# Parameter Estimation of the Bishop Photovoltaic Model Using a Genetic Algorithm
## 5 Discussion and Conclusions  
Comparing the results of the two stages of the parameter estimation, it was established that the estimation of the complete set of parameters of the Bishop model achieved a better performance than that obtained by estimating only the five SDM parameters and using the second-quadrant parameters reported in [18]. A comparison of the parameter estimation results (Stages 1 and 2) shows that the parameters for the first quadrant were similar for both Cell 1 and Cell 2. The most significant difference in the estimation stages was \(R_{sh}\), which affected the second quadrant behavior in the Bishop model. For that parameter, Cell 1 exhibited differences of \(36.6(\Omega)\) between SDM and the Bishop model from its mean values (see Tables 3 and 10) and \(28.5(\Omega)\) from the best results (see Tables 5 and 9). For Cell 2, those values were \(302.1(\Omega)\) and \(90.8(\Omega)\), respectively. This analysis shows that I-V experimental curves, which include the first and second quadrant, are necessary for estimating the parameters of the Bishop model. This study found differences in the behavior of the I-V curve of mc-SI and pc-SI cells at important points, such as the short-circuit current \(I_{sc}\) and the maximum power point \((V_{mpp},I_{mpp})\). Those variations are reflected in the estimation of the parameters of the Bishop model, as shown in Table 9. Such differences are noticeable not only in the first quadrant, but also in the second quadrant, since the three parameters defining that behavior (\(a\), \(m\) and \(V_{br}\)) show considerable variations depending on the type of cell technology. Therefore,  
Figure 15: Summary of the proposed methodology. not only parameters but also search ranges should be defined according to the technology of the cells under analysis. It is important to emphasize that the parameters of the first quadrant also affected both the result of estimating the parameters of the second quadrant and the reproduction of I-V curve in that quadrant; therefore, using values taken from the literature can introduce significant errors in the estimation of the I-V curve. Thus, the solution presented in this paper is a tool to improve the analysis of the cell when it is exposed to partial shading, enabling an accurate representation using the Bishop model. In this way, tools oriented to quantifying shading losses and studies of degradation caused by hot-spots and aging, among other issues, can be developed by using the proposed methodology; this providing a suitable compromise between accuracy and complexity. Finally, future studies should be focused on evaluating the performance of other optimization techniques for estimating the parameters of photovoltaic cells, for both the first and second quadrant, using the Bishop model. Moreover, performing experiments on a large number of commercial PV cells with different technologies (thin-film, bi-facial and PERC, among others) could be useful for the scientific community, since accurate parameters for both the first and second quadrant could be provided. On the other hand, it is important to evaluate the performance of the proposed approach by considering dynamic operating conditions in terms of temperature and irradiance. Conceptualization, B.J.-C., J.M., C.A.R.-P., L.A.T.-G. and M.L.O.-G.; methodology, [PERSON]-C., J.M., [PERSON]-P., L.A.T.-G. and M.L.O.-G.; software, [PERSON]-C. and J.M. ; validation, [PERSON]-C., J.M., C.A.R.-P., L.A.T.-G. and M.L.O.-G.; writing--original draft preparation, [PERSON]-C. and J.M. ; writing--review and editing, [PERSON]-C., J.M., [PERSON]-P., L.A.T.-G. and M.L.O.-G. All authors have read and agreed to the published version of the manuscript.