# How can i calculate five unknown parameters??

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Charalampos Ioannou on 16 Nov 2017
Edited: Walter Roberson on 22 Dec 2019
Hello everyone,
I want to calculate the five unknown parameters for the following equations. Please could you give me a hint on how to do it?
Some of the parameters i already know them so i define them n = 1; k = 1.38064852 * 10^-23; T = 8; q = 1.60217662 * 10^-19; Vt = n*k*T/q; Np = 5; Ns = 12; Voc = 36.48; Isc = 8.12; Im = 7.62; Vm = 29.47;
These are the unknown parameters i am looking for: (Iph I_o Vt Rs Rp)
These are the equations i have and i want to solve them 1) Vt = (n*k*T)/q; 2) Np*Iph - Np*I_o*exp((Voc/Ns*Vt) - 1) - (Np/Ns) * (Voc/Rp) = 0; 3) Isc == Np*Iph - Np*I_o*exp((Isc*Rs)/(Np*Vt) -1) - ((Isc*Rs)/Rp); 4) Im == Np*Iph - Np*I_o*exp((((Vm/Ns)+((Im/Np)*Rs))/Vt) - 1) - Np* (((Vm/Ns) + ((Im/Np)*Rs))/Rp); 5) (Im/Vm) == ((Np/Ns*Vt)*I_o*exp(((Vm + Im*((Ns/Np)*Rs))/(Ns*Vt)) + (1/(Ns*Np)*Rp))) / (1 + (Rs/Vt)*I_o*exp((Vm + (Im*(Ns*Np)*Rs))/(Ns*Vt)) + (Rs/Rp)); 6) (-(1/Rp)) == ((-(Np/Ns*Vt))*I_o*exp((Isc*(Ns/Np)*Rs)/(Ns*Vt)) - (1/(Ns*Np)*Rp)) / (1 + (Rs/Vt)*I_o*exp((Isc*(Ns/Np)*Rs)/(Ns*Vt)) + (Rs/Rp)), Iph);
Regards,
Charalampos

Star Strider on 16 Nov 2017
Edited: Star Strider on 16 Nov 2017
Use the Optimization Toolbox fsolve (link) function.
Star Strider on 21 Nov 2017
Nonlinear optimization algorithms can be sensitive to initial parameter estimates, if the function being optimized has a number of local minima, a flat response hypersurface, a hypersurface charaterised by ‘saddle points’ (in which a global minimum might not exist), or other problems. If you know approximately what the optimum parameter values should be, start with those.
Another option would be to use one of the Global Optimization Toolbox functions to see if you can find the global minimum with an algorithm that does not use a gradient-descent approach.

Alex Sha on 22 Dec 2019
There are multi-solutions for Charalampos's problem:
1:
iph: -12.4464463252524
io: -889977.402184639
n: -4891.45375599277
rp: -3.43888384438778
rs: 29.2716150287422
Vt: -3.37210182925269
2:
iph: -1.58509863749155
io: -25.8943258325875
n: -2509.22818093014
rp: -1.9797561075646
rs: 1.83150481082548
Vt: -1.72982785098611
3:
iph: -6.55480935306723
io: -431499.497847303
n: -4852.19727384217
rp: -6.49397053909992
rs: 22.7965518323771
Vt: -3.34503894327367