I am using fsolve and receiving errors

Question

Charalampos Ioannou 2017-11-24

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评论： Charalampos Ioannou 2017-11-24

I have the following function which i am defining some of the parameters as follows:

function F = solar5d(x)
q   = 1.60217662*10^-19;
k   = 1.38064852*10^-23;
T   = 298.15; % Temperature in degrees 25. This one is in Kelvin.
Ns  = 72;
Np  = 1;
Voc = 44.6;
Vm  = 35.43;
Isc = 5.43;
Im  = 4.95;
n   = 1.086;

These are my unknown parameters i am looking for:

Iph = x(1);
Io  = x(2);
Rs  = x(3);
Rp  = x(4);
Vt  = x(5);

The following are the six questions i have to solve the system:

F(1) = Vt - n*k*T/q;
F(2) = Np*Iph - Np*Io*(exp(Voc/Ns*Vt)-1) - (Np*Voc)/(Ns*Rp);
F(3) = Np*Iph - Np*Io*(exp((Isc*Rs)/(Np*Vt)) - 1) - (Isc*Rs)/Rp - Isc;
F(4) = Np*Iph - Np*Io*(exp(((Vm/Ns)+(Im*Rs)/Np)/Vt) - 1) - Np*((((Vm/Ns)+((Im*Rs)/Np))/Rp)) - Im;
F(5) = (((Np/Ns*Vt)*Io*(exp((Vm + ((Im*Ns*Rs)/Np))/Ns*Vt)) + (1/(Ns*Rp)/Np))/(1 + (Rs*Vt)*Io*(exp((Vm + ((Im*Ns*Rs)/Np))/Ns*Vt)) + (Rs/Rp))) - (Im/Vm);
F(6) = (((-Np/Ns*Vt)*Io*(exp(Voc/Ns*Vt)) - (1/Ns*Rp/Np)) / (1 + (Rs/Vt)*Io*(exp(Voc/Ns*Vt)) + (Rs/Rp))) + 1/Rs;
end

But i am receiving the following error:

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle
non-square systems; using Levenberg-Marquardt algorithm instead. 
> In fsolve (line 298) 
Error using levenbergMarquardt (line 16)
Objective function is returning undefined values at initial point.
fsolve cannot continue.
Error in fsolve (line 397)
        levenbergMarquardt(funfcn,x,verbosity,options,defaultopt,f,JAC,caller,
        ...

Please could you help me to solve my problem??

Thanks in advance.

Regards,

Charalampos

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Walter Roberson 2017-11-24

You did not happen to show you call to fsolve, with your initial conditions.

Stephen23 2017-11-24

编辑：Stephen23 2017-11-24

在 MATLAB Online 中打开

Note that

q = 1.60217662*10^-19;

requires three numbers and two expensive operations to generate the output value, whereas

q = 1.60217662e-19;

is efficiently defined as that value, without any operations.

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Answer 1

Torsten 2017-11-24

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在 MATLAB Online 中打开

Add

disp(F)

at the end of solar5d.

I suspect that the array F contains Inf, NaN or something similar.

Take care that your initial values for the variables don't produce division by zero or undefined expressions.

Best wishes

Torsten.

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Charalampos Ioannou 2017-11-24

The pictures i post above are the equations i am using in the algorithm i post. The first 3 equations i rearranged them to be equal to zero the 4 one the same and then i choose question (15) to be as my fifth equation and i rearrange it to be equal to zero again.

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Answer 2

Are Mjaavatten 2017-11-24

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It seems that you try to solve an overdetermined system. You have six equations in five unknowns. You should re-examine your problem to see if one of your equations is superfluous.

Also, it is good practice (although not strictly necessary) to pre-allocate memory to F: Insert the command

F = zeros(6,1) % Or zeros(5,1)?

before you define the components of F.

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Charalampos Ioannou 2017-11-24

在 MATLAB Online 中打开

Hello Are,

I could take out equation F(1) i can calculate it manually and define the value instead of having the equation there as an unknown parameter.

function F = solar5d(x)

% q = 1.60217662*10^-19;

% k = 1.38064852*10^-23;

% T = 298.15; % Temperature in degrees 25. This one is in Kelvin.

Ns = 72;

Np = 1;

Voc = 44.6;

Vm = 35.43;

Isc = 5.43;

Im = 4.95;

% n = 1.086;

Vt = 0.028;

Iph = x(1);

Io = x(2);

Rs = x(3);

Rp = x(4);

F(1) = Np*Iph - Np*Io*(exp(Voc/Ns*Vt)-1) - (Np*Voc)/(Ns*Rp);

F(2) = Np*Iph - Np*Io*(exp((Isc*Rs)/(Np*Vt)) - 1) - (Isc*Rs)/Rp - Isc;

F(3) = Np*Iph - Np*Io*(exp(((Vm/Ns)+(Im*Rs)/Np)/Vt) - 1) - Np*((((Vm/Ns)+((Im*Rs)/Np))/Rp)) - Im;

F(4) = (((Np/Ns*Vt)*Io*(exp((Vm + ((Im*Ns*Rs)/Np))/Ns*Vt)) + (1/(Ns*Rp)/Np))/(1 + (Rs*Vt)*Io*(exp((Vm + ((Im*Ns*Rs)/Np))/Ns*Vt)) + (Rs/Rp))) - (Im/Vm);

F(5) = (((-Np/Ns*Vt)*Io*(exp(Voc/Ns*Vt)) - (1/Ns*Rp/Np)) / (1 + (Rs/Vt)*Io*(exp(Voc/Ns*Vt)) + (Rs/Rp))) + 1/Rs;

disp(F)

end

But still i am receiving the same error:

>> fun = @solar5d;

>> x0 = [0,0,0,0];

>> x = fsolve(fun,x0)

-Inf NaN -Inf NaN NaN

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.

> In fsolve (line 298) Error using levenbergMarquardt (line 16) Objective function is returning undefined values at initial point. fsolve cannot continue.

Error in fsolve (line 397) levenbergMarquardt(funfcn,x,verbosity,options,defaultopt,f,JAC,caller, ...

>>

Are Mjaavatten 2017-11-24

Did you check that fsolve converged at all? If so, if you plug the resulting x into solar5d the result should be a set of very small numbers. Solving a set of nonlinear equations is not always easy. In the general case, a solution may not even exist.

If you have some knowledge of what the solution should be, try with a starting vector close to this estimate. It may also be a good idea to double-check that your equations and parameters are all correct

Charalampos Ioannou 2017-11-24