## 1 Introduction
### Methodology Proposed to Calculate the Maximum Power Point (MPP)  
In the present work, an alternative analytical method is proposed to extract the 1-diode/2-resistor equivalent circuit parameters from a reduced number of experimental measurements. Bearing in mind that measuring both short-circuit and open-circuit points are also simple operations, the main problem remains the maximum power point (MPP) determination, as the operating voltage of this point is, in principle, unknown. In the proposed methodology, equations corresponding to the maximum power point and its derivative are replaced by their equivalents at any other point (\(I_{i}\), \(V_{i}\)). This procedure is similar to other parameter-extraction methods that do not require the MPP, and use another point of the _I-V_ curve instead. For example, [PERSON] et al. [16] developed a non-direct iterative method that avoids using the MPP. The works by other authors such as [PERSON] et al. [17], [PERSON] et al. [18], [PERSON] et al. [19] should be also mentioned, as they fit the equivalent circuit model to the _I-V_ curve with a limited number of points. Once the equivalent circuit parameters have been extracted, the proposed analytical method can be used to predict the MPP location on the _I-V_ curve. Furthermore, the use of the proposed analytical method for maximum peak power tracking (MPPT) is analyzed, as proposed by some of the aforementioned authors [17; 18; 19]. The proposed calculation procedure can be briefly summarized as follows:  
* Obtain the short circuit current, \(I_{sc}\), and the inverse of the _I-V_ curve's slope at that point, \(R_{sh0}\), of the solar cell/panel as in MPPT offline methods (short circuiting the panel or with pilot cells). * Obtain the open circuit voltage, \(V_{oc}\), of the solar cell/panel like in MPPT offline methods (opening the circuit or with pilot cells). * Monitor the solar panel to obtain the instantaneous working point, that is, the operation point (\(I_{i}\), \(V_{i}\)) and \(\mathrm{d}I/\mathrm{d}V\,|_{i}\). * Extract the 1-diode/2-resistor equivalent circuit model parameters. * Calculate the maximum power point \(I_{mp}\), \(V_{mp}\). As mentioned, this methodology has advantages in both offline and online methods. On the one hand, in the case of the offline methods the method allows for the instantaneous calculation of the desired value of the operating voltage, but with higher precision. On the other hand, in the online methods, there is feedback that improves the accuracy in each step, because the operating point is used to recalculate the maximum power point, which increases the accuracy of the calculation as the operating point approaches to the maximum power point. The use of the characteristic points (short circuit and open voltage) can be a problem if they are measured during the solar panel operation, as it could represent \"an unacceptable power loss\" [19]. Nevertheless, on the one hand, this power loss will depend on the data acquisition frequency; on the other hand, pilot cells could overcome this drawback, as mentioned above. The present work is the last contribution from the IDR/UPM Institute within the research framework on space solar panel performance analysis. This project has proven to be successful from both the scientific and academic points of view (the results from the research on solar panels, once obtained, are immediately used by the students of the Master in Space Systems (MUSE), organized by the IDR/UPM Institute [20; 21; 22]). It should be pointed out that one of the aims of the work carried out at the IDR/UPM is to obtain procedures that obtain the quickest results in relation to foreseeing the behavior of the photovoltaic systems (within a reasonable accuracy level), as in autonomous systems such as the space systems, the fastest solutions are normally preferred. The results obtained with the aforementioned analytical methods, together with some mathematical approaches [23], have been used for the solar power supply estimations related to UPMSat-2 [24] and Lian-He/UNION missions.