CN105116346A

CN105116346A - Series-connected battery system and method for estimating state of charge thereof

Info

Publication number: CN105116346A
Application number: CN201510593040.6A
Authority: CN
Inventors: 孙烨; 彭思敏; 陈明明
Original assignee: Yancheng Vocational Institute of Industry Technology
Current assignee: Yancheng Vocational Institute of Industry Technology
Priority date: 2015-09-15
Filing date: 2015-09-15
Publication date: 2015-12-02

Abstract

The invention discloses a series lithium ion battery system and a charge state estimation method thereof. The series lithium ion battery system is composed of N battery lithium ion monomers connected in series. The method is as follows: establish an equivalent circuit model of the series lithium-ion battery system based on the state of charge of the battery, establish a space state equation of the series lithium-ion battery system in combination with the meaning of the battery state of charge, and use an unscented Kalman filter to analyze the series lithium-ion battery system. The state of charge of the ion battery system is estimated, and the gain matrix is updated by comparing the output voltage of the battery system with the estimated value of the voltage on-line, and the estimated value of the state of charge of the series lithium-ion battery system is obtained by cyclic recursion. The present invention adopts the state-of-charge estimation algorithm of the series lithium-ion battery system, which is more accurate and robust than the extended Kalman filter algorithm, and is applicable to both the series-type lithium-ion battery system and other battery types, such as lead-acid, Nickel-cadmium batteries, etc.

Description

A series lithium ion battery system and its state of charge estimation method

技术领域technical field

本发明属于智能电网中MW级电池储能系统设计与控制技术领域，涉及一种串联型锂离子电池系统及其荷电状态估计方法。The invention belongs to the technical field of design and control of a MW-level battery energy storage system in a smart grid, and relates to a series lithium-ion battery system and a state-of-charge estimation method thereof.

背景技术Background technique

随着风电、光伏发电等可再生能源及电网智能化的大力发展，电池系统作为电池储能系统能量存储的主要载体，已越来越多地受到世界各国的关注和应用。同时可再生能源规模的不断扩大及用电负荷的快速增长，也将促使电池系统向大容量化(MW级)方向发展，通过多个电池单体的串联可实现电池容量的扩大，即串联型锂离子电池系统(Series-connectedBatterySystem，SBS)。然而，由于应用环境的复杂性(如秒级波动功率平滑、一次高频等高动态场合)及电池电量不能直接测量等因素，准确估计电池系统荷电状态(StateofCharge，SOC)不仅直接决定电池系统能否安全、可靠、高效运行，且对电池系统优化配置、设计与控制等至关重要。With the vigorous development of renewable energy such as wind power and photovoltaic power generation and the intelligentization of power grids, battery systems, as the main carrier of energy storage in battery energy storage systems, have attracted more and more attention and applications from all over the world. At the same time, the continuous expansion of the scale of renewable energy and the rapid growth of electricity load will also promote the development of the battery system in the direction of large capacity (MW level). The expansion of battery capacity can be achieved by connecting multiple battery cells in series, that is, the series type Lithium-ion battery system (Series-connectedBatterySystem, SBS). However, due to the complexity of the application environment (such as second-level fluctuating power smoothing, high-frequency occasions such as primary frequency) and the inability to directly measure the battery power, accurate estimation of the battery system state of charge (State of Charge, SOC) not only directly determines the battery system Whether it can operate safely, reliably and efficiently is crucial to the optimal configuration, design and control of the battery system.

传统的SOC估计算法主要有：安时法、阻抗法、开路电压法等，近年来相继出现了神经网络、模糊逻辑法、支持向量机及标准卡尔曼滤波法、EKF等高级算法。安时法因其算法简单、易行等优点，已得到广泛应用，但存在自身开环、误差时间积累等缺点，其精度受限；开路电压法适合稳态下SOC估计，不宜于在线估计；神经网络、模糊逻辑等高级算法适宜于恒负载、恒流充放电状态下不同类型电池SOC估计，但存在训练数据量大、训练方法对估计误差影响大的局限；标准卡尔曼滤波法具有鲁棒性高、抗扰动能力强等优点，适宜于线性系统的SOC估计，然而电池系统是一种非线性时变系统，其精度仍受限；为此，针对非线性时变的电池系统，目前常采用EKF，并取得良好的效果，然而由于EKF存在自身计算复杂、忽略高阶项等问题，必会产生一定误差，使电池的SOC估计精度仍待进一步研究。The traditional SOC estimation algorithms mainly include: ampere-time method, impedance method, open circuit voltage method, etc. In recent years, neural network, fuzzy logic method, support vector machine, standard Kalman filter method, EKF and other advanced algorithms have appeared one after another. The ampere-time method has been widely used because of its simple algorithm and easy operation, but it has its own shortcomings such as open loop and error time accumulation, and its accuracy is limited; the open-circuit voltage method is suitable for SOC estimation in steady state, not suitable for online estimation; Advanced algorithms such as neural network and fuzzy logic are suitable for SOC estimation of different types of batteries under constant load and constant current charging and discharging conditions, but there are limitations in the large amount of training data and the large impact of training methods on estimation errors; the standard Kalman filter method is robust It has the advantages of high performance and strong anti-disturbance ability, and is suitable for SOC estimation of linear systems. However, the battery system is a nonlinear time-varying system, and its accuracy is still limited. Therefore, for nonlinear time-varying battery systems, currently EKF is used and good results are achieved. However, due to the complex calculation of EKF and the neglect of high-order terms, certain errors will inevitably occur, so that the SOC estimation accuracy of the battery still needs further research.

发明内容Contents of the invention

本发明解决的问题是在于提供一种基于无迹卡尔曼滤波(UnscentedKalmanFilter，UKF)的串联型锂离子电池系统荷电状态估计方法，解决串联型锂离子电池系统性能参数受SOC影响、扩展卡尔曼滤波法计算复杂、精度不高而导致电池系统SOC难以被准确测量、估算的问题，达到准确估计串联型锂离子电池系统SOC的目的。The problem solved by the present invention is to provide a method for estimating the state of charge of a series lithium-ion battery system based on an Unscented Kalman Filter (UnscentedKalmanFilter, UKF), which solves the problem that the performance parameters of the series lithium-ion battery system are affected by the SOC and the extended Kalman The calculation of the filtering method is complex and the accuracy is not high, which makes it difficult to accurately measure and estimate the SOC of the battery system, so as to achieve the purpose of accurately estimating the SOC of the series lithium-ion battery system.

本发明目的是通过以下技术方案来实现：The object of the invention is to realize through the following technical solutions:

本发明提供一种串联型锂离子电池系统，该系统由N个锂离子电池单体串联而成，其中N均为大于1的自然数。The invention provides a series lithium ion battery system, which is composed of N lithium ion battery cells connected in series, wherein N is a natural number greater than 1.

本发明提供的一种基于无迹卡尔曼滤波的串联型锂离子电池系统荷电状态估计方法如下：根据已知锂离子电池单体性能参数，利用并联电路工作特性及其充放电工作特性确定串联型锂离子电池系统性能参数与电池单体性能参数的关系，再结合基尔霍夫定律KVC确定电池系统输出端电压方程，建立串联型锂离子电池系统等效模型(1)；将串联型锂离子电池系统的荷电状态SOC及等效模型中2个RC并联电路的端电压作为状态变量，以电池系统的电流及输出电压分别作为系统输入量与输出量，结合串联型锂离子电池系统等效电路模型，得串联型锂离子电池系统空间状态方程(2)；将串联型锂离子电池系统空间状态方程(2)中的电池系统SOC、2个RC并联电路的端电压作为无迹卡尔曼滤波算法UKF的状态变量；以串联型锂离子电池系统空间状态方程(2)的输入状态空间方程、输出电压状态空间方程分别作为UKF算法的非线性状态方程及测量方程；通过电压传感器测量串联型锂离子电池系统端电压(4)的实际值与UKF算法获得的电池端电压估计值来更新增益矩阵(5)，最后由UKF算法经循环迭代，从而实时得到电池系统SOC的估计值。A method for estimating the state of charge of a series lithium-ion battery system based on an unscented Kalman filter provided by the present invention is as follows: According to the known performance parameters of lithium-ion battery cells, the operating characteristics of the parallel circuit and its charging and discharging characteristics are used to determine the The relationship between the performance parameters of the small lithium-ion battery system and the performance parameters of the battery cells, combined with Kirchhoff's law KVC to determine the output voltage equation of the battery system, and establish the equivalent model of the series lithium-ion battery system (1); The state of charge SOC of the ion battery system and the terminal voltage of the two RC parallel circuits in the equivalent model are used as state variables, and the current and output voltage of the battery system are used as the input and output of the system, respectively, combined with a series lithium-ion battery system, etc. The effective circuit model is used to obtain the space state equation (2) of the series lithium-ion battery system; the battery system SOC in the space state equation (2) of the series lithium-ion battery system and the terminal voltage of two RC parallel circuits are taken as the unscented Kalman The state variables of the filtering algorithm UKF; the input state space equation and the output voltage state space equation of the series lithium-ion battery system space state equation (2) are respectively used as the nonlinear state equation and measurement equation of the UKF algorithm; the series type is measured by a voltage sensor The actual value of the lithium-ion battery system terminal voltage (4) and the estimated value of the battery terminal voltage obtained by the UKF algorithm are used to update the gain matrix (5). Finally, the UKF algorithm undergoes cyclic iterations to obtain the estimated value of the battery system SOC in real time.

所述串联型锂离子电池系统等效电路模型(1)为二阶等效电路模型，模型主电路由2个RC并联电路、受控电压源U_s0(SOC)及电池内阻R_s等组成。建立准确的电池系统等效电路模型关键在于如何根据电池工作特性来确定电池系统性能参数与电池单体性能参数的关系。本发明中串联型锂离子电池系统性能参数与电池单体性能参数关系式为：The equivalent circuit model (1) of the series lithium-ion battery system is a second-order equivalent circuit model, and the main circuit of the model is composed of two RC parallel circuits, a controlled voltage source U _s0 (SOC) and a battery internal resistance R _s , etc. . The key to establishing an accurate battery system equivalent circuit model is how to determine the relationship between battery system performance parameters and battery cell performance parameters according to battery operating characteristics. In the present invention, the relational expression between the performance parameter of the series lithium ion battery system and the performance parameter of the battery cell is:

$\{\begin{matrix} {U u}_{s the s 00} ((t t)) = = {Σ Σ}_{i i = = 11}^{n no} {U u}_{i i 00} ((t t)) \\ {R R}_{s the s} ((t t)) = = {Σ Σ}_{i i = = 11}^{n no} {R R}_{i i} ((t t)) \\ {R R}_{s the s s the s} ((t t)) = = {Σ Σ}_{i i = = 11}^{n no} {R R}_{i i s the s} ((t t)) \\ \frac{11}{{C C}_{s the s s the s} ((t t))} = = {Σ Σ}_{i i = = 11}^{n no} \frac{11}{{C C}_{i i s the s} ((t t))} \\ {R R}_{s the s 11} ((t t)) = = {Σ Σ}_{i i = = 11}^{n no} {R R}_{i i 11} ((t t)) \\ \frac{11}{{C C}_{s the s 11} ((t t))} = = {Σ Σ}_{i i = = 11}^{n no} \frac{11}{{C C}_{i i 11} ((t t))} \end{matrix}$

式中，R_ss、R_s1、C_ss、C_s1分别表示电池系统模型中2个RC并联电路的电阻和电容；下标i表示第i个电池单体；U_i0、R_i分别表示电池单体的开路电压、内阻；R_is、R_i1、C_is、C_i1分别表示电池单体模型中2个RC并联电路的电阻和电容；U_i0、R_i、R_is、R_i1、C_is、C_i1均与SOC有关，SOC的定义为：其中，SOC₀为电池单体SOC初始值，一般为0～1的常数；Q_u(t)为电池单体不可用容量，Q₀为电池单体额定容量。U_i0(SOC)、R_is、R_i1和C_is、C_i1、R_i的计算分别如下： $U_{i 0} (S O C) = a_{0} e^{- a_{1} S O C (t)} + a_{2} + a_{3} S O C (t) - a_{4} {SOC}^{2} (t) + a_{5} {SOC}^{3} (t),$ $R_{i s} (t) = c_{0} e^{- c_{1} S O C (t)} + c_{2}, C_{i s} (t) = d_{0} e^{- d_{1} S O C (t)} + d_{2}, R_{i 1} (t) = e_{0} e^{- e_{1} S O C (i)} + e_{2},$ $C_{i 1} (t) = f_{0} e^{- f_{1} S O C (t)} + f_{2}, R_{i} (t) = b_{0} e^{- b_{1} S O C (t)} + b_{2} + b_{3} S O C (t) - b_{4} {SOC}^{2} (t) + b_{5} {SOC}^{3} (t),$ 其中，a₀～a₅、c₀～c₂、d₀～d₂、e₀～e₂、f₀～f₂、b₀～b₅均为模型系数，可由电池测量数据经拟合而得。In the formula, R _ss , R _s1 , C _ss , and C _s1 respectively represent the resistance and capacitance of two RC parallel circuits in the battery system model; the subscript i represents the i-th battery cell; U _i0 and R _i represent the battery cell The open circuit voltage and internal resistance of the body; R _is , R _i1 , C _is , and C _i1 respectively represent the resistance and capacitance of two RC parallel circuits in the battery cell model; U _i0 , R _i , R _is , R _i1 , C _is , C _i1 are related to SOC, the definition of SOC is: Among them, SOC ₀ is the initial value of the SOC of the battery cell, which is generally a constant between 0 and 1; Qu ( _t ) is the unusable capacity of the battery cell, and Q ₀ is the rated capacity of the battery cell. The calculations of U _i0 (SOC), R _is , R _i1 and C _is , C _i1 , R _i are as follows: $u_{i 0} (S o C) = a_{0} e^{- a_{1} S o C (t)} + a_{2} + a_{3} S o C (t) - a_{4} {SOC}^{2} (t) + a_{5} {SOC}^{3} (t),$ $R_{i the s} (t) = c_{0} e^{- c_{1} S o C (t)} + c_{2}, C_{i the s} (t) = d_{0} e^{- d_{1} S o C (t)} + d_{2}, R_{i 1} (t) = e_{0} e^{- e_{1} S o C (i)} + e_{2},$ $C_{i 1} (t) = f_{0} e^{- f_{1} S o C (t)} + f_{2}, R_{i} (t) = b_{0} e^{- b_{1} S o C (t)} + b_{2} + b_{3} S o C (t) - b_{4} {SOC}^{2} (t) + b_{5} {SOC}^{3} (t),$ Among them, a ₀ ~ a ₅ , c ₀ ~ c ₂ , d ₀ ~ d ₂ , e ₀ ~ e ₂ , f ₀ ~ f ₂ , b ₀ ~ b ₅ are all model coefficients, which can be obtained by fitting the battery measurement data have to.

所述串联型锂离子电池系统空间状态方程(2)的建立如下：a、以电池系统的荷电状态SOC_s及等效模型中2个RC并联电路的端电压作为状态变量，以电池系统的电流I_s为系统输入量，根据等效电路模型建立电池系统空间状态方程为The establishment of the space state equation (2) of the series lithium-ion battery system is as follows: a, with the state of charge SOC _s of the battery system and the terminal voltages of the two RC parallel circuits in the equivalent model as state variables, with the battery system's The current I _s is the input quantity of the system, and the space state equation of the battery system is established according to the equivalent circuit model as

$[\begin{matrix} S S O o {C C}_{s the s,, k k + + 11} \\ {U u}_{s the s s the s,, k k + + 11} \\ {U u}_{s the s 11,, k k + + 11} \end{matrix}] = = [\begin{matrix} 11 & 00 & 00 \\ 00 & exp exp ((- - Δ Δ t t / / {τ τ}_{11})) & 00 \\ 00 & 00 & exp exp ((- - Δ Δ t t / / {τ τ}_{22})) \end{matrix}] \times \times [\begin{matrix} S S O o {C C}_{s the s,, k k} \\ {U u}_{s the s s the s,, k k} \\ {U u}_{s the s 11,, k k} \end{matrix}] + + [\begin{matrix} \frac{- - η η Δ Δ t t}{{Q Q}_{N N}} \\ {R R}_{s the s s the s} [[11 - - exp exp ((- - Δ Δ t t / / {τ τ}_{11}))]] \\ {R R}_{s the s 11} [[11 - - exp exp ((- - Δ Δ t t / / {τ τ}_{22}))]] \end{matrix}] {I I}_{s the s,, k k} + + {w w}_{k k}$

式中，U_ss、U_s1为2个RC并联电路端电压，R_ss、R_s1为2个RC并联电路的电阻，Q_N为电池系统额定电量，τ₁、τ₂为时间常数，w_k为系统观过程噪声，Δt为采样周期，k为大于1的自然数；b、根据基尔霍夫电压定律，结合电池系统等效电路模型，可得电池系统输出电压方程空间状态方程为： $U_{s, k + 1} (t) = U_{s 0, k + 1} (t) - R_{s, k + 1} (t) I_{s, k + 1} (t) - [\begin{matrix} 0 & 1 & 1 \end{matrix}] \times [\begin{matrix} S O C_{s, k + 1} \\ U_{s s, k + 1} \\ U_{s 1, k + 1} \end{matrix}],$ 式中，U_s为电池系统端电压，R_s为电池系统内阻。In the formula, U _ss and U _s1 are the terminal voltages of the two RC parallel circuits, R _ss and R _s1 are the resistances of the two RC parallel circuits, Q _N is the rated power of the battery system, τ ₁ and τ ₂ are the time constants, w _k is the system-view process noise, Δt is the sampling period, and k is a natural number greater than 1; b. According to Kirchhoff’s voltage law, combined with the equivalent circuit model of the battery system, the space state equation of the output voltage equation of the battery system can be obtained as: $u_{the s, k + 1} (t) = u_{the s 0, k + 1} (t) - R_{the s, k + 1} (t) I_{the s, k + 1} (t) - [\begin{matrix} 0 & 1 & 1 \end{matrix}] \times [\begin{matrix} S o C_{the s, k + 1} \\ u_{the s the s, k + 1} \\ u_{the s 1, k + 1} \end{matrix}],$ In the formula, U _s is the terminal voltage of the battery system, and R _s is the internal resistance of the battery system.

所述无迹卡尔曼滤波算法UKF的主要步骤为：1)初始化状态变量x均值E()和均方误差P₀： ${\hat{x}}_{0} = E (x_{0}), {\hat{P}}_{0} = E [(x_{0} - {\hat{x}}_{0}) {(x_{0} - {\hat{x}}_{0})}^{T}];$ 2)获取采样点x_i及对应权重ω： $\{\begin{matrix} x_{0, k - 1} = {\hat{x}}_{k - 1} \\ x_{i, k - 1} = {\hat{x}}_{k - 1} + {(\sqrt{(n + γ) P_{i, k - 1}})}_{i}, i = 1, 2, ..., n \\ x_{i + n, k - 1} = {\hat{x}}_{k - 1} + {(\sqrt{(n + γ) P_{i, k - 1}})}_{i}, i = n + 1, n + 2, ..., 2 n \end{matrix},$ $\{\begin{matrix} ω_{0}^{m} = λ / (n + λ) \\ ω_{0}^{c} = λ / (n + λ) + (1 + β - α^{2}) \\ ω_{i}^{m} = ω_{i}^{c} = 1 / 2 (n + λ), i &NotEqual; 0 \end{matrix}$ 式中，λ＝α²(n+h)-n；3)状态估计及均方误差的时间更新：状态估计时间更新为 $\{\begin{matrix} x_{i, k / k - 1} = f_{k - 1} (x_{i, k - 1}) + q_{k - 1}, i = 0, 1, ..., 2 n \\ {\hat{x}}_{k / k - 1} = Σ_{i = 0}^{2 n} ω_{i}^{m} f_{k - 1} (x_{i, k - 1}) + q_{k - 1} \end{matrix},$ 均方误差时间更新为 $P_{k / k - 1} = Σ_{i = 0}^{2 n} ω_{i}^{c} (x_{i, k / k - 1} - {\hat{x}}_{k / k - 1}) {(x_{i, k / k - 1} - {\hat{x}}_{k / k - 1})}^{T} + Q_{k - 1},$ 系统输出时间更新为 $\{\begin{matrix} χ_{i, k / k - 1} = g_{k - 1} (x_{i, k - 1}) + r_{k - 1} \\ {\hat{y}}_{k / k - 1} = Σ_{i = 0}^{2 n} ω_{i}^{m} g_{k - 1} (x_{i, k - 1}) + r_{k - 1} \end{matrix}$ 式中，g_k-1(·)为测量方程；4)计算增益矩阵(5)：式中， $\{\begin{matrix} P_{y, k} = Σ_{i = 0}^{2 n} ω_{i}^{c} (χ_{i, k / k - 1} - {\hat{y}}_{k / k - 1}) {(χ_{i, k / k - 1} - {\hat{y}}_{k / k - 1})}^{T} \\ P_{x y, k} = Σ_{i = 0}^{2 n} ω_{i}^{c} (x_{i, k / k - 1} - {\hat{x}}_{k / k - 1}) {(χ_{i, k / k - 1} - {\hat{y}}_{k / k - 1})}^{T} \end{matrix};$ 5)状态估计及均方误差的测量更新：状态估计测量更新为均方误差测量更新为 $P_{k} = P_{k / k - 1} - L_{k} P_{y, k} L_{k}^{T} .$ The main steps of the unscented Kalman filter algorithm UKF are: 1) initializing the state variable x mean value E() and mean square error P ₀ : ${\hat{x}}_{0} = E. (x_{0}), {\hat{P}}_{0} = E. [(x_{0} - {\hat{x}}_{0}) {(x_{0} - {\hat{x}}_{0})}^{T}];$ 2) Obtain the sampling point x _i and the corresponding weight ω: $\{\begin{matrix} x_{0, k - 1} = {\hat{x}}_{k - 1} \\ x_{i, k - 1} = {\hat{x}}_{k - 1} + {(\sqrt{(no + γ) P_{i, k - 1}})}_{i}, i = 1, 2, ..., no \\ x_{i + no, k - 1} = {\hat{x}}_{k - 1} + {(\sqrt{(no + γ) P_{i, k - 1}})}_{i}, i = no + 1, no + 2, ..., 2 no \end{matrix},$ $\{\begin{matrix} ω_{0}^{m} = λ / (no + λ) \\ ω_{0}^{c} = λ / (no + λ) + (1 + β - α^{2}) \\ ω_{i}^{m} = ω_{i}^{c} = 1 / 2 (no + λ), i &NotEqual; 0 \end{matrix}$ In the formula, λ=α ² (n+h)-n; 3) Time update of state estimation and mean square error: state estimation time update is $\{\begin{matrix} x_{i, k / k - 1} = f_{k - 1} (x_{i, k - 1}) + q_{k - 1}, i = 0, 1, ..., 2 no \\ {\hat{x}}_{k / k - 1} = Σ_{i = 0}^{2 no} ω_{i}^{m} f_{k - 1} (x_{i, k - 1}) + q_{k - 1} \end{matrix},$ The mean square error time is updated as $P_{k / k - 1} = Σ_{i = 0}^{2 no} ω_{i}^{c} (x_{i, k / k - 1} - {\hat{x}}_{k / k - 1}) {(x_{i, k / k - 1} - {\hat{x}}_{k / k - 1})}^{T} + Q_{k - 1},$ The system output time is updated as $\{\begin{matrix} χ_{i, k / k - 1} = g_{k - 1} (x_{i, k - 1}) + r_{k - 1} \\ {\hat{the y}}_{k / k - 1} = Σ_{i = 0}^{2 no} ω_{i}^{m} g_{k - 1} (x_{i, k - 1}) + r_{k - 1} \end{matrix}$ In the formula, g _k-1 ( ) is the measurement equation; 4) Calculate the gain matrix (5): In the formula, $\{\begin{matrix} P_{the y, k} = Σ_{i = 0}^{2 no} ω_{i}^{c} (χ_{i, k / k - 1} - {\hat{the y}}_{k / k - 1}) {(χ_{i, k / k - 1} - {\hat{the y}}_{k / k - 1})}^{T} \\ P_{x the y, k} = Σ_{i = 0}^{2 no} ω_{i}^{c} (x_{i, k / k - 1} - {\hat{x}}_{k / k - 1}) {(χ_{i, k / k - 1} - {\hat{the y}}_{k / k - 1})}^{T} \end{matrix};$ 5) The measurement update of state estimation and mean square error: the state estimation measurement is updated as The mean squared error measure is updated to $P_{k} = P_{k / k - 1} - L_{k} P_{the y, k} L_{k}^{T} .$

与采用扩展卡尔曼滤波算法EKF进行串联型锂离子电池系统SOC估计相比，本发明具有以下有益的技术效果：一是整个放电过程，本发明所采用的UKF算法比EKF算法进行串联型锂离子电池系统SOC估计时UKF估计精度更高，尤其是放电初期和末期效果更明显；二是所采用的UKF算法比EKF算法能更快收敛于实验数据，鲁棒性更好。Compared with using the extended Kalman filter algorithm EKF to estimate the SOC of the series lithium-ion battery system, the present invention has the following beneficial technical effects: one is the whole discharge process, the UKF algorithm adopted by the present invention is better than the EKF algorithm for the series lithium-ion battery system. The estimation accuracy of UKF is higher when estimating the SOC of the battery system, especially at the beginning and end of discharge. Second, the UKF algorithm used can converge to the experimental data faster than the EKF algorithm, and has better robustness.

附图说明Description of drawings

图1串联型锂离子电池系统的荷电状态估计方法实施流程框图Figure 1 Flow chart of the implementation of the state of charge estimation method for the series lithium-ion battery system

图2为串联型锂离子电池系统结构示意图；Fig. 2 is a schematic structural diagram of a series lithium-ion battery system;

图3为含6个电池单体的串联型锂离子电池系统结构示意图；Fig. 3 is a schematic structural diagram of a tandem lithium-ion battery system containing 6 battery cells;

图4为含2个RC并联电路的串联型锂离子电池系统等效电路模型图；Figure 4 is an equivalent circuit model diagram of a series lithium-ion battery system containing two RC parallel circuits;

图5为无迹卡尔曼滤波算法流程图；Fig. 5 is the unscented Kalman filtering algorithm flowchart;

图6-1～图6-4为SOC₀不同时电池恒流放电特性，其中图6-1为SOC₀＝1时SOC变化情况，图6-2为SOC₀＝1时电池系统端电压变化情况，图6-3为SOC₀＝0.8时SOC变化情况，图6-4为SOC₀＝0.8时电池系统端电压变化情况；Figure 6-1 to Figure 6-4 show the constant current discharge characteristics of the battery when SOC ₀ is different. Figure 6-1 shows the change of SOC when SOC ₀ =1, and Figure 6-2 shows the change of terminal voltage of the battery system when SOC ₀ =1 Figure 6-3 shows the change of SOC when SOC ₀ =0.8, and Figure 6-4 shows the change of battery system terminal voltage when SOC ₀ =0.8;

图7-1～图7-4为SOC₀不同时电池脉冲放电特性，其中图7-1为SOC₀＝1时SOC变化情况，图7-2为SOC₀＝1时电池系统端电压变化情况，图7-3为SOC₀＝0.8时SOC变化情况，图7-4为SOC₀＝0.8时电池系统端电压变化情况。Figure 7-1 to Figure 7-4 show the pulse discharge characteristics of the battery when SOC ₀ is different, where Figure 7-1 shows the change of SOC when SOC ₀ = 1, and Figure 7-2 shows the change of battery system terminal voltage when SOC ₀ = 1 , Fig. 7-3 shows the change of SOC when SOC ₀ =0.8, and Fig. 7-4 shows the change of battery system terminal voltage when SOC ₀ =0.8.

具体实施方式Detailed ways

下面结合具体的实例对本发明作进一步的详细说明，所述为对本发明的解释而不是限定。The present invention will be further described in detail below in conjunction with specific examples, which are for explanation of the present invention rather than limitation.

本发明提供的一种串联型锂离子电池系统的荷电状态估计方法具体实施流程框图如图1所示。A specific implementation flow chart of a method for estimating the state of charge of a series lithium-ion battery system provided by the present invention is shown in FIG. 1 .

1、串联型锂离子电池系统及其等效电路模型(1)1. Series lithium-ion battery system and its equivalent circuit model (1)

1.1串联型锂离子电池系统1.1 Series lithium-ion battery system

串联型锂离子电池系统是由由N个锂离子电池单体串联而成，其结构图如图2所示。为便于分析，本实例中假设串联型锂离子电池系统由6个电池单体经串联而成，即6×1串联型锂离子电池系统，如图3所示。串联型锂离子电池系统中每个电池单体的额定电压为3.2V，额定容量为25Ah，放电截止电压为2.5V。The tandem lithium-ion battery system is composed of N lithium-ion battery cells connected in series, and its structure diagram is shown in Figure 2. For the convenience of analysis, in this example, it is assumed that the series-type lithium-ion battery system is composed of six battery cells connected in series, that is, a 6×1 series-type lithium-ion battery system, as shown in Figure 3. The rated voltage of each battery cell in the series lithium-ion battery system is 3.2V, the rated capacity is 25Ah, and the discharge cut-off voltage is 2.5V.

1.2串联型锂离子电池系统等效电路模型(1)1.2 Equivalent circuit model of series lithium-ion battery system (1)

串联型锂离子电池系统等效电路模型(1)为二阶等效电路模型，模型主电路由2个RC并联电路、受控电压源U_s0(SOC)及电池内阻R_s等组成，如图4所示。串联型锂离子电池系统性能参数通过与电池单体性能参数的关系来获取，具体计算如下：The equivalent circuit model (1) of the series lithium-ion battery system is a second-order equivalent circuit model. The main circuit of the model is composed of two RC parallel circuits, a controlled voltage source U _s0 (SOC) and the internal resistance R _s of the battery, as shown in Figure 4 shows. The performance parameters of the series lithium-ion battery system are obtained through the relationship with the performance parameters of the battery cells, and the specific calculation is as follows:

$\{\begin{matrix} {U u}_{s the s 00} ((t t)) = = {Σ Σ}_{i i = = 11}^{66} {U u}_{i i 00} ((t t)) \\ {R R}_{s the s} ((t t)) = = {Σ Σ}_{i i = = 11}^{66} {R R}_{i i} ((t t)) \\ {R R}_{s the s s the s} ((t t)) = = {Σ Σ}_{i i = = 11}^{66} {R R}_{i i s the s} ((t t)) \\ \frac{11}{{C C}_{s the s s the s} ((t t))} = = {Σ Σ}_{i i = = 11}^{66} \frac{11}{{C C}_{i i s the s} ((t t))} \\ {R R}_{s the s 11} ((t t)) = = {Σ Σ}_{i i = = 11}^{66} {R R}_{i i 11} ((t t)) \\ \frac{11}{{C C}_{s the s 11} ((t t))} = = {Σ Σ}_{i i = = 11}^{66} \frac{11}{{C C}_{i i 11} ((t t))} \end{matrix}$

上式中，电池单体性能参数U₀(t)、R_s(t)、R₁(t)和C_s(t)、C₁(t)的计算分别如下： $U_{0} (t) = a_{0} e^{- a_{1} S O C (t)} + a_{2} + a_{3} S O C (t) - a_{4} {SOC}^{2} (t) + a_{5} {SOC}^{3} (t), R_{s} (t) = c_{0} e^{- c_{1} S O C (t)} + c_{2},$ $C_{s} (t) = d_{0} e^{- d_{1} S O C (t)} + d_{2}, R_{1} (t) = e_{0} e^{- e_{1} S O C (t)} + e_{2}, C_{1} (t) = f_{0} e^{- f_{1} S O C (t)} + f_{2},$ $R (t) = b_{0} e^{- b_{1} S O C (t)} + b_{2} + b_{3} S O C (t) - b_{4} {SOC}^{2} (t) + b_{5} {SOC}^{3} (t),$ 其中，a₀～a₅取值分别为-0.602、-10.365、3.395、0.267、-0.202、0.105，c₀～c₂取值分别为0.1058、-59.96、0.0036，d₀～d₂取值分别为-196、-142、295，e₀～e₂取值分别为0.00697、-60.8、0.0022，f₀～f₂取值分别为-2996、-175、5122，b₀～b₅取值分别为-0.0558、-29.96、0.0055、0.0062、0.0121、0.0066。In the above formula, the battery cell performance parameters U ₀ (t), R _s (t), R ₁ (t) and C _s (t), C ₁ (t) are calculated as follows: $u_{0} (t) = a_{0} e^{- a_{1} S o C (t)} + a_{2} + a_{3} S o C (t) - a_{4} {SOC}^{2} (t) + a_{5} {SOC}^{3} (t), R_{the s} (t) = c_{0} e^{- c_{1} S o C (t)} + c_{2},$ $C_{the s} (t) = d_{0} e^{- d_{1} S o C (t)} + d_{2}, R_{1} (t) = e_{0} e^{- e_{1} S o C (t)} + e_{2}, C_{1} (t) = f_{0} e^{- f_{1} S o C (t)} + f_{2},$ $R (t) = b_{0} e^{- b_{1} S o C (t)} + b_{2} + b_{3} S o C (t) - b_{4} {SOC}^{2} (t) + b_{5} {SOC}^{3} (t),$ Among them, the values of a ₀ ~ a ₅ are -0.602, -10.365, 3.395, 0.267, -0.202, 0.105 respectively, the values of c ₀ ~ c ₂ are 0.1058, -59.96, 0.0036 respectively, and the values of d ₀ ~ d ₂ are respectively are -196, -142, 295, the values of e ₀ ~ e ₂ are 0.00697, -60.8, 0.0022 respectively, the values of f ₀ ~ f ₂ are -2996, -175, 5122 respectively, and the values of b ₀ ~ b ₅ are respectively are -0.0558, -29.96, 0.0055, 0.0062, 0.0121, 0.0066.

2、串联型锂离子电池系统空间状态方程(2)2. Space state equation of series lithium-ion battery system (2)

a、以串联型锂离子电池系统的荷电状态SOC_s及等效模型中2个RC并联电路的端电压U_ss、U_s1作为状态变量，以串联型锂离子电池系统的电流I_s为系统输入量，根据等效电路模型(1)建立串联型锂离子电池系统输入状态空间方程为a. Take the state of charge SOC _s of the series lithium-ion battery system and the terminal voltages U _ss and U _s1 of the two RC parallel circuits in the equivalent model as state variables, and take the current I _s of the series lithium-ion battery system as the system Input quantity, according to the equivalent circuit model (1), the input state space equation of the series lithium-ion battery system is established as

式中，U_ss、U_s1为2个RC并联电路端电压，R_ss、R_s1为2个RC并联电路的电阻，Q_N为电池系统额定电量，τ₁、τ₂为时间常数，w_k为系统观过程噪声，Δt为采样周期，k为大于1的自然数。In the formula, U _ss and U _s1 are the terminal voltages of the two RC parallel circuits, R _ss and R _s1 are the resistances of the two RC parallel circuits, Q _N is the rated power of the battery system, τ ₁ and τ ₂ are the time constants, w _k is the system view process noise, Δt is the sampling period, and k is a natural number greater than 1.

b、根据基尔霍夫电压定律，结合串联型锂离子电池系统等效电路模型，可得串联型锂离子电池系统输出电压方程为： $U_{s, k + 1} (t) = U_{s 0, k + 1} (t) - R_{s, k + 1} (t) I_{s, k + 1} (t) - [\begin{matrix} 0 & 1 & 1 \end{matrix}] \times [\begin{matrix} S O C_{s, k + 1} \\ U_{s s, k + 1} \\ U_{s 1, k + 1} \end{matrix}],$ 式中，U_s为电池系统端电压，R_s为电池系统内阻，k为大于1的自然数。b. According to Kirchhoff's voltage law, combined with the equivalent circuit model of the series lithium-ion battery system, the output voltage equation of the series lithium-ion battery system can be obtained as: $u_{the s, k + 1} (t) = u_{the s 0, k + 1} (t) - R_{the s, k + 1} (t) I_{the s, k + 1} (t) - [\begin{matrix} 0 & 1 & 1 \end{matrix}] \times [\begin{matrix} S o C_{the s, k + 1} \\ u_{the s the s, k + 1} \\ u_{the s 1, k + 1} \end{matrix}],$ In the formula, U _s is the terminal voltage of the battery system, R _s is the internal resistance of the battery system, and k is a natural number greater than 1.

3、无迹卡尔曼滤波法(3)3. Unscented Kalman filter method (3)

将串联型锂离子电池系统空间状态方程中的电池系统SOC、2个RC并联电路的端电压作为无迹卡尔曼滤波算法UKF的状态变量x；将串联型锂离子电池系统的输入状态空间方程、输出电压状态空间方程分别作为UKF算法的非线性状态方程f_k-1(·)及测量方程g_k-1(·)；通过电压传感器测量电池系统端电压(4)的实际值y_k与UKF算法获得的电池端电压估计值来更新增益矩阵(5)，最后由UKF算法进行循环迭代，具体流程如图5所示，在迭代过程中，状态变量x初值为[100]，α取值为1、β取值为2，h取值为0；最后实时得到串联型锂离子电池系统SOC的估计值SOC_k。The battery system SOC in the space state equation of the series lithium-ion battery system and the terminal voltage of two RC parallel circuits are used as the state variable x of the unscented Kalman filter algorithm UKF; the input state space equation of the series lithium-ion battery system, The output voltage state space equation is used as the nonlinear state equation f _k-1 ( ) and the measurement equation g _k-1 ( ) of the UKF algorithm respectively; the actual value y _k of the battery system terminal voltage (4) is measured by the voltage sensor and UKF The battery terminal voltage estimate obtained by the algorithm to update the gain matrix (5), and finally the UKF algorithm performs cyclic iterations. The specific process is shown in Figure 5. During the iteration process, the initial value of the state variable x is [100], the value of α is 1, and the value of β is 2 , the value of h is 0; finally, the estimated value SOC _k of the SOC of the series lithium-ion battery system is obtained in real time.

4、系统仿真结果及效果对比4. System simulation results and effect comparison

仿真试验主要包括恒流与脉冲两种工况，一是恒流工况，即电池以恒流方式(25A)向外供电；二是脉冲工况，即以脉冲电流方式向外供电放电，具体为：先以25A恒流工作600s，静置600s后，再以25A恒流工作600s，如此循环。为验证UKF的高鲁棒性，在恒流与脉冲两种工况分别以SOC₀为1、0.8两种情况进行对比分析。图6-1～图6-4为SOC₀不同时电池恒流放电特性，其中图6-1为SOC₀＝1时SOC变化情况，图6-2为SOC₀＝1时电池系统端电压变化情况，图6-3为SOC₀＝0.8时SOC变化情况，图6-4为SOC₀＝0.8时电池系统端电压变化情况；由图6-1和图6-2可知，整个放电过程中，EKF和UKF都能很好地预测电池系统SOC及其端电压的变化，但UKF在放电末期(3000s)的精度更高，证明在恒流工况下UKF比EKF更准确。由图6-3和图6-4可知，UKF在放电初期(500s前)及放电末期(3000s后)精度更高，且在放电初期比EKF更快地收敛于实验数据，验证了在恒流工况下UKF比EKF精度及鲁棒均好。The simulation test mainly includes two working conditions of constant current and pulse. One is the constant current working condition, that is, the battery supplies power to the outside with a constant current (25A); It is: first work with 25A constant current for 600s, after standing still for 600s, then work with 25A constant current for 600s, and so on. In order to verify the high robustness of UKF, a comparative analysis was carried out under two conditions of constant current and pulse with SOC ₀ of 1 and 0.8 respectively. Figure 6-1 to Figure 6-4 show the constant current discharge characteristics of the battery when SOC ₀ is different. Figure 6-1 shows the change of SOC when SOC ₀ =1, and Figure 6-2 shows the change of terminal voltage of the battery system when SOC ₀ =1 Figure 6-3 shows the change of SOC when SOC ₀ =0.8, and Figure 6-4 shows the change of battery system terminal voltage when SOC ₀ =0.8; from Figure 6-1 and Figure 6-2, we can see that during the entire discharge process, Both EKF and UKF can predict the SOC of the battery system and its terminal voltage very well, but the accuracy of UKF at the end of discharge (3000s) is higher, which proves that UKF is more accurate than EKF under constant current conditions. From Figure 6-3 and Figure 6-4, it can be seen that UKF has higher accuracy at the initial stage of discharge (before 500s) and at the end of discharge (after 3000s), and it converges to the experimental data faster than EKF at the initial stage of discharge, which verifies that in constant current Under working conditions, UKF has better accuracy and robustness than EKF.

图7-1～图7-4为SOC₀不同时电池脉冲放电特性，其中图7-1为SOC₀＝1时SOC变化情况，图7-2为SOC₀＝1时电池系统端电压变化情况，图7-3为SOC₀＝0.8时SOC变化情况，图7-4为SOC₀＝0.8时电池系统端电压变化情况。由图7-1和图7-2可知，整个放电过程中，UKF比EKF预测精度更高，尤其是在放电末期(3000s后)。由图7-3和图7-4可知，整个放电过程中，UKF与EKF均能快速跟随实验数据变化，但在放电初期时，因UKF比EKF计算量小，其收敛速度更快，而且在放电末期，因EKF本身忽略高阶项，UKF比EKF仿真结果更接近实验数据，进一步验证了在脉冲工况下UKF比EKF估计精度高且鲁棒性更好。Figure 7-1 to Figure 7-4 show the pulse discharge characteristics of the battery when SOC ₀ is different, where Figure 7-1 shows the change of SOC when SOC ₀ = 1, and Figure 7-2 shows the change of battery system terminal voltage when SOC ₀ = 1 , Fig. 7-3 shows the change of SOC when SOC ₀ =0.8, and Fig. 7-4 shows the change of battery system terminal voltage when SOC ₀ =0.8. It can be seen from Figure 7-1 and Figure 7-2 that during the entire discharge process, the prediction accuracy of UKF is higher than that of EKF, especially at the end of discharge (after 3000s). It can be seen from Figure 7-3 and Figure 7-4 that both UKF and EKF can quickly follow the changes of experimental data during the entire discharge process, but at the initial stage of discharge, because UKF has a smaller calculation amount than EKF, its convergence speed is faster, and in At the end of the discharge, because the EKF itself ignores high-order terms, the UKF simulation results are closer to the experimental data than the EKF, which further verifies that the UKF has higher estimation accuracy and better robustness than the EKF under pulse conditions.

Claims

1. The present invention discloses a tandem lithium-ion battery system and a method for estimating its state of charge, which is characterized in that the tandem lithium-ion battery system is composed of N lithium-ion battery cells connected in series, wherein N is is a natural number greater than 1.

The method comprises the steps of:

According to the known performance parameters of lithium-ion battery cells, the relationship between the performance parameters of the series lithium-ion battery system and the performance parameters of the battery cells is determined by using the operating characteristics of the parallel circuit and the charging and discharging characteristics, and then combined with Kirchhoff's law KVC to determine the battery Based on the voltage equation at the output of the system, the equivalent model of the series lithium-ion battery system is established (1).

The state of charge SOC of the series lithium-ion battery system and the terminal voltage of the two RC parallel circuits in the equivalent model are used as state variables, and the current and output voltage of the battery system are used as the system input and output respectively. Based on the equivalent circuit model of the ion battery system, the space state equation (2) of the series lithium ion battery system is obtained.

The battery system SOC and the terminal voltage of two RC parallel circuits in the space state equation (2) of the series lithium-ion battery system are used as the state variables of the unscented Kalman filter algorithm UKF; the space state equation (2) of the series lithium-ion battery system )'s input state space equation and output voltage state space equation are used as the nonlinear state equation and measurement equation of the UKF algorithm respectively; the actual value of the terminal voltage (4) of the series lithium-ion battery system measured by the voltage sensor and the battery terminal voltage obtained by the UKF algorithm The gain matrix (5) is updated by the estimated value of the voltage, and finally the UKF algorithm is iterated to obtain the estimated value of the SOC of the series lithium-ion battery system in real time.

2. A kind of series type lithium-ion battery system and its state of charge estimation method thereof according to claim 1, it is characterized in that the established series type lithium-ion battery system model (1) is two RC parallel circuits containing 2 first-order equivalent circuit model.

3. a kind of tandem lithium-ion battery system and its state of charge estimation method according to claim 1, it is characterized in that described tandem lithium-ion battery system space state equation (2) is as follows: system state space equation and The output equations of the system are

[\begin{matrix} {SOC}_{p, k + 1} \\ u_{p the s, k + 1} \\ u_{p l, k + 1} \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & \exp (- Δ t / τ_{1}) & 0 \\ 0 & 0 & \exp (- Δ t / τ_{2}) \end{matrix}] \times [\begin{matrix} {SOC}_{p, k} \\ u_{p the s, k} \\ u_{p l, k} \end{matrix}] + [\begin{matrix} \frac{- η Δ t}{Q_{N}} \\ R_{p the s} [1 - \exp (- Δ t / τ_{1})] \\ R_{p l} [1 - \exp (- Δ t / τ_{2})] \end{matrix}] I_{p, k} + w_{k}

、[U _{p, k} ]=U _{p0, k} - R _{p, k} I _{p, k} - U _{ps, k} - U _{p1, k} + v _k , where SOC _p is the state of charge of the series lithium-ion battery system, U _ps and U _p1 are the terminal voltages of two RC parallel circuits, R _ps and R _p1 are the resistances of two RC parallel circuits, τ ₁ and τ ₂ are time constants, v _k and w _k are system observation noise and process noise respectively , Δt is the sampling period, U _p and U _p0 are the battery system terminal voltage and open circuit terminal voltage respectively, R _p and I _p are the internal resistance and current of the battery system respectively, Q _N is the rated power of the battery system, and k is a natural number greater than 1 .

4. a kind of series type lithium-ion battery system and state of charge estimation method thereof according to claim 1, it is characterized in that described unscented Kalman filter UKF algorithm step is as follows: 1) initialization state variable x average value E( ) and mean square error P ₀ ; 2) Obtain sampling point x _i and corresponding weight ω; 3) Time update of state estimation and mean square error; 4) Calculation of gain matrix; 5) State estimation and measurement update of mean square error.

5. A series lithium-ion battery system and its state-of-charge estimation method according to claim 1, characterized in that said state-of-charge estimation method is not only applicable to series-type lithium-ion battery systems, but also can be applied to Other types of batteries, such as lead-acid, nickel-cadmium batteries, etc.