I am using fsolve and receiving errors

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

[Walter Roberson]

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

[Stephen23]

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.

Answer 1

[Torsten]

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.

[Charalampos Ioannou]

Hello Torsten

I am calling the following in the matlab command:

fun = @solar5d; x0 = [0,0,0,0,0]; x = fsolve(fun,x0)

But i am receiving the error i mentioned above

[Torsten]

And what do you get for F in solar5d ?

You divide by Rp, Rs and Vt. This is not possible for your vector of initial values.

Best wishes

Torsten.

[Charalampos Ioannou]

>> fun = @solar5d;

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

>> x = fsolve(fun,x0) -0.0279 -Inf NaN NaN 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, ...

[Charalampos Ioannou]

[Charalampos Ioannou]

[Charalampos Ioannou]

[Charalampos Ioannou]

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.

Answer 2

[Are Mjaavatten]

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.

[Charalampos Ioannou]

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, ...

>>

[Torsten]

And ? Did you change x0 to a vector without zeros ? No, you didn't.

Best wishes

Torsten.

[Charalampos Ioannou]

I already did it but i am not receiving the correct values again.

I change my vector to x0 = [1,1,1,1,1];

Thanks for your help!!!!

[Torsten]

So it works now, but you get an unexpected result ?

Best wishes

Torsten.

[Charalampos Ioannou]

Yes i am not receiving the correct results i want.

These are the results i am receiving:

 x =

    0.7116   -0.0000    1.0583    0.8775    0.2934

For the last on its supposed to be 0.028 is the only one i can calculate manually but i am getting wrong results.

[Matt J]

If you know x(5) is supposed to be .028 why are you initializing with x(5)=1? For that matter, why are you doing the extra work of solving numerically for x(5) when you can get it analytically? It makes life easier for fsolve if you have fewer unknowns.

[Charalampos Ioannou]

I wanted to calculate it but it self instead of define it. What i am trying to do is to include the simultaneous equations i mentioned above using the nonlinear equation solver 'fsolve', which is embedded with 'Levenberg-Marquardt and 'Gauss-Newton'

[Are Mjaavatten]

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]

Hello Are,

I have the solutions from a different source so i will try to get that solutions include them in the equations and see if i will get zero.

If i am getting zero that means the equations are correct i will try to doing it now and see. Thanks for your help :)