## 5 Resilience Assessment for Smart Power and Telecommunication: Case Study
In this case study, the performance of the scrutinized system is evaluated using two distinct measurements, each addressing unique aspects of the infrastructure's characteristics. The first measurement centers around the total quantity of available transmission lines, a parameter that directly reflects the system's topology. The second measurement, on the other hand, assesses the precise amount of power demand that the system can cater to, offering insights into its functional capabilities. To further investigate the performance, a multi-objective optimization problem (MOP) is defined for the Supervisory Control and Data Acquisition (SCADA) system, an integral part of the infrastructure. This selected MOP is intrinsically tied to the system's topology, focusing specifically on the total number of Remote Terminal Units (RTUs) at its disposal. It is vital to recognize that the selection of a suitable MOP for the SCADA system is influenced by various factors, including the overarching goals of the system, the resources at its disposal, and the system's specific constraints. Consequently, the selected  
Figure 19: The high voltage Swiss electric power transmission system. Figure 18: The representation of the EPSS in three subsystems (layers). MOP should be in harmony with the performance metrics employed for evaluating the system's effectiveness. To facilitate comparisons, the MOPs are normalized within the range of [0, 1]. This normalization process helps in keeping the diverse measurements within a standard scale, enabling a more accurate and fair comparison. In the broader setting, the case study provides a comprehensive analytical framework that captures key elements of system resilience while addressing the inherent complexities and interdependencies within the infrastructure. \[MOP_{SUC1}=\frac{\text{number of available transmission lines}}{\text{number of total transmission lines}}\in[0,1] \tag{18}\]  
\[MOP_{SUC2}=\frac{\text{actual power demand served (MW)}}{\text{total power demand (MW)}}\in[0,1] \tag{19}\]  
\[MOP_{SCADA1}=\frac{\text{number of available RTU devices}}{\text{number of total RTU devices}}\in[0,1] \tag{20}\]  
To conduct a thorough and effective assessment of the resilience metric, General Resilience (GR), vis-a-vis alternative strategies, it is imperative to calculate a couple of additional performability metrics. These metrics provide complementary perspectives on system performance and enhance our understanding of the system's resilience. The first metric is the Average Substation Service Availability Index (ASSAI). This index quantifies the proportion of the total hours during which all operational substations render service in relation to the total hours wherein the service is demanded. This index offers a comprehensive view of the service available throughout the entire system, taking into account the operational status of all substations. By comparing the ASSAI values of various solutions, one can gain a deeper understanding of their capacity to provide a dependable service over an extended period. This comparison provides an analytical perspective that is invaluable in understanding the system's resilience and effectiveness. Notably, the ASSAI serves as an essential tool for evaluating the dependability and robustness of the system's service, hence playing a pivotal role in the overall resilience assessment. These combined metrics--GR and ASSAI--allow for a more holistic and nuanced understanding of system resilience. By integrating various aspects of system performance, they provide a comprehensive picture of system resilience, thereby facilitating informed decision making in the design and operation of resilient infrastructures. \[\text{ASSAI}=\frac{N_{S}\times\text{number of hours}-\sum_{i=1}^{N_{S}}Res_{i}}{N _{S}\times\text{number of hours}}\in[0,1] \tag{21}\]  
where \(Res_{i}\) represents the restoration time for the \(i-th\) substation if service interruption exists and \(N_{S}\) represents the total number of substations.