## 4 Application of the Developed PV System Models
### Case 1  
This studies the reliability contribution of the three different PV technologies as a function of the system peak load. The system LOLE and LOEE are evaluated for different PV topologies. Figures 12 and 13, respectively, show the LOLE and LOEE of the SIPS when 30% of PV is added to the system. The historical solar irradiation data of Al-Madinah in Saudi Arabia located at 24.91\({}^{\circ}\) N, 46.41\({}^{\circ}\) E, is used to evaluate the power generation from the PV system [16]. It can be noticed in Figures 12 and 13 that the LOLE and LOEE increase as the peak load increases with all PV topologies. These two figures additionally show that using the micro-inverter topology can provide more incremental reliability benefits compared to other PV topologies. However, this increment decreases at certain percentages of the PV system installed where no further benefit can be obtained by further increasing installed PV capacity as discussed in the next section.  
Figure 14 represents the system adequacy for different PV topologies for the addition of 30% of the PV capacity to the SIPS at a peak load of 80 kW. Clearly, the results obtained from this analysis show that there is reliability improvement from adding solar power to SIPS using different PV topologies, but not to the same level. The analysis indicates that there is significant impact on system reliability in using different PV topologies. This shows that micro-inverter PV topology provides the largest reliability benefit among other topologies.  
This work evaluates the optimum conventional generation capacity that can be replaced by PV generation. This study compares replacing diesel generation with a PV system, considering different PV topologies. The analysis involves adding a proper PV unit to provide an acceptable system reliability level. The 40 kW of conventional generation capacity is removed from SIPS. Table 7 represents the capacity of the PV unit required to replace the 40 kW in order to maintain the acceptable criteria of 32.26 h/year. The LOLE increases when the 40 kW conventional unit is removed for system. When the central PV capacity is used, the LOLE is restored to 32.26 h/year if 270 kW of PV is added. This indicates that 270 kW of PV capacity using central PV system is able to replace a 40 kW conventional generation unit. However, 180 and 98 kW of string and micro-inverter PV capacity is required in order to meet the system risk level of 32.26 h/year.  
The equivalence between replaced conventional generation unit and added PV systems can be expressed by the ratio of PV capacity to conventional generation unit and this ratio is known as the risk-based equivalent capacity ratio (RBECR) [31]. Equation (25) is used to determine the RBECR. The results indicates that one unit of conventional capacity is approximately equivalent to 7, 5 and 3 units of central, string and micro-inverter PV capacity, respectively, as shown in Table 7.  
Figure 14: System Adequacy for Different PV Topologies.  
Figure 13: Variation in risk level (LOEE) with system demand load for different PV topologies.  
\[\text{RBECR}\ =\frac{\text{Total amount of installed PV capacity}}{\text{Total amount of replaced conventional generation capacity}} \tag{25}\]