What are the crucial parameters that are to considered in the state space model while estimating the state of charge of batteries ?

Here estimation of charge is carried out using extended Kalman filtering, I am unclear how do we model the uncertainties involving the battery , howto incorporate them in our state space ekf model for estimation.

I am unable to get a correct estimation. I am using Matlab scripting to realize the EKF. I am not sure why the script fails to estimate accurately

How do we choose noise parameter Q and R here.

Kindly someone explain to me what exactly is to be considered in these places.

%For this filter I use: %x: state vector, containing the state of charge (%) and a voltage (V) %I_meas: current measures %U_meas: voltage measures %h_est: voltage prediction %f: state function, giving its values to x %Loading of the measures data = SimData;%csvread('Measurements.csv'); % Opens of the measures file %len=size(data,1); % Number of data samples len=size(SimData)-5000; time=data(:,1)-5000; % 2nd column of the file: time U_meas=data(:,4); % 5th column: voltage I_meas=data(:,3); % 6th column: current

% Circuit and measure variables of electric battery model eta=1; % Coulombic efficiency: 1 for discharge, <1 for charge tau_Diff=L_Rdiff*L_Cd; % [s] Time constant of the RC ladder Cnom=18; % [Ah] Battery capacity dt=time(2)-time(1); %dt=1;

% Uncertainties initialization n=2; % Number of states: x(1):SoC, x(2):V_Diff q=0.2979; % Stdiv of process (voltage) % is it standard deviation or variance of the or the whole terminal voltage itself r=4.0028; % Stdiv of measurement (current)% is it the current as a whole to be considered or error current Q=q^2*eye(n); % Covariance of process R=r^2; % Covariance of measurement

% Initial states x_k_1 = [100;3.4910]; % Initial state: Soc=100%, U=0 P_k_1 = eye(n); % Initial state covariance

% OCV(SoC) model %how do we choose the right model i used poly fit\poly % trend OCV=@(socm)((3.82 * 10^-10) * socm^5 - (1.21 * 10^-7) * socm^4 + (1.51 * 10^-5) * socm^3 - (9.3 * 10^-4) * socm^2 + (0.0295* socm) + 2.85); %L_VOC = a8 * M_SOC.^8 + a7 * M_SOC.^7 +a6 * M_SOC.^6 + a5 * M_SOC.^5 + a4 * M_SOC.^4 + a3 * M_SOC.^3 + a2 * M_SOC.^2 + a1 * M_SOC.^1 + a0 % Function definition matrices Ak=[1 0;0 exp(-dt*eta/(L_Rdiff*L_Cd))]; Bk=[-dt*eta/L_Cd;L_Rdiff(1-exp(-dt/L_Rdiff*L_Cd))];

% Main loop

for k=1:len

    % Observation function
    h_est=@(x)(OCV(x(1))-((I_meas(k)*Ini_Ri)-x(2)));

    % State prediction function
    f=@(x)(Ak*x+Bk*I_meas(k));

    % *** START OF EKF ***

        % Calculation of the Jacobians
        [x1,A]=jaccsd(f,x_k_1); % Constant value 
        [z1,H]=jaccsd(h_est,x1); % Varies with OCV(SoC)

        % *** PREDICTION ***

        x_k_ = Ak*x_k_1+Bk*I_meas(k); 

        % Prediction of the plant covariance
        P_k_ = Ak*P_k_1*(Ak)' + Q;

        % *** UPDATE ***

        % Kalman gain
        K = P_k_*H'*inv(H*P_k_*H'+R);

        % Update estimate with measurement U_meas 
        x_k = x_k_ + K*(U_meas(k)-h_est(x_k_));

        % Update the error covariance
          P_k = (eye(n)-K*H)*P_k_;

    % *** END OF EKF ***

    % STORING OF VALUES

    x_store(k,:)=x_k;
    x_store_(k,:)=x_k_;
    h_store(k)=h_est(x_k_);

    % PREPARATION OF THE VARIABLES FOR THE NEXT K

     x_k_1=x_k;
     P_k_1=P_k;

if(k<(len-1)) dt=time(k+1)-time(k); end if (dt==0) if (k>1) dt=(time(k-1)+time(k+1))/2; else dt=1; jk = jk+1; end end

end

% Results plot

% State of charge figure(1) subplot(3,1,1) plot(time,data(:,2),time,x_store(:,1)) title('State of Charge') h_legend = legend('Actual value','Update',2); set(h_legend,'Interpreter','none')

% I current subplot(3,1,2) plot(time,I_meas,'-') title('I: battery current')

% U voltage subplot(3,1,3) plot(time,U_meas,'-',time,h_store,'--') title('U: battery voltage')

Error = x_store(:,1) - data(:,2); variance = var(Error)

% figure(2) % subplot(3,1,1) % plot(time,data(:,2),time,x_store(:,1)) % title('State of Charge') % h_legend = legend('Actual value','Update',2); % set(h_legend,'Interpreter','none') % % % error % subplot(2,1,2) % plot(time,Error,'-',variance,'***'); % title('Error and Variance')

Answer 1

[Sabin]

A good place to start is Simscape Battery. Check out the SOC Estimator (Kalman Filter) doc page for more insights into how the estimator is designed.

https://www.mathworks.com/help/simscape-battery/ref/socestimatorkalmanfilter.html