## 2 Basic Reliability Evaluation Concepts and Indices  
The reliability system indices can be defined as the ability of its power generation to satisfy the total load demand within acceptable risk levels. Firstly, developing a generation model of the conventional generation system is required. Secondly, this model is then combined with a load model only without PV to evaluate the basic system adequacy as shown in Figure 1. The generation model is generally formatted as a series of states, each of which has a capacity level and probability. This formation is called a capacity outage probability table (COPT) [4] which are utilized in this project to calculate the system risk indices of LOLE and loss of energy exception (LOEE). These two indices are considered the most widely used reliability evaluation indices [7]. The LOLE can be defined as the expected period of time during which the system load exceeds the available generating capacity. The LOEE can be defined as the amount of energy that will not be supplied in a given year. The LOLE and LOEE are determined using Equations (1) and (2), respectively, as shown in Figure 2.  
\[\text{LOLE}=\sum_{k=1}^{n}p_{k}\times t_{k}=\sum_{k=1}^{n}P_{k}\times(t_{k}-t_{ k-1}) \tag{1}\]  
\[\text{LOEE}=\sum_{k=1}^{n}p_{k}\times E_{k} \tag{2}\]  
where \(n\) is the number of capacity outage states; \(O_{k}\) is the \(k\)th outage of COPT; \(p_{k}\) is the probability of the capacity outage \(O_{k}\); \(t_{k}\) is the time for which load loss will occur due to \(O_{k}\); \(P_{k}\) is cumulative outage probability for capacity state \(O_{k}\); and \(E_{k}\) is energy not supplied. The capacity value contribution with the added renewable energy system is expressed in terms of physical capacity (W). The ELCC and CC factors are used in this paper to evaluate the capacity value contribution of the solar system installed. The rationale for calculating ELCC is described in [11; 12]. Figure 3 shows the mathematical method for the estimation of ELCC. The physical meaning of ELCC from this figure is the additional load that can be carried with addition of new generation while maintaining the LOLE constant. The ELCC is a useful index for estimating the solar capacity value as it depends on many factors such as the size of the existing and added generating units, the unit FOR, the system peak load variation and the system risk criterion. The CC is another important parameter in capacity value evaluation and has been applied extensively to assess the contribution of a power  
Figure 1: Basic Reliability Evaluation Model for a photovoltaic (PV)-integrated Power System. Figure 2: Evaluation of loss of load expectation (LOLE) and loss of energy expectation (LOEE) using an hourly load curve. generating source to meet the load carrying capability of the system at an acceptable risk level. The CC of the PV system is obtained using Equation (3). \[\text{CC}=\frac{\text{ELCC}}{\text{C}_{A}}\times 100 \tag{3}\]  
where \(C_{A}\) is the rated capacity of the added generating unit. The PV system is commonly used in SIPS [13]. The application of PV in large systems has also received considerable attention. This study considers a SIPS to evaluate the reliability contribution of the PV system generation; however, the modeling and proposed reliability assessment approach can be applied to larger systems. A SIPS is located in a remote area. This system may or may not have a transmission line. The SIPS used in this paper has one 70 kW and two 40 kW [13] generation units with a total system capacity of 150 kW. The system peak load is 80 kW. The data on the failure rate (\(\lambda\)) and repair rate (\(\mu\)) are important to evaluate the FOR or unavailability and availability. The reciprocals of \(\lambda\) and \(\mu\) are known as the mean time to failure (MTTF) and mean time to repair (MTTR) respectively. The unavailability (\(U\)) and availability (\(A\)) can be defined using Equations (4) and (5), respectively [7].