# Probabilistic Resilience Analysis of the Icelandic Power System under Extreme Weather
## 5 Conclusions  
This paper developed a probabilistic resilience assessment methodology, explicitly taking into account the impact of weather conditions on the availability of the system infrastructure. Focusing on a storm event, we relied on real-life data as inputs to an already established model of the component  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Start** & **Peak** & **End** \\ \hline \(\sigma_{\text{sev}}/\hat{s}\hat{e}\)v(\%) & 53.33 & 48.15 & 33.04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Worst-case outage severity coefficient of variation.  
Figure 3: Summary of sampled system configurations.  
failure probability in function of the anticipated wind-speed. We combined this model with a worst-case assessment framework, relying on bi-level optimization to quantify the worst-possible loss of load from any new component outage, given the (randomly sampled) prior failures the system may have already sustained. We analyzed the resulting metrics at different characteristic phases throughout the storm, to capture resilience in terms of the relative ability of the system to absorb further degradation.  
The presented case study concerns the islanded power system of Iceland and it is based on data that were prepared in anticipation of one of the most extreme weather events, which happened in December of 2019. Our results validate the resilience of the Icelandic system in the face of this storm event. We have shown that at the peak threat instance, when the system infrastructure may already be partially unavailable and a new outage is most probable, the worst-case new outage is expected to only cause involuntary shedding 2.35% of the consumer demand. Further, at that storm end instance, when a large part of the infrastructure should have failed and before any restorative maintenance, a new outage is expected to only cause involuntary shedding 4.42% of the consumer demand in the worst-case. This implies that the ability of the system to withstand failures degrades much slower than the degradation in its available infrastructure.  
Landsnet records contain 17 distinct events of shedding of consumer demand during the studied period. Of these, 11 represent disconnections of 1% or less of consumer demand, and five others represent 1 to 2.4% of consumer demand. The remaining largest disconnection event represented 5.9% of consumer demand; however, in this particular case, 40% of the shedding was voluntary as a result of pre-existing wide-area control systems. Therefore, the proportion of involuntary load shed was 3.5%, which is within the bounds determined by the bi-level attacker defender model. Hence, the system is indeed resilient.  
Future work concerns extending the framework introduced in this paper towards evaluating the impact of several measures for enhancing the system resilience. As a first-step, we plan to develop and integrate a credible restorative maintenance model, explicitly recognizing the particular difficulties present during the storm event. This will allow for quantifying the value of restorative maintenance for power system resilience and analyze which parameters of the restorative maintenance infrastructure (e.g., capacity of maintenance crews, geographical dispersion, availability of spare parts) are of critical value. In a similar manner, the framework will also be extended by modeling bespoke resilience-enhancing resources, such as back-up generation.  
E.K. developed and implemented the probabilistic resilience assessment framework. S.P. developed and implemented the probabilistic threat modeling framework. E.K. and S.P. jointly analyzed the case study results, wrote and edited the manuscript. L.W. provided consultation on the development of the methodology and reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.