# Probabilistic Resilience Analysis of the Icelandic Power System under Extreme Weather
## 4 Results & Discussion
### System Resilience  
We proceed by comparing the ability of the system to sustain the worst possible outage at the three identified characteristic instances by means of Monte Carlo simulation. Recalling that the worst possible outage depends on the prior sustained failures, Table 1 summarizes the results in terms of expected worst-case load shed. All the results of this table have been obtained using 5500 samples of the respective probability distribution, with the 3 rd column showing the standard deviation of the estimated quantity. Table 1 showcases the resilience of the Icelandic system. Indeed, at any phase of the storm, and despite having already sustained different failures, the system could still cope reasonably well with the additional worst-case outage. At the most extreme case, having realized the full effect of the storm, a new outage could lead to not serving at most 4.42% of the end-user demand. Further, given the cumulative effects of the storm, we argue that the progressive increase of the expected worst-case severity between the three phases of the storm is certainly moderate. Here we recall that the results shown in Table 1 are computed under the conservative assumption that no maintenance activity is performed throughout the storm. The small difference in the magnitude of the worst-case impact from between the start, peak and end of the storm should, thus, in practice, turn out to be even smaller. The coefficient of variation (i.e., ratio of standard deviation to the expected value) of the worst-case outage severity is an additional indicator to perceive the system resilience. To establish this point, Figure 3 presents the frequency of the different sampled system configurations at the three storm phases. The three sampled instances correspond to a very vast diversity of system configurations, \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \(\mathbf{s\hat{\varepsilon}v}\) (MW) & \(\mathbf{s\hat{\varepsilon}v}\) (\%) & \(\mathbf{\sigma_{sve}}\) (MW) \\ \hline start & 24 & 1.07 & 12.8 \\ peak & 48.8 & 2.35 & 23.5 \\ end & 95.16 & 4.42 & 31.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Worst-case outage severity (load shed). Figure 2: Temporal evolution of survival & new outage probabilities. as this figure shows. Notably, at the end of the storm, the system is at least in an N-9 configuration, which of course implies an atypically large number of component outage combinations. The system is clearly capable of absorbing the diversity in the possible component failures, as the worst-case outage severity coefficient variation is decreasing with the progression of the storm, Table 2. This implies that the system can respond to the storm progression in a rather stable manner. Keeping in mind Figure 3, additional evidence of the system resilience can also be found by looking into the identified worst-case outages at the different storm phases. Over this very diverse range of configurations, very few 'critical' branches stand-out as the additional outage that would cause the worst-case severity. At the instance prior to the storm, and as the system would still be most-likely intact, the outage of the branch HRU-GLE (as shown in Figure 1) was identified as the next worst-case outage in approximately 97% of the studied samples. During the moment of peak threat, we found two striking worst-case outages, and specifically the outages of branches RAN-VAR and HVO-RIM with respective frequencies of 26.3% and 70.4%. These two outages are also dominantly the identified worst-cases at the end of the storm with frequencies of 73% and 25.8%, respectively.The maximum severity of these outages during the moment of peak threat was estimated to be 1.65% and 0.63% in terms of percent of load disconnected due to involuntary shedding, respectively. Note that more severe worst-case outages were experienced in only 0.3% of simulations, up to a maximum severity of 5.7%.