Solver stopped prematurely. fsolve stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 2.000000e+02.
13 views (last 30 days)
Show older comments
I want to solve a system of equations containing two non-linear equations, one of which is Psh==Pse,the other is Qs==0, but solving it with the fsolve function doesn't achieve the given constraints, how can I solve this problem?
V_s=10*1e3/sqrt(3);
n_t=25*sqrt(3);
V_r=400/sqrt(3);
theta_r=pi/12;
Srate=100*1e3/3;
Zbase=(V_r)^2/Srate;
X_r=0.4*Zbase;
X_t=400^2/(150*1e3)*4/100;
rho=0:2*pi/24:2*pi;
V_se=0.2*V_r;
Z_r=j*X_r;
for m=1:25
fun=@(x)myfun(x,rho(m));
x0=[0 0];
[x,fval,exitflag(m),~]=fsolve(fun,x0);
gamma(m)=x(1);
I_sh(m)=x(2);
I_r(m)=1/(Z_r+j*X_t)*(sqrt(3)*V_s*exp(j*pi/6)/n_t+V_se*exp(j*rho(m))-V_r*exp(j*theta_r)-j*X_t*I_sh(m)*exp(j*gamma(m)));
V_c1(m)=sqrt(3)*V_s*exp(j*pi/6)/n_t-j*X_t*(I_sh(m)*exp(j*gamma(m))+I_r(m));
Psh(m)=real(V_c1(m)*conj(I_sh(m)*exp(j*gamma(m))));
Pse(m)=real(V_se*exp(j*rho(m))*conj(I_r(m)));
Pr(m)=real(V_r*exp(j*theta_r)*conj(I_r(m)));
Qr(m)=imag(V_r*exp(j*theta_r)*conj(I_r(m)));
Sr(m)=sqrt(Pr(m)^2+Qr(m)^2);
Ps(m)=real(sqrt(3)*V_s*exp(j*pi/6)/n_t*conj(I_r(m)+I_sh(m)*exp(j*gamma(m))));
Qs(m)=imag(sqrt(3)*V_s*exp(j*pi/6)/n_t*conj(I_r(m)+I_sh(m)*exp(j*gamma(m))));
Ss(m)=sqrt(Ps(m)^2+Qs(m)^2);
end
plot( Ps/Srate,Qs/Srate,LineWidth=2,color='[0.9290 0.6940 0.1250]')
function y=myfun(x,rho)
V_s=10*1e3/sqrt(3);
n_t=25*sqrt(3);
V_r=400/sqrt(3);
theta_r=pi/12;
Srate=100*1e3/3;
Zbase=(V_r)^2/Srate;
X_r=0.4*Zbase;
X_t=400^2/(150*1e3)*4/100;
V_se=0.2*V_r;
Z_r=j*X_r;
%%%%%%%%%%%%%%%%Two constraints,Psh==Pse,Qs==0
gamma=x(1);
I_sh=x(2);
I_r=1/(Z_r+j*X_t)*(sqrt(3)*V_s*exp(j*pi/6)/n_t+V_se*exp(j*rho)-V_r*exp(j*theta_r)-j*X_t*I_sh*exp(j*gamma));
V_c1=sqrt(3)*V_s*exp(j*pi/6)/n_t-j*X_t*(I_sh*exp(j*gamma)+I_r);
Psh=real(V_c1*conj(I_sh*exp(j*gamma)));
Pse=real(V_se*exp(j*rho)*conj(I_r));
Qs=imag(sqrt(3)*V_s*exp(j*pi/6)/n_t*conj(I_r+I_sh*exp(j*gamma)));
y=[Psh-Pse; Qs];
end
0 Comments
Accepted Answer
Anagha Mittal
on 24 Jul 2024
Hi,
"fsolve" function is not giving you the desired solution as it is not able to handle the constraints. I would rather suggest to use "fmincon" function. I have made a few changes in your code accordingly, please take a look below:
% Given constants
V_s = 10*1e3/sqrt(3);
n_t = 25*sqrt(3);
V_r = 400/sqrt(3);
theta_r = pi/12;
Srate = 100*1e3/3;
Zbase = (V_r)^2/Srate;
X_r = 0.4*Zbase;
X_t = 400^2/(150*1e3)*4/100;
rho = 0:2*pi/24:2*pi;
V_se = 0.2*V_r;
Z_r = 1i * X_r;
% Initial guess
x0 = [0 0];
% Options for fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'iter');
% Constraints
lb = [];
ub = [];
% Solve for each rho
for m = 1:25
% Define the nonlinear constraint function
fun = @(x) myfun(x, rho(m));
% Use fmincon to solve the problem
[x, fval, exitflag(m), output] = fmincon(@(x) 0, x0, [], [], [], [], lb, ub, fun, options);
% Extract solutions
gamma(m) = x(1);
I_sh(m) = x(2);
% Compute derived quantities
I_r(m) = 1 / (Z_r + 1i * X_t) * (sqrt(3) * V_s * exp(1i * pi/6) / n_t + V_se * exp(1i * rho(m)) - V_r * exp(1i * theta_r) - 1i * X_t * I_sh(m) * exp(1i * gamma(m)));
V_c1(m) = sqrt(3) * V_s * exp(1i * pi/6) / n_t - 1i * X_t * (I_sh(m) * exp(1i * gamma(m)) + I_r(m));
Psh(m) = real(V_c1(m) * conj(I_sh(m) * exp(1i * gamma(m))));
Pse(m) = real(V_se * exp(1i * rho(m)) * conj(I_r(m)));
Pr(m) = real(V_r * exp(1i * theta_r) * conj(I_r(m)));
Qr(m) = imag(V_r * exp(1i * theta_r) * conj(I_r(m)));
Sr(m) = sqrt(Pr(m)^2 + Qr(m)^2);
Ps(m) = real(sqrt(3) * V_s * exp(1i * pi/6) / n_t * conj(I_r(m) + I_sh(m) * exp(1i * gamma(m))));
Qs(m) = imag(sqrt(3) * V_s * exp(1i * pi/6) / n_t * conj(I_r(m) + I_sh(m) * exp(1i * gamma(m))));
Ss(m) = sqrt(Ps(m)^2 + Qs(m)^2);
end
% Plot results
plot(Ps/Srate, Qs/Srate, 'LineWidth', 2, 'Color', [0.9290 0.6940 0.1250]);
% Nonlinear constraint function
function [c, ceq] = myfun(x, rho)
V_s = 10*1e3/sqrt(3);
n_t = 25*sqrt(3);
V_r = 400/sqrt(3);
theta_r = pi/12;
Srate = 100*1e3/3;
Zbase = (V_r)^2/Srate;
X_r = 0.4*Zbase;
X_t = 400^2/(150*1e3)*4/100;
V_se = 0.2*V_r;
Z_r = 1i * X_r;
% Extract variables
gamma = x(1);
I_sh = x(2);
% Compute intermediate quantities
I_r = 1 / (Z_r + 1i * X_t) * (sqrt(3) * V_s * exp(1i * pi/6) / n_t + V_se * exp(1i * rho) - V_r * exp(1i * theta_r) - 1i * X_t * I_sh * exp(1i * gamma));
V_c1 = sqrt(3) * V_s * exp(1i * pi/6) / n_t - 1i * X_t * (I_sh * exp(1i * gamma) + I_r);
% Constraints
Psh = real(V_c1 * conj(I_sh * exp(1i * gamma)));
Pse = real(V_se * exp(1i * rho) * conj(I_r));
Qs = imag(sqrt(3) * V_s * exp(1i * pi/6) / n_t * conj(I_r + I_sh * exp(1i * gamma)));
% Nonlinear equality constraints
ceq = [Psh - Pse; Qs];
c = [];
end
For more information on "fmincon", refer to the following documentation:
Also, you may refer to the following documentation to read about constraints while solving non-linear equations:
Hope this helps!
More Answers (0)
See Also
Categories
Find more on Systems of Nonlinear Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!