## 5 Smart Grid Reliability Assessment
### The Algorithm Used  
The reliability simulations are based on the time sequential Monte Carlo technique. This method has been adapted into the proposed approach of Smart Grid reliability assessment. The algorithm used to compute reliability indices of electric power distribution systems (EPS), communications networks (ICT) and integrated Smart Grid (SG) system is presented in a block diagram in Figure 6.  
The program starts with definition of system input data such as network topology with location of the components, failure and repair rates and connected loads. The number of sample years (N) and simulation period (T) are also entered in this step. The simulation begins with generating random numbers [0,1] for each element in the system and converting them into time to failure (TTF) using equation 4. In the next step, the element with the shortest TTF is determined, i.e., the component that will fail first. In the conditional block, it is then checked to see if the found minimal TTF value matches within one year. If this is not a case, it means that the TTF is longer than 8760 h and within this year no failure occurs. Further steps will be skipped and random numbers of TTF are computed again for all elements. If the TTF is shorter than 8760 h, the time to repair (TTR) will be computed for that element which indicates its out of operation state duration. Moreover, its location in the interconnection matrix as well as the location of any load nodes which can be influenced by the given component is also determined. After that, a new random number is generated for that component and converted into new TTF. Simulation time has to be updated for each element according to Equation (11).  
\[\text{TTF}=\text{t}+\text{TTR}+\text{TTF}_{\_}\text{new} \tag{11}\]  
Figure 5: Methodology of smart grid co-simulation: (**a**) EPS, ICT and Smart Grid in operation, (**b**) outage in EPS, ICT in operation, shortening the failure in Smart Grid, (**c**) failure in EPS, failure in ICT, shortening the failure in Smart Grid, (**d**) EPS in operation, failure in ICT, Smart Grid in operation [80,81].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & **Failure Rate (\(\lambda\))** & \
\begin{tabular}{c} **Mean Time to Repair** \\ **(MTTR) [h]** \\ \end{tabular} &
\begin{tabular}{c} **MTTR\({}_{\text{SG}}\) with com.** \\ **Network [h]** \\ \end{tabular} \\ \hline Distribution lines & 0.8 & 50 & 40 \\ Transformers & 0.1 & 100 & 80 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Values of the reliability parameters used for the simulations.  
The updated TTF value indicates subsequent time of failure occurrence and is compared with previously generated TTFs of other components. After that, the TTR for other elements can be computed. These procedures are repeated in a loop for each element until the simulation period (e.g., one year) is completed and all of the simulation sequences comprising the defined number of years are finished. Then, the reliability parameters of each component, such as failure and repair rate as well as unavailability, are computed. Finally, based on these parameters, the reliability indices for the whole system are calculated for the total sample number of years (N).  
Figure 6: Sequential Monte Carlo algorithm [81,82].