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

4 次查看（过去 30 天）
xin
xin 2024-7-27
评论： xin 2024-7-28
Ran in:
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

请先登录，再回答此问题。

采纳的回答

Torsten
Torsten 2024-7-27
编辑：Torsten 2024-7-27
Ran in:
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 个评论
显示 1更早的评论
Torsten
Torsten 2024-7-27
编辑：Torsten 2024-7-27
Ran in:
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

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Systems of Nonlinear Equations 的更多信息

标签

产品


版本

R2020b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by