## 5 CTMC Estimation of improvement in Blackout Recovery Time with Autarkic Microgrids
* **Test Case 1, Scenario 2: blackout recovery using autarkic microgrids:** autarkic blackout recovery is performed in the microgrid using MTC-based MAS communications but without the IOPS function, so that, if the eNodeB loses service from the mobile core network, the communication in the MAS fails. It is assumed that the eNodeBs are equipped with emergency power supplies, so that they continue to provide service in the blackout. Here, the microgrids autarkically perform black starts. The steps in the blackout recovery procedure in the microgrid are, firstly, to identify which nodes in the MAS are working; secondly, to identify the current microgrid topology and DER capacity; and, thirdly, to re-energise the microgrid and the loads. The CTMC states and conservative estimates of the state transition values are given in Tables 2 and 5. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Transition** & **Transition Purpose: Time to** & **Value (hours)** \\ \hline T\_SCADA & bring up SCADA & 1 \\ T\_GEN & bring up the generators & 10 \\ T\_NET & energise the transmission grid & 4 \\ T\_LOADRES & restore the load & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CTMC Transitions in conventional hierarchical top-down blackout recovery (Scenario 1). \begin{table}
\begin{tabular}{c c} \hline \hline
**State** & **State Meaning** \\ \hline S1\_MG & Blackout \\ S2\_MG & MG controller up, real time MG capability and topology identified \\ S3\_MG & Microgrids restored \\ S1\_MG & Blackout \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CTMC States in autarkic microgrids blackout recovery (Scenario 2). Figure 6: (a,b) CTMC Models for Test Case 1. * **Test Case 1, Scenario 3: Improved blackout recovery using autarkic microgrids and continuous preparation for blackout**: this is a further development of Scenario 2, but with the MAS continuously preparing during normal operation for blackout. It continuously monitors which agents are reachable, and deduces the current microgrid topology and what the DER production is. Based on this situational awareness, it knows whether it is able to perform black start in case of all possible combinations of nodes failing. Table 3 shows the neighbour identification time (T_MG_NBR_IDENTIFICATION), which includes the identification of the working MAS nodes and the actual grid topology. Furthermore, the value assumed for the time to coordinate the different MAS nodes to restore the microgrid (T_MG_CON_RES) is also shown. Figure 7 shows the mean blackout recovery time and the probability of blackout recovery for the three scenarios of Test Case 1. It can be seen that the grid is restored faster with the autarkic microgrid-based blackout recovery where individual microgrids are energised in parallel and quicker than in the traditional top-down method of Scenario 1. The mean restoration time is reduced by a factor of the order of 10 for the restoration with autarkic microgrids (Scenario 2) and reduced further by more than 10 times for the restoration with autarkic microgrids with continuous preparation (Scenario 3), where the steps of restoration are faster due to having pre-processed information regarding the identification of the available MAS nodes and the consequent contingency. Test Case 2 shows how the availability of the communication infrastructure is improved with the public safety (IOPS) function [17]: as shown in Figure 8, IOPS ensures that eNodeB continues to function if the mobile core network fails. Figure 7: Test Case 1: (**a**) Blackout Recovery Time and (**b**) Probability of Restoration for Conventional and Autarkic Microgrid Scenarios. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Transition** & **Transition Purpose: Time to** & **Value (hours)** \\ \hline T\_MG\_NBR\_IDENTIFICATION & bring up SCADA & 0.75 \\ T\_MG\_CON\_RES & bring up the generators & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CTMC Transitions in autarkic microgrids blackout recovery (Scenario 2).