Refinement of the co-content function, through an integration of a polynomial fit of $$I-I_{sc}$$ I - I sc . Part 1 theoretical analysis and proposal - Victor-Tapio Rangel-Kuoppa (Discover Electronics)
Abstract In this Part 1 article of this series of articles, a new methodology to refine the Co-Content function $$\left(CC\left(V,I\right)\right)$$ C C V , I is proposed, consisting on fitting the current minus the short-circuit current $$(I-I_{sc})$$ ( I - I sc ) , to an $$N-1$$ N - 1 order polynomial, where $${N}_{points}=N$$ N points = N , is the number of measured current–voltage $$\left(IV\right)$$ I V points, and integrating it to calculate $$CC\left(V,I\right)$$ C C V , I . The shunt resistance $$\left(R_{sh}\right)$$ R sh , the series resistance $$\left(R_{s}\right)$$ R s , the ideality factor $$\left(n\right)$$ n , the light current $$\left(I_{lig}\right)$$ I lig , and the saturation current $$\left(I_{sat}\right)$$ I sat , are then deduced, in the case of a constant percentage noise or a percentage noise of the maximum current $$\left(I_{max}\right)$$ I max . In the former case, $${R}_{s}$$ R s , $${R}_{sh}, n, \text{and } I_{lig},$$ R sh , n , and I lig , can be deduced with less than 10% error, using only $${P}_{V}=$$ P V = 51 $$\frac{number\, of \,points}{V}$$ n u m b e r o f p o i n t s V , even if the noise is as large as $${p}_{n}=0.1\text{%}$$ p n = 0.1 % , with a computation time around 80 ms. $${I}_{sat}$$ I sat needs $${p}_{n}=0.05\text{%}$$ p n = 0.05 % or less, and $${P}_{V}$$ P V equal or larger than 501 $$\frac{number\, of\, points}{V}$$ n u m b e r o f p o i n t s V . For the latter case, $${R}_{s}$$ R s , $$\text{and } I_{lig},$$ and I lig , can be obtained with less than 10% error, using only $${P}_{V}=$$ P V = 251 $$\frac{number\, of\, points}{V}$$ n u m b e r o f p o i n t s V , and $${p}_{n}=0.1\text{%}$$ p n = 0.1 % , or smaller, with total computation time around 49 s. $${R}_{sh}, I_{sat}, \text{and } n$$ R sh , I sat , and n needs that $${p}_{n}\le 0.05\text{%}$$ p n ≤ 0.05 % , and $${P}_{V}=$$ P V = 751 $$\frac{number\, of \,points}{V}$$ n u m b e r o f p o i n t s V or larger. A computation time expression of the form $$time=E{N_{points}}^{m}$$ t i m e = E N points m , is deduced. The methodology proposed in this article is appliable to unevenly/randomly distributed IV data points, and it is implemented in Part 2 in solar cells’ and photovoltaic modules’ experimental $$IV$$ IV reported in the literature, to deduce their five solar cell parameters.