CN102289557B - Battery model parameter and residual battery capacity joint asynchronous online estimation method - Google Patents
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Abstract
本发明涉及一种电池模型参数与剩余电量联合异步在线估计方法。现有方法一般都假设同类型的电池其内阻等参数基本不变,因此难以克服由于电池老化对电池剩余电量估计精度的影响。本发明方法通过测量在时刻的电池端电压和电池供电电流,依据合理的电池模型,在合适的初始化基础上,首先基于时刻电池模型参数的估计结果,采用采样点卡尔曼滤波算法进行时刻电池剩余电量的估计,然后利用时刻所估计出的电池剩余电量,采用采样点卡尔曼滤波算法完成电池模型参数的估计。电池剩余电量与电池模型参数的估计异步交替在线完成。本发明方法可以方便地进行电池剩余电量的在线估计,收敛速度快、估计精度高,受电池老化影响较小。The invention relates to a combined asynchronous online estimation method of battery model parameters and remaining power. Existing methods generally assume that the internal resistance and other parameters of the same type of battery are basically unchanged, so it is difficult to overcome the impact of battery aging on the estimation accuracy of the remaining battery power. The method of the present invention is measured in battery terminal voltage at time and battery supply current , according to a reasonable battery model, on the basis of a suitable initialization, first based on The estimated results of the battery model parameters at any time, using the sampling point Kalman filter algorithm time to estimate the remaining battery power, and then use the The remaining battery power estimated at the time is estimated by the sampling point Kalman filter algorithm to complete the estimation of the battery model parameters. The estimation of remaining battery power and battery model parameters is done asynchronously and alternately online. The method of the invention can conveniently perform on-line estimation of battery remaining power, has fast convergence speed, high estimation precision, and is less affected by battery aging.
Description
技术领域 technical field
本发明属于电池技术领域,具体涉及一种电池模型参数与剩余电量联合异步在线估计方法。 The invention belongs to the technical field of batteries, and in particular relates to a combined asynchronous online estimation method of battery model parameters and remaining power.
背景技术 Background technique
电池作为备用电源已在通讯、电力系统、军事装备等领域得到了广泛的应用。同传统燃油汽车相比,电动汽车可实现零排放,因此是未来汽车的主要发展方向。在电动汽车中电池直接作为主动能量供给部件,因此其工作状态的好坏直接关系到整个汽车的行驶安全性和运行可靠性。为确保电动汽车中的电池组性能良好,延长电池组使用寿命,须及时、准确地了解电池的运行状态,对电池进行合理有效的管理和控制。 As a backup power source, batteries have been widely used in communications, power systems, military equipment and other fields. Compared with traditional fuel vehicles, electric vehicles can achieve zero emissions, so they are the main development direction of future vehicles. In an electric vehicle, the battery is directly used as an active energy supply component, so its working condition is directly related to the driving safety and operational reliability of the entire vehicle. In order to ensure the good performance of the battery pack in electric vehicles and prolong the service life of the battery pack, it is necessary to know the operating status of the battery in a timely and accurate manner, and manage and control the battery reasonably and effectively.
电池荷电状态(State of Charge,以下简称SOC)的精确估算是电池能量管理系统中最核心的技术。电池的SOC无法用一种传感器直接测得,它必须通过对一些其他物理量的测量,并采用一定的数学模型和算法来估计得到。 The accurate estimation of the battery state of charge (State of Charge, hereinafter referred to as SOC) is the core technology in the battery energy management system. The SOC of the battery cannot be directly measured by a sensor, it must be estimated by measuring some other physical quantities and using certain mathematical models and algorithms.
目前常用的电池SOC估计方法有开路电压法、安时法等。开路电压法进行电池SOC估计时电池必须静置较长时间以达到稳定状态,而且只适用于电动汽车在停车状态下的SOC估计,不能满足在线检测要求。安时法易受到电流测量精度的影响,在高温或电流波动剧烈情况下,精度很差。另一方面,已有方法一般都假设同类型的电池其内阻等参数基本不变,从而对同一类型电池进行SOC估计时均采用同一组模型参数,这种假设在电池没有发生老化时往往是成立的,但是当电池老化较严重时,电池内阻等会发生较大的变化,此时再基于原有模型参数进行SOC估计势必会发生较大程度的偏差。 At present, the commonly used battery SOC estimation methods include the open circuit voltage method and the ampere-hour method. When the battery SOC is estimated by the open circuit voltage method, the battery must stand for a long time to reach a stable state, and it is only suitable for the SOC estimation of the electric vehicle in the parking state, which cannot meet the requirements of online detection. The ampere-hour method is easily affected by the accuracy of current measurement, and the accuracy is very poor in the case of high temperature or severe current fluctuation. On the other hand, the existing methods generally assume that the internal resistance and other parameters of the same type of battery are basically unchanged, so that the same set of model parameters are used to estimate the SOC of the same type of battery, which is often the case when the battery is not aging. However, when the battery aging is serious, the internal resistance of the battery will change greatly. At this time, the SOC estimation based on the original model parameters will inevitably have a large degree of deviation.
发明内容 Contents of the invention
本发明的目的就是克服现有技术的不足,提出一种电池模型参数与剩余电量联合异步在线估计方法,在在线估计出电池SOC的同时,可以对模型参数进行联合异步在线估计,从而克服由于电池老化带来的电池参数变化对电池SOC估计准确性的影响。本发明方法可以适用于所有电池,且估计精度较高。 The purpose of the present invention is to overcome the deficiencies of the prior art, and propose a method for joint asynchronous online estimation of battery model parameters and remaining power. The impact of battery parameter changes brought about by aging on the accuracy of battery SOC estimation. The method of the invention can be applied to all batteries, and has high estimation accuracy.
本发明的电池模型参数与剩余电量联合异步在线估计方法,具体步骤是: The specific steps of the combined asynchronous online estimation method of battery model parameters and remaining power in the present invention are as follows:
步骤(1)测量在 时刻的电池端电压和电池供电电流,。 Step (1) measure at battery terminal voltage at time and battery supply current , .
步骤(2)用状态方程和观测方程表示电池的各个时刻的荷电状态依赖关系: Step (2) Use the state equation and the observation equation to express the state-of-charge dependence of the battery at each moment:
状态方程: Equation of state:
观测方程: Observation equation:
其中为电池的荷电状态,即剩余电量;为电池的放电比例系数,反映的是放电速率、温度等因素对电池SOC的影响程度,本发明中只考虑放电速率的影响;是电池在室温25条件下、以1/30倍额定电流的放电速率放电时所能得到的额定总电量,是测量时间间隔,为处理噪声。为电池观测模型的参数,是一个列向量;为电池的内阻,为观测噪声。 in is the state of charge of the battery, that is, the remaining power; is the discharge proportional coefficient of the battery, which reflects the degree of influence of factors such as discharge rate and temperature on the SOC of the battery, and only the influence of the discharge rate is considered in the present invention; is the battery at room temperature 25 The rated total electricity that can be obtained when discharging at a discharge rate of 1/30 times the rated current under the specified conditions, is the measurement time interval, to deal with noise. is the parameter of the battery observation model, which is a column vector; is the internal resistance of the battery, is the observation noise.
放电比例系数的确定方法为: Discharge proportional coefficient The determination method is:
(a)将完全充满电的电池以不同放电速率(,为电池的额定放电电流)恒流放电次,计算相应放电速率下的电池总电量,。 (a) Discharging a fully charged battery at different rates ( , is the rated discharge current of the battery) constant current discharge times, calculate the total battery charge at the corresponding discharge rate , .
(b)根据最小二乘方法拟合出与间的二次曲线关系,即在最小均方误差准则下求出同时满足,为最优系数。 (b) According to the least squares method fitting out and The quadratic curve relationship among them, that is, under the criterion of the minimum mean square error, it is found that both satisfies , is the optimal coefficient.
(c)在放电电流为时,对应的放电比例系数为: (c) When the discharge current is , the corresponding discharge proportional coefficient for:
此处,由于放电比例系数与电池老化等无关,因此,最优系数对于同一类型的电池只需确定一次,确定后可作为已知常数直接用于所有同类型电池的剩余电量估计。 Here, since the discharge proportional coefficient has nothing to do with battery aging, etc., the optimal coefficient For the battery of the same type, it only needs to be determined once, and after determination, it can be directly used as a known constant to estimate the remaining power of all batteries of the same type.
步骤(3)执行如下初始化过程: Step (3) performs the following initialization process:
(a)电池剩余电量估计的初始化: (a) Initialization of battery remaining power estimation:
起始状态及其方差分别为: initial state and its variance They are:
, ,
处理噪声的方差、观测噪声的方差分别为: deal with noise Variance , observation noise Variance They are:
, ,
尺度参数为: Scale parameter for:
扩展后的状态向量及其协方差为: The expanded state vector and its covariance for:
, ,
均值加权系数和方差加权系数分别为: mean weighting factor and variance weighting coefficient They are:
,,, , , ,
(b)电池模型参数估计的初始化: (b) Initialization of battery model parameter estimation:
任意选取初始模型参数 Choose the initial model parameters arbitrarily
设定的平方根均方差矩阵为,;其中为的单位矩阵; set up The square root mean square error matrix of is , ;in for the identity matrix;
选取比例常数,; Choose a constant of proportionality , ;
设定变量; set variable ;
设定加权系数,。 set weighting factor , .
步骤(4)采用采样点卡尔曼滤波算法进行循环递推: Step (4) adopts sampling point Kalman filtering algorithm to carry out loop recursion:
在时刻,根据测得的电池端电压及电池的供电电流,按下列步骤迭代进行电池模型参数与剩余电量的联合异步估计: at the moment , according to the measured battery terminal voltage and battery supply current , perform the joint asynchronous estimation of the battery model parameters and the remaining power iteratively according to the following steps:
(a)电池剩余电量的估计流程 (a) Estimation process of remaining battery capacity
①根据时刻的扩展状态向量及其协方差,计算该时刻的所有的采样点序列: ① According to The extended state vector at time and its covariance , calculate all the sampling point sequences at this moment :
②根据状态方程进行时间域更新: ②Update in the time domain according to the state equation:
由采样点序列,根据状态方程计算采样点更新: sequence of sampling points , according to the state equation to calculate the sampling point update :
对采样点更新进行加权,计算状态估计: Update the sampling point weighted to calculate the state estimate :
计算状态估计的方差: Computing State Estimates Variance :
③根据观测方程完成测量更新: ③Complete the measurement update according to the observation equation:
由采样点更新及时刻的参数估计值,根据观测方程计算测量更新: updated by sample point and Estimated values of parameters at time , computing the measurement update from the observation equation :
对测量更新进行加权,计算测量估计: Update on measurements weighting, calculation of measurement estimates :
计算测量估计的方差: Calculate Measurement Estimate Variance :
计算与的互协方差: calculate and cross-covariance of :
计算卡尔曼增益: Calculate the Kalman gain :
计算状态更新: Compute Status Update :
计算状态更新的方差: Compute Status Update Variance :
通过上述流程,所得到的状态更新值即为当前时刻所估计得到的电池剩余电量。 Through the above process, the obtained state update value the current moment Estimated remaining battery charge.
(b)电池模型参数的估计流程: (b) Estimation process of battery model parameters:
①计算模型参数的估计值: ① Calculate the estimated value of the model parameters :
计算模型参数的平方根均方差矩阵的估计值:,其中,,为对应矩阵的对角线元素构成的列向量。 Computes an estimate of the square root mean square error matrix of the model parameters : ,in, , is a column vector corresponding to the diagonal elements of the matrix.
②计算的采样点序列: ② calculation The sequence of sampling points :
为6×1列向量,为6×6矩阵,故为6×13矩阵。 is a 6×1 column vector, is a 6×6 matrix, so It is a 6×13 matrix.
③按下列各式计算测量更新: ③ Calculate the measurement update according to the following formula:
计算采样点的观测序列:,为6×13矩阵; Calculate the sequence of observations for the sampling points : , is a 6×13 matrix;
计算观测序列的估计值:,为的第列; Calculate the sequence of observations estimated value of : , for First List;
计算观测序列的平方根均方差矩阵: Calculate the sequence of observations The square root mean square error matrix of :
计算协方差矩阵:; Compute the covariance matrix : ;
计算卡尔曼增益:; Calculate the Kalman gain : ;
计算参数更新:; Calculation parameter update : ;
计算临时变量:; Calculate temporary variable : ;
计算模型参数的平方根均方差矩阵的更新:; Computes the update of the square root mean square error matrix of the model parameters : ;
其中表示求矩阵的正交三角分解,并返回得到的上三角矩阵;为矩阵的转置操作;表示求矩阵的Cholesky分解。 in Represents the orthogonal triangular decomposition of the matrix and returns the obtained upper triangular matrix; is the transpose operation of the matrix; Indicates seeking a matrix Cholesky decomposition.
通过上述流程,所得到的即为当前时刻所估计得到的电池模型参数。 Through the above process, the obtained the current moment The estimated battery model parameters.
在每一时刻,上述步骤4(a)、4(b)交替进行,因此,电池剩余电量的估计依赖于上一时刻电池模型参数的估计结果,另一方面,电池模型参数的估计则基于当前时刻所估计得到的电池剩余电量完成。整个循环递推过程是在线完成的,即在电池实际工作过程中在线异步完成各时刻电池剩余电量的估计与电池模型参数的估计。 At each moment, the above-mentioned steps 4(a) and 4(b) are carried out alternately. Therefore, the estimation of the remaining battery capacity depends on the estimation result of the battery model parameters at the previous moment. On the other hand, the estimation of the battery model parameters is based on the current The time to estimate the remaining battery power is completed. The whole cyclic recursion process is completed online, that is, the estimation of the remaining power of the battery at each moment and the estimation of the parameters of the battery model are completed online and asynchronously during the actual working process of the battery.
本发明可以方便地进行电池SOC的快速估计,且可以克服电池老化对模型参数的影响。该方法收敛速度快,估计精度高,而且适用于各种电池SOC的快速估计。 The invention can conveniently perform fast estimation of battery SOC, and can overcome the influence of battery aging on model parameters. This method has fast convergence speed and high estimation accuracy, and is suitable for fast estimation of SOC of various batteries.
根据本发明的第一方面,公开了一种用于电池模型参数与剩余电量联合异步在线估计方法所依赖的测量量,分别为电池的端电压和电池的供电电流。 According to the first aspect of the present invention, a method for joint asynchronous online estimation of battery model parameters and remaining power is disclosed. The measured quantities are respectively the terminal voltage of the battery and the supply current of the battery.
根据本发明的第二方面,公开了一种用于电池模型参数与剩余电量联合异步在线估计方法中的状态方程和观测方程。 According to the second aspect of the present invention, a state equation and an observation equation used in a combined asynchronous online estimation method of battery model parameters and remaining power are disclosed.
根据本发明的第三方面,公开了一种用于电池模型参数与剩余电量联合异步在线估计方法所依赖的初始值。包括电池剩余电量估计的初始化值及电池模型参数估计的初始值等。这些初始值不必很准确,在采样点卡尔曼滤波的后续迭代过程中它们会很快收敛到真实值附近。 According to the third aspect of the present invention, an initial value used for the combined asynchronous online estimation method of battery model parameters and remaining power is disclosed. Including the initialization value of the remaining battery capacity estimation and the initial value of the battery model parameter estimation, etc. These initial values do not have to be very accurate, and they will quickly converge to near the true value during the subsequent iterations of the sampling point Kalman filter.
根据本发明的第四方面,公开了一种应用采样点卡尔曼滤波迭代进行电池模型参数与电池剩余电量联合异步在线估计的具体流程。电池剩余电量的估计依赖于上一时刻电池模型参数的估计结果,而电池模型参数的估计则基于当前时刻所估计得到的电池剩余电量完成,两种估计流程交替异步进行。 According to the fourth aspect of the present invention, it discloses a specific process for performing joint asynchronous online estimation of battery model parameters and remaining battery power by applying sampling point Kalman filter iteratively. The estimation of the remaining battery power depends on the estimation result of the battery model parameters at the previous moment, while the estimation of the battery model parameters is completed based on the estimated remaining battery power at the current moment, and the two estimation processes are carried out alternately and asynchronously.
具体实施方式 Detailed ways
电池模型参数与剩余电量联合异步在线估计方法,具体步骤是: The joint asynchronous online estimation method of battery model parameters and remaining power, the specific steps are:
步骤(1)测量在时刻的电池端电压和电池供电电流,。 Step (1) measure at battery terminal voltage at time and battery supply current , .
步骤(2)用状态方程和观测方程表示电池的各个时刻的荷电状态依赖关系: Step (2) Use the state equation and the observation equation to express the state-of-charge dependence of the battery at each moment:
状态方程: Equation of state:
观测方程: Observation equation:
其中为电池的荷电状态,即剩余电量;为电池的放电比例系数,反映的是放电速率、温度等因素对电池SOC的影响程度,本发明中只考虑放电速率的影响;是电池在室温25条件下、以1/30倍额定电流的放电速率放电时所能得到的额定总电量,是测量时间间隔,为处理噪声。为电池观测模型的参数,是一个列向量;为电池的内阻,为观测噪声。 in is the state of charge of the battery, that is, the remaining power; is the discharge proportional coefficient of the battery, which reflects the degree of influence of factors such as discharge rate and temperature on the SOC of the battery, and only the influence of the discharge rate is considered in the present invention; is the battery at room temperature 25 The rated total electricity that can be obtained when discharging at a discharge rate of 1/30 times the rated current under the specified conditions, is the measurement time interval, to deal with noise. is the parameter of the battery observation model, which is a column vector; is the internal resistance of the battery, is the observation noise.
放电比例系数的确定方法为: Discharge proportional coefficient The determination method is:
(a)将完全充满电的电池以不同放电速率(,为电池的额定放电电流)恒流放电次,计算相应放电速率下的电池总电量,。 (a) Discharging a fully charged battery at different rates ( , is the rated discharge current of the battery) constant current discharge times, calculate the total battery charge at the corresponding discharge rate , .
(b)根据最小二乘方法拟合出与间的二次曲线关系,即在最小均方误差准则下求出同时满足, 为最优系数。 (b) According to the least squares method fitting out and The quadratic curve relationship among them, that is, under the criterion of the minimum mean square error, it is found that both satisfies , is the optimal coefficient.
(c)在放电电流为时,对应的放电比例系数为: (c) When the discharge current is , the corresponding discharge proportional coefficient for:
此处,由于放电比例系数与电池老化等无关,因此,最优系数对于同一类型的电池只需确定一次,确定后可作为已知常数直接用于所有同类型电池的剩余电量估计。 Here, since the discharge proportional coefficient has nothing to do with battery aging, etc., the optimal coefficient For the battery of the same type, it only needs to be determined once, and after determination, it can be directly used as a known constant to estimate the remaining power of all batteries of the same type.
步骤(3)执行如下初始化过程: Step (3) performs the following initialization process:
(a)电池剩余电量估计的初始化: (a) Initialization of battery remaining power estimation:
起始状态及其方差分别为: initial state and its variance They are:
, ,
处理噪声的方差、观测噪声的方差分别为: deal with noise Variance , observation noise Variance They are:
, ,
尺度参数为: Scale parameter for:
扩展后的状态向量及其协方差为: The expanded state vector and its covariance for:
, ,
均值加权系数和方差加权系数分别为: mean weighting factor and variance weighting coefficient They are:
,,, , , ,
(b)电池模型参数估计的初始化: (b) Initialization of battery model parameter estimation:
任意选取初始模型参数 Choose the initial model parameters arbitrarily
设定的平方根均方差矩阵为,;其中为的单位矩阵; set up The square root mean square error matrix of is , ;in for the identity matrix;
选取比例常数,; Choose a constant of proportionality , ;
设定变量; set variable ;
设定加权系数,。 set weighting factor , .
步骤(4)采用采样点卡尔曼滤波算法进行循环递推: Step (4) adopts sampling point Kalman filtering algorithm to carry out loop recursion:
在时刻,根据测得的电池端电压及电池的供电电流,按下列步骤迭代进行电池模型参数与剩余电量的联合异步估计: at the moment , according to the measured battery terminal voltage and battery supply current , perform the joint asynchronous estimation of the battery model parameters and the remaining power iteratively according to the following steps:
(a)电池剩余电量的估计流程 (a) Estimation process of remaining battery capacity
①根据时刻的扩展状态向量及其协方差,计算该时刻的所有的采样点序列: ① According to The extended state vector at time and its covariance , calculate all the sampling point sequences at this moment :
②根据状态方程进行时间域更新: ②Update in the time domain according to the state equation:
由采样点序列,根据状态方程计算采样点更新: sequence of sampling points , according to the state equation to calculate the sampling point update :
对采样点更新进行加权,计算状态估计: Update the sampling point weighted to calculate the state estimate :
计算状态估计的方差: Computing State Estimates Variance :
③根据观测方程完成测量更新: ③Complete the measurement update according to the observation equation:
由采样点更新及时刻的参数估计值,根据观测方程计算测量更新: updated by sample point and Estimated values of parameters at time , computing the measurement update from the observation equation :
对测量更新进行加权,计算测量估计: Update on measurements weighting, calculation of measurement estimates :
计算测量估计的方差: Calculate Measurement Estimate Variance :
计算与的互协方差: calculate and cross-covariance of :
计算卡尔曼增益: Calculate the Kalman gain :
计算状态更新: Compute Status Update :
计算状态更新的方差: Compute Status Update Variance :
通过上述流程,所得到的状态更新值即为当前时刻所估计得到的电池剩余电量。 Through the above process, the obtained state update value the current moment Estimated remaining battery charge.
(b)电池模型参数的估计流程: (b) Estimation process of battery model parameters:
①计算模型参数的估计值: ① Calculate the estimated value of the model parameters :
计算模型参数的平方根均方差矩阵的估计值:,其中,,为对应矩阵的对角线元素构成的列向量。 Computes an estimate of the square root mean square error matrix of the model parameters : ,in, , is a column vector corresponding to the diagonal elements of the matrix.
②计算的采样点序列: ② calculation The sequence of sampling points :
为6×1列向量,为6×6矩阵,故为6×13矩阵。 is a 6×1 column vector, is a 6×6 matrix, so It is a 6×13 matrix.
③按下列各式计算测量更新: ③ Calculate the measurement update according to the following formula:
计算采样点的观测序列:,为6×13矩阵; Calculate the sequence of observations for the sampling points : , is a 6×13 matrix;
计算观测序列的估计值:,为的第列; Calculate the sequence of observations estimated value of : , for First List;
计算观测序列的平方根均方差矩阵: Calculate the sequence of observations The square root mean square error matrix of :
计算协方差矩阵:; Compute the covariance matrix : ;
计算卡尔曼增益:; Calculate the Kalman gain : ;
计算参数更新:; Calculation parameter update : ;
计算临时变量:; Calculate temporary variable : ;
计算模型参数的平方根均方差矩阵的更新:; Computes the update of the square root mean square error matrix of the model parameters : ;
其中表示求矩阵的正交三角分解,并返回得到的上三角矩阵;为矩阵的转置操作;表示求矩阵的Cholesky分解。 in Represents the orthogonal triangular decomposition of the matrix, and returns the obtained upper triangular matrix; is the transpose operation of the matrix; Indicates seeking a matrix Cholesky decomposition.
通过上述流程,所得到的即为当前时刻所估计得到的电池模型参数。 Through the above process, the obtained the current moment The estimated battery model parameters.
在每一时刻,上述步骤4(a)、4(b)交替进行,因此,电池剩余电量的估计依赖于上一时刻电池模型参数的估计结果,另一方面,电池模型参数的估计则基于当前时刻所估计得到的电池剩余电量完成。整个循环递推过程是在线完成的,即在电池实际工作过程中在线异步完成各时刻电池剩余电量的估计与电池模型参数的估计。 At each moment, the above-mentioned steps 4(a) and 4(b) are carried out alternately. Therefore, the estimation of the remaining battery capacity depends on the estimation result of the battery model parameters at the previous moment. On the other hand, the estimation of the battery model parameters is based on the current The time to estimate the remaining battery power is completed. The whole cyclic recursion process is completed online, that is, the estimation of the remaining power of the battery at each moment and the estimation of the parameters of the battery model are completed online and asynchronously during the actual working process of the battery.
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