## 4 Conclusions  
In this paper, a modified layered fault tree model is proposed in order to distinguish and separate the two different power supply modes of utility supply and local supply, focusing on a potential islanded local framework of a specific smart grid architecture. Fault tree analysis has been a favorable method in reliability and safety evaluation, providing insights into the structure of the complex systems. It is an effective visual tool for engineering and management. The proposed fault tree construction procedure makes the model greatly simplified and unitized compared to the conventional fault tree model, with the layering procedure and inadequacy judgment function integrated. Revised importance measures for components considering load priority are presented and are applicable to find the weak parts of the system in order to improve the design and using. Corresponding \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**IEM**} & \multicolumn{3}{c}{**Failure rate (failures/hour)**} \\ \cline{2-4}  & **1.00 \(\times\) 10\({}^{-8}\)** & **1.00 \(\times\) 10\({}^{-7}\)** & **1.00 \(\times\) 10\({}^{-6}\)** \\ \hline Unreliability of Load 1 & 4.50 \(\times\) 10\({}^{-4}\) & 1.24 \(\times\) 10\({}^{-3}\) & 9.13 \(\times\) 10\({}^{-3}\) \\ Unreliability of Load 8 & 1.41 \(\times\) 10\({}^{-1}\) & 1.42 \(\times\) 10\({}^{-1}\) & 1.49 \(\times\) 10\({}^{-1}\) \\ \hline \multirow{2}{*}{**Communication**} & \multicolumn{3}{c}{**Failure rate (failures/hour)**} \\ \cline{2-4}  & **1.00 \(\times\) 10\({}^{-8}\)** & **1.00 \(\times\) 10\({}^{-7}\)** & **1.00 \(\times\) 10\({}^{-6}\)** \\ \hline Unreliability of Load 1 & 4.50 \(\times\) 10\({}^{-4}\) & 2.06 \(\times\) 10\({}^{-3}\) & 1.79 \(\times\) 10\({}^{-2}\) \\ Unreliability of Load 8 & 1.41 \(\times\) 10\({}^{-1}\) & 1.42 \(\times\) 10\({}^{-1}\) & 1.55 \(\times\) 10\({}^{-1}\) \\ \hline \multirow{2}{*}{**IFM**} & \multicolumn{3}{c}{**Failure rate (failures/hour)**} \\ \cline{2-4}  & **1.00 \(\times\) 10\({}^{-8}\)** & **1.00 \(\times\) 10\({}^{-7}\)** & **1.00 \(\times\) 10\({}^{-6}\)** \\ \hline Unreliability of Load 1 & 4.50 \(\times\) 10\({}^{-4}\) & 4.55 \(\times\) 10\({}^{-4}\) & 8.42 \(\times\) 10\({}^{-4}\) \\ Unreliability of Load 8 & 1.41 \(\times\) 10\({}^{-1}\) & 1.41 \(\times\) 10\({}^{-1}\) & 1.42 \(\times\) 10\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Unreliability assessment of selected loads with different failure rate settings for selected components. hierarchical Monte Carlo simulation method for reliability assessment is proposed for the layered fault tree model, with integration of state transition process of different power supply modes. The proposed layered fault tree model and reliability evaluation process combine power adequacy assessment with system failure logic, delivering a comprehensive insight into system failure. With the layering procedure and inadequacy judgment function integrated, the fault tree model will be greatly simplified and unitized compared to the conventional fault tree model. It also needs to be concerned that the evaluation process may require huge amount of computation, taking the dynamic aspect of DGs and loads as well as the increasing scale of system into consideration. The lack of pertinent failure-rate data makes it difficult to evaluate the reliability of the system. Sensitivity analysis has to be applied to evaluate the influence of deficient data. The proposed procedure is successfully tested on a case study of the FREEDM system. Thanks to the advanced automation and communication infrastructures along with the standardized structure of smart grids, the procedures proposed can be accomplished and applicable to other forms of smart grids.