MATLAB: Unable to find explicit solution for “solve”

solve

Code summary: Trying to calculate an array of 'Inet' values, one for every 'V' value. All of the other values are individul numbers. The code is below. The reason I believe it is not working is that there are 'Inet' variables on each side of the equation.

V = 0:.01:3;
syms Inet;
I = solve(Inet == Isc - Is.*(exp(q.*(V+Inet*Rs)./(n*kB*Tc))-1)-(V+Inet*Rs)./Rsh, Inet);

Here is the output warning:

Warning: Unable to find explicit solution. For options, see help.

After running the code, 'I' has no value. I would like it to be an array of 301 numbers, just like 'V'. Can anybody see what I'm doing wrong? Any help is appreciated

Best Answer

Hi,

solve numeric:

% Values for constants - I took some fantasy values...
Isc = 0.1;
Is = 1;
q = 2;
Rs = 0.0135;
Rsh = -2;
n = 4;
kB = 0.4;
Tc = 10;
% Definition of V as column vector
V = (0:.01:3)';
% Solve for Inet
x0 = ones(size(V,1),1);
Inet = fsolve(@(x)solve_Inet(x,Isc,Is,q,V,Rs,Rsh,n,kB,Tc),x0);
% Inet Function
function F = solve_Inet(x,Isc,Is,q,V,Rs,Rsh,n,kB,Tc)
    Inet = x;
    F = Isc - Is.*(exp(q.*(V+Inet*Rs)./(n*kB*Tc))-1)-(V+Inet*Rs)./Rsh - Inet;
end

Best regards

Stephan

Related Solutions

MATLAB: Error fsolve undefined function or variable x.

One problem is that you are calling fsolve from within the ‘prova’ function.

Try this:

function F = prova(x)
k=1.38E-23;
Tc=298.15;
q=1.6E-19;
VT=k*Tc/q;
Isc=5.96;
Voc=62.18;
Imp=5.65;
Vmp=50.61;
Rs=0;
F(1)= x(1)-Isc-x(2)*(exp((Isc*Rs)/(x(3)*VT))-1);
F(2)= x(1)-Imp-x(2)*(exp((Vmp+Imp*Rs)/(x(3)*VT))-1);
F(3)= x(1)-x(2)*(exp((Voc)/(x(3)*VT))-1);
F=[F(1),F(2),F(3)];
end
x0=[6 0.5 1.2];
x=fsolve(@prova,x0);

However solving that problem throws::

Error using trustnleqn (line 28)
Objective function is returning undefined values at initial point. FSOLVE cannot continue.

Running this:

Q = prova(x0)

produces:

Q =
         0.04         -Inf         -Inf

This is most likely due to the vanishingly small values for ‘k’ and ‘q’. You have to solve that. (Scaling may be an option, such that al the constants are multiplied by 1E+10 or some such, then the ‘x’ values are appropriately re-scaled, if necessary.)

MATLAB: Solving a system of 5 dependent non-linear equations

Hi Frederico

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

Actually, command fsolve works pretty well here, let me explain:

Since V(5) unknown only shows up in the 1st equation I decided to put off the 1st equation, let's solve the remaining system with fsolve

clear all;clc;close all
syms m Rsh Rs Io Is
Vmp = 31.1;
Imp = 8.67;
Voc = 38.2;
Isc = 9.19;
K = 1.38 * 10^-23;
T = 298.15;
q = -1.6 * 10^-19; 
Vt = K*T/q;
V = [m, Rsh, Rs, Io];
 F = @(V) [  (Isc - (Voc - V(3)*Isc)/ V(2)) * exp(-Voc/ (V(1)*Vt)) - V(4);
          Isc - (Vmp + V(3)*Imp + V(3)*Isc)/ V(2) - (Isc - (Voc - V(3)*Isc)/ V(2)) * exp((Vmp + V(3)*Imp - Voc)/ (V(1)*Vt)) - Imp;
          Imp + ((-(V(2)*Isc - Voc + V(3)*Isc) * exp((Vmp + V(3)*Imp - Voc)/ (V(1)*Vt))/ (V(2) * V(1)*Vt) - 1/V(2))/ (1 + V(3) * (V(2)*Isc - Voc + V(3)*Isc) * exp((Vmp + V(3)*Imp - Voc)/ (V(1)*Vt))/ (V(2) * V(1)*Vt) + V(3)/V(2))) * Vmp;
          (-(V(2)*Isc - Voc + V(3)*Isc) * exp((V(3)*Isc - Voc)/ (V(1)*Vt))/ (V(2) * V(1)*Vt) - 1/V(2))/ (1 + V(3) * (V(2)*Isc - Voc + V(3)*Isc) * exp((V(3)*Isc - Voc)/ (V(1)*Vt))/ (V(2) * V(1)*Vt) + V(3)/V(2)) + 1/V(2)];
InitialGuess = [50; 0.1; .01; 1];
options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt,'MaxFunctionEvaluations',2000);
XY = fsolve(F, InitialGuess,options);
XY =
  51.755945628868020
   3.071518542695716
   1.085173513887406
  -1.062922141399835

These are semiconductor equations, I like reading what is what, so I am putting back the initial variable names

m=XY(1)
Rsh=XY(2)
Rs=XY(3)
Io=XY(4)

Now the initial equation is trivial

Is=  Io * exp(Voc/ (m*Vt) )+ Voc/Rsh
Is =
  12.436844990189343

fsolve even produces the optimality graph ending up in 3.5e9 quite high.

I was wondering, should your 1st equation have an inverted polarity, then Is would be

Is=  Io * exp(-Voc/ (m*Vt) )+ Voc/Rsh
Is =
    -3.101249033198816e+12

Please note that function fsolve has a default amount if iterations equal to 400. If not changed, for this equations system, fsolve completes all the loops, without a solution, but warns that it may have a solution if increasing such default value.

To so, just change in advance the options field

'MaxFunctionEvaluations'

to for instance

Frederico

Cosi fan tutte :)

If you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

Best Answer

Related Solutions

MATLAB: Error fsolve undefined function or variable x.

MATLAB: Solving a system of 5 dependent non-linear equations

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