阅读说明：本技术 一种基于开路电压的电池容量估计方法 (Battery capacity estimation method based on open-circuit voltage ) 是由 郑岳久 沈安琪 崔一凡 陆天溪 晏莉琴 吕桃林 解晶莹 于 2020-05-22 设计创作，主要内容包括：本发明提出了一种基于开路电压的电池容量估计方法。其方法包括如下步骤：S1：建立一阶RC等效模型,利用带遗忘因子的递归最小二乘法进行参数在线辨识,估算出电池的欧姆内阻与OCV；S2：绘制SOC与OCV关系的标定曲线图,将OCV代入标定曲线图,获得对应的SOC；S3：根据电量变化与对应SOC变化的线性关系,绘制电量与SOC关系的拟合曲线图,将SOC代入并利用加权最小二乘法,获得对应的斜率值,即为电池容量的第一容量值；S4：通过离散化Arrhenius寿命模型估计获得电池容量的第二容量值；S5：使用卡尔曼滤波算法将第一容量值和第二容量值进行融合估计,获得电池容量的第三容量值。本发明的好处是通过采用加权最小二乘法的方法来进行容量估计以提高其估计精度。与现有的基于开路电压进行容量估计的方法相比,本发明具有较高的容量精度。(The invention provides a battery capacity estimation method based on open-circuit voltage. The method comprises the following steps: s1: establishing a first-order RC equivalent model, performing parameter online identification by using a recursive least square method with forgetting factors, and estimating the ohmic internal resistance and the OCV of the battery; s2: drawing a calibration curve graph of the relation between the SOC and the OCV, and substituting the OCV into the calibration curve graph to obtain a corresponding SOC; s3: drawing a fitting curve graph of the relation between the electric quantity and the SOC according to the linear relation between the electric quantity change and the corresponding SOC change, substituting the SOC into the fitting curve graph and obtaining a corresponding slope value, namely a first capacity value of the battery capacity by using a weighted least square method; s4: estimating and obtaining a second capacity value of the battery capacity through a discretized Arrhenius life model; s5: and performing fusion estimation on the first capacity value and the second capacity value by using a Kalman filtering algorithm to obtain a third capacity value of the battery capacity. The method has the advantage that the capacity estimation is carried out by adopting a weighted least square method so as to improve the estimation precision. Compared with the existing method for estimating the capacity based on the open-circuit voltage, the method has higher capacity precision.)

1. A method for estimating battery capacity based on open circuit voltage is characterized in that the method comprises the following steps:

s1: establishing a first-order RC equivalent model of a sample battery, performing parameter online identification by using a recursive least square method (FFRLS) with a forgetting factor, and estimating ohmic internal resistance and OCV of the sample battery;

s2: drawing a calibration curve graph of the relation between the SOC and the OCV, and substituting the OCV into the calibration curve graph to obtain a corresponding SOC;

s3: drawing a fitting curve graph of the relation between the electric quantity and the SOC according to the linear relation between the electric quantity change of the sample battery and the corresponding SOC change, substituting the SOC into the fitting curve graph, and obtaining a corresponding slope value by using a weighted least square method, wherein the slope value is a first capacity value of the battery capacity of the sample battery;

s4: estimating and obtaining a second capacity value of the battery capacity of the sample battery through a discretized Arrhenius life model;

s5: and performing fusion estimation on the first capacity value and the second capacity value by using a Kalman filtering algorithm to obtain a third capacity value of the battery capacity of the sample battery.

2. The method of claim 1, wherein the external characteristic equation of the first-order RC equivalent model is as follows:

wherein: r₁For polarizing internal resistance, tau₁Is a time constant, R₀Ohmic internal resistance;

the expressions of the output vector, the observation vector and the vector to be estimated in the recursive least square method are respectively as follows:

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

3. The method of claim 2, wherein the algorithm for the online parameter identification is recursive as follows:

wherein: y is_kIn order to output the vector for the system,

the R is₁And τ₁According to said R, for a known parameter₁And τ₁By looking up the SOC table to obtain R_1,kAnd τ_1,kIntroduction of said R into_1,kAnd τ_1,kSubstituting the parameters into a recursion formula for online parameter identification to obtain the OCV, wherein an output equation is as follows:

y_k＝U_1,k+U_t,k＝OCV_k-I_kR_0,k

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

4. The method of claim 1, wherein the first capacity value C is obtained from a change in charge and discharge power and a corresponding change in SOC based on a two-point cumulative power method_batThe formula is as follows:

the above formula is transformed and merged into a matrix form:

Y＝X₀A+V

wherein: a ═ k, b]In order to obtain the coefficients to be calculated,v is a random error term;

obtaining A ═ X according to the weighted least squares method (WRLS)₀ ^TWX₀)^-1X₀ ^TWY，

5. The method according to claim 4, wherein if the random error term V satisfies E (V) 0, E (V) is satisfied^TV) is R, then when the weight W is R^-1And then, the variance of the SOC error is minimum, and the coefficient to be solved is as follows:

6. the method according to claim 1, wherein the k-time is a time of dayThe first capacity value is C_bat(n_k) And said second capacity value at time k is C_cap(n_k) The third capacity value is C_D(n_k+1) The external characteristic equation of the discretized Arrhenius life model is as follows:

wherein ξ (n) is relative capacity decrement of the battery after n times of battery circulation, and has unit of%_aFor activation energy, the unit is J/mol; r is a gas constant and has the unit of J/(mol.k); t is the absolute temperature in K; n is the cycle number; z is an index.

Technical Field

The invention belongs to the field of battery capacity estimation, and particularly relates to a battery capacity estimation method based on open-circuit voltage for improving the estimation precision of battery capacity.

Background

In recent years, our country has a fast development of new energy vehicles, especially pure electric vehicles are driven by electric power completely, and no tail gas caused by pollution is generated, so the development of the new energy vehicles has important significance for environmental protection and reduction of consumption of petroleum resources. The national and local governments have corresponding subsidy policies for pure electric vehicles, which plays a very large role in promoting the rapid development of the pure electric vehicles. The vehicle-mounted BMS is an indispensable part of the current electric vehicle in order to improve the operating performance of the battery and extend the service life of the battery. The SOC and battery capacity estimation of the battery are the most core functions of the BMS, and the estimation accuracy and the practicality thereof are particularly important. Accurate battery capacity estimation is necessary to efficiently manage the battery.

The research on the on-line estimation of the battery capacity is more, and Farmann et al thoroughly reviews and classifies the current on-line estimation method of the capacity. However, if the fundamental approach of capacity estimation is achieved by analyzing various methods, it can be found that the currently mainstream methods basically follow two different approaches: the first method is to estimate the capacity based on the battery attenuation law, and specifically comprises an open loop estimation method based on a capacity attenuation model, an IC/DV curve method based on an attenuation mechanism and the like. The estimation method based on the attenuation model and the estimation method based on the IC/DV curve are both established on the basis of the known battery attenuation rule, the service life test needs to be carried out on line, and the actual estimation precision is difficult to ensure due to the fact that the online application environment is different from the test condition. The second method is to estimate based on capacity definition, specifically including a two-point accumulated energy method, a model-based closed-loop estimation method, and the like, and is more suitable for online occasions. The method for accumulating the electric quantity between two points is relatively simpler, and the key point of the method is the estimation precision of the SOC values at two different moments. The accuracy of the model-based closed-loop estimation algorithm depends largely on the model accuracy, and the calculation amount of the algorithm is relatively large.

The capacity fading degree of the battery characterizes the service life of the battery, and is one of important parameters for measuring the aging of the battery, so the capacity of the battery needs to be estimated. The present invention also provides a method for estimating battery capacity.

Disclosure of Invention

The invention improves the method for estimating the SOC based on the open-circuit voltage, and provides a method capable of improving the capacity online estimation precision. The method is beneficial to reducing the capacity estimation error, more accurately evaluating the health state of the battery and improving the safety of the new energy vehicle taking the lithium battery as the power source.

The purpose of the invention can be realized by the following technical scheme:

a method for estimating a capacity of a battery based on an open circuit voltage, the method comprising the steps of:

s1: establishing a first-order RC equivalent model of a sample battery, performing parameter online identification by using a recursive least square method (FFRLS) with a forgetting factor, and estimating ohmic internal resistance and OCV of the sample battery;

s2: drawing a calibration curve graph of the relation between the SOC and the OCV, and substituting the OCV into the calibration curve graph to obtain a corresponding SOC;

s3: drawing a fitting curve graph of the relation between the electric quantity and the SOC according to the linear relation between the electric quantity change of the sample battery and the corresponding SOC change, substituting the SOC into the fitting curve graph, and obtaining a corresponding slope value by using a weighted least square method, wherein the slope value is a first capacity value of the battery capacity of the sample battery;

s4: estimating and obtaining a second capacity value of the battery capacity of the sample battery through a discretized Arrhenius life model;

s5: and performing fusion estimation on the first capacity value and the second capacity value by using a Kalman filtering algorithm to obtain a third capacity value of the battery capacity of the sample battery.

Preferably, in the method for estimating battery capacity based on open-circuit voltage, the external characteristic equation of the first-order RC equivalent model is as follows:

wherein: r₁For polarizing internal resistance, tau₁Is a time constant, R₀Ohmic internal resistance;

the expressions of the output vector, the observation vector and the vector to be estimated in the recursive least square method are respectively as follows:

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

Preferably, in the method for estimating battery capacity based on open-circuit voltage, the algorithm recursive process of parameter online identification is as follows:

wherein: y is_kIn order to output the vector for the system,for measurement vectors consisting of observations, θ_kFor the vector to be estimated containing the parameter to be estimated, e_kFor estimation error of system output, K_kTo gain, P_kThe method is characterized in that the method is a covariance matrix, lambda is a forgetting factor, and the value range of lambda is between 0 and 1 according to the definition;

the R is₁And τ₁According to said R, for a known parameter₁And τ₁By looking up the SOC table to obtain R_1,kAnd τ_1,kIntroduction of said R into_1,kAnd τ_1,kSubstituting the parameters into a recursion formula for online parameter identification to obtain the OCV, wherein an output equation is as follows:

y_k＝U_1,k+U_t,k＝OCV_k-Ik_R0,k

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

Preferably, the method for estimating the capacity of the battery based on the open circuit voltage obtains the first capacity value C based on a two-point cumulative electric quantity method by a change in electric quantity during charge and discharge and a corresponding change in SOC_batThe formula is as follows:

the above formula is transformed and merged into a matrix form:

Y＝X₀A+V

wherein: a ═ k, b]In order to obtain the coefficients to be calculated,v is a random error term;

obtaining from the weighted least squares method (WRLS)

Preferably, in the method for estimating battery capacity based on open-circuit voltage, if the random error term V satisfies E (V) 0, E (V)^TV) is R, then when the weight W is R^-1And then, the variance of the SOC error is minimum, and the coefficient to be solved is as follows:

preferably, in the method for estimating battery capacity based on open-circuit voltage, the first capacity value at the time k is C_bat(n_k) And said second capacity value at time k is C_cap(n_k) The third capacity value is C_D(n_k+1) The external characteristic equation of the discretized Arrhenius life model is as follows:

wherein ξ (n) is relative capacity decrement of the battery after n times of battery circulation, and has unit of%_aFor activation energy, the unit is J/mol; r is a gas constant and has the unit of J/(mol.k); t is the absolute temperature in K; n is the cycle number; z is an index.

The invention has the characteristics and beneficial effects that:

compared with the existing method for estimating the capacity based on the open-circuit voltage, the method for estimating the capacity of the battery based on the open-circuit voltage has higher capacity precision. The invention is based on a first-order RC model of a circuit, and the parameters of the battery are identified by using a least square method with forgetting factors, so that the optimal estimation of the parameters can be sought. The battery capacity is estimated by using a weighted least square method in consideration of the influence of the SOC error on the estimation of the battery capacity, and the method is high in reliability and high in accuracy. And finally, the battery capacity is fused and estimated by using a Kalman filtering method, so that the capacity estimation precision is further improved.

Drawings

FIG. 1 is a flow chart of a method of open circuit voltage based battery capacity estimation in accordance with the present invention;

FIG. 2 is a circuit diagram of a first order RC equivalent model in the present invention;

FIG. 3 is the OCV graph after identification by the recursive least squares method (FFRLS);

FIG. 4 is a fitting graph of the relationship between the amount of charge and the SOC in the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.

Hereinafter, a preferred embodiment of the present invention will be explained in detail with reference to fig. 1.

S1: as shown in fig. 2, the first-order RC equivalent model of the sample battery is established, the model has a simple structure and relatively small computational complexity, and the external characteristic equation of the first-order RC equivalent model is as follows:

wherein: r₁For polarizing internal resistance, tau₁Is a time constant, R₀Ohmic internal resistance;

based on a first-order RC equivalent model, a recursive least square method (FFRLS) with forgetting factors is used for parameter online identification, and in order to improve the reliability of the algorithm of the parameter online identification, polarization internal resistance R is used₁And time constant τ₁As a known parameter to estimate the ohmic internal resistance R of the sample cell₀And OCV, the algorithmic recursion process of online parameter identification is as follows:

wherein: y is_kIn order to output the vector for the system,for measurement vectors consisting of observations, θ_kFor the vector to be estimated containing the parameter to be estimated, e_kFor estimation error of system output, K_kTo gain, P_kThe method is characterized in that the method is a covariance matrix, lambda is a forgetting factor, and the value range of lambda is between 0 and 1 according to the definition;

meanwhile, according to an external characteristic equation of a first-order RC equivalent model, expressions of an output vector, an observation vector and a vector to be estimated in a recursive least squares (FFRLS) algorithm are respectively obtained as follows:

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

Based on the known parameter R of the sample cell₁And τ₁By looking up the current SOC table, R can be obtained_1,kAnd τ_1,kR is to be_1,kAnd τ_1,kSubstituting the parameters into a recursion formula for online identification to obtain the OCV, wherein the identification result is shown in FIG. 3, and the output equation of the OCV is as follows:

y_k＝U_1,k+U_t,k＝OCV_k-I_kR_0,k

wherein: u shape_1,kAnd U_t,kAs an output vector, I_kAs an observation vector, OCV_kAnd R_0,kIs the vector to be estimated.

S2: drawing a calibration curve graph of the relation between the SOC and the OCV, and substituting the OCV into the calibration curve graph to obtain a corresponding SOC;

s3: based on the method of accumulating electric energy between two points, a fitting curve chart of the relation between the electric energy and the SOC as shown in FIG. 4 is drawn according to the linear relation between the electric energy change during charging and discharging and the corresponding SOC change, and the SOC is substituted into the fitting curve chart to obtain a first capacity value C_batThe formula is as follows:

the above formula is transformed and merged into a matrix form:

Y＝X₀A+V

wherein: a ═ k, b]In order to obtain the coefficients to be calculated,v is a random error term;

under the condition of considering SOC error, the capacity estimation precision is improved by using weighted least square method (WRLS), and the capacity estimation precision is obtained by using weighted least square method (WRLS)

And obtain a corresponding slopeThe value of slope is the battery capacity C of the sample battery_batA first capacity value of, i.e.

As can be seen from the markov estimation in the weighted least square estimation, if the random error term V satisfies E (V) 0, E (V)^TV) is R, then when the weight W is R^-1And then, the variance of the SOC error is minimum, and the coefficient to be solved is as follows:

s4: obtaining a second capacity value C of the battery capacity of the sample battery through discretization Arrhenius life model estimation_capThe external characteristic equation of the discretized Arrhenius life model is as follows:

wherein ξ (n) is relative capacity decrement of the battery after n times of battery circulation, and has unit of%_aFor activation energy, the unit is J/mol; r is a gas constant and has the unit of J/(mol.k); t is the absolute temperature in K; n is the cycle number; z is an index. Parameters A, E of first order RC equivalent model_athe/R, z is to be obtained by a true result fit of the capacities of the sample cells at different stages of aging.

S5: using a Kalman Filter algorithm to measure the first capacity value C_batAnd a second capacity value C_capPerforming a fusion estimation, i.e. obtaining a first capacity value C at time k_bat(n_k) And a second capacity value C at time k_cap(n_k) And fusing by using a Kalman filter to obtain a third capacity value C of the battery capacity of the sample battery_D(n_k+1) And realizing the fused estimation of the capacity.

Specifically, step S5 is divided into the following steps:

S5₁the state variable time updates are as follows:

S5₂the error covariance time update is as follows:

S5₃the kalman gain matrix is updated as follows:

S5₄the state variable measurements are updated as follows:

S5₅the error covariance measurement is updated as follows:

while embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be taken as limiting the invention. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.