In this paper
On the analytical approach for modeling photovoltaic systems
behavior by Javier Cubas
I tried to derive the an implicit expression of the series resistor, from the following 4 equations which are ued by author:
I_pv≡(R_sh+R_s)/R_sh I_sc………………………………………………(7)
I_0=((R_sh+R_S ) I_Sc-V_oc)/(R_sh exp(V_oc/(aV_T )) ) …………………………………………(9)
(I_SC-&(I_sc-(V_oc-R_S I_sc)/R_sh )[exp((V_mp+I_mp R_S-V_oc)/(aV_T )) ]@-&(V_mp+I_mp R_S-I_sc R_S)/R_sh =I_mp.) ……………..(11)
dI/dV=-I_0/(aV_T ) (1+dI/dV R_S )[exp((V+IR_S)/(aV_T )) ]-1/R_sh (1+dI/dV R_S ) ……(15)
A pdf file shows the equations summarized which he used to derive series and shunt resistanc explicit equations.
I need to know the derivision from those 4 eqautions to get the Rs and Rsh equations :
(aV_T V_mp (2I_mp-I_SC ))/((V_mp I_SC+V_oc (I_mp-I_SC ))(V_mp-I_mp R_S )-aV_T (V_mp I_SC-V_oc I_mp ) )= exp((V_mp+I_mp R_S-V_oc)/(aV_T )) (2)
R_sh=(V_mp-I_mp R_S )(V_mp-R_S (I_SC-I_mp )-aV_T )/((V_mp-I_mp R_S )(I_SC-I_mp )-aV_T I_mp ) (3)
After permission is granted from Prof. Javier Cubas.
Prof. Javier Cubas sent to me the proof of this equation to get implicit equation in Rs and ideality factor a.
I attach 2 files original one from Prof. Javier Cubas and the other one by my hand writing to simplify steps for researchers. Best wishes.
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