Solver stopped prematurely. fsolve stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 2.000000e+02.
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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
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Akzeptierte Antwort
Anagha Mittal
am 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!
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