# I'm having trouble solving a system of nonlinear equations with the fmincon function.

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xin il 27 Lug 2024
Commentato: xin il 28 Lug 2024
I want to solve a system of equations containing two non-linear equations, one of which is Psh_newhv == Pse_newhv,the other is Qs_newhv==0, but solving it with the fmincon function doesn't achieve the first constraint, how can I solve this problem?
% 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/(300*1e3)*4/100;
rho = 0:2*pi/72:2*pi;
V_se = 0.2*V_r;
V_se_newhv = 0.2*V_s;
Z_r = 1i * X_r;
% Initial guess
x0 = [0 0];
% Options for fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'off','ConstraintTolerance',1e-6);
% Constraints
lb = [];
ub = [];
% Solve for each rho
for m = 1:73
% Define the nonlinear constraint function
fun_newhv = @(x_newhv) myfun_newhv(x_newhv, rho(m));
% Use fmincon to solve the problem
[x_newhv, fval_newhv, exitflag_newhv(m), output_newhv] = fmincon(@(x_newhv) 0, x0, [], [], [], [], lb, ub, fun_newhv, options);
% Extract solutions
gamma_newhv(m) = x_newhv(1);
I_sh_newhv(m) = x_newhv(2);
I_r_newhv(m)=1/(Z_r+j*X_t)*(sqrt(3)*(V_s+V_se_newhv*exp(j*rho(m)))*exp(j*pi/6)/n_t-V_r*exp(j*theta_r));
V_tap_newhv=0.5*(V_s+V_se_newhv*exp(j*rho(m)))*exp(j*-pi/3);
Pr_newhv(m)=real(V_r*exp(j*theta_r)*conj( I_r_newhv(m)));
Qr_newhv(m)=imag(V_r*exp(j*theta_r)*conj( I_r_newhv(m)));
I_s_newhv(m)=0.5*I_sh_newhv(m)*exp(j*gamma_newhv(m))*exp(j*pi/3)+sqrt(3)/n_t* I_r_newhv(m)*exp(j*-pi/6);
Ps_newhv(m)=real(V_s*conj(I_s_newhv(m)));
Qs_newhv(m)=imag(V_s*conj(I_s_newhv(m)));
Psh_newhv(m)=real(V_tap_newhv*conj(I_sh_newhv(m)*exp(j*gamma_newhv(m))));
Qsh_newhv(m)=imag(V_tap_newhv*conj(I_sh_newhv(m)*exp(j*gamma_newhv(m))));
Ssh_newhv(m) = sqrt(Psh_newhv(m)^2 + Qsh_newhv(m)^2);
Pse_newhv(m)=real(V_se_newhv*exp(j*rho(m))*conj(I_sh_newhv(m)));
Qse_newhv(m)=imag(V_se_newhv*exp(j*rho(m))*conj(I_sh_newhv(m)));
Sse_newhv(m) = sqrt(Pse_newhv(m)^2 + Qse_newhv(m)^2);
end
polarplot( (Psh_newhv - Pse_newhv)/Srate,LineWidth=2)
hold on
polarplot( Qs_newhv/Srate,LineWidth=2)
% Nonlinear constraint function
function [c, ceq] = myfun_newhv(x_newhv, 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/(300*1e3)*4/100;
V_se_newhv = 0.2*V_s;
Z_r = 1i * X_r;
% Extract variables
gamma_newhv = x_newhv(1);
I_sh_newhv = x_newhv(2);
% Compute intermediate quantities
I_r_newhv=1/(Z_r+j*X_t)*(sqrt(3)*(V_s+V_se_newhv*exp(j*rho))*exp(j*pi/6)/n_t-V_r*exp(j*theta_r));
I_s_newhv=0.5*I_sh_newhv*exp(j*gamma_newhv)*exp(j*pi/3)+sqrt(3)/n_t* I_r_newhv*exp(j*-pi/6);
Qs_newhv=imag(V_s*conj(I_s_newhv));
V_tap_newhv=0.5*(V_s+V_se_newhv*exp(j*rho))*exp(j*-pi/3);
Psh_newhv=real(V_tap_newhv*conj(I_sh_newhv*exp(j*gamma_newhv)));
Pse_newhv=real(V_se_newhv*exp(j*rho)*conj(I_s_newhv));
% Constraints
% Nonlinear equality constraints
ceq = [ Psh_newhv - Pse_newhv;Qs_newhv];
c = [];
end
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

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### Risposta accettata

Torsten il 27 Lug 2024
Modificato: Torsten il 27 Lug 2024
Use
% Options for fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'off','ConstraintTolerance',1e-12);
instead of
% Options for fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'off','ConstraintTolerance',1e-6);
But why do you use "fmincon" to solver a system of two nonlinear equations ? "fsolve" usually is the solver of choice.
rho = 0:2*pi/72:2*pi;
% Initial guess
x0 = [0 0];
% Options for fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'off','ConstraintTolerance',1e-12);
% Constraints
lb = [];
ub = [];
% Solve for each rho
for m = 1:73
% Define the nonlinear constraint function
fun_newhv = @(x_newhv) myfun_newhv(x_newhv, rho(m));
% Use fmincon to solve the problem
[x_newhv, fval_newhv, exitflag_newhv(m), output_newhv] = fmincon(@(x_newhv) 0, x0, [], [], [], [], lb, ub, fun_newhv, options);
% Extract solutions
gamma_newhv(m) = x_newhv(1);
I_sh_newhv(m) = x_newhv(2);
[~,ceq(:,m)] = fun_newhv(x_newhv);
end
hold on
plot(1:m,ceq(1,:),'b')
plot(1:m,ceq(2,:),'r')
hold off
grid on
% Nonlinear constraint function
function [c, ceq] = myfun_newhv(x_newhv, 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/(300*1e3)*4/100;
V_se_newhv = 0.2*V_s;
Z_r = 1i * X_r;
% Extract variables
gamma_newhv = x_newhv(1);
I_sh_newhv = x_newhv(2);
% Compute intermediate quantities
I_r_newhv=1/(Z_r+j*X_t)*(sqrt(3)*(V_s+V_se_newhv*exp(j*rho))*exp(j*pi/6)/n_t-V_r*exp(j*theta_r));
I_s_newhv=0.5*I_sh_newhv*exp(j*gamma_newhv)*exp(j*pi/3)+sqrt(3)/n_t* I_r_newhv*exp(j*-pi/6);
Qs_newhv=imag(V_s*conj(I_s_newhv));
V_tap_newhv=0.5*(V_s+V_se_newhv*exp(j*rho))*exp(j*-pi/3);
Psh_newhv=real(V_tap_newhv*conj(I_sh_newhv*exp(j*gamma_newhv)));
Pse_newhv=real(V_se_newhv*exp(j*rho)*conj(I_s_newhv));
% Constraints
% Nonlinear equality constraints
ceq = [ Psh_newhv - Pse_newhv;Qs_newhv];
c = [];
end
##### 3 CommentiMostra 1 commento meno recenteNascondi 1 commento meno recente
Torsten il 27 Lug 2024
Modificato: Torsten il 27 Lug 2024
rho = 0:2*pi/72:2*pi;
% Initial guess
x0 = [0 0];
% Options for fsolve
options = optimoptions('fsolve', 'Display', 'off');
% Solve for each rho
for m = 1:73
% Define the equations
fun_newhv = @(x_newhv) myfun_newhv(x_newhv, rho(m));
% Use fsolve to solve the problem
[x_newhv, fval_newhv, exitflag_newhv(m), output_newhv] = fsolve(fun_newhv, x0, options);
% Extract solutions
gamma_newhv(m) = x_newhv(1);
I_sh_newhv(m) = x_newhv(2);
res(:,m) = fval_newhv;
x0 = x_newhv;
end
hold on
plot(1:m,res(1,:),'b')
plot(1:m,res(2,:),'r')
hold off
grid on
% Nonlinear equations
function res = myfun_newhv(x_newhv, 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/(300*1e3)*4/100;
V_se_newhv = 0.2*V_s;
Z_r = 1i * X_r;
% Extract variables
gamma_newhv = x_newhv(1);
I_sh_newhv = x_newhv(2);
% Compute intermediate quantities
I_r_newhv=1/(Z_r+j*X_t)*(sqrt(3)*(V_s+V_se_newhv*exp(j*rho))*exp(j*pi/6)/n_t-V_r*exp(j*theta_r));
I_s_newhv=0.5*I_sh_newhv*exp(j*gamma_newhv)*exp(j*pi/3)+sqrt(3)/n_t* I_r_newhv*exp(j*-pi/6);
Qs_newhv=imag(V_s*conj(I_s_newhv));
V_tap_newhv=0.5*(V_s+V_se_newhv*exp(j*rho))*exp(j*-pi/3);
Psh_newhv=real(V_tap_newhv*conj(I_sh_newhv*exp(j*gamma_newhv)));
Pse_newhv=real(V_se_newhv*exp(j*rho)*conj(I_s_newhv));
res = [ Psh_newhv - Pse_newhv;Qs_newhv];
end
xin il 28 Lug 2024
Good job, thanks.

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