## 2 Materials and Methods  
### Risk-Based Methodology  
A large body of work on power systems follows the classic definition of risk by [PERSON] [84] whereby risk is defined as the impact of an event times the probability of occurrence for this event. Similarly, to the data-driven approach in this paper, other works have used large datasets and statistical or probabilistic approaches to the analysis of power system events in terms of quantifying risk [84; 85; 86; 44; 87]. With enough data available, one can also use these datasets as a source of features and train modern machine learning approaches to predicting and quantifying risk [78; 86]. Machine learning and artificial intelligence approaches also can provide timely recommendations to the operator in charge of remedial actions [76; 78]. Common sources of data that recent research increasingly incorporates to risk and reliability studies are those characterizing renewable resources [88; 89].  
There is not a unique definition for resilience today, but the majority of published definitions focus on the power system ability to anticipate, absorb, and rapidly recover from an external, high-impact, low-probability event. A conceptual framework of power system resilience covers the following steps [46; 86]:  
* Step 1: Threat/Event characterization,
* Step 2: Vulnerability of system's components,
* Step 3: System response, and
* Step 4: System restoration.  
The key attributes of a resilient power system are robustness, resistance, resourcefulness, and redundancy. Due to the limitations mentioned above our study does not cover all these attributes and results are primarily related to step 1. To measure for example the robustness of a power system a comprehensive study needs to be performed to establish a threshold value of the consequence beyond which the performance of the system is considered to be unacceptable.  
It is important to note the similarities and differences on risk studies versus resilience studies. Reference [90] provides the definition for resilience of an infrastructure as \"the ability to anticipate,prepare for, and adapt to changing conditions and withstand, respond to, and recover rapidly from disruption\". It also states that resilience management goes beyond risk management to address the complexities of a power grid and the uncertainty of future treats, as it includes risk analysis as a central component. Risk analysis depends on characterization of the threats, vulnerabilities, and consequences of adverse events to determine the expected loss of critical functionality [90]. Due to the scope of this paper and the datasets we are leveraging, the authors are not applying the traditional risk-based methodology presented in [91] but focusing on the risk factors that come from the outages included in the analysis. Therefore, authors have used the results on cluster statistics to evaluate an aggregated risk at operating entity level that could be helpful to TOs to identify mitigation measures to prevent or minimize the impacts of those outages.  
CIGRE WG C4.47 proposed the reliability framework under a broader perspective to cover three components: adequacy, security, and resilience. A system that is resilient is not necessarily reliable. However, a reliable system must be resilient to extreme events, otherwise it would not satisfy the general definition of reliability. This perspective is supported also by EERC--Federal Energy Regulatory Commission--which indicates in [92] that \"resilience is a component of reliability in relation to an event\", and by NERC which states in [79] that \"a bulk power system that provides an adequate level of reliability is a resilient one\".