11} {ψ ψ}_{k k | | k k - - 11}^{T T} + + {Q Q}_{k k - - 11} - - - - - - ((1212))$

其中Q_k是系统零均值随机过程噪声w_k的协方差矩阵。where Qk is the covariance _matrix of the system's zero-mean stochastic process noise _wk .

iii、滤波增益矩阵iii. Filter gain matrix

${K K}_{k k} = = {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} {(({H h}_{k k} {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} + + {R R}_{k k}))}^{- - 11} - - - - - - ((1313))$

其中，观测矩阵：Among them, the observation matrix:

$\begin{matrix} {H h}_{x x 11} ((k k)) = = {\frac{{&PartialD; &PartialD; Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} | |}_{X x = = \overset{^^}{S S} o o {C C}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\} - - - - - - ((1414))$

其中是k时刻SoC的预估值，即状态预测矩阵第1行第1列的数据；R_k是系统测量噪声v_k的协方差；in is the estimated value of SoC at time k, that is, the state prediction matrix The data in the first row and the first column; R _k is the covariance of the system measurement noise v _k ;

iv、状态估算矩阵iv. State estimation matrix

${\overset{^^}{X x}}_{k k | | k k} = = {\overset{^^}{X x}}_{k k | | k k - - 11} + + {K K}_{k k} (({Y Y}_{m m | | k k} - - {\overset{^^}{Y Y}}_{k k})) - - - - - - ((1515))$

其中，状态估算矩阵的第1行第1列数据是SoC_k的最优估算值；Y_m|k是k时刻电池输出端电压的观测值，包含测量噪声v_k；是k时刻电池输出端电压估算值，通过下式计算所得：Among them, the state estimation matrix The data in row 1 and column 1 of is the optimal estimated value of SoC _k ; Y _m|k is the observed value of battery output terminal voltage at time k, including measurement noise v _k ; is the estimated value of the battery output terminal voltage at time k, calculated by the following formula:

$\begin{matrix} {\overset{^^}{Y Y}}_{k k} = = OCV OCV ((\overset{^^}{S S} o o {C C}_{k k - - 11})) - - {I I}_{k k} {R R}_{00} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} - - {U u}_{k k}^{33} \\ {U u}_{k k}^{11} = = {U u}_{k k - - 11}^{11} {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} + + {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{22} = = {U u}_{k k - - 11}^{22} {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} + + {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{33} = = {U u}_{k k - - 11}^{33} {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} + + {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) {I I}_{k k - - 11} \end{matrix}\} - - - - - - ((1616))$

在计算过程中，根据第一步得到的开路电压OCV与SOC之间的非线性模型，并结合已得到的开路电压OCV和前一时刻SoC_k-1值可估算得到第(8)、(16)式中开路电压OCV(SoC_k-1)。In the calculation process, according to the nonlinear model between the open circuit voltage OCV and SOC obtained in the first step, combined with the obtained open circuit voltage OCV and the value of SoC _k-1 at the previous moment, the first (8), (16 ) where the open circuit voltage OCV (SoC _k-1 ).

v、估算误差方差矩阵v. Estimated error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1 (17)P _k|k ＝(IK _k H _k )P _k|k-1 (17)

步骤i到v就是状态变量X1＝SoC_k估算过程，在给定状态估算矩阵和估算误差方差矩阵P_k|k各元素的初值，取为0.001～0.005，通过递归就可得到其第1行第1列数据就是SoC_k的最优估算值。Steps i to v are state variable X1=SoC _k estimation process, in a given state estimation matrix and the initial value of each element of the estimated error variance matrix P _k|k , which is taken as 0.001~0.005, can be obtained by recursion The data in row 1 and column 1 is the optimal estimated value of SoC _k .

根据上述本发明动力锂离子电池的电荷状态估算方法设计的动力锂离子电池的电荷状态估算系统，包括微处理器、电流传感器、电压传感器、模数(A/D)转换器、程序存储器、可编程存储器、定时器及显示器。模数转换器、程序存储器、可编程存储器、定时器及显示器分别与微处理器连接，电流传感器串联在待测动力锂离子电池与负载连接构成的电路中，电压传感器则并联在该电路上。电流传感器和电压传感器的输出接入模数转换器，传送所测量的动力锂离子电池连接负载后的电路电流和输出端电压。According to the state of charge estimation system of the power lithium ion battery of the present invention, the state of charge estimation system of the power lithium ion battery design includes a microprocessor, a current sensor, a voltage sensor, an analog-to-digital (A/D) converter, a program memory, and Program memory, timer and display. The analog-to-digital converter, program memory, programmable memory, timer and display are respectively connected to the microprocessor, the current sensor is connected in series to the circuit formed by connecting the power lithium-ion battery to be tested and the load, and the voltage sensor is connected in parallel to the circuit. The output of the current sensor and the voltage sensor is connected to the analog-to-digital converter to transmit the measured circuit current and output terminal voltage after the power lithium-ion battery is connected to the load.

可编程存储器存储实验所得的动力锂离子电池等效模型参数，包括欧姆内阻R₀₀，电容C₁、C₂、C₃，极化内阻R₁、R₂、R₃，开路电压与SoC_k-1的非线性模型参数k₁～k₉。程序存储器中存储卡尔曼滤波SoC_k估算模型和开路电压OCV(SOC_K-1)与SoC_k-1非线性关系模型；The programmable memory stores the equivalent model parameters of the power lithium-ion battery obtained from the experiment, including ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , polarization internal resistance R ₁ , R ₂ , R ₃ , open circuit voltage and SoC _k-1 nonlinear model parameters k ₁ to k ₉ . The Kalman filter SoC _k estimation model and the open circuit voltage OCV (SOC _K-1 ) and SoC _k-1 nonlinear relationship model are stored in the program memory;

卡尔曼滤波SoC_k估算模型包括：The Kalman filter SoC _k estimation model includes:

i、状态预测矩阵i. State prediction matrix

${\overset{^^}{X x}}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {\overset{^^}{X x}}_{k k - - 11 | | k k - - 11} + + {Γ Γ}_{k k - - 11} {I I}_{k k - - 11}$

其中，状态转移矩阵：Among them, the state transition matrix:

${ψ ψ}_{k k | | k k - - 11} = = (\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} & 00 & 00 \\ 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} & 00 \\ 00 & 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} \end{matrix})$

系统控制输入矩阵：System control input matrix:

${Γ Γ}_{k k - - 11} = = {[\begin{matrix} - - \frac{ηΔt ηΔt}{{C C}_{n no}} & {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) & {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) & {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) \end{matrix}]}^{T T}$

ii、预测误差方差矩阵ii. Forecast error variance matrix

${P P}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {P P}_{k k - - 11 | | k k - - 11} {ψ ψ}_{k k | | k k - - 11}^{T T} + + {Q Q}_{k k - - 11}$

其中Q_k是系统零均值随机过程噪声w_k的协方差矩阵；where Q _k is the covariance matrix of the system’s zero-mean stochastic process noise w _k ;

iii、滤波增益矩阵iii. Filter gain matrix

${K K}_{k k} = = {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} {(({H h}_{k k} {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} + + {R R}_{k k}))}^{- - 11}$

其中，观测矩阵：Among them, the observation matrix:

$\begin{matrix} {H h}_{x x 11} ((k k)) = = {\frac{{&PartialD; &PartialD; Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} | |}_{X x = = \overset{^^}{S S} o o {C C}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\}$

iv、状态估算矩阵iv. State estimation matrix

${\overset{^^}{X x}}_{k k | | k k} = = {\overset{^^}{X x}}_{k k | | k k - - 11} + + {K K}_{k k 11} (({Y Y}_{m m | | k k} - - {\overset{^^}{Y Y}}_{k k}))$

$\begin{matrix} {\overset{^^}{Y Y}}_{k k} = = OCV OCV ((\overset{^^}{S S} o o {C C}_{k k - - 11})) - - {I I}_{k k} {R R}_{00} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} - - {U u}_{k k}^{33} \\ {U u}_{k k}^{11} = = {U u}_{k k - - 11}^{11} {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} + + {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{22} = = {U u}_{k k - - 11}^{22} {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} + + {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{33} = = {U u}_{k k - - 11}^{33} {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} + + {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) {I I}_{k k - - 11} \end{matrix}\};;$

其中：是SoC_k-1的预估值，开路电压OCV(SOC_K-1)与SoC_k-1非线性关系模型如下：in: is the estimated value of SoC _k -1, the nonlinear relationship model between open circuit voltage OCV(SOC _K-1 ) and SoC _k-1 is as follows:

$OCV OCV (({SoC SoC}_{k k - - 11})) = = {k k}_{11} {SoC SoC}_{k k - - 11}^{88} + + {k k}_{22} {SoC SoC}_{k k - - 11}^{77} + + {k k}_{33} {SoC SoC}_{k k - - 11}^{66} + + {k k}_{44} {SoC SoC}_{k k - - 11}^{55} + + {k k}_{55} {SoC SoC}_{k k - - 11}^{44}$

$+ + {k k}_{66} {SoC SoC}_{k k - - 11}^{33} + + {k k}_{77} {SoC SoC}_{k k - - 11}^{22} + + {k k}_{88} {SoC SoC}_{k k - - 11} + + {k k}_{99} . .$

根据SoC_k-1的估算值得到 Estimated value based on SoC _k-1 get

v、估算误差方差矩阵v. Estimated error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1 ；P _k|k ＝(IK _k H _k )P _k|k-1 ;

定时器控制程序存储器中SoC_k估算程序启动和中断的运行，微处理器的运行结果的当前SoC_k估算值，通过显示器实时显示。The timer controls the start and interrupt operation of the SoC _k estimation program in the program memory, and the current SoC _k estimation value of the operating result of the microprocessor is displayed in real time through the display.

与现有技术相比，本发明动力锂离子电池的电荷状态估算方法与系统的优点为：1、在扩展的卡尔曼算法(EKF)的基础上，根据叠加原理，分解测量方程，将多状态变量分别独立估算，消除了状态变量之间的耦合，减小了SoC_k状态估算的运算量，提高了SoC_k估算精度，实验证明，状态分解估算的EKF卡尔曼滤波增益矩阵与经典的EKF相比，修正作用更强、更稳定；2、考虑到在动力电池实际应用中的噪声，降低估算结果的误差，防止出现滤波估算发散，实验证明本发明SoC估算的精度可达1％；3、估算程序可存储于基于微处理器的系统内，可实时准确得到动力电池的电荷状态值，为动力电池安全运行提供重要参数。Compared with the prior art, the advantages of the state of charge estimation method and system of the power lithium-ion battery of the present invention are: 1. On the basis of the extended Kalman algorithm (EKF), according to the superposition principle, the measurement equation is decomposed, and the multi-state The variables are estimated independently, which eliminates the coupling between state variables, reduces the calculation amount of SoC _k state estimation, and improves the estimation accuracy of SoC _k . 2. Taking into account the noise in the practical application of the power battery, the error of the estimation result is reduced, and the divergence of the filtering estimation is prevented. The experiment proves that the SoC estimation accuracy of the present invention can reach 1%; 3. The estimation program can be stored in the microprocessor-based system, which can accurately obtain the charge state value of the power battery in real time, and provide important parameters for the safe operation of the power battery.

附图说明Description of drawings

图1为本动力锂离子电池的电荷状态估算方法实施例动力锂离子电池的三阶RC等效电路模型示意图；Fig. 1 is the schematic diagram of the third-order RC equivalent circuit model of the power lithium-ion battery embodiment of the state of charge estimation method of the power lithium-ion battery;

图2为本动力锂离子电池的电荷状态估算方法实施例动力锂离子电池充电、恒流放电和静置实验所得的电压和时间的曲线图；Fig. 2 is the curve diagram of the voltage and time obtained from power lithium ion battery charging, constant current discharge and static experiment of the embodiment of the method for estimating the state of charge of the power lithium ion battery;

图3为本动力锂离子电池的电荷状态估算系统实施例结构示意图。Fig. 3 is a schematic structural diagram of an embodiment of the charge state estimation system of the power lithium-ion battery.

具体实施方式Detailed ways

动力锂离子电池的电荷状态估算方法实施例Embodiment of the method for estimating the state of charge of a power lithium-ion battery

I、建立模型I. Build a model

建立一个等效动力锂离子电池的三阶RC等效电路模型，如图1所示，极化电阻R₁、R₂和R₃分别和电容C₁、C₂和C₃构成三个RC电路，串联的三个RC电路再串联动力锂离子电池的开路电压OCV和欧姆内阻R₀₀，该等效电路模型的端电压为动力锂离子电池的输出端电压Y_L。Establish a third-order RC equivalent circuit model of an equivalent power lithium-ion battery, as shown in Figure 1, polarization resistors R ₁ , R ₂ and R ₃ form three RC circuits with capacitors C ₁ , C ₂ and C ₃ respectively , and three RC circuits connected in series to open-circuit voltage OCV and ohmic internal resistance R ₀₀ of the power lithium-ion battery. The terminal voltage of this equivalent circuit model is the output terminal voltage Y _L of the power lithium-ion battery.

$\begin{matrix} \frac{{dU U}^{11}}{dt dt} = = - - \frac{{U u}^{11}}{{R R}_{11} {C C}_{11}} + + \frac{I I}{{C C}_{11}} \\ \frac{{dU U}^{22}}{dt dt} = = - - \frac{{U u}^{22}}{{R R}_{22} {C C}_{22}} + + \frac{I I}{{C C}_{22}} \\ \frac{{dU U}^{33}}{dt dt} = = - - \frac{{U u}^{33}}{{R R}_{33} {C C}_{33}} + + \frac{I I}{{C C}_{33}} \\ {Y Y}_{L L} = = OCV OCV ((SoC SoC)) - - {IR IR}_{0000} - - {U u}^{11} - - {U u}^{22} - - {U u}^{33} \end{matrix}\}$

$SoC SoC = = {SoC SoC}_{initial initial} + + \frac{11}{{C C}_{n no}} &Integral; &Integral; ηIdt ηIdt$

本例测试实验设备为美国Arbin公司的电动车电池测试系统-EVTS。动力锂离子电池额定容量C_n＝60Ah，η为库仑效率，在充电时η＝0.95，放电时η＝1。The test equipment in this example is the electric vehicle battery test system-EVTS of Arbin Company of the United States. The rated capacity of the power lithium-ion battery is C _n =60Ah, η is the coulombic efficiency, η=0.95 when charging, and η=1 when discharging.

辨识模型参数的实验包括动力锂离子电池充电、恒流放电和静置过程，整个过程在常温下进行，在实验过程中，高精度测量动力锂离子电池连接负载的电路的电流和输出端电压，采样周期为1秒，得到实验过程的电压和时间的曲线，如图2所示。The experiment to identify the model parameters includes charging, constant current discharge and standing process of the power lithium-ion battery. The whole process is carried out at room temperature. During the experiment, the current and output terminal voltage of the circuit connecting the power lithium-ion battery to the load are measured with high precision. The sampling period is 1 second, and the curve of voltage and time in the experimental process is obtained, as shown in Fig. 2 .

II-1、充电II-1. Charging

动力锂离子电池恒流恒压充电，达到图2中的A点，电池输出端额定电压的U₀＝79.48V；The power lithium-ion battery is charged at constant current and constant voltage to reach point A in Figure 2, and the rated voltage of the battery output terminal is U ₀ =79.48V;

II-2、恒流放电II-2. Constant current discharge

常温下恒流放电，电池额定容量为60Ah，放电电流I＝60*20％＝12A，放电时间T＝700s，动力锂离子电池输出端电压Y_Lx迅速下降，至图2中的B点，对应电池输出端电压为U_B＝77.8V，停止恒流放电；Constant current discharge at room temperature, the rated capacity of the battery is 60Ah, the discharge current I = 60*20% = 12A, the discharge time T = 700s, the output voltage Y _Lx of the power lithium-ion battery drops rapidly to point B in Figure 2, corresponding to The battery output terminal voltage is U _B = 77.8V, stop constant current discharge;

II-3、在停止恒流放电的瞬间，电池输出端电压跳变上升到图2中的B′点为U_B’＝79.18V；B点和B′点为拐点，BB与水平线的角度近于90度；其突变电压与恒流的比为欧姆内阻R₀₀参数值；II-3. At the moment when the constant current discharge is stopped, the voltage of the battery output jumps up to point B' in Figure 2, which is U _B '=79.18V; points B and B' are inflection points, and the angle between BB and the horizontal line is close to at 90 degrees; the ratio of the sudden change voltage to the constant current is the ohmic internal resistance R ₀₀ parameter value;

II-4、静置II-4. Stand still

停止恒流之后静置，本例持续时间4300s，动力锂离子电池输出端电压Y_Ls缓慢上升，直到前后两次采样的电压差值在此处电压值的5％以内，进入稳态，本例稳态电压U_C＝79.4V，即图2中的C点，U_C是本电池的开路电压OCV。Stand still after stopping the constant current, the duration of this example is 4300s, the voltage Y _Ls of the output terminal of the power lithium-ion battery rises slowly until the voltage difference between the two samples before and after is within 5% of the voltage value here, and enters a steady state, in this example Steady-state voltage U _C =79.4V, which is point C in Figure 2, where U _C is the open-circuit voltage OCV of the battery.

III-1、在步骤II-4动力锂离子电池输出端电压上升段BB’中3个阻容环节电压特性为零输入响应，电池的输出端电压值III-1. In the step II-4 power lithium-ion battery output terminal voltage rise section BB', the voltage characteristics of the three resistance-capacitance links are zero input response, and the output terminal voltage value of the battery is

${Y Y}_{Ls ls} = = {b b}_{00} - - {b b}_{11} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{11}})))) - - {b b}_{22} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{22}})) - - {b b}_{33} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{33}}))$

其中：Y_LS是电池上升段电压输出值，τ₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃。(2)式中t₁为结束放电时刻到进入电压稳态、静置结束的时间区间内的任意时刻，结束放电时刻t₁＝0。Wherein: Y _LS is the voltage output value of the rising stage of the battery, τ ₁ =R ₁ C ₁ , τ ₂ =R ₂ C ₂ , τ ₃ =R ₃ C ₃ . In the formula (2), t ₁ is any time between the end of the discharge time and the time interval between entering the voltage steady state and ending the rest, and the discharge end time t ₁ =0.

根据步骤II-4所得的时间电压实验数据，采用最小二乘法就，求得待定系数b₀、b₁、b₂、b₃、τ₁、τ₂、τ₃。According to the time and voltage experimental data obtained in step II-4, use the least square method to obtain the undetermined coefficients b ₀ , b ₁ , b ₂ , b ₃ , τ ₁ , τ ₂ , τ ₃ .

III-2、在步骤II动力锂离子电池输出端电压下降段AB的电压输出III-2. The voltage output of step II power lithium-ion battery output terminal voltage drop section AB

${Y Y}_{Lx Lx} = = {U u}_{00} - - {IR IR}_{11} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{11}})))) - - {IR IR}_{22} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{22}})))) - - {IR IR}_{33} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{33}}))))$

其中，Y_LX是电池下降段电压输出值，U₀是步骤I充电完成后A点的动力锂离子电池输出端电压，将式(2)求得的参数τ₁、τ₂、τ₂代入式(3)，根据步骤II所得的时间电压实验数据，采用最小二乘法，得到极化电阻R₁、R₂、R₃。(3)式t₂为从开始放电时刻到停止放电时间区间的任意时刻，开始放电时刻t₂＝0。Among them, Y _LX is the voltage output value of the falling section of the battery, U ₀ is the output terminal voltage of the power lithium-ion battery at point A after the charging in step I is completed, and the parameters τ ₁ , τ ₂ , τ ₂ obtained in formula (2) are substituted into the formula (3) According to the time-voltage experimental data obtained in step II, the polarization resistances R ₁ , R ₂ , and R ₃ are obtained by using the least square method. (3) Equation t ₂ is any time in the time interval from the start of discharge to the stop of discharge, and the time of start of discharge t ₂ =0.

以上步骤II的实验重复3次，每次实验后按III-1和III-2计算所得各参数，各次实验所得的参数分别取平均值，作为对应参数值。The experiment of the above step II was repeated 3 times, and each parameter was calculated according to III-1 and III-2 after each experiment, and the parameters obtained in each experiment were respectively averaged as corresponding parameter values.

III-3、在不同恒流值充放电过程中，高精度测量动力锂离子电池连接负载后的电路的电流和对应开路电压，同时根据SoC的定义得到与开路电压对应的SoC值，根据实验得到欧姆内阻R₀₀，电容C₁、C₂、C₃，极化内阻R₁、R₂、R₃的参数值，即可由上述电池三阶RC等效电路数学模型方程组(1)获得开路电压OCV与SoC的非线性关系OCV(SoC_k-1)的多项式模型如下：III-3. In the process of charging and discharging with different constant current values, the current and the corresponding open circuit voltage of the circuit after the power lithium-ion battery is connected to the load are measured with high precision, and the SoC value corresponding to the open circuit voltage is obtained according to the definition of SoC. According to the experiment The parameter values of ohmic internal resistance R ₀₀ , capacitors C ₁ , C ₂ , and C ₃ , and polarization internal resistances R ₁ , R ₂ , and R ₃ can be obtained from the mathematical model equations (1) of the above-mentioned third-order RC equivalent circuit of the battery The polynomial model of the nonlinear relationship between open circuit voltage OCV and SoC OCV(SoC _k-1 ) is as follows:

$\begin{matrix} OCV OCV (({SoC SoC}_{k k - - 11})) = = {k k}_{11} {SoC SoC}_{k k - - 11}^{88} + + {k k}_{22} {SoC SoC}_{k k - - 11}^{77} + + {k k}_{33} {SoC SoC}_{k k - - 11}^{66} + + {k k}_{44} {SoC SoC}_{k k - - 11}^{55} + + {k k}_{55} {SoC SoC}_{k k - - 11}^{44} \\ + + {k k}_{66} {SoC SoC}_{k k - - 11}^{33} + + {k k}_{77} {SoC SoC}_{k k - - 11}^{22} + + {k k}_{88} {SoC SoC}_{k k - - 11} + + {k k}_{99} . . \end{matrix}$

式中SoC_k为当前采样时刻，k时刻的SoC，SoC_k-1是前一采样时刻，k-1时刻的SoC。In the formula, SoC _k is the SoC at the current sampling time at time k, and SoC _k-1 is the SoC at the time k-1 at the previous sampling time.

开路电压OCV与SoC的非线性关系OCV(SoC_k-1)Nonlinear relationship between open circuit voltage OCV and SoC OCV(SoC _k-1 )

i、状态预测矩阵i. State prediction matrix

其中，状态转移矩阵：Among them, the state transition matrix:

系统控制输入矩阵：System control input matrix:

ii、预测误差方差矩阵ii. Forecast error variance matrix

iii、滤波增益矩阵iii. Filter gain matrix

其中，观测矩阵：Among them, the observation matrix:

$\begin{matrix} {H h}_{x x 11} ((k k)) = = \frac{{&PartialD; &PartialD; Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} {| |}_{X x = = \overset{^^}{S S} o o {C C}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\}$

其中是k时刻SoC的预估值，即状态预测矩阵第1行第1列的数据；R_k是系统测量噪声v_k的协方差；本例估算X1时，根据测试数据结合协方差定义估算，本例取R_k＝0.0473，则本例系统零均值随机过程噪声w_k的协方差矩阵：in is the estimated value of SoC at time k, that is, the state prediction matrix The data in the first row and the first column; R _k is the covariance of the system measurement noise v _k ; when estimating X1 in this example, it is estimated based on the test data combined with the covariance definition. In this example, R _k = 0.0473, then the system zero mean in this example Covariance matrix of stochastic process noise w _k :

${Q Q}_{k k} = = (\begin{matrix} 0.012 0.012 & 00 & 00 & 00 \\ 00 & 00 & 00 & 00 \\ 00 & 00 & 00 & 00 \\ 00 & 00 & 00 & 00 \end{matrix})$

iv、状态估算矩阵iv. State estimation matrix

${\overset{^^}{X x}}_{k k | | k k} = = {\overset{^^}{X x}}_{k k | | k k - - 11} + + {K K}_{k k} (({Y Y}_{m m | | k k} - - {\overset{^^}{Y Y}}_{k k}))$

$\begin{matrix} {\overset{^^}{Y Y}}_{k k} = = OCV OCV ((\overset{^^}{S S} {oC oC}_{k k - - 11})) - - {I I}_{k k} {R R}_{00} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} - - {U u}_{k k}^{33} \\ {U u}_{k k}^{11} = = {U u}_{k k - - 11}^{11} {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} + + {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{22} = = {U u}_{k k - - 11}^{22} {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} + + {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{33} = = {U u}_{k k - - 11}^{33} {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} + + {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) {I I}_{k k - - 11} \end{matrix}\}$

v、估算误差方差矩阵v. Estimated error variance matrix

P_k|k=(I-K_kH_k)P_k|k-1 P _k|k =(IK _k H _k )P _k|k-1

步骤i到v是状态变量X1=SoC_k估算过程，令k=2是开始时刻，在给定状态估算矩阵和估算误差方差矩阵P_k|k的初值，取和P_k|k两个矩阵各元素为0.001，通过递归就可得到状态估算矩阵其第1行第1列数据是SoC_k的最优估算值。在计算过程中，根据第一步得到的开路电压OCV与SOC之间的非线性模型，并结合已得到的开路电压OCV和前一时刻SoC_k-1值可估算得到第(16)式中开路电压OCV(SoC_k-1)。Steps i to v are state variables X1=SoC _k estimation process, let k=2 be the start time, in a given state estimation matrix and the initial value of the estimated error variance matrix P _k|k , take Each element of the two matrices and P _k|k is 0.001, and the state estimation matrix can be obtained by recursion The data in row 1 and column 1 is the optimal estimated value of SoC _k . In the calculation process, according to the nonlinear model between the open circuit voltage OCV and SOC obtained in the first step, combined with the obtained open circuit voltage OCV and the value of SoC _k-1 at the previous moment, the open circuit in formula (16) can be estimated Voltage OCV(SoC _k-1 ).

通过i到v的递归计算，本例得到SoC_k的最优估算值，其估算精度1％。Through the recursive calculation from i to v, this example obtains the optimal estimation value of SoC _k , and its estimation accuracy is 1%.

动力锂离子电池的电荷状态估算系统实施例Embodiment of charge state estimation system for power lithium-ion battery

本动力锂离子电池的电荷状态估算系统实施例如图3所示，包括微处理器、电流传感器、电压传感器、模数(A/D)转换器、程序存储器、可编程存储器、定时器及显示器。模数转换器、程序存储器、可编程存储器、定时器及显示器分别与微处理器连接，电流传感器串联在待测动力锂离子电池与负载连接的电路中，电压传感器则并联在该电路上。电流传感器和电压传感器的输出接入模数转换器，传送所测量的动力锂离子电池的负载电流和输出端电压。本例的微处理器、模数转换器、程序存储器、可编程存储器和定时器安装在同一计算机主板上。The implementation of the state of charge estimation system of the power lithium-ion battery is shown in Figure 3, including a microprocessor, a current sensor, a voltage sensor, an analog-to-digital (A/D) converter, a program memory, a programmable memory, a timer and a display. The analog-to-digital converter, program memory, programmable memory, timer and display are respectively connected to the microprocessor, the current sensor is connected in series to the circuit connecting the power lithium-ion battery to be tested and the load, and the voltage sensor is connected in parallel to the circuit. The output of the current sensor and the voltage sensor is connected to the analog-to-digital converter to transmit the measured load current and output terminal voltage of the power lithium-ion battery. In this example, the microprocessor, analog-to-digital converter, program memory, programmable memory, and timer are installed on the same computer motherboard.

可编程存储器存储动力锂离子电池参数，包括电池额定容量，欧姆内阻R₀₀，电容C₁、C₂、C₃，极化内阻R₁、R₂、R₃、开路电压与SoC_k-1的非线性模型参数k₁～k₉。Programmable memory stores power lithium-ion battery parameters, including battery rated capacity, ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , polarization internal resistance R ₁ , R ₂ , R ₃ , open circuit voltage and SoC _{k- 1} nonlinear model parameters k ₁ ˜k ₉ .

程序存储器中存储卡尔曼滤波SoC_k估算模型和开路电压OCV(SOC_K-1)与SoC_k-1非线性关系模型；The Kalman filter SoC _k estimation model and the open circuit voltage OCV (SOC _K-1 ) and SoC _k-1 nonlinear relationship model are stored in the program memory;

i、状态预测矩阵i. State prediction matrix

其中，状态转移矩阵：Among them, the state transition matrix:

${ψ ψ}_{k k | | k k - - 11} = = [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} & 00 & 00 \\ 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} & 00 \\ 00 & 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} \end{matrix}]$

系统控制输入矩阵：System control input matrix:

ii、预测误差方差矩阵ii. Forecast error variance matrix

iii、滤波增益矩阵iii. Filter gain matrix

其中，观测矩阵：Among them, the observation matrix:

$\begin{matrix} {H h}_{x x 11} ((k k)) = = \frac{&PartialD; &PartialD; {Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} {| |}_{X x = = \overset{^^}{S S} {oC oC}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\}$

iv、状态估算矩阵iv. State estimation matrix

其中状态估算矩阵的第1行第1列数据是SoC_k的最优估算值；Y_m|k是k时刻电池输出端电压的观测值，包含测量噪声v_k；是k时刻电池输出端电压估算值，通过下式计算所得：where the state estimation matrix The data in row 1 and column 1 of is the optimal estimated value of SoC _k ; Y _m|k is the observed value of battery output terminal voltage at time k, including measurement noise v _k ; is the estimated value of the battery output terminal voltage at time k, calculated by the following formula:

其中，是SoC_k-1的预估值，开路电压OCV(SOC_K-1)与SoC_k-1非线性关系模型如下：in, is the estimated value of SoC _k -1, the nonlinear relationship model between open circuit voltage OCV(SOC _K-1 ) and SoC _k-1 is as follows:

v、估算误差方差矩阵v. Estimated error variance matrix

P_k|k=(I-K_kH_k)P_k|k-1；P _k|k =(IK _k H _k )P _k|k-1 ;

本例的显示器为LCD显示器，可编程存储器为电可擦除E²PROM可编程存储器。The display in this example is an LCD display, and the programmable memory is an electrically erasable E ² PROM programmable memory.

上述实施例，仅为对本发明的目的、技术方案和有益效果进一步详细说明的具体个例，本发明并非限定于此。凡在本发明的公开的范围之内所做的任何修改、等同替换、改进等，均包含在本发明的保护范围之内。The above-mentioned embodiments are only specific examples for further specifying the purpose, technical solutions and beneficial effects of the present invention, and the present invention is not limited thereto. Any modifications, equivalent replacements, improvements, etc. made within the disclosed scope of the present invention are included in the protection scope of the present invention.

Claims

1. The state of charge estimation method for power lithium-ion batteries is divided into two steps,

The first step, model building, experiment and formula identification model parameters

Ⅰ. Model building

Establish a third-order RC equivalent circuit model of an equivalent power lithium-ion battery. The composition of the model is as follows: Polarization resistors R ₁ , R ₂ and R ₃ and capacitors C ₁ , C ₂ and C ₃ respectively form three RC circuits , the three RC circuits in series are connected in series with the open circuit voltage OCV and ohmic internal resistance R ₀₀ of the power lithium-ion battery, and the terminal voltage of this equivalent circuit model is the output terminal voltage Y _L of the power lithium-ion battery;

The corresponding mathematical model is as follows:

\begin{matrix} \frac{{dU U}^{11}}{dt dt} = = - - \frac{{U u}^{11}}{{R R}_{11} {C C}_{11}} + + \frac{I I}{{C C}_{11}} \\ \frac{{dU U}^{22}}{dt dt} = = - - \frac{{U u}^{22}}{{R R}_{22} {C C}_{22}} + + \frac{I I}{{C C}_{22}} \\ \frac{d d {U u}^{33}}{dt dt} = = - - \frac{{U u}^{33}}{{R R}_{33} {C C}_{33}} + + \frac{I I}{{C C}_{33}} \\ {Y Y}_{L L} = = OCV OCV ((SoC SoC)) - - {IR IR}_{0000} - - {U u}^{11} - - {U u}^{22} - - {U u}^{33} \end{matrix}\} - - - - - - ((11))

Among them, Y _L is the output terminal voltage of the power lithium-ion battery, R ₀₀ is the internal resistance in ohms, U ¹ , U ² , and U ³ represent the terminal voltages of capacitors C ₁ , C ₂ , and C ₃ , respectively; R ₁ , R ₂ , _R3 is the polarization internal resistance, and I is the current value in the equivalent circuit model;

The definition of the state-of-charge SoC mathematical model of a power lithium-ion battery is:

SoC SoC = = {SoC SoC}_{initial initial} + + \frac{11}{{C C}_{n no}} &Integral; &Integral; ηIdt ηIdt

SoC _initial is the initial value of SoC, η is the Coulombic efficiency, and C _n is the rated capacity of the power lithium-ion battery;

Ⅱ. Power lithium-ion battery charging, constant current discharge and static experiment

The experiment of identifying model parameters includes charging, constant current discharge and standing process of the power lithium-ion battery. The voltage at the battery output terminal is sampled, the sampling period is 0.5-2 seconds, and the curve of voltage and time during the experiment process is obtained;

Ⅱ-1. Charging

The power lithium-ion battery is charged with constant current and constant voltage, and the output terminal voltage reaches the rated voltage U ₀ of the battery output terminal;

Ⅱ-2. Constant current discharge

Constant current discharge at room temperature, assuming that the rated capacity of the battery is M ampere hours, the discharge current value is 18-22%, that is, the discharge rate is 0.18-0.22, the output voltage Y _Lx of the power lithium-ion battery drops rapidly, and the continuous discharge lasts for 500s～ 2000s, stop constant current discharge, at this time the corresponding battery output voltage is _UB ;

Ⅱ-3. At the moment when the constant current discharge is stopped, the voltage at the output terminal of the battery jumps up to U _B' , and the ratio of the sudden change voltage to the constant current is the parameter value of the ohmic internal resistance R ₀₀ ;

Right now

R_{00} = \frac{u_{B^{'}} - u_{B}}{I}

Ⅱ-4. Stand still

Stand still after stopping the constant current discharge, the output voltage Y _Ls of the power lithium-ion battery rises slowly, and the voltage difference between the two samples before and after the voltage is within 5% of the voltage value here, that is, it enters a steady state, and the steady state voltage is U _C , U _C is the open circuit voltage OCV;

Ⅲ. Obtain the nonlinear relationship between open circuit voltage OCV and SoC

Ⅲ-1. In step Ⅱ-4, the output terminal voltage of the power lithium-ion battery rises, the voltage characteristics of the three resistance-capacitance circuits are the voltage output values of the zero input response, so

{Y Y}_{Ls ls} = = {b b}_{00} - - {b b}_{11} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{11}})))) - - {b b}_{22} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{22}})) - - {b b}_{33} exp exp ((- - \frac{{t t}_{11}}{{τ τ}_{33}}))

Among them: Y _Ls is the voltage output value of the rising stage of the battery, τ ₁ = R ₁ C ₁ , τ ₂ = R ₂ C ₂ , τ ₃ = R ₃ C ₃ ; where t ₁ is the time from the end of discharge to the voltage steady state, At any time within the time interval of the end of standing, the discharge end time t ₁ =0;

According to the time and voltage experimental data obtained in step Ⅱ-4, use the least square method to obtain the undetermined coefficients b ₀ , b ₁ , b ₂ , b ₃ , τ ₁ , τ ₂ , τ ₃ ;

Ⅲ-2. In step Ⅱ, the voltage output of the power lithium-ion battery output terminal voltage drops

{Y Y}_{Lx Lx} = = {U u}_{00} - - {IR IR}_{11} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{11}})))) - - {IR IR}_{22} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{22}})))) - - {IR IR}_{33} ((11 - - exp exp ((- - \frac{{t t}_{22}}{{τ τ}_{33}})))) - - - - - - ((33))

Among them, Y _LX is the voltage output value of the battery falling section, U ₀ is the output terminal voltage of the power lithium-ion battery after the charging in step I is completed, and the parameters τ ₁ , τ ₂ , τ ₃ obtained in formula (2) are substituted into formula (3 ), according to the time-voltage experimental data obtained in step II, using the least squares method, the polarization resistances R ₁ , R ₂ , R ₃ are obtained; (3) where t ₂ is the time interval from the start of discharge to the stop of discharge At any time of , start discharge time t ₂ =0;

Ⅲ-3. In the process of charging and discharging with different constant current values, measure the current and the corresponding open circuit voltage U _C of the circuit after the power lithium-ion battery is connected to the load with high precision, and obtain the SoC value corresponding to the open circuit voltage according to the definition of SoC. The parameter values of ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , and polarization internal resistance R ₁ , R ₂ , R ₃ are obtained from the experiment, which can be obtained from the mathematical model of the third-order RC equivalent circuit of the battery in the above step Ⅰ The equation set obtains the nonlinear relationship OCV(SoC _k-1 ) between open circuit voltage OCV and SoC;

\begin{matrix} OCV OCV (({SoC SoC}_{k k - - 11})) = = {k k}_{11} {SoC SoC}_{k k - - 11}^{88} + + {k k}_{22} {SoC SoC}_{k k - - 11}^{77} + + {k k}_{33} {SoC SoC}_{k k - - 11}^{66} + + {k k}_{44} {SoC SoC}_{k k - - 11}^{55} + + {k k}_{55} {SoC SoC}_{k k - - 11}^{44} \\ + + {k k}_{66} {SoC SoC}_{k k - - 11}^{33} + + {k k}_{77} {SoC SoC}_{k k - - 11}^{22} + + {k k}_{88} {SoC SoC}_{k k - - 11} + + {k k}_{99} . . \end{matrix}

Among them, SoC _k is the current sampling time, the SoC at k time, SoC _k-1 is the previous sampling time, and the SoC at k-1 time;

Estimated value based on SoC _k-1 get

Use the least square method to calculate the nonlinear relationship model parameters k ₁ ~ k ₉ between OCV and SoC;

The second step, SoC estimation based on Kalman filter

The state prediction of the extended Kalman algorithm recursive process for nonlinear systems is as follows:

ⅰ. State prediction matrix

{\overset{^^}{X x}}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {\overset{^^}{X x}}_{k k - - 11 | | k k - - 11} + + {Γ Γ}_{k k - - 11} {I I}_{k k - - 11}

Among them, the state transition matrix:

{ψ ψ}_{k k | | k k - - 11} = = (\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} & 00 & 00 \\ 00 & 00 & - - \frac{Δt Δt}{{τ τ}_{22}} & 00 \\ 00 & 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} \end{matrix})

System control input matrix:

{Γ Γ}_{k k - - 11} = = {[\begin{matrix} - - \frac{ηΔt ηΔt}{{C C}_{n no}} & {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) & {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) & {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) \end{matrix}]}^{T T}

ii. Forecast error variance matrix

{P P}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {P P}_{k k - - 11 | | k k - - 11} {ψ ψ}_{k k | | k k - - 11}^{T T} + + {Q Q}_{k k - - 11}

where Q _k is the covariance matrix of the system’s zero-mean stochastic process noise w _k ;

ⅲ, filter gain matrix

{K K}_{k k} = = {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} {(({H h}_{k k} {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} + + {R R}_{k k}))}^{- - 11}

Among them, the observation matrix:

\begin{matrix} {H h}_{x x 11} ((k k)) = = \frac{{&PartialD; &PartialD; Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} {| |}_{X x = = \overset{^^}{S S} o o {C C}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\}

in is the estimated value of SoC at time k, that is, the state prediction matrix The data in the first row and the first column; R _k is the covariance of the system measurement noise v _k ;

ⅳ. State estimation matrix

{\overset{^^}{X x}}_{k k | | k k} = = {\overset{^^}{X x}}_{k k | | k k - - 11} + + {K K}_{k k} (({Y Y}_{m m | | k k} - - {\overset{^^}{Y Y}}_{k k}))

Among them, the state estimation matrix The data in row 1 and column 1 of is the optimal estimated value of SoC _k ; Y _m|k is the observed value of battery output terminal voltage at time k, including measurement noise v _k ; is the estimated value of the battery output terminal voltage at time k, calculated by the following formula:

\begin{matrix} {\overset{^^}{Y Y}}_{k k} = = OCV OCV ((\overset{^^}{S S} {oC oC}_{k k - - 11})) - - {I I}_{k k} {R R}_{00} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} - - {U u}_{k k}^{33} \\ {U u}_{k k}^{11} = = {U u}_{k k - - 11}^{11} {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} + + {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{22} = = {U u}_{k k - - 11}^{22} {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} + + {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{33} = = {U u}_{k k - - 11}^{33} {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} + + {R R}_{33} ((11 {- - e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) {I I}_{k k - - 11} \end{matrix}\}

in, is the terminal voltage of capacitor _C1 at time k; is the terminal voltage of capacitor C ₂ at time k; is the terminal voltage of capacitor C ₃ at time k;

ⅴ. Estimated error variance matrix

P _k|k ＝(IK _k H _k )P _k|k-1

Steps i to v are state variables X1=SoC _k estimation process, in a given state estimation matrix and estimated error variance matrix P _k|k each element is taken as 0.001 ~ 0.005, and the optimal estimated value of SoC _k is obtained by recursion; in the calculation process, according to the nonlinear model between the open circuit voltage OCV and SOC obtained in the first step , and combine the obtained open circuit voltage OCV and the value of SoC _k-1 at the previous moment to estimate the open circuit voltage OCV(SoC _k-1 ).

2. The method for estimating the state of charge of the power lithium-ion battery according to claim 1, characterized in that:

The experiment of step II was repeated 3 to 5 times, and each parameter was calculated according to III-1 and III-2 after each experiment, and the parameters obtained in each experiment were respectively averaged as corresponding parameter values.

3. The state of charge estimation system of the power lithium ion battery according to the state of charge estimation method design of the power lithium ion battery according to claim 1 or 2, is characterized in that:

Including microprocessor, current sensor, voltage sensor, analog-to-digital converter, program memory, programmable memory, timer and display; analog-to-digital converter, program memory, programmable memory, timer and display are respectively connected to the microprocessor , the current sensor is connected in series in the circuit composed of the power lithium-ion battery to be tested and the load, and the voltage sensor is connected in parallel on the circuit; the output of the current sensor and the voltage sensor is connected to the analog-to-digital converter to transmit the measured power lithium-ion battery load current and output voltage;

The programmable memory stores the equivalent model parameters of the power lithium-ion battery obtained from the experiment, including ohmic internal resistance R ₀₀ , capacitance C ₁ , C ₂ , C ₃ , polarization internal resistance R ₁ , R ₂ , R ₃ , open circuit voltage and SoC _k-1 nonlinear model parameters k ₁ ~k ₉ ;

The Kalman filter SoC _k estimation model and the open circuit voltage OCV (SOC _K-1 ) and SoC _k-1 nonlinear relationship model are stored in the program memory;

The Kalman filter SoC _k estimation model includes:

ⅰ. State prediction matrix

{\overset{^^}{X x}}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {\overset{^^}{X x}}_{k k - - 11 | | k k - - 11} + + {Γ Γ}_{k k - - 11} {I I}_{k k - - 11}

Among them, the state transition matrix:

{ψ ψ}_{k k | | k k - - 11} = = (\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} & 00 & 00 \\ 00 & 00 & - - \frac{Δt Δt}{{τ τ}_{22}} & 00 \\ 00 & 00 & 00 & {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} \end{matrix})

System control input matrix:

{Γ Γ}_{k k - - 11} = = {[\begin{matrix} - - \frac{ηΔt ηΔt}{{C C}_{n no}} & {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) & {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) & {R R}_{33} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) \end{matrix}]}^{T T}

ii. Forecast error variance matrix

{P P}_{k k | | k k - - 11} = = {ψ ψ}_{k k | | k k - - 11} {P P}_{k k - - 11 | | k k - - 11} {ψ ψ}_{k k | | k k - - 11}^{T T} + + {Q Q}_{k k - - 11}

ⅲ, filter gain matrix

{K K}_{k k} = = {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} {(({H h}_{k k} {P P}_{k k | | k k - - 11} {H h}_{k k}^{T T} + + {R R}_{k k}))}^{- - 11}

Among them, the observation matrix:

\begin{matrix} {H h}_{x x 11} ((k k)) = = \frac{{&PartialD; &PartialD; Y Y}_{k k,, x x 11}}{&PartialD; &PartialD; X x} {| |}_{X x = = \overset{^^}{S S} o o {C C}_{k k}} \\ {H h}_{k k} = = [\begin{matrix} {H h}_{x x 11} ((k k)) & 00 & 00 & 00 \end{matrix}] \end{matrix}\}

ⅳ. State estimation matrix

{\overset{^^}{X x}}_{k k | | k k} = = {\overset{^^}{X x}}_{k k | | k k - - 11} + + {K K}_{k k} (({Y Y}_{m m | | k k} - - {\overset{^^}{Y Y}}_{k k}))

where the state estimation matrix The data in row 1 and column 1 of is the optimal estimated value of SoC _k ; Y _m|k is the observed value of battery output terminal voltage at time k, including measurement noise v _k ; is the estimated value of the battery output terminal voltage at time k, calculated by the following formula:

\begin{matrix} {\overset{^^}{Y Y}}_{k k} = = OCV OCV ((\overset{^^}{S S} {oC oC}_{k k - - 11})) - - {I I}_{k k} {R R}_{00} - - {U u}_{k k}^{11} - - {U u}_{k k}^{22} - - {U u}_{k k}^{33} \\ {U u}_{k k}^{11} = = {U u}_{k k - - 11}^{11} {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}} + + {R R}_{11} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{11}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{22} = = {U u}_{k k - - 11}^{22} {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}} + + {R R}_{22} ((11 - - {e e}^{- - \frac{Δt Δt}{{τ τ}_{22}}})) {I I}_{k k - - 11} \\ {U u}_{k k}^{33} = = {U u}_{k k - - 11}^{33} {e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}} + + {R R}_{33} ((11 {- - e e}^{- - \frac{Δt Δt}{{τ τ}_{33}}})) {I I}_{k k - - 11} \end{matrix}\}

in, is the estimated value of SoC _k -1, the nonlinear relationship model between open circuit voltage OCV(SOC _K-1 ) and SoC _k-1 is as follows:

\begin{matrix} OCV OCV (({SoC SoC}_{k k - - 11})) = = {k k}_{11} {SoC SoC}_{k k - - 11}^{88} + + {k k}_{22} {SoC SoC}_{k k - - 11}^{77} + + {k k}_{33} {SoC SoC}_{k k - - 11}^{66} + + {k k}_{44} {SoC SoC}_{k k - - 11}^{55} + + {k k}_{55} {SoC SoC}_{k k - - 11}^{44} \\ + + {k k}_{66} {SoC SoC}_{k k - - 11}^{33} + + {k k}_{77} {SoC SoC}_{k k - - 11}^{22} + + {k k}_{88} {SoC SoC}_{k k - - 11} + + {k k}_{99} . . \end{matrix}

ⅴ. Estimated error variance matrix

P _k|k ＝(IK _k H _k )P _k|k-1 ;

The timer controls the start and interrupt operation of the SoC _k estimation program in the program memory, and the current SoC _k estimation value of the operating result of the microprocessor is displayed in real time through the display.