CN105353314A - Estimation method of state of charge of parallel-connected battery system - Google Patents

Abstract

The invention discloses a method for estimating the state of charge of a parallel battery system. The parallel battery system is composed of N battery cells connected in parallel. The method is as follows: establish an equivalent circuit model of the parallel battery system based on the state of charge of the battery, establish a space state equation of the parallel battery system in combination with the meaning of the battery state of charge, and use an unscented Kalman filter to charge the parallel battery system State estimation, and update the gain matrix by comparing the output voltage of the battery system with the estimated value of the voltage on-line, and obtain the estimated value of the battery state of charge by cyclic recursion. The present invention uses a parallel battery system state of charge estimation algorithm that is more accurate and robust than the extended Kalman filter algorithm, and is applicable to both parallel battery systems and parallel battery modules or battery strings.

Description

A State of Charge Estimation Method for Parallel Battery System

technical field

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 method for estimating the state of charge of a parallel battery system.

Background technique

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 renewable energy scale and the rapid growth of electricity load will also promote the development of battery systems in the direction of large capacity (MW level). The expansion of battery capacity can be realized through the parallel connection of multiple battery cells, that is, parallel connection Battery system (Parallel-connected Battery System, PBS). However, due to the complexity of the application environment (such as second-level fluctuating power smoothing, high-frequency occasions such as high frequency) and the fact that the battery power cannot be directly measured, accurate estimation of the state of charge (State of Charge, SOC) of the battery system not only directly determines the state of charge of the battery system. Whether it can operate safely, reliably and efficiently is crucial to the optimal configuration, design and control of the battery system.

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.

Contents of the invention

The problem to be solved by the present invention is to provide a method for estimating the state of charge of a parallel battery system based on Unscented Kalman Filter (UKF), which solves the problem that the performance parameters of the parallel battery system are affected by the SOC and the calculation of the extended Kalman filter method is complicated. , The low accuracy 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 parallel battery system.

The object of the invention is to realize through the following technical solutions:

The invention provides a parallel battery system, which is formed by parallel connection of N battery cells, where N is a natural number greater than 1.

A method for estimating the state of charge of a parallel battery system is as follows: According to the known performance parameters of lithium-ion battery cells, the relationship between the performance parameters of the parallel battery system and the performance parameters of the battery cells is determined by using the operating characteristics of the parallel circuit and its charging and discharging characteristics , combined with Kirchhoff's law KVC to determine the output terminal voltage equation of the battery system, and establish the equivalent model of the parallel battery system (1); the state of charge SOC of the parallel battery system and the two RC parallel circuits in the equivalent model The terminal voltage is used as the state variable, and the current and output voltage of the battery system are used as the system input and output respectively, combined with the equivalent circuit model of the parallel battery system, the space state equation (2) of the parallel battery system is obtained; the parallel battery system The battery system SOC in the space state equation (2) and the terminal voltage of two RC parallel circuits are used as the state variables of the unscented Kalman filter algorithm UKF; the input state space equation and the output of the parallel battery system space state equation (2) The voltage state space equation is used as the nonlinear state equation and measurement equation of the UKF algorithm respectively; the gain matrix (5) is updated by the actual value of the terminal voltage (4) measured by the voltage sensor and the estimated value of the battery terminal voltage obtained by the UKF algorithm , and finally the UKF algorithm undergoes cyclic iterations to obtain the estimated value of the SOC of the battery system in real time.

The parallel battery system equivalent circuit model (1) 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 _b0 (SOC) and a battery internal resistance R _b . 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 relationship between the performance parameters of the parallel battery system and the performance parameters of the battery cells is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula, R _ps , R _pl , C _ps , and C _pl 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 _il , C _is , C _il represent the resistance and capacitance of two RC parallel circuits in the battery cell model respectively; U _i0 , R _i , R _is , R _il , C _is , C _il 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 _il and C _is , C _il , R _i are as follows: $u_{i0}\left(\mathrm{SOC}\right)=a_0{e}^{{-a}_1\mathrm{SOC}\left(t\right)}+a_2+a_3\mathrm{SOC}\left(t\right)-a_4{\mathrm{SOC}}^2\left(t\right)+a_5{\mathrm{SOC}}^3\left(t\right),R_{\mathrm{is}}\left(t\right)=c_0{e}^{{-c}_1\mathrm{SOC}\left(t\right)}+c_2,$ $C_{\mathrm{is}}\left(t\right)=d_0{e}^{{-d}_1\mathrm{SOC}\left(t\right)}+d_2,R_{i1}\left(t\right)=e_0{e}^{{-e}_1\mathrm{SOC}\left(t\right)}+e_2,C_{i1}\left(t\right)=f_0{e}^{{-f}_1\mathrm{SOC}\left(t\right)}+f_2,$ $R_i\left(t\right)=b_0{e}^{{-b}_1\mathrm{SOC}\left(t\right)}+b_2+b_3\mathrm{SOC}\left(t\right)-b_4{\mathrm{SOC}}^2\left(t\right)+b_5{\mathrm{SOC}}^3\left(t\right),$ 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.

The establishment of the parallel battery system space state equation (2) is as follows: a. The state of charge SOC _p of the battery system and the terminal voltages of the two RC parallel circuits in the equivalent model are used as state variables, and the current I of the battery system is _p 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

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; SOC</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; SOC</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right]{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

In the formula, U _ps and U _pl are the terminal voltages of the two RC parallel circuits, R _ps and R _pl 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:

$u_{p,k+1}\left(t\right)=u_{p0,k+1}\left(t\right)-R_{p,k+1}\left(t\right)I_{p,k+1}\left(t\right)-\&lsqb;\begin{array}{ccc}0& 1& 1\end{array}\&rsqb;\&times;\left[\begin{array}{c}So{C}_{p,k+1}\\ u_{p\mathrm{the\; s},k+1}\\ u_{pl,k+1}\end{array}\right],$ In the formula, U _p is the terminal voltage of the battery system, and R _p is the internal resistance of the battery system.

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 : ${\hat{x}}_0=\mathrm{E.}\left(x_0\right),P_0=\mathrm{E.}\left((x_0-{\hat{x}}_0){(x_0-{\hat{x}}_0)}^T\right);$ 2) Obtain the sampling point x _i and the corresponding weight ω: $\left\{\begin{array}{c}{x}_{0,k-1}={\hat{x}}_{k-1}\\ x_{i,k-1}={\hat{x}}_{k-1}+{\left(\sqrt{\left(\mathrm{no}+\mathrm{\&lambda;}\right)P_{i,k-1}}\right)}_i,i=1,2,\mathrm{...},\mathrm{no}\\ x_{i,k-1}={\hat{x}}_{k-1}-{\left(\sqrt{\left(\mathrm{no}+\mathrm{\&lambda;}\right)P_{i,k-1}}\right)}_i,i=\mathrm{no}+1,\mathrm{no}+2,\mathrm{...},2\mathrm{no}\end{array}\right.,$ $\left\{\begin{array}{c}{\mathrm{\&omega;}}_0^m=\mathrm{\&lambda;}/(\mathrm{no}+\mathrm{\&lambda;})\\ {\mathrm{\&omega;}}_0^c=\mathrm{\&lambda;}/(\mathrm{no}+\mathrm{\&lambda;})+(1+\mathrm{\&beta;}-{\mathrm{\&alpha;}}^2)\\ {\mathrm{\&omega;}}_i^m={\mathrm{\&omega;}}_i^c=1/2(\mathrm{no}+\mathrm{\&lambda;}),i\&NotEqual;0\end{array}\right.$ In the formula, λ=α ² (n+h)-n, ω ^m and ω ^c represent the weight of the variance and the mean value respectively, α and β represent the particle distribution distance in the sampling point and the error size of the high-order item respectively; 3) state estimation and the time update of the mean square error: the state estimation time is updated as $\left\{\begin{array}{c}{x}_{i,k/k-1}=f_{k-1}\left(x_{i,k-1}\right),i=0,1,...,2\mathrm{no}\\ {\hat{x}}_{k/k-1}=\underset{i=0}{\overset{2\mathrm{no}}{\&Sigma;}}{\mathrm{\&omega;}}_i^m{f}_{k-1}\left(x_{i,k-1}\right)\end{array}\right.,$ The mean square error time is updated as $P_{k/k-1}=\underset{i=0}{\overset{2\mathrm{no}}{\&Sigma;}}{\mathrm{\&omega;}}_i^c(x_{i,k/k-1}-{\hat{x}}_{k/k-1}){(x_{i,k/k-1}-{\hat{x}}_{k/k-1})}^T,$ The system output time is updated as $\left\{\begin{array}{c}{\mathrm{\&chi;}}_{i,k/k-1}=g_{k-1}\left(x_{i,k-1}\right)\\ {\widehat{\mathrm{the\; y}}}_{k/k-1}=\underset{i=0}{\overset{2\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^m{g}_{k-1}\left(x_{i,k-1}\right)\end{array}\right.$ In the formula, g _k-1 ( ) is the measurement equation; 4) Calculate the gain matrix (5): $L_k=P_{x\mathrm{the\; y},k}{P}_{\mathrm{the\; y},k}^{-1},$ In the formula, $\left\{\begin{array}{c}{P}_{\mathrm{the\; y},k}=\underset{i=0}{\overset{2\mathrm{no}}{\&Sigma;}}{\mathrm{\&omega;}}_i^c({\mathrm{\&chi;}}_{i,k/k-1}-{\widehat{\mathrm{the\; y}}}_{k/k-1}){({\mathrm{\&chi;}}_{i,k/k-1}-{\widehat{\mathrm{the\; y}}}_{k/k-1})}^T\\ P_{x\mathrm{the\; y},k}=\underset{i=0}{\overset{2\mathrm{no}}{\&Sigma;}}{\mathrm{\&omega;}}_i^c(x_{i,k/k-1}-{\hat{x}}_{k/k-1}){({\mathrm{\&chi;}}_{i,k/k-1}-{\widehat{\mathrm{the\; y}}}_{k/k-1})}^T\end{array}\right.;$ 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 $P_k=P_{k/k-1}-L_k{P}_{\mathrm{the\; y},k}{L}_k^T.$

Compared with using the extended Kalman filter algorithm EKF to estimate the SOC of the parallel battery system, the present invention has the following beneficial technical effects: First, the UKF algorithm used in the present invention is better than the EKF algorithm for the SOC estimation of the parallel battery system during the entire discharge process. When the UKF estimation accuracy is higher, especially the effect at the beginning and end of the discharge is more obvious; second, the UKF algorithm used can converge to the experimental data faster than the EKF algorithm, and the robustness is better.

Description of drawings

Fig. 1 is a flow chart of a method for estimating the state of charge of a parallel battery system;

Figure 2 is a schematic structural diagram of a parallel battery system;

Fig. 3 is a schematic structural diagram of a parallel battery system containing two battery cells;

Figure 4 is an equivalent circuit model diagram of a parallel battery system containing two RC parallel circuits;

Fig. 5 is the unscented Kalman filter algorithm flowchart;

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;

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.

detailed description

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.

According to an embodiment of the present invention, as shown in FIG. 1 , FIG. 2 , FIG. 3 , FIG. 4 and FIG. 5 , a method for estimating the state of charge of a parallel battery system is provided. The flow chart of the embodiment is shown in FIG. 1 , mainly Include the following steps:

1. Establish an equivalent circuit model of a parallel battery system

1) Parallel battery system

The parallel battery system is composed of N battery cells connected in parallel, and its structure diagram is shown in Figure 2. For the convenience of analysis, it is assumed in this example that the parallel battery system consists of two battery cells connected in parallel, that is, a 1×2 parallel battery system, as shown in Figure 3. The rated voltage of each battery cell in the parallel battery system is 3.2V, the rated capacity is 25Ah, and the discharge cut-off voltage is 2.5V.

2) Establish an equivalent circuit model of a 1×2 battery system

The parallel battery system equivalent circuit model (1) 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 _p0 (SOC) and battery internal resistance R _p , etc., as shown in Figure 4 shown. The performance parameters of the parallel battery system are obtained through the relationship with the performance parameters of the battery cells, and the specific calculation is as follows: $\left\{\begin{array}{c}{u}_{p0}\left(t\right)=u_{i0}\left(t\right)\\ \frac{1}{R_p\left(t\right)}=\underset{i=1}{\overset{2}{\&Sigma;}}\frac{1}{R_i\left(t\right)}\\ \frac{1}{R_{p\mathrm{the\; s}}\left(t\right)}=\underset{i=1}{\overset{2}{\&Sigma;}}\frac{1}{R_{i\mathrm{the\; s}}\left(t\right)}\\ C_{p\mathrm{the\; s}}\left(t\right)=C_{i\mathrm{the\; s}}\left(t\right)\\ \frac{1}{R_{p1}\left(t\right)}=\underset{i=1}{\overset{2}{\&Sigma;}}\frac{1}{R_{i1}\left(t\right)}\\ C_{p1}\left(t\right)=C_{i1}\left(t\right)\end{array}\right.$

In the above formula, the battery cell performance parameters U ₀ (t), R _s (t), R _l (t) and C _s (t), C _l (t) are calculated as follows: $u_0\left(t\right)=a_0{e}^{{-a}_1\mathrm{SOC}\left(t\right)}+a_2+a_3\mathrm{SOC}\left(t\right)-a_4{\mathrm{SOC}}^2\left(t\right)+a_5{\mathrm{SOC}}^3\left(t\right),R_{\mathrm{the\; s}}\left(t\right)=c_0{e}^{{-c}_1\mathrm{SOC}\left(t\right)}+c_2,$ $C_{\mathrm{the\; s}}\left(t\right)=d_0{e}^{{-d}_1\mathrm{SOC}\left(t\right)}+d_2,R_1\left(t\right)=e_0{e}^{{-e}_1\mathrm{SOC}\left(t\right)}+e_2,C_1\left(t\right)=f_0{e}^{{-f}_1\mathrm{SOC}\left(t\right)}+f_2,$ $R\left(t\right)=b_0{e}^{{-b}_1\mathrm{SOC}\left(t\right)}+b_2+b_3\mathrm{SOC}\left(t\right)-b_4{\mathrm{SOC}}^2\left(t\right)+b_5{\mathrm{SOC}}^3\left(t\right),$ 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. Parallel battery system space state equation

a. Taking the state of charge SOC _P of the parallel battery system and the terminal voltages U _ps and U _pl of the two RC parallel circuits in the equivalent model as state variables, and taking the current I _p of the parallel battery system as the system input, according to Equivalent circuit model (1) Establish the input state space equation of the parallel battery system as

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; SOC</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; SOC</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right]{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

In the formula, U _ps and U _pl are the terminal voltages of the two RC parallel circuits, R _ps and R _pl 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 parallel battery system, the output voltage equation of the parallel battery system can be obtained as: $u_{p,k+1}\left(t\right)=u_{p0,k+1}\left(t\right)-R_{p,k+1}\left(t\right)I_{p,k+1}\left(t\right)-\&lsqb;\begin{array}{ccc}0& 1& 1\end{array}\&rsqb;\&times;\left[\begin{array}{c}So{C}_{p,k+1}\\ u_{p\mathrm{the\; s},k+1}\\ u_{pl,k+1}\end{array}\right],$ In the formula, U _p is the terminal voltage of the battery system, R _p is the internal resistance of the battery system, and k is a natural number greater than 1.

3. State of charge estimation of parallel battery system based on Kalman filter method

The battery system SOC in the space state equation of the parallel 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 parallel battery system, the output voltage state space The equations are respectively used as the nonlinear state equation f _k-1 ( ) and the measurement equation g _k-1 ( ) of the UKF algorithm; the actual value y _k of the battery system terminal voltage (4) measured by the voltage sensor and the battery obtained by the UKF algorithm terminal voltage estimate to update the gain matrix (5), and finally the UKF algorithm performs loop iterations, as shown in Figure 5, during the iteration process, the initial value of the state variable x is [100], the value of α is 1, the value of β is 2, h The value is 0; finally, the estimated value SOC _k of the SOC of the parallel battery system is obtained in real time.

System simulation results and effect comparison

According to the battery system state of charge estimation method based on unscented Kalman filter, the state of charge of a 1×2 battery system composed of a certain type of lithium battery is estimated, and EKF is used to estimate the state of charge of the battery system. Through simulation The comparison of the results and experimental data verifies that the battery system state of charge estimation method based on the unscented Kalman filter has higher accuracy and stronger robustness. 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 parallel battery system and its terminal voltage well, but UKF has higher accuracy, especially at the end of discharge (3000s). It can be seen from Figure 6-3 and Figure 6-4 that both algorithms can converge to the experimental data well, no matter it is the SOC or terminal voltage of the parallel battery system, which proves that both algorithms have good robustness. But not only at the initial stage of discharge, because UKF has a smaller calculation amount than EKF, its convergence speed is faster, but also at the end of discharge, because EKF itself ignores higher-order terms, UKF is closer to the experimental data than EKF simulation results, which proves that in constant current discharge Under certain circumstances, UKF is more accurate and robust than EKF prediction results.

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. It can be seen from Figure 7-3 and Figure 7-4 that during the entire discharge process, the UKF simulation results are more consistent with the experimental data than the EKF, especially the two stages of the initial discharge period (before 600s) and the final period (after 6000s); at the same time, the UKF can The faster convergence to the experimental data further verifies that UKF can more accurately estimate the SOC value of the parallel battery system under pulse conditions, and has better robustness.

Claims (5)

1. The present invention discloses a method for estimating the state of charge of a parallel battery system, which is characterized in that the parallel battery system is composed of N battery cells connected in parallel, where N 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 parallel battery system and the performance parameters of the battery cells is determined by using the operating characteristics of the parallel circuit and its charging and discharging characteristics, and then combined with Kirchhoff's law KVC to determine the output of the battery system Based on the terminal voltage equation, an equivalent model of a parallel battery system is established (1). The state of charge SOC of the parallel 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 the parallel battery system, etc. The effective circuit model is used to obtain the space state equation (2) of the parallel battery system. The battery system SOC in the space state equation (2) of the parallel battery system and the terminal voltage of the two RC parallel circuits are used as the state variables of the unscented Kalman filter algorithm UKF; the input state of the space state equation (2) of the parallel battery system The space equation and the output voltage state space equation are respectively used as the nonlinear state equation and measurement equation of the UKF algorithm; the gain is updated by measuring the actual value of the terminal voltage (4) of the parallel battery system with the voltage sensor and the estimated value of the battery terminal voltage obtained by the UKF algorithm Matrix (5), and finally the UKF algorithm undergoes cyclic iterations to obtain the estimated value of the SOC of the parallel battery system in real time. 2. A method for estimating the state of charge of a parallel battery system according to claim 1, characterized in that the established parallel battery system model (1) is a second-order equivalent circuit model containing two RC parallel circuits. 3. A method for estimating the state of charge of a parallel battery system according to claim 1, wherein the space state equation (2) of the parallel battery system is as follows: the system state space equation and the system output equation are respectively $\left[\begin{array}{c}{\mathrm{SOC}}_{p,k+1}\\ u_{p\mathrm{the\; s},k+1}\\ u_{pl,k+1}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \exp (-\mathrm{\&Delta;}t/{\mathrm{\&tau;}}_1)& 0\\ 0& 0& \exp (-\mathrm{\&Delta;}t/{\mathrm{\&tau;}}_2)\end{array}\right]\&times;\left[\begin{array}{c}{\mathrm{SOC}}_{p,k}\\ u_{p\mathrm{the\; s},k}\\ u_{pl,k}\end{array}\right]+\left[\begin{array}{c}\frac{-\mathrm{\&eta;}\mathrm{\&Delta;}t}{Q_N}\\ R_{p\mathrm{the\; s}}\&lsqb;1-\exp (-\mathrm{\&Delta;}t/{\mathrm{\&tau;}}_1)\&rsqb;\\ R_{pl}\&lsqb;1-\exp (-\mathrm{\&Delta;}t/{\mathrm{\&tau;}}_2)\&rsqb;\end{array}\right]I_{p,k}+w_k$ 、[U _p,k ]＝U _p0,k -R _p,k I _p,k -U _ps,k -U _pl,k +v _k , where SOC _p is the state of charge of the parallel battery system, U _ps , U _pl are the terminal voltages of the two RC parallel circuits, R _ps and R _pl are the resistances of the two RC parallel circuits, τ ₁ and τ ₂ are the time constants, v _k and w _k are the 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 method for estimating the state of charge of a parallel battery system according to claim 1, characterized in that the steps of the Unscented Kalman Filter UKF algorithm are as follows: 1) Initialize the state variable x mean 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) Measurement update of state estimation and mean square error. 5. A method for estimating the state of charge of a parallel battery system according to claim 1, characterized in that the modeling method is not only applicable to parallel battery systems, but also applicable to parallel battery modules or battery strings.