CN105353315A - Estimation method of state of charge of battery system on the basis of Unscented Kalman Filter - Google Patents

Abstract

The invention discloses a battery system charge state estimation method based on unscented Kalman filter. The battery system is an M×N battery system, that is, M battery cells are connected in series to form a battery string, and then N batteries connected in series. The method is as follows: establish an equivalent circuit model of the battery system based on the state of charge of the battery, establish a space state equation of the battery system in combination with the meaning of the state of charge of the battery, use an unscented Kalman filter to estimate the state of charge of the battery system, and use the online The output voltage of the battery system and the estimated value of the voltage are detected to update the gain matrix of the unscented Kalman filter, and a new estimated value of the battery state of charge is obtained by cyclic recursion. The battery system charge state estimation algorithm adopted by the invention is more accurate and robust than the extended Kalman filter algorithm, and is applicable to both the battery system and the battery monomer.

Description

A battery system state of charge estimation method based on unscented Kalman filter

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 battery system based on an unscented Kalman filter.

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). 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, extended Kalman filter method (ExtendedKalmanFilter, EKF) and other advanced algorithms. For nonlinear time-varying battery systems, EKF is often used at present and has achieved good results. However, due to the complex calculation of EKF itself and the neglect of high-order terms, certain errors will inevitably occur, so that the accuracy of the SOC estimation of the battery still needs to be further improved. Research.

Contents of the invention

The problem to be solved by the present invention is to provide a battery system state of charge estimation method based on Unscented Kalman Filter (UKF), which solves the problem that the performance parameters of the battery system are affected by the SOC, and the extended Kalman filter method has complex calculations and low precision. As a result, the SOC of the battery system is difficult to be accurately measured and estimated, and the purpose of accurately estimating the SOC of the battery system is achieved.

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

The invention provides a battery system, which is formed by connecting M battery cells in series to form a battery string, and then connecting N batteries in series and parallel, wherein M and N are both natural numbers greater than 1.

A battery system state of charge estimation method based on unscented Kalman filter is as follows: According to the known performance parameters of lithium-ion battery cells, the performance parameters of the battery system and the performance parameters of the battery cells are determined by using the operating characteristics of the series and parallel circuits and the screening method combined with Kirchhoff's law KVC to determine the output voltage equation of the battery system, and establish an equivalent model of the battery system (1); the state of charge SOC of the battery system and the terminal voltage of the two RC parallel circuits in the equivalent model As state variables, 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 battery system, the battery system space state equation (2) is obtained; the battery system space state equation (2) is The battery system SOC 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 voltage state space equation of the battery system space state equation (2) are respectively used as the nonlinearity of the UKF algorithm The state equation and measurement equation; the gain matrix (5) is updated by the actual value of the battery system 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 battery in real time. An estimate of the system SOC.

The 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 battery system and the performance parameters of the battery cells is:

In the formula, R _bs , R _bl , C _bs , and C _bl 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: 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 battery system space state equation (2) is as follows: a. The state of charge SOC _b 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 _b of the battery system is The system input quantity, according to the equivalent circuit model to establish the space state equation of the battery system is

In the formula, U _bs and U _bl are the terminal voltages of the two RC parallel circuits, R _bs and R _bl 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 output voltage equation of the battery system can be obtained as: U _b (t) =U _b0 (t)-R _b (t)I _b (t)-U _bl (t)-U _bs (t), where U _b is the terminal voltage of the battery system, and R _b 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 : 2) Obtain the sampling point x _i and the corresponding weight ω: 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 The mean square error time is updated as The system output time is updated as In the formula, g _k-1 ( ) is the measurement equation; 4) Calculate the gain matrix L _k (5): In the formula, 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

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

Description of drawings

Fig. 1 is a flowchart of a method for estimating the state of charge of a battery system based on an unscented Carr filter;

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

Figure 3 is a schematic structural diagram of a 12×2 battery system;

Figure 4 is an equivalent circuit model diagram of a 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 battery system based on an unscented Kalman filter is provided, and the flow chart of the embodiment is shown in Fig. 1, mainly includes the following steps:

1. Establish an equivalent circuit model of the battery system

1) Battery system

The battery system is formed by connecting M battery cells in series to form a battery string, and then connecting N batteries in series and parallel. Its structure diagram is shown in Figure 2. For the convenience of analysis, in this example, it is assumed that the battery system consists of 12 battery cells connected in series to form a battery string, and then 2 battery strings connected in parallel, that is, a 12×2 battery system, as shown in Figure 3. The rated voltage of each battery cell in the 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 12×2 battery system

The 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 _b0 (SOC) and a battery internal resistance R _b , as shown in Figure 4 . The performance parameters of the battery system are obtained through the relationship with the performance parameters of the battery cells. The specific calculations are as follows: U _b0 (t)=12*U ₀ (t), R _b (t)=6*R(t), R _bs ( t)=6*R _s (t), C _bs (t)=C _s (t)/6, R _bl (t)=6*R _l (t), C _bl (t)=C _l (t) /6. In each of the above formulas, the calculations of battery cell performance parameters U ₀ (t), R _s (t), R _l (t) and C _s (t), C _l (t) are as follows: 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. Establish the space state equation of the battery system

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

In the formula, U _bs and U _bl are the terminal voltages of the two RC parallel circuits, R _bs and R _bl 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 output voltage equation of the battery system can be obtained as: In the formula, U _b is the terminal voltage of the battery system, R _b is the internal resistance of the battery system, and k is a natural number greater than 1.

3. Using the Kalman filter method to estimate the state of charge of the battery system

The battery system SOC in the battery system space state equation 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 and the output voltage state space equation of the battery system space state equation are respectively As the nonlinear state equation f _k-1 ( ) and 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 terminal voltage obtained by the UKF algorithm estimated value 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 battery system SOC is obtained in real time.

System simulation verification and effect comparison

According to the battery system state of charge estimation method based on unscented Kalman filter, the state of charge of a 12×2 battery system composed of a certain type of lithium battery is estimated. At the same time, 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 battery system SOC and its terminal voltage changes very 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 the two algorithms can converge to the experimental data well regardless of the battery system SOC or terminal voltage, which proves that both algorithms have good robustness, but not only In the early stage of discharge, because UKF has a smaller calculation amount than EKF, its convergence speed is faster, and in the end of discharge, because EKF itself ignores high-order terms, UKF is closer to the experimental data than EKF simulation results, which proves that in the case of constant current discharge UKF prediction results are more accurate and robust than EKF.

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 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 estimate the SOC value of the battery system more accurately and has better robustness under pulse conditions.

Claims (5)

1. The present invention discloses a method for estimating the state of charge of a battery system based on an unscented Kalman filter, It is characterized in that the battery system is composed of M battery cells connected in series to form a battery string, and then N batteries connected in parallel, wherein M and N are both natural numbers 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 battery system and the performance parameters of the battery cells is determined by using the operating characteristics of the series and parallel circuits and the screening method, and then combined with Kirchhoff's law KVC to determine the output voltage equation of the battery system , to establish the battery system equivalent model (1). Taking the state of charge SOC of the battery system and the terminal voltages of two RC parallel circuits in the equivalent model as state variables, taking the current and output voltage of the battery system as the system input and output respectively, combined with the equivalent circuit model of the battery system, The space state equation (2) of the battery system is obtained. The battery system SOC in the battery system 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 of the battery system space state equation (2), the output 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 battery system 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 estimated value of the SOC of the battery system is obtained in real time by the UKF algorithm through cyclic iterations. 2. A method for estimating the state of charge of a battery system based on an unscented Kalman filter according to claim 1, wherein the established battery system model (1) is a second-order equivalent of two RC parallel circuits circuit model. 3. A battery system state of charge estimation method based on unscented Kalman filter according to claim 1, characterized in that said battery system space state equation (2) is as follows: system state space equation and system output equation respectively $\left[\begin{array}{c}{\mathrm{SOC}}_{b,k+1}\\ u_{b\mathrm{the\; s},k+1}\\ u_{bl,k+1}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)& 0\\ 0& 0& \exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\end{array}\right]\×\left[\begin{array}{c}{\mathrm{SOC}}_{b,k}\\ u_{b\mathrm{the\; s},k}\\ u_{bl,k}\end{array}\right]+\left[\begin{array}{c}\frac{-\mathrm{\η}\mathrm{\Δ}t}{Q_N}\\ R_{b\mathrm{the\; s}}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)\]\\ R_{bl}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\]\end{array}\right]I_{b,k}+w_k$ $,\[u_{b,k}\]=u_{bo,k}-R_{b,k}{I}_{b,k}-u_{b\mathrm{the\; s},k}-u_{bl,k}+v_k,$ In the formula, SOC _b is the state of charge of the battery system, U _bs and U _bl are the terminal voltages of the two RC parallel circuits, R _bs and R _bl are the resistances of the two RC parallel circuits, τ ₁ and τ ₂ are the time constants, v _k , w _k are system observation noise and process noise respectively, Δt is sampling period, U _b , U _b0 are battery system terminal voltage and open circuit terminal voltage respectively, R _b , I _b are battery system internal resistance and current respectively, Q _N is The rated power of the battery system, k is a natural number greater than 1. 4. A method for estimating the state of charge of a battery system based on an Unscented Kalman Filter according to claim 1, wherein the steps of the Unscented Kalman Filter UKF algorithm are as follows: 1) initializing 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 battery system based on an unscented Kalman filter according to claim 1, wherein the modeling method is not only applicable to the battery system, but also applicable to battery modules or cells .