## 3 Case Study
### Reliability Assessment  
Figure 7 shows the fault tree taking outage for the load points in IEM 1 as the top event. Concerning this specific architecture of FREEDM system, the differences in the fault tree for different load points only lie in the component number of the primary fault tree, and the sections of output flow paths in the secondary fault tree. The IEMs and IEMs, corresponding to intelligent control and protection systems of the FREEDM system, are not further analyzed and decomposed. The basic events for the fault tree are listed in Table 2.  
Generally, the life of the electric equipment is exponentially distributed. Fault rates of the key components refer to literature [30]. The fault rate of starting failure of diesel generator is a fixed value of 0.05 [31]. For communication failure, no data found can be directly transformed to fault rate. Considering the target bit error rate (BER) of the fiber optic transmission is as low as \(1.00\times 10^{-15}\), and the fault-tolerance mechanisms of error checking and retransmission is introduced during the process of sending and receiving, communication in the FREEDM system can get a high reliability. It is assumed that the order of magnitude for the fault rate of communication is \(1.00\times 10^{-8}\) failures/hour. \begin{table}
\begin{tabular}{c c c c} \hline
**Load point** & **Priority** & **Priority factor** & **Power demand (kW)** \\ \hline Load 1 & 1 & 1.000 & 5 \\ Load 2 & 2 & 0.875 & 3 \\ Load 3 & 3 & 0.750 & 5 \\ Load 4 & 4 & 0.625 & 5 \\ Load 5 & 5 & 0.500 & 2 \\ Load 6 & 6 & 0.375 & 2.5 \\ Load 7 & 7 & 0.250 & 5 \\ Load 8 & 8 & 0.125 & 2.5 \\ \hline \end{tabular}
\end{table} 
Table 1: The settings of loads in the local framework. The same dilemma of failure data is also with the IEM and IFM devices, an order of magnitude of \(1.00\times 10^{-8}\) failures/hour is given for these components, considering their paramount importance in the system. For the renewable DGs, the data of their output power refer to online database [32,33], taking the real data of generated wind power and solar power of year 2013 in the Belgium area and transforming the data to the power levels of given renewable DGs. With layered fault tree model, we tend to analyze the reliability for different loads in the local framework of FREEDM system, using the simulation procedure for reliability assessment. The assessment is executed within a one-year cycle and the islanded cycle is set as one week (168 h). Results of reliability for load points in the local framework are presented in Table 3. Reliability for different loads is decreased with priority, which accords with the original intention of the system design. The modified Loss of load probability (_LOLP_*) is evaluated as \(8.34\times 10^{-3}\), and unreliability contribution of each load is listed in Table 3. The effect of priority factor is reflected, avoiding overemphasis on the low-priority loads with higher unreliability. It contributes to a rational systematic outcome, which weighs more on the high-priority loads and reflects the concern of the users. The loads with the biggest unreliability contribution are still Load 7 and Load 8, both with a relatively higher unreliability measure. Processes of unreliability growth over time for the loads in the local framework are also recorded and shown in Figure 8. The curves are generally separated into three groups. For the loads with higher priorities from Load 1 to Load 3, their unreliability measures are very low and the unreliability curves take on an approximate linear growth trend. For Load from 4 to 6, the yearly unreliability measures are still lower than 1%. It reflects the robustness of the system architecture in a sense. As for Load 7 and Load 8, the values of unreliability are significantly greater and there is a rapid growth process in the early period. This difference mainly caused by the different reliability levels of different kinds of DGs, in that batteries have higher reliability and can only supply 20 kW power.