# Quantification of the Benefits for Power System of Resilience Boosting Measures
## 2 A Framework to Model Power System Resilience
### A Risk Based Perspective to Analyse Power System Resilience  
The assessment of power system resilience and its enhancement requires the re-definition of the boundaries of the system subject to the analysis. In fact, while the conventional concepts of security and adequacy are mainly focused on the power system only, resilience is a multifaceted subproperty which encompasses the relationship between power system and the (natural and human) environment. Resilience analysis hence focuses on the study of the interactions between the environment and the power system. The environment affects the system in different ways:  
* Environmental threats can affect the infrastructure and energy supply service of power systems. * Weather also influences the available generation and the load demand, thus the operating conditions of the power system (e.g., the large use of air conditioning systems in case of hot temperatures, the renewable generation as a function of wind speed and solar irradiation, and the cutoff of wind turbines due to excessive wind). A resilience analysis always starts from the modeling of the root causes (e.g., wet snow storm) of the outages, namely natural or man-made threats. To this purpose, the bow tie model [20] provides a useful conceptual scheme to describe the connections between the different aspects of the resilience assessment framework. In particular, Figure 2 shows the bow-tie model used to qualitatively describe the connections between threats, component vulnerabilities, and power system contingencies. The left side of the scheme in Figure 2 suggests possible classifications for threats, in particular two categories are highlighted: natural threats versus man-related threats, where the latter are in turn classified into internal or external to the power system. Threats act on power system components by means of stress variables (e.g., wet snow loads for a wet snow event) and they cause the faults of components by exploiting their vulnerabilities. Component faults lead to the occurrence of a contingency which may affect more or less components on the basis of the response of protection and automation systems. The contingency may lead to an initial impact which in turn can exploit other vulnerabilities, triggering a cascading process that finally results in load disruptions (up to widespread blackout). The barriers represented in Figure 2 stop (or at least make less probable) the overall process which leads from threats to load disruptions: For example, a barrier can either reduce the intensity of the threat or reduce the vulnerability of the component to the threat. Given a certain set of faulty components, barriers allow to reduce the extent and the severity of a contingency. The same contingency may in turn cause less impact if suitable barriers are deployed. This process from threats to power system impacts is modelled in the proposed framework taking into account:  
* The differences among the application contexts (long term planning, operational planning, real time control), which affect the types of measures that can be adopted in each time frame. Figure 2: The bow tie model. * The uncertainties affecting the assessment process, which depend on the chosen application context. For example, in long term planning strong uncertainties affect both load and generation patterns as well as the extreme values of weather variables, while operational planning considers the short term forecasts of load and renewable generation, the conventional generation schedule, as well as the short term forecasts of the weather conditions in the subsequent 24-72 h. In real time control, the main uncertainties regard the response of protection, defense and automation systems during the shock absorption phase and on repair crew work in the recovery phase. In this context, risk is a key enabler to take advantage of the concept of resilience.