Last time, I shared a code for estimating SOC with extended Kalman filter, which got support from many friends. Today, I will share a very useful program for estimating SOC with extended Kalman filter. Use MATLAB language to complete the program writing.
For the derivation and principle of EKF, please see another blog I wrote: SOC estimation based on extended Kalman filter (with MATLAB code) article link: SOC estimation based on extended Kalman filter (with MATLAB code) Blog-CSDN blog_soc extended Kalman filter
Let's start the detailed analysis of the code:
1. Determination of sampling time, total step size, state vector, parameters P, Q, R. The state vector is set to a zero matrix with 3 rows and N columns. The covariance matrix P is set as an identity matrix, Q=0.1; R=0.1; the setting of this value is not fixed, and can be obtained by an optimization algorithm or adjusted based on experience.
T=1;%采样时间为1s
N=20042/T;%总步长
x=zeros(3,N);%定义状态向量x,定义一个3行N列的零矩阵。
x(:,1)=[0;0;1];%状态向量x初值设定
global P; %global 声明全局变量
P=eye(3);%定义协方差 EKF,生成一个3行3列的单位矩阵
Q=0.1;R=0.1;
global Q_1;2. Import current, voltage, SOC data, and set the battery capacity to 24Ah.
%ii(1,:)=I;uu(1,:)=Ub;soc(1,:)=SOC;%输入参数
i = xlsread('i.xlsx'); %读取电流数据
u = xlsread('v.xlsx'); %读取电压数据
soc1 = xlsread('soc.xlsx'); %读取soc数据
ii = i'; %将电流数据变成行向量
uu = u'; %将电压数据变成行向量
soc = soc1'; %将soc数据变成行向量
I = ii(1,:);Ub = uu(1,:);SOC = soc(1,:); %访问数组第一行的所有元素？？？
Cn=24;%电池容量3. Through the data fitting method, based on Matlab's curve fitting toolbox cftool combined with the parameters identified by hppc.
for i=2:N
R1=0.03023*x(3,i-1)^6-0.1141*x(3,i-1)^5+0.1689*x(3,i-1)^4-0.1243*x(3,i-1)^3+0.04728*x(3,i-1)^2-0.008527*x(3,i-1)+0.0006967;
R2=0.003971*x(3,i-1)^6-0.005341*x(3,i-1)^5-0.006872*x(3,i-1)^4+0.01435*x(3,i-1)^3-0.007282*x(3,i-1)^2+0.001231*x(3,i-1)+0.0002082;
C1=510100*x(3,i-1)^6-1276000*x(3,i-1)^5+1031000*x(3,i-1)^3-176300*x(3,i-1)^2+69310*x(3,i-1)+909;
C2=-12940000*x(3,i-1)^6+39640000*x(3,i-1)^5-45050000*x(3,i-1)^4+23320000*x(3,i-1)^3-5467000*x(3,i-1)^2+523200*x(3,i-1)+52340;
A=[1-(1/(R1*C1)) 0 0;0 1-(1/(R2*C2)) 0;0 0 1];%系数矩阵A 3行3列
B=[1/C1 1/C2 1/(3600*Cn)]';%系数矩阵B 3行1列
H=(66.48+54.18*ii(1,i-1))*x(3,i-1)^5-(127.9+196.8*ii(1,i-1))*x(3,i-1)^4+(70.16+262.88*ii(1,i-1))*x(3,i-1)^3-(3.48-163.38*ii(1,i-1))*x(3,i-1)^2....
-(4.58-48.42*ii(1,i-1))*x(3,i-1)-5.77*ii(1,i-1)+1.26; %求一阶泰勒近似
C=[1,1,H];%系数矩阵C 1行3列
if ii(1,:)>=0 %R0区分充放电来拟合，也是关于SOC的函数
R0=(-0.1313*x(3,i-1)^3+0.4812*x(3,i-1)^2-0.5452*x(3,i-1)+2.96)/1000;%充电时欧姆内阻三阶拟合,除1000表示毫Ω化Ω
else
R0=(9.033*x(3,i-1)^6-39.36*x(3,i-1)^5+65.72*x(3,i-1)^4-54.46*x(3,i-1)^3+24.21*x(3,i-1)^2 -5.774*x(3,i-1)+2.58)/1000;%放电时欧姆内阻6阶拟合 除1000表示毫Ω化Ω
end
Ppre=A*P*A'+eye(3)*Q;%协方差预测更新 3行3列
xpre(:,i-1)=A*x(:,i-1)+B*ii(1,i-1);%状态x的预测更新 3行1列 第一行为U1,；第二行为U2；第三行为SOC
Usoc=11.08*xpre(3,i-1)^6-25.58*xpre(3,i-1)^5+17.54*xpre(3,i-1)^4-1.159*xpre(3,i-1)^3-2.386*xpre(3,i-1)^2....
+1.263*xpre(3,i-1)+3.422;%开路电压Usoc是关于SOC的函数
K(:,i-1)=Ppre*C'*inv(C*Ppre*C'+R);%卡尔曼增益更新
Um(1,i-1)=Usoc+xpre(1,i-1)+xpre(2,i-1)+ii(1,i-1)*R0;%预测的电池端电压
e(1,i-1)=uu(1,i-1)-Um(1,i-1);%新息
x(:,i)=xpre(:,i-1)+K(:,i-1)*e(1,i-1);%状态的后验估计 / 状态估计测量更新
P=(eye(3)-K(:,i-1)*C)*Ppre;%协方差更新
end4. Drawing, through the plot command of MATLAB, draw the comparison diagram between the SOC estimated by EKF and the real SOC, as shown in Figure 1, and the error diagram of SOC is shown in Figure 2.
figure
hold on;box on;
plot(x(3,:),'r','Linewidth',5);
plot(soc(1,:),'b','Linewidth',5);
xlabel('time s');
ylabel('SOC');
figure
hold on;box on;
plot(soc(1,:)-x(3,:),'c','Linewidth',3);
Figure 1 Comparison of SOC estimated by EKF and real SOC
Figure 2 Error diagram of SOC
All the program codes during the master's and doctoral period are more than 2 g in total. I can give you guidance and give you a half-hour voice call to answer questions. Battery data + identification program + various Kalman filter algorithms are all in it, and new models will be updated in the future. Quick Start BMS Software. A goose: 2629471989