# Electrical and Thermal Behaviour of Crystalline Photovoltaic Solar Modules in Shading Conditions
## 3 Results and Discussion  
In order to explain the dependence of the electric output current, the bypass diode current, and the output voltage established in a PV module, the results obtained in test 1 are discussed. In test 1, I-V curves plotting the total output and the bypass diode current were obtained in each of these conditions:  
Condition 1: Operation without any covered PV cell. Condition 2: Operation with a covered PV cell, E3, in substring 1. Condition 3: Operation with two covered PV cells, E3 and C4, in substring 1 and 2, respectively. Condition 4: Operation with three covered PV cells, E3, C4, and B6, in substring 1, 2, and 3, respectively. Figure 4 shows the solar PV module I-V characteristic curve in condition 1 with an average irradiance of 839 W/m\({}^{2}\). A normal response of the PV module is shown, with no current flowing through any bypass diode. Figure 5 shows the solar PV module I-V characteristic curve in condition 2 with an average irradiance of 946 W/m\({}^{2}\). No bypass diode was turned on when the systems worked in a voltage range between 26 and 41 V, while the total output current was considerably reduced in comparison with the current in MPP in Figure 4. To lower voltage operating values than 26 V the current increased to short circuit values, and the substring bypass diode with the covered PV cell started to lead the current, which can be obtained applying the next expression:  
\[I_{di}=I_{p}-I_{p^{\prime}} \tag{1}\]  
where:  
\(I_{di}\): Bypass diode current, \(i\), in the sub-module with the covered PV cell. \(I_{p}\): Total PV module current when \(V_{p}<V_{\infty}-V_{S}\)  
where:  
\(V_{p}\): Operating voltage of the solar PV module. \(V_{\infty}\): Open circuit PV module voltage. \(V_{S}\): Open circuit PV module voltage of the sub-module with the covered PV cell, \(i\), which can be obtained as:  
\[V_{S}=N_{S}\cdot V_{f} \tag{2}\]  
Figure 4: Experimental monocrystalline solar module I-V characteristic curve in condition 1.  
where:  
\(N_{5}\): Number of PV cells in a sub-module protected by a bypass diode, \(i\). \(V_{f}\): Crystalline silicon cell forward voltage. \(I_{p}\): Total PV module current when \(V_{p}\geq V_{\infty}-V_{S}\)  
Figure 6 shows the solar PV module I-V characteristic curve in condition 3 with an average irradiance of 1008 W/m\({}^{2}\). Firstly, in this condition, there existed two sub-modules with a covered PV cell, so when the voltage operation value was \(V_{p}<V_{\infty}-(2\cdot V_{S})\), each sub-module bypass diode carried an electrical current, which could be calculable as it is shown in (1). The total output PV module current was close to the short circuit PV module current in STC (Standard Tests Conditions). Secondly, to an operating voltage level of \(V_{p}>V_{\infty}-(2\cdot V_{S})\), no bypass diode was turned on, but the total output PV module current suffered a considerable reduction. Figure 7 shows the solar PV module I-V characteristic curve in condition 4 with an average irradiance of 1047 W/m\({}^{2}\). In this condition, the short circuit PV module measured current is far lower than in Figure 4. Furthermore, in a big part of the characteristic I-V curve, no bypass diode was turned on since all the failures made in each PV cell of different sub-modules were similar. However, there were two bypass diodes turned on when the operation voltage value was below 15 V. This could  
Figure 5: Experimental monocrystalline solar module I-V characteristic curve in condition 2. Figure 6: Experimental monocrystalline solar module I-V characteristic curve in condition 3.  
have been produced due to the sensibility of the different PV cells exposed to failure or mismatching between the photovoltaic current produced by each one of them. Once the dependence of the electric output current, the bypass diode current, and the output voltage in a PV module were studied, the electrical and thermal results of tests 1 and 2 were presented. Figure 8 shows the electrical results obtained in test 2.