[go: up one dir, main page]

CN102289557B - Battery model parameter and residual battery capacity joint asynchronous online estimation method - Google Patents

Battery model parameter and residual battery capacity joint asynchronous online estimation method Download PDF

Info

Publication number
CN102289557B
CN102289557B CN 201110127479 CN201110127479A CN102289557B CN 102289557 B CN102289557 B CN 102289557B CN 201110127479 CN201110127479 CN 201110127479 CN 201110127479 A CN201110127479 A CN 201110127479A CN 102289557 B CN102289557 B CN 102289557B
Authority
CN
China
Prior art keywords
battery
estimation
model parameters
matrix
calculate
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN 201110127479
Other languages
Chinese (zh)
Other versions
CN102289557A (en
Inventor
何志伟
高明煜
曾毓
黄继业
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hangzhou Dianzi University
Original Assignee
Hangzhou Dianzi University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hangzhou Dianzi University filed Critical Hangzhou Dianzi University
Priority to CN 201110127479 priority Critical patent/CN102289557B/en
Publication of CN102289557A publication Critical patent/CN102289557A/en
Application granted granted Critical
Publication of CN102289557B publication Critical patent/CN102289557B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Landscapes

  • Secondary Cells (AREA)
  • Tests Of Electric Status Of Batteries (AREA)

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

Figure DEST_PATH_IMAGE002
时刻的电池端电压
Figure DEST_PATH_IMAGE004
和电池供电电流
Figure DEST_PATH_IMAGE006
,依据合理的电池模型,在合适的初始化基础上,首先基于
Figure DEST_PATH_IMAGE008
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
Figure 690356DEST_PATH_IMAGE002
时刻电池剩余电量的估计,然后利用
Figure 684987DEST_PATH_IMAGE002
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
Figure DEST_PATH_IMAGE002
battery terminal voltage at time
Figure DEST_PATH_IMAGE004
and battery supply current
Figure DEST_PATH_IMAGE006
, according to a reasonable battery model, on the basis of a suitable initialization, first based on
Figure DEST_PATH_IMAGE008
The estimated results of the battery model parameters at any time, using the sampling point Kalman filter algorithm
Figure 690356DEST_PATH_IMAGE002
time to estimate the remaining battery power, and then use the
Figure 684987DEST_PATH_IMAGE002
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

一种电池模型参数与剩余电量联合异步在线估计方法A joint asynchronous online estimation method of battery model parameters and remaining power

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                                                

Figure 2011101274791100002DEST_PATH_IMAGE001
时刻的电池端电压
Figure 261102DEST_PATH_IMAGE002
和电池供电电流
Figure 193024DEST_PATH_IMAGE004
。 Step (1) measure at
Figure 2011101274791100002DEST_PATH_IMAGE001
battery terminal voltage at time
Figure 261102DEST_PATH_IMAGE002
and battery supply current ,
Figure 193024DEST_PATH_IMAGE004
.

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:

Figure DEST_PATH_IMAGE005
Equation of state:
Figure DEST_PATH_IMAGE005

观测方程:

Figure 722225DEST_PATH_IMAGE006
Observation equation:
Figure 722225DEST_PATH_IMAGE006

其中

Figure DEST_PATH_IMAGE007
为电池的荷电状态,即剩余电量;
Figure 58922DEST_PATH_IMAGE008
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;
Figure 2011101274791100002DEST_PATH_IMAGE009
是电池在室温25
Figure 897434DEST_PATH_IMAGE010
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,
Figure DEST_PATH_IMAGE011
是测量时间间隔,
Figure 552537DEST_PATH_IMAGE012
为处理噪声。
Figure DEST_PATH_IMAGE013
为电池观测模型的参数,是一个列向量;为电池的内阻,
Figure DEST_PATH_IMAGE015
为观测噪声。 in
Figure DEST_PATH_IMAGE007
is the state of charge of the battery, that is, the remaining power;
Figure 58922DEST_PATH_IMAGE008
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;
Figure 2011101274791100002DEST_PATH_IMAGE009
is the battery at room temperature 25
Figure 897434DEST_PATH_IMAGE010
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,
Figure DEST_PATH_IMAGE011
is the measurement time interval,
Figure 552537DEST_PATH_IMAGE012
to deal with noise.
Figure DEST_PATH_IMAGE013
is the parameter of the battery observation model, which is a column vector; is the internal resistance of the battery,
Figure DEST_PATH_IMAGE015
is the observation noise.

放电比例系数

Figure 201267DEST_PATH_IMAGE008
的确定方法为: Discharge proportional coefficient
Figure 201267DEST_PATH_IMAGE008
The determination method is:

(a)将完全充满电的电池以不同放电速率

Figure 836779DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE017
Figure 477713DEST_PATH_IMAGE018
为电池的额定放电电流)恒流放电
Figure DEST_PATH_IMAGE019
次,计算相应放电速率下的电池总电量
Figure 551980DEST_PATH_IMAGE020
Figure DEST_PATH_IMAGE021
。 (a) Discharging a fully charged battery at different rates
Figure 836779DEST_PATH_IMAGE016
(
Figure DEST_PATH_IMAGE017
,
Figure 477713DEST_PATH_IMAGE018
is the rated discharge current of the battery) constant current discharge
Figure DEST_PATH_IMAGE019
times, calculate the total battery charge at the corresponding discharge rate
Figure 551980DEST_PATH_IMAGE020
,
Figure DEST_PATH_IMAGE021
.

(b)根据最小二乘方法拟合出

Figure 648287DEST_PATH_IMAGE020
Figure 454701DEST_PATH_IMAGE016
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
Figure DEST_PATH_IMAGE023
为最优系数。 (b) According to the least squares method fitting out
Figure 648287DEST_PATH_IMAGE020
and
Figure 454701DEST_PATH_IMAGE016
The quadratic curve relationship among them, that is, under the criterion of the minimum mean square error, it is found that both satisfies ,
Figure DEST_PATH_IMAGE023
is the optimal coefficient.

(c)在放电电流为

Figure 585522DEST_PATH_IMAGE003
时,对应的放电比例系数为: (c) When the discharge current is
Figure 585522DEST_PATH_IMAGE003
, the corresponding discharge proportional coefficient for:

   

Figure 335490DEST_PATH_IMAGE024
   
Figure 335490DEST_PATH_IMAGE024

此处,由于放电比例系数与电池老化等无关,因此,最优系数

Figure 577115DEST_PATH_IMAGE023
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
Figure 577115DEST_PATH_IMAGE023
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

Figure DEST_PATH_IMAGE025
及其方差
Figure 930867DEST_PATH_IMAGE026
分别为: initial state
Figure DEST_PATH_IMAGE025
and its variance
Figure 930867DEST_PATH_IMAGE026
They are:

Figure DEST_PATH_IMAGE027
Figure 685590DEST_PATH_IMAGE028
Figure DEST_PATH_IMAGE027
,
Figure 685590DEST_PATH_IMAGE028

处理噪声的方差

Figure DEST_PATH_IMAGE029
、观测噪声
Figure 625044DEST_PATH_IMAGE015
的方差分别为: deal with noise Variance
Figure DEST_PATH_IMAGE029
, observation noise
Figure 625044DEST_PATH_IMAGE015
Variance They are:

,

Figure 575737DEST_PATH_IMAGE032
,
Figure 575737DEST_PATH_IMAGE032

尺度参数为: Scale parameter for:

Figure 409701DEST_PATH_IMAGE034
Figure 409701DEST_PATH_IMAGE034

扩展后的状态向量

Figure DEST_PATH_IMAGE035
及其协方差
Figure 173389DEST_PATH_IMAGE036
为: The expanded state vector
Figure DEST_PATH_IMAGE035
and its covariance
Figure 173389DEST_PATH_IMAGE036
for:

Figure DEST_PATH_IMAGE037
Figure 118211DEST_PATH_IMAGE038
Figure DEST_PATH_IMAGE037
,
Figure 118211DEST_PATH_IMAGE038

均值加权系数和方差加权系数

Figure 785209DEST_PATH_IMAGE040
分别为: mean weighting factor and variance weighting coefficient
Figure 785209DEST_PATH_IMAGE040
They are:

Figure DEST_PATH_IMAGE041
Figure 603124DEST_PATH_IMAGE042
Figure DEST_PATH_IMAGE043
Figure DEST_PATH_IMAGE041
,
Figure 603124DEST_PATH_IMAGE042
,
Figure DEST_PATH_IMAGE043
,

(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

Figure DEST_PATH_IMAGE045
Choose the initial model parameters arbitrarily
Figure DEST_PATH_IMAGE045

设定

Figure 101156DEST_PATH_IMAGE046
的平方根均方差矩阵为
Figure DEST_PATH_IMAGE047
Figure 370463DEST_PATH_IMAGE048
;其中
Figure DEST_PATH_IMAGE049
Figure 296962DEST_PATH_IMAGE050
的单位矩阵; set up
Figure 101156DEST_PATH_IMAGE046
The square root mean square error matrix of is
Figure DEST_PATH_IMAGE047
,
Figure 370463DEST_PATH_IMAGE048
;in
Figure DEST_PATH_IMAGE049
for
Figure 296962DEST_PATH_IMAGE050
the identity matrix;

选取比例常数

Figure DEST_PATH_IMAGE051
,
Figure 284510DEST_PATH_IMAGE052
; Choose a constant of proportionality
Figure DEST_PATH_IMAGE051
,
Figure 284510DEST_PATH_IMAGE052
;

设定变量

Figure DEST_PATH_IMAGE053
; set variable
Figure DEST_PATH_IMAGE053
;

设定加权系数

Figure 885649DEST_PATH_IMAGE054
Figure DEST_PATH_IMAGE055
。 set weighting factor
Figure 885649DEST_PATH_IMAGE054
,
Figure DEST_PATH_IMAGE055
.

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

Figure 25774DEST_PATH_IMAGE004
,根据测得的电池端电压及电池的供电电流
Figure 519389DEST_PATH_IMAGE003
,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
Figure 25774DEST_PATH_IMAGE004
, according to the measured battery terminal voltage and battery supply current
Figure 519389DEST_PATH_IMAGE003
, 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

Figure 547388DEST_PATH_IMAGE056
时刻的扩展状态向量
Figure DEST_PATH_IMAGE057
及其协方差
Figure 40555DEST_PATH_IMAGE058
,计算该时刻的所有的采样点序列
Figure DEST_PATH_IMAGE059
: ① According to
Figure 547388DEST_PATH_IMAGE056
The extended state vector at time
Figure DEST_PATH_IMAGE057
and its covariance
Figure 40555DEST_PATH_IMAGE058
, calculate all the sampling point sequences at this moment
Figure DEST_PATH_IMAGE059
:

Figure 558124DEST_PATH_IMAGE060
Figure 558124DEST_PATH_IMAGE060

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

Figure 5417DEST_PATH_IMAGE059
,根据状态方程计算采样点更新
Figure DEST_PATH_IMAGE061
Figure 633845DEST_PATH_IMAGE062
sequence of sampling points
Figure 5417DEST_PATH_IMAGE059
, according to the state equation to calculate the sampling point update
Figure DEST_PATH_IMAGE061
:
Figure 633845DEST_PATH_IMAGE062

对采样点更新

Figure 261746DEST_PATH_IMAGE061
进行加权,计算状态估计
Figure DEST_PATH_IMAGE063
Figure 950216DEST_PATH_IMAGE064
Update the sampling point
Figure 261746DEST_PATH_IMAGE061
weighted to calculate the state estimate
Figure DEST_PATH_IMAGE063
:
Figure 950216DEST_PATH_IMAGE064

计算状态估计

Figure 71756DEST_PATH_IMAGE063
的方差
Figure DEST_PATH_IMAGE065
Figure 254607DEST_PATH_IMAGE066
Computing State Estimates
Figure 71756DEST_PATH_IMAGE063
Variance
Figure DEST_PATH_IMAGE065
:
Figure 254607DEST_PATH_IMAGE066

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

Figure 270153DEST_PATH_IMAGE056
时刻的参数估计值,根据观测方程计算测量更新
Figure 190574DEST_PATH_IMAGE068
Figure DEST_PATH_IMAGE069
updated by sample point and
Figure 270153DEST_PATH_IMAGE056
Estimated values of parameters at time , computing the measurement update from the observation equation
Figure 190574DEST_PATH_IMAGE068
:
Figure DEST_PATH_IMAGE069

对测量更新

Figure 160804DEST_PATH_IMAGE068
进行加权,计算测量估计
Figure 984534DEST_PATH_IMAGE070
Figure DEST_PATH_IMAGE071
Update on measurements
Figure 160804DEST_PATH_IMAGE068
weighting, calculation of measurement estimates
Figure 984534DEST_PATH_IMAGE070
:
Figure DEST_PATH_IMAGE071

计算测量估计

Figure 14807DEST_PATH_IMAGE070
的方差
Figure 110939DEST_PATH_IMAGE072
Figure DEST_PATH_IMAGE073
Calculate Measurement Estimate
Figure 14807DEST_PATH_IMAGE070
Variance
Figure 110939DEST_PATH_IMAGE072
:
Figure DEST_PATH_IMAGE073

计算

Figure 137058DEST_PATH_IMAGE061
的互协方差
Figure 203420DEST_PATH_IMAGE074
: 
Figure DEST_PATH_IMAGE075
calculate
Figure 137058DEST_PATH_IMAGE061
and cross-covariance of
Figure 203420DEST_PATH_IMAGE074
:
Figure DEST_PATH_IMAGE075

计算卡尔曼增益

Figure 599897DEST_PATH_IMAGE076
Figure DEST_PATH_IMAGE077
Calculate the Kalman gain
Figure 599897DEST_PATH_IMAGE076
:
Figure DEST_PATH_IMAGE077

计算状态更新 Compute Status Update :

计算状态更新

Figure 271105DEST_PATH_IMAGE078
的方差
Figure 580863DEST_PATH_IMAGE080
Figure DEST_PATH_IMAGE081
Compute Status Update
Figure 271105DEST_PATH_IMAGE078
Variance
Figure 580863DEST_PATH_IMAGE080
:
Figure DEST_PATH_IMAGE081

通过上述流程,所得到的状态更新值

Figure 464637DEST_PATH_IMAGE078
即为当前时刻
Figure 580360DEST_PATH_IMAGE001
所估计得到的电池剩余电量。 Through the above process, the obtained state update value
Figure 464637DEST_PATH_IMAGE078
the current moment
Figure 580360DEST_PATH_IMAGE001
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

Figure 420140DEST_PATH_IMAGE082
Figure DEST_PATH_IMAGE083
① Calculate the estimated value of the model parameters
Figure 420140DEST_PATH_IMAGE082
:
Figure DEST_PATH_IMAGE083

计算模型参数的平方根均方差矩阵的估计值

Figure 215314DEST_PATH_IMAGE084
Figure DEST_PATH_IMAGE085
,其中,
Figure DEST_PATH_IMAGE087
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
Figure 215314DEST_PATH_IMAGE084
:
Figure DEST_PATH_IMAGE085
,in, ,
Figure DEST_PATH_IMAGE087
is a column vector corresponding to the diagonal elements of the matrix.

②计算

Figure 302536DEST_PATH_IMAGE082
的采样点序列
Figure 996823DEST_PATH_IMAGE088
: ② calculation
Figure 302536DEST_PATH_IMAGE082
The sequence of sampling points
Figure 996823DEST_PATH_IMAGE088
:

Figure DEST_PATH_IMAGE089
Figure DEST_PATH_IMAGE089

Figure 225547DEST_PATH_IMAGE082
为6×1列向量,
Figure 67602DEST_PATH_IMAGE084
为6×6矩阵,故
Figure 462811DEST_PATH_IMAGE088
为6×13矩阵。
Figure 225547DEST_PATH_IMAGE082
is a 6×1 column vector,
Figure 67602DEST_PATH_IMAGE084
is a 6×6 matrix, so
Figure 462811DEST_PATH_IMAGE088
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

Figure 277183DEST_PATH_IMAGE090
Figure DEST_PATH_IMAGE091
Figure 975012DEST_PATH_IMAGE090
为6×13矩阵; Calculate the sequence of observations for the sampling points
Figure 277183DEST_PATH_IMAGE090
:
Figure DEST_PATH_IMAGE091
,
Figure 975012DEST_PATH_IMAGE090
is a 6×13 matrix;

计算观测序列

Figure 242045DEST_PATH_IMAGE090
的估计值
Figure DEST_PATH_IMAGE093
Figure 486655DEST_PATH_IMAGE094
Figure 480019DEST_PATH_IMAGE090
的第
Figure DEST_PATH_IMAGE095
列; Calculate the sequence of observations
Figure 242045DEST_PATH_IMAGE090
estimated value of :
Figure DEST_PATH_IMAGE093
,
Figure 486655DEST_PATH_IMAGE094
for
Figure 480019DEST_PATH_IMAGE090
First
Figure DEST_PATH_IMAGE095
List;

计算观测序列

Figure 47397DEST_PATH_IMAGE090
的平方根均方差矩阵
Figure 846726DEST_PATH_IMAGE096
: Calculate the sequence of observations
Figure 47397DEST_PATH_IMAGE090
The square root mean square error matrix of
Figure 846726DEST_PATH_IMAGE096
:

Figure DEST_PATH_IMAGE097
Figure DEST_PATH_IMAGE097

计算协方差矩阵

Figure 681696DEST_PATH_IMAGE098
Figure DEST_PATH_IMAGE099
; Compute the covariance matrix
Figure 681696DEST_PATH_IMAGE098
:
Figure DEST_PATH_IMAGE099
;

计算卡尔曼增益

Figure 173857DEST_PATH_IMAGE100
Figure DEST_PATH_IMAGE101
; Calculate the Kalman gain
Figure 173857DEST_PATH_IMAGE100
:
Figure DEST_PATH_IMAGE101
;

计算参数更新

Figure DEST_PATH_IMAGE103
; Calculation parameter update :
Figure DEST_PATH_IMAGE103
;

计算临时变量

Figure 565972DEST_PATH_IMAGE104
Figure DEST_PATH_IMAGE105
; Calculate temporary variable
Figure 565972DEST_PATH_IMAGE104
:
Figure DEST_PATH_IMAGE105
;

计算模型参数的平方根均方差矩阵的更新

Figure 512239DEST_PATH_IMAGE106
Figure DEST_PATH_IMAGE107
; Computes the update of the square root mean square error matrix of the model parameters
Figure 512239DEST_PATH_IMAGE106
:
Figure DEST_PATH_IMAGE107
;

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;

Figure DEST_PATH_IMAGE109
为矩阵的转置操作;
Figure 514010DEST_PATH_IMAGE110
表示求矩阵
Figure DEST_PATH_IMAGE111
的Cholesky分解。 in Represents the orthogonal triangular decomposition of the matrix and returns the obtained upper triangular matrix;
Figure DEST_PATH_IMAGE109
is the transpose operation of the matrix;
Figure 514010DEST_PATH_IMAGE110
Indicates seeking a matrix
Figure DEST_PATH_IMAGE111
Cholesky decomposition.

通过上述流程,所得到的

Figure 904409DEST_PATH_IMAGE102
即为当前时刻
Figure 402386DEST_PATH_IMAGE001
所估计得到的电池模型参数。 Through the above process, the obtained
Figure 904409DEST_PATH_IMAGE102
the current moment
Figure 402386DEST_PATH_IMAGE001
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

Figure 235027DEST_PATH_IMAGE004
。 Step (1) measure at battery terminal voltage at time and battery supply current ,
Figure 235027DEST_PATH_IMAGE004
.

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:

Figure 177575DEST_PATH_IMAGE005
Equation of state:
Figure 177575DEST_PATH_IMAGE005

观测方程:

Figure 677827DEST_PATH_IMAGE006
Observation equation:
Figure 677827DEST_PATH_IMAGE006

其中

Figure 98444DEST_PATH_IMAGE007
为电池的荷电状态,即剩余电量;
Figure 885528DEST_PATH_IMAGE008
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;
Figure 998977DEST_PATH_IMAGE009
是电池在室温25
Figure 924208DEST_PATH_IMAGE010
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,
Figure 210833DEST_PATH_IMAGE011
是测量时间间隔,
Figure 272330DEST_PATH_IMAGE012
为处理噪声。
Figure 369730DEST_PATH_IMAGE013
为电池观测模型的参数,是一个列向量;
Figure 782256DEST_PATH_IMAGE014
为电池的内阻,
Figure 810255DEST_PATH_IMAGE015
为观测噪声。 in
Figure 98444DEST_PATH_IMAGE007
is the state of charge of the battery, that is, the remaining power;
Figure 885528DEST_PATH_IMAGE008
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;
Figure 998977DEST_PATH_IMAGE009
is the battery at room temperature 25
Figure 924208DEST_PATH_IMAGE010
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,
Figure 210833DEST_PATH_IMAGE011
is the measurement time interval,
Figure 272330DEST_PATH_IMAGE012
to deal with noise.
Figure 369730DEST_PATH_IMAGE013
is the parameter of the battery observation model, which is a column vector;
Figure 782256DEST_PATH_IMAGE014
is the internal resistance of the battery,
Figure 810255DEST_PATH_IMAGE015
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

Figure 243828DEST_PATH_IMAGE016
Figure 143651DEST_PATH_IMAGE017
为电池的额定放电电流)恒流放电
Figure 323014DEST_PATH_IMAGE019
次,计算相应放电速率下的电池总电量
Figure 745905DEST_PATH_IMAGE020
Figure 133024DEST_PATH_IMAGE021
。 (a) Discharging a fully charged battery at different rates
Figure 243828DEST_PATH_IMAGE016
(
Figure 143651DEST_PATH_IMAGE017
, is the rated discharge current of the battery) constant current discharge
Figure 323014DEST_PATH_IMAGE019
times, calculate the total battery charge at the corresponding discharge rate
Figure 745905DEST_PATH_IMAGE020
,
Figure 133024DEST_PATH_IMAGE021
.

(b)根据最小二乘方法拟合出

Figure 502825DEST_PATH_IMAGE020
Figure 206470DEST_PATH_IMAGE016
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
Figure 3525DEST_PATH_IMAGE022
, 为最优系数。 (b) According to the least squares method fitting out
Figure 502825DEST_PATH_IMAGE020
and
Figure 206470DEST_PATH_IMAGE016
The quadratic curve relationship among them, that is, under the criterion of the minimum mean square error, it is found that both satisfies
Figure 3525DEST_PATH_IMAGE022
, is the optimal coefficient.

(c)在放电电流为

Figure 848170DEST_PATH_IMAGE003
时,对应的放电比例系数
Figure 858852DEST_PATH_IMAGE008
为: (c) When the discharge current is
Figure 848170DEST_PATH_IMAGE003
, the corresponding discharge proportional coefficient
Figure 858852DEST_PATH_IMAGE008
for:

   

Figure 141322DEST_PATH_IMAGE024
   
Figure 141322DEST_PATH_IMAGE024

此处,由于放电比例系数与电池老化等无关,因此,最优系数

Figure 237454DEST_PATH_IMAGE023
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
Figure 237454DEST_PATH_IMAGE023
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

Figure 949058DEST_PATH_IMAGE025
及其方差
Figure 876563DEST_PATH_IMAGE026
分别为: initial state
Figure 949058DEST_PATH_IMAGE025
and its variance
Figure 876563DEST_PATH_IMAGE026
They are:

Figure 15420DEST_PATH_IMAGE027
Figure 411897DEST_PATH_IMAGE028
Figure 15420DEST_PATH_IMAGE027
,
Figure 411897DEST_PATH_IMAGE028

处理噪声

Figure 661613DEST_PATH_IMAGE012
的方差
Figure 646887DEST_PATH_IMAGE029
、观测噪声
Figure 18962DEST_PATH_IMAGE015
的方差
Figure 89686DEST_PATH_IMAGE030
分别为: deal with noise
Figure 661613DEST_PATH_IMAGE012
Variance
Figure 646887DEST_PATH_IMAGE029
, observation noise
Figure 18962DEST_PATH_IMAGE015
Variance
Figure 89686DEST_PATH_IMAGE030
They are:

Figure 454677DEST_PATH_IMAGE031
,
Figure 454677DEST_PATH_IMAGE031
,

尺度参数为: Scale parameter for:

Figure 129875DEST_PATH_IMAGE034
Figure 129875DEST_PATH_IMAGE034

扩展后的状态向量

Figure 986973DEST_PATH_IMAGE035
及其协方差为: The expanded state vector
Figure 986973DEST_PATH_IMAGE035
and its covariance for:

Figure 145870DEST_PATH_IMAGE037
Figure 145870DEST_PATH_IMAGE037
,

均值加权系数

Figure 648712DEST_PATH_IMAGE039
和方差加权系数分别为: mean weighting factor
Figure 648712DEST_PATH_IMAGE039
and variance weighting coefficient They are:

Figure 867095DEST_PATH_IMAGE042
Figure 65995DEST_PATH_IMAGE043
Figure 531611DEST_PATH_IMAGE044
,
Figure 867095DEST_PATH_IMAGE042
,
Figure 65995DEST_PATH_IMAGE043
,
Figure 531611DEST_PATH_IMAGE044

(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

Figure 357933DEST_PATH_IMAGE046
的平方根均方差矩阵为
Figure 94945DEST_PATH_IMAGE047
Figure 618330DEST_PATH_IMAGE048
;其中
Figure 110491DEST_PATH_IMAGE049
Figure 86537DEST_PATH_IMAGE050
的单位矩阵; set up
Figure 357933DEST_PATH_IMAGE046
The square root mean square error matrix of is
Figure 94945DEST_PATH_IMAGE047
,
Figure 618330DEST_PATH_IMAGE048
;in
Figure 110491DEST_PATH_IMAGE049
for
Figure 86537DEST_PATH_IMAGE050
the identity matrix;

选取比例常数,Choose a constant of proportionality , ;

设定变量

Figure 917462DEST_PATH_IMAGE053
; set variable
Figure 917462DEST_PATH_IMAGE053
;

设定加权系数

Figure 708700DEST_PATH_IMAGE054
Figure 787515DEST_PATH_IMAGE055
。 set weighting factor
Figure 708700DEST_PATH_IMAGE054
,
Figure 787515DEST_PATH_IMAGE055
.

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

Figure 98542DEST_PATH_IMAGE004
,根据测得的电池端电压
Figure 604609DEST_PATH_IMAGE002
及电池的供电电流
Figure 820827DEST_PATH_IMAGE003
,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
Figure 98542DEST_PATH_IMAGE004
, according to the measured battery terminal voltage
Figure 604609DEST_PATH_IMAGE002
and battery supply current
Figure 820827DEST_PATH_IMAGE003
, 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

Figure 765649DEST_PATH_IMAGE056
时刻的扩展状态向量
Figure 118133DEST_PATH_IMAGE057
及其协方差,计算该时刻的所有的采样点序列
Figure 637349DEST_PATH_IMAGE059
: ① According to
Figure 765649DEST_PATH_IMAGE056
The extended state vector at time
Figure 118133DEST_PATH_IMAGE057
and its covariance , calculate all the sampling point sequences at this moment
Figure 637349DEST_PATH_IMAGE059
:

Figure 57966DEST_PATH_IMAGE060
Figure 57966DEST_PATH_IMAGE060

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

Figure 592853DEST_PATH_IMAGE059
,根据状态方程计算采样点更新
Figure 365954DEST_PATH_IMAGE062
sequence of sampling points
Figure 592853DEST_PATH_IMAGE059
, according to the state equation to calculate the sampling point update :
Figure 365954DEST_PATH_IMAGE062

对采样点更新

Figure 403311DEST_PATH_IMAGE061
进行加权,计算状态估计
Figure 730387DEST_PATH_IMAGE063
Figure 77055DEST_PATH_IMAGE064
Update the sampling point
Figure 403311DEST_PATH_IMAGE061
weighted to calculate the state estimate
Figure 730387DEST_PATH_IMAGE063
:
Figure 77055DEST_PATH_IMAGE064

计算状态估计的方差

Figure 745168DEST_PATH_IMAGE066
Computing State Estimates Variance :
Figure 745168DEST_PATH_IMAGE066

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

Figure 200420DEST_PATH_IMAGE061
Figure 162560DEST_PATH_IMAGE056
时刻的参数估计值
Figure 728671DEST_PATH_IMAGE067
,根据观测方程计算测量更新
Figure 764760DEST_PATH_IMAGE068
Figure 203962DEST_PATH_IMAGE069
updated by sample point
Figure 200420DEST_PATH_IMAGE061
and
Figure 162560DEST_PATH_IMAGE056
Estimated values of parameters at time
Figure 728671DEST_PATH_IMAGE067
, computing the measurement update from the observation equation
Figure 764760DEST_PATH_IMAGE068
:
Figure 203962DEST_PATH_IMAGE069

对测量更新进行加权,计算测量估计

Figure 757621DEST_PATH_IMAGE070
Figure 913795DEST_PATH_IMAGE071
Update on measurements weighting, calculation of measurement estimates
Figure 757621DEST_PATH_IMAGE070
:
Figure 913795DEST_PATH_IMAGE071

计算测量估计

Figure 710850DEST_PATH_IMAGE070
的方差
Figure 634200DEST_PATH_IMAGE072
Figure 807693DEST_PATH_IMAGE073
Calculate Measurement Estimate
Figure 710850DEST_PATH_IMAGE070
Variance
Figure 634200DEST_PATH_IMAGE072
:
Figure 807693DEST_PATH_IMAGE073

计算

Figure 880691DEST_PATH_IMAGE061
Figure 848647DEST_PATH_IMAGE068
的互协方差:  calculate
Figure 880691DEST_PATH_IMAGE061
and
Figure 848647DEST_PATH_IMAGE068
cross-covariance of :

计算卡尔曼增益

Figure 334620DEST_PATH_IMAGE076
Figure 473477DEST_PATH_IMAGE077
Calculate the Kalman gain
Figure 334620DEST_PATH_IMAGE076
:
Figure 473477DEST_PATH_IMAGE077

计算状态更新

Figure 119222DEST_PATH_IMAGE078
Compute Status Update
Figure 119222DEST_PATH_IMAGE078
:

计算状态更新

Figure 665796DEST_PATH_IMAGE078
的方差
Figure 975555DEST_PATH_IMAGE080
Figure 108596DEST_PATH_IMAGE081
Compute Status Update
Figure 665796DEST_PATH_IMAGE078
Variance
Figure 975555DEST_PATH_IMAGE080
:
Figure 108596DEST_PATH_IMAGE081

通过上述流程,所得到的状态更新值

Figure 162002DEST_PATH_IMAGE078
即为当前时刻
Figure 1782DEST_PATH_IMAGE001
所估计得到的电池剩余电量。 Through the above process, the obtained state update value
Figure 162002DEST_PATH_IMAGE078
the current moment
Figure 1782DEST_PATH_IMAGE001
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

Figure 295492DEST_PATH_IMAGE082
Figure 587933DEST_PATH_IMAGE083
① Calculate the estimated value of the model parameters
Figure 295492DEST_PATH_IMAGE082
:
Figure 587933DEST_PATH_IMAGE083

计算模型参数的平方根均方差矩阵的估计值

Figure 445030DEST_PATH_IMAGE084
Figure 201634DEST_PATH_IMAGE085
,其中,
Figure 167709DEST_PATH_IMAGE086
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
Figure 445030DEST_PATH_IMAGE084
:
Figure 201634DEST_PATH_IMAGE085
,in,
Figure 167709DEST_PATH_IMAGE086
, is a column vector corresponding to the diagonal elements of the matrix.

②计算

Figure 608235DEST_PATH_IMAGE082
的采样点序列
Figure 219345DEST_PATH_IMAGE088
: ② calculation
Figure 608235DEST_PATH_IMAGE082
The sequence of sampling points
Figure 219345DEST_PATH_IMAGE088
:

Figure 307386DEST_PATH_IMAGE089
Figure 307386DEST_PATH_IMAGE089

Figure 387469DEST_PATH_IMAGE082
为6×1列向量,为6×6矩阵,故
Figure 989669DEST_PATH_IMAGE088
为6×13矩阵。
Figure 387469DEST_PATH_IMAGE082
is a 6×1 column vector, is a 6×6 matrix, so
Figure 989669DEST_PATH_IMAGE088
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

Figure 310928DEST_PATH_IMAGE090
Figure 799679DEST_PATH_IMAGE091
Figure 802270DEST_PATH_IMAGE090
为6×13矩阵; Calculate the sequence of observations for the sampling points
Figure 310928DEST_PATH_IMAGE090
:
Figure 799679DEST_PATH_IMAGE091
,
Figure 802270DEST_PATH_IMAGE090
is a 6×13 matrix;

计算观测序列

Figure 637239DEST_PATH_IMAGE090
的估计值
Figure 105447DEST_PATH_IMAGE093
Figure 646150DEST_PATH_IMAGE094
Figure 24041DEST_PATH_IMAGE090
的第
Figure 437836DEST_PATH_IMAGE095
列; Calculate the sequence of observations
Figure 637239DEST_PATH_IMAGE090
estimated value of :
Figure 105447DEST_PATH_IMAGE093
,
Figure 646150DEST_PATH_IMAGE094
for
Figure 24041DEST_PATH_IMAGE090
First
Figure 437836DEST_PATH_IMAGE095
List;

计算观测序列

Figure 901179DEST_PATH_IMAGE090
的平方根均方差矩阵
Figure 307889DEST_PATH_IMAGE096
: Calculate the sequence of observations
Figure 901179DEST_PATH_IMAGE090
The square root mean square error matrix of
Figure 307889DEST_PATH_IMAGE096
:

Figure 805867DEST_PATH_IMAGE097
Figure 805867DEST_PATH_IMAGE097

计算协方差矩阵

Figure 311934DEST_PATH_IMAGE098
; Compute the covariance matrix
Figure 311934DEST_PATH_IMAGE098
: ;

计算卡尔曼增益

Figure 725172DEST_PATH_IMAGE100
Figure 139972DEST_PATH_IMAGE101
; Calculate the Kalman gain
Figure 725172DEST_PATH_IMAGE100
:
Figure 139972DEST_PATH_IMAGE101
;

计算参数更新

Figure 816941DEST_PATH_IMAGE102
Figure 254876DEST_PATH_IMAGE103
; Calculation parameter update
Figure 816941DEST_PATH_IMAGE102
:
Figure 254876DEST_PATH_IMAGE103
;

计算临时变量

Figure 961112DEST_PATH_IMAGE105
; Calculate temporary variable :
Figure 961112DEST_PATH_IMAGE105
;

计算模型参数的平方根均方差矩阵的更新

Figure 136878DEST_PATH_IMAGE106
Figure 62109DEST_PATH_IMAGE107
; Computes the update of the square root mean square error matrix of the model parameters
Figure 136878DEST_PATH_IMAGE106
:
Figure 62109DEST_PATH_IMAGE107
;

其中

Figure 286417DEST_PATH_IMAGE108
表示求矩阵的正交三角分解,并返回得到的上三角矩阵;
Figure 925078DEST_PATH_IMAGE109
为矩阵的转置操作;
Figure 209428DEST_PATH_IMAGE110
表示求矩阵
Figure 418693DEST_PATH_IMAGE111
的Cholesky分解。 in
Figure 286417DEST_PATH_IMAGE108
Represents the orthogonal triangular decomposition of the matrix, and returns the obtained upper triangular matrix;
Figure 925078DEST_PATH_IMAGE109
is the transpose operation of the matrix;
Figure 209428DEST_PATH_IMAGE110
Indicates seeking a matrix
Figure 418693DEST_PATH_IMAGE111
Cholesky decomposition.

通过上述流程,所得到的

Figure 446692DEST_PATH_IMAGE102
即为当前时刻
Figure 628274DEST_PATH_IMAGE001
所估计得到的电池模型参数。 Through the above process, the obtained
Figure 446692DEST_PATH_IMAGE102
the current moment
Figure 628274DEST_PATH_IMAGE001
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.

Claims (1)

1.一种电池模型参数与剩余电量联合异步在线估计方法,其特征在于该方法的具体步骤是:1. A joint asynchronous online estimation method of battery model parameters and residual power, characterized in that the specific steps of the method are: 步骤(1)测量在k时刻的电池端电压yk和电池供电电流ik,k=1,2,3,…;Step (1) Measure the battery terminal voltage y k and the battery supply current i k at time k , k=1,2,3,...; 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: z k + 1 = f ( z k , i k ) + w k = z k - ( &eta; i &Delta;t Q n ) i k + w k Equation of state: z k + 1 = f ( z k , i k ) + w k = z k - ( &eta; i &Delta;t Q no ) i k + w k 观测方程: y k = g ( z k , i k ; p k ) + v k = K 0 - Ri k - K 1 z k - K 2 z k + K 3 ln z k + K 4 ln ( 1 - z k ) + v k Observation equation: the y k = g ( z k , i k ; p k ) + v k = K 0 - Ri k - K 1 z k - K 2 z k + K 3 ln z k + K 4 ln ( 1 - z k ) + v k == 11 -- ii kk -- 11 zz kk -- zz kk lnln zz kk lnln (( 11 -- zz kk )) &CenterDot;&Center Dot; pp kk 其中z为电池的荷电状态,即剩余电量;ηi为电池的放电比例系数,反映的是放电速率、温度因素对电池SOC的影响程度,本发明中只考虑放电速率的影响;Qn是电池在室温25°C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,Δt是测量时间间隔,wk为处理噪声;pk=[K0 R K1 K2 K3 K4]T为电池观测模型的参数,是一个列向量;R为电池的内阻,vk为观测噪声;Wherein z is the state of charge of the battery, i.e. the remaining power; η i is the discharge proportional coefficient of the battery, which reflects the degree of influence of the discharge rate and temperature factors on the battery SOC, and only considers the impact of the discharge rate in the present invention; Q n is The rated total power that can be obtained when the battery is discharged at a discharge rate of 1/30 times the rated current at a room temperature of 25°C, Δt is the measurement time interval, w k is the processing noise; p k =[K 0 R K 1 K 2 K 3 K 4 ] T is the parameter of the battery observation model, which is a column vector; R is the internal resistance of the battery, and v k is the observation noise; 放电比例系数ηi的确定方法为:The method of determining the discharge proportional coefficient η i is: (a)将完全充满电的电池以不同放电速率Ci恒流放电N次,计算相应放电速率下的电池总电量Qi,1≤i≤N,0<Ci≤C,N>10,C为电池的额定放电电流;(a) Discharge the fully charged battery N times at a constant current at different discharge rates C i , and calculate the total battery capacity Q i at the corresponding discharge rate, 1≤i≤N, 0<C i ≤C, N>10, C is the rated discharge current of the battery; (b)根据最小二乘方法拟合出Qi与Ci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
Figure FDA00003110207600014
a,b,c为最优系数;
(b) According to the least squares method, the quadratic curve relationship between Q i and C i is fitted, that is, under the criterion of minimum mean square error, it is found that both satisfies
Figure FDA00003110207600014
a, b, c are optimal coefficients;
(c)在放电电流为ik时,对应的放电比例系数ηi为:(c) When the discharge current is i k , the corresponding discharge proportional coefficient η i is: &eta;&eta; ii == QQ nno aiai kk 22 ++ bibi kk ++ cc 此处,由于放电比例系数与电池老化无关,因此最优系数a,b,c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, the optimal coefficients a, b, and c only need to be determined once for the same type of battery, and can be directly used as known constants to estimate the remaining power of all batteries of the same type after determination; 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
Figure FDA000031102076000213
及其方差P0分别为:
initial state
Figure FDA000031102076000213
and its variance P 0 are:
zz ^^ 00 ++ 100100 %% ,, PP 00 == varvar (( zz 00 )) == 1010 -- 22 处理噪声wk的方差Rw、观测噪声vk的方差Rv分别为:The variance R w of processing noise w k and the variance R v of observation noise v k are respectively: Rw=10-5,Rv=10-2 R w =10 -5 , R v =10 -2 尺度参数γ为:The scale parameter γ is: &gamma;&gamma; == 33 扩展后的状态向量
Figure FDA00003110207600024
及其协方差
Figure FDA00003110207600025
为:
The expanded state vector
Figure FDA00003110207600024
and its covariance
Figure FDA00003110207600025
for:
zz ^^ kk aa == zz kk 00 00 TT ,, PP kk aa == PP kk 00 00 00 RR ww 00 00 00 RR vv 均值加权系数
Figure FDA00003110207600027
i=0,1,2,...,6和方差加权系数
Figure FDA00003110207600028
i=0,1,2,...,6分别为:
mean weighting factor
Figure FDA00003110207600027
i=0,1,2,...,6 and variance weighting coefficient
Figure FDA00003110207600028
i=0,1,2,...,6 are:
w z 0 ( m ) = 0 , w z 0 ( c ) = 2 , w z i ( m ) = w z i ( c ) = 1 / 6 , 1≤i≤6 w z 0 ( m ) = 0 , w z 0 ( c ) = 2 , w z i ( m ) = w z i ( c ) = 1 / 6 , 1≤i≤6 (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
Figure FDA000031102076000212
Choose the initial model parameters arbitrarily
Figure FDA000031102076000212
设定p0的平方根均方差矩阵为Sp0,Sp0=I6,其中I6为6×6的单位矩阵;Set the square root mean square error matrix of p 0 as S p0 , S p0 =I 6 , where I 6 is a 6×6 identity matrix; 选取比例常数h,h>1;Select the constant of proportionality h, h>1; 设定变量 R r = 10 - 3 I 6 ; set variable R r = 10 - 3 I 6 ; 设定加权系数 W p 0 ( m ) = h 2 - 7 h 2 , W p j ( m ) = 1 2 h 2 , W p j ( c 1 ) = 1 2 h , W p j ( c 2 ) = h 2 - 1 2 h 2 , j=1,2,…,12;set weighting factor W p 0 ( m ) = h 2 - 7 h 2 , W p j ( m ) = 1 2 h 2 , W p j ( c 1 ) = 1 2 h , W p j ( c 2 ) = h 2 - 1 2 h 2 , j=1,2,...,12; 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k=1,2,3,…,根据测得的电池端电压yk及电池的供电电流ik,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 time k=1, 2, 3,..., according to the measured battery terminal voltage y k and the battery supply current ik , iteratively perform the joint asynchronous estimation of battery model parameters and remaining power 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k-1时刻的扩展状态向量
Figure FDA00003110207600036
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 k-1
Figure FDA00003110207600036
and its covariance Calculate all the sampling point sequences at this moment
Figure FDA00003110207600039
Figure FDA00003110207600039
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
Figure FDA000031102076000310
根据状态方程计算采样点更新
Figure FDA000031102076000311
Figure FDA000031102076000312
sequence of sampling points
Figure FDA000031102076000310
Compute sample point updates from state equations
Figure FDA000031102076000311
Figure FDA000031102076000312
对采样点更新
Figure FDA000031102076000313
进行加权,计算状态估计
Figure FDA000031102076000314
Update the sampling point
Figure FDA000031102076000313
weighted to calculate the state estimate
Figure FDA000031102076000314
计算状态估计
Figure FDA000031102076000315
的方差
Figure FDA000031102076000316
Figure FDA000031102076000317
Computing State Estimates
Figure FDA000031102076000315
Variance
Figure FDA000031102076000316
Figure FDA000031102076000317
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
Figure FDA000031102076000318
及k-1时刻的参数估计值
Figure FDA000031102076000319
根据观测方程计算测量更新
updated by sample point
Figure FDA000031102076000318
And the estimated value of the parameter at time k-1
Figure FDA000031102076000319
Calculate measurement updates from observation equations
对测量更新
Figure FDA000031102076000324
进行加权,计算测量估计
Update on measurements
Figure FDA000031102076000324
weighting, calculation of measurement estimates
计算测量估计
Figure FDA000031102076000322
的方差
Figure FDA000031102076000323
Calculate Measurement Estimate
Figure FDA000031102076000322
Variance
Figure FDA000031102076000323
计算
Figure FDA00003110207600042
的互协方差
Figure FDA000031102076000431
calculate and
Figure FDA00003110207600042
cross-covariance of
Figure FDA000031102076000431
计算卡尔曼增益Kk Compute the Kalman gain K k : 计算状态更新 z ^ k = z k - + K k ( y k - y ^ k - ) ; Compute Status Update z ^ k = z k - + K k ( the y k - the y ^ k - ) ; 计算状态更新
Figure FDA00003110207600046
的方差
Figure FDA00003110207600047
Compute Status Update
Figure FDA00003110207600046
Variance
Figure FDA00003110207600047
通过上述流程,所得到的状态更新值
Figure FDA00003110207600048
即为当前时刻k所估计得到的电池剩余电量;
Through the above process, the obtained state update value
Figure FDA00003110207600048
That is, the remaining battery power estimated by k at the current moment;
(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
Figure FDA00003110207600049
① Calculate the estimated value of the model parameters
Figure FDA00003110207600049
计算模型参数的平方根均方差矩阵的估计值
Figure FDA000031102076000410
其中, D r k - 1 = - diag { S p k - 1 } + diag { S p k - 1 } 2 + diag { R r } , diag{·}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
Figure FDA000031102076000410
in, D. r k - 1 = - diag { S p k - 1 } + diag { S p k - 1 } 2 + diag { R r } , diag{ } is a column vector composed of diagonal elements of the corresponding matrix;
②计算
Figure FDA000031102076000412
的采样点序列
② calculation
Figure FDA000031102076000412
The sequence of sampling points
Figure FDA000031102076000414
Figure FDA000031102076000414
Figure FDA000031102076000415
为6×1列向量,
Figure FDA000031102076000416
为6×6矩阵,故
Figure FDA000031102076000417
为6×13矩阵;
Figure FDA000031102076000415
is a 6×1 column vector,
Figure FDA000031102076000416
is a 6×6 matrix, so
Figure FDA000031102076000417
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
Figure FDA000031102076000418
Figure FDA000031102076000419
为6×13矩阵;
Calculate the sequence of observations for the sampling points
Figure FDA000031102076000418
Figure FDA000031102076000419
is a 6×13 matrix;
计算观测序列
Figure FDA000031102076000420
的估计值
Figure FDA000031102076000421
Figure FDA000031102076000422
Figure FDA000031102076000423
的第j列;
Calculate the sequence of observations
Figure FDA000031102076000420
estimated value of
Figure FDA000031102076000421
Figure FDA000031102076000422
for
Figure FDA000031102076000423
column j of
计算观测序列
Figure FDA000031102076000424
的平方根均方差矩阵
Figure FDA000031102076000425
Calculate the sequence of observations
Figure FDA000031102076000424
The square root mean square error matrix of
Figure FDA000031102076000425
计算协方差矩阵
Figure FDA000031102076000430
Compute the covariance matrix
Figure FDA000031102076000430
计算卡尔曼增益K′k K k &prime; = ( P p k d k / S d ~ k T ) / S d ~ k ; Compute the Kalman gain K′ k : K k &prime; = ( P p k d k / S d ~ k T ) / S d ~ k ; 计算参数更新 p ^ k : p ^ k = p ^ k - + K k &prime; ( y k - d ^ k - ) ; Calculation parameter update p ^ k : p ^ k = p ^ k - + K k &prime; ( the y k - d ^ k - ) ; 计算临时变量U:
Figure FDA00003110207600052
Compute the temporary variable U:
Figure FDA00003110207600052
计算模型参数的平方根均方差矩阵的更新
Figure FDA00003110207600057
Computes the update of the square root mean square error matrix of the model parameters
Figure FDA00003110207600057
:
SS pp kk == cholupdatecholupdate {{ SS pp kk -- ,, Uu ,, -- 11 }} ;; 其中qr{·}表示求矩阵的正交三角分解,并返回得到的上三角矩阵;(·)T为矩阵的转置操作;
Figure FDA00003110207600054
表示求矩阵
Figure FDA00003110207600055
的Cholesky分解;
Where qr{ } means to find the orthogonal triangular decomposition of the matrix, and return the obtained upper triangular matrix; ( ) T is the transpose operation of the matrix;
Figure FDA00003110207600054
Indicates seeking a matrix
Figure FDA00003110207600055
The Cholesky decomposition of;
通过上述流程,所得到的
Figure FDA00003110207600056
即为当前时刻k所估计得到的电池模型参数;
Through the above process, the obtained
Figure FDA00003110207600056
That is, the battery model parameters estimated at the current moment k;
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 remaining power of the battery estimated at each moment is completed; the entire cyclic recursion process is completed online, that is, the estimation of the remaining battery power at each time and the estimation of the battery model parameters are completed online and asynchronously during the actual working process of the battery.
CN 201110127479 2011-05-17 2011-05-17 Battery model parameter and residual battery capacity joint asynchronous online estimation method Expired - Fee Related CN102289557B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN 201110127479 CN102289557B (en) 2011-05-17 2011-05-17 Battery model parameter and residual battery capacity joint asynchronous online estimation method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN 201110127479 CN102289557B (en) 2011-05-17 2011-05-17 Battery model parameter and residual battery capacity joint asynchronous online estimation method

Publications (2)

Publication Number Publication Date
CN102289557A CN102289557A (en) 2011-12-21
CN102289557B true CN102289557B (en) 2013-08-07

Family

ID=45335981

Family Applications (1)

Application Number Title Priority Date Filing Date
CN 201110127479 Expired - Fee Related CN102289557B (en) 2011-05-17 2011-05-17 Battery model parameter and residual battery capacity joint asynchronous online estimation method

Country Status (1)

Country Link
CN (1) CN102289557B (en)

Families Citing this family (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102298118A (en) * 2011-05-17 2011-12-28 杭州电子科技大学 On-line synchronous estimating method for model parameters and remaining power of battery
CN102928783B (en) * 2012-07-19 2014-09-03 北京金山安全软件有限公司 Method and device for estimating available time of battery power and mobile equipment
CN103077291B (en) * 2013-01-25 2016-05-18 华北电力大学 The battery charge and discharge process digital simulation method of initial state-of-charge can be set
CN103995464B (en) * 2014-05-26 2016-04-13 北京理工大学 A kind ofly estimate the parameter of the power system of electric vehicle and the method for state
CN107122578A (en) * 2016-02-23 2017-09-01 林德(中国)叉车有限公司 A kind of accurate method for calculating forklift battery dump energy
CN107421543B (en) * 2017-06-22 2020-06-05 北京航空航天大学 Implicit function measurement model filtering method based on state dimension expansion
CN108318823B (en) * 2017-12-28 2020-06-02 上海交通大学 Lithium battery state of charge estimation method based on noise tracking
CN108008320B (en) * 2017-12-28 2020-03-17 上海交通大学 Lithium ion battery state of charge and model parameter self-adaptive joint estimation method
CN109375111A (en) * 2018-10-12 2019-02-22 杭州电子科技大学 A UHF-based method for estimating remaining battery power
CN109782177B (en) * 2018-12-29 2021-04-20 北京新能源汽车股份有限公司 Method and device for acquiring electric quantity of battery and automobile
CN109975739B (en) * 2019-04-11 2021-01-08 宁夏隆基宁光仪表股份有限公司 High-precision intelligent electric energy meter debugging and measuring method
CN110161423A (en) * 2019-06-26 2019-08-23 重庆大学 A kind of dynamic lithium battery state joint estimation method based on various dimensions coupling model
CN118665273B (en) * 2024-06-18 2024-12-27 淮阴工学院 A battery equalization method and system based on gas-liquid thermal coupling model

Family Cites Families (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000075967A (en) * 1998-08-27 2000-03-14 Matsushita Electric Ind Co Ltd Battery level evaluation method and apparatus for portable personal computer
CN101212071B (en) * 2006-12-31 2011-07-06 比亚迪股份有限公司 Method for estimating charge state of power cell
CN100492751C (en) * 2007-03-09 2009-05-27 清华大学 Estimation method of state of charge of Ni-MH power battery based on standard battery model
JP5038258B2 (en) * 2008-08-25 2012-10-03 日本電信電話株式会社 Remaining capacity estimation method and remaining capacity estimation apparatus
CN101604005B (en) * 2009-06-29 2011-04-13 杭州电子科技大学 Estimation method of battery dump energy based on combined sampling point Kalman filtering
CN101598769B (en) * 2009-06-29 2011-04-20 杭州电子科技大学 Method for estimating remaining capacity of battery based on sampling points Kalman filtering
CN101625397B (en) * 2009-08-06 2011-04-06 杭州电子科技大学 Mixed rapid estimation method for residual energy of battery

Also Published As

Publication number Publication date
CN102289557A (en) 2011-12-21

Similar Documents

Publication Publication Date Title
CN102289557B (en) Battery model parameter and residual battery capacity joint asynchronous online estimation method
CN101604005B (en) Estimation method of battery dump energy based on combined sampling point Kalman filtering
CN101625397B (en) Mixed rapid estimation method for residual energy of battery
CN101598769B (en) Method for estimating remaining capacity of battery based on sampling points Kalman filtering
CN102169168B (en) Battery dump energy estimation method based on particle filtering
CN111722118B (en) Lithium ion battery SOC estimation method based on SOC-OCV optimization curve
CN103020445B (en) A kind of SOC and SOH Forecasting Methodology of electric-vehicle-mounted ferric phosphate lithium cell
CN105717460B (en) A kind of power battery SOC methods of estimation and system based on nonlinear observer
CN102680795B (en) Real-time on-line estimation method for internal resistance of secondary battery
CN110824363B (en) Lithium battery SOC and SOE joint estimation method based on improved CKF
CN110261779A (en) A kind of ternary lithium battery charge state cooperates with estimation method with health status online
CN108761340A (en) The battery evaluation method of strong tracking volume Kalman filtering based on noise jamming
CN109633479B (en) On-line estimation method of lithium battery SOC based on embedded volumetric Kalman filter
CN107402353A (en) A kind of state-of-charge to lithium ion battery is filtered the method and system of estimation
CN103529398A (en) On-line SOC Estimation Method of Li-ion Battery Based on Extended Kalman Filter
CN102645637A (en) Method for estimating SOC (state of charge) of equalized batteries
CN105699910A (en) Method for on-line estimating residual electric quantity of lithium battery
CN110795851A (en) Lithium ion battery modeling method considering environmental temperature influence
CN111707953A (en) An online SOC estimation method for lithium batteries based on a backward smoothing filter framework
CN106772067A (en) The method that Multiple Time Scales IAPF filters estimated driving force battery charge state and health status
CN106772081A (en) Battery limit charging and discharging current estimation method based on extended equivalent circuit model
CN105093129B (en) A kind of energy-storage battery residual capacity detection method
CN110687462A (en) A joint estimation method of power battery SOC and capacity full life cycle
CN109375111A (en) A UHF-based method for estimating remaining battery power
CN110095723A (en) A kind of Li-ion battery model parameter and SOC online joint estimation method

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant
EE01 Entry into force of recordation of patent licensing contract

Application publication date: 20111221

Assignee: SOYEA TECHNOLOGY Co.,Ltd.

Assignor: HANGZHOU DIANZI University

Contract record no.: X2019330000056

Denomination of invention: Battery model parameter and residual battery capacity joint asynchronous online estimation method

Granted publication date: 20130807

License type: Common License

Record date: 20191226

EE01 Entry into force of recordation of patent licensing contract
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20130807

CF01 Termination of patent right due to non-payment of annual fee