# Operational Resilience Metrics for Complex Inter-Dependent Electrical Networks
## 3 The RecSIM Tool
For instance, in case of an outage in some of the substations on the MV line 1 in Figure 8, the descendant substations of the failed substation can be restored using line 2 or 3 using the \"frontier\" nodes (D1, C2, C3). Furthermore, in the RecSim models, there are dependencies between the EDN SCADA components and the telecommunication components providing the communication service. As shown in Figure 9, the tele-controlled substations use the communication service that is provided by telecommunication network components (i.e., the Base Transceiver Station of the tlc network ); this also works in the other direction--the BTS are fed by the secondary substations of the EDN. In this work, we assume that the BTS do not have battery backup. Then, if a BTS \(B_{x}\) depends on a substation \(S_{y}\) and \(S_{y}\) is in a damaged or disconnected status, the consequence is that \(B_{x}\) will immediately stop functioning. Assessing Robustness of Electrical Distribution Network Components and Possible Physical Damage Scenarios  
This section describes how to assess the physical damage that a possible shock might cause on EDN components, causing a loss of \(QoS\) that from the unit value will fall to the \(mQoS\) of Figure 2. The entity of \(mQoS\) will depend, among other factors, on the level of physical damage induced by the shock on the EDN components, if they are not totally robust to the shock. Properly designed components according to the most advanced design standard will guarantee a good level of robustness. However, it is usually not possible or, in any case, economically not feasible to guarantee full robustness of EDNs components to the different shocks that might arise from extreme natural events. Therefore, it might be useful to be able to assess their vulnerability (i.e., the propensity to be affected by perturbation of certain types, which can be considered as the complementary term of the robustness) and the physical damage that a shock might induce on them. A first step toward the assessment of vulnerability is the collection of relevant information related to the design level and the geometric and constructive features of the components. Table 1 proposes a taxonomy for assessing the vulnerability of EDNs. Figure 8: An example of frontier substations. Figure 7: The RecSim electrical model. Figure 9: An electrical distribution network SCADA system and TLC mutual dependencies. The assessment of a possible damage scenario can then be carried out by overlaying and convoluting information on the exposed EDNs components, including those regarding their vulnerability to the specific hazard under analysis (referred to as vulnerability factors in Table 1), and the perturbation intensity at the location of the exposed EDNs. This concept is summarized in the equation below, where the symbol \(*\) expresses convolution among factors:  
\[Damage=Hazard*Vulnerability*Exposure\]  
Damage can be described with different metrics for different types of EDN components (Table 1). Damage to infrastructure nodes is represented in CICCast-DSS according to a four-level damage scale, i.e., D1 slight/minor damage, D2 moderate damage, D3 extensive damage and D4 total disruption; with D0 representing the absence of damage. Damage of infrastructure nodes should consider both the physical damage and operational failure. Although components are located inside buildings, it may be necessary to separately assess the operational state of the equipment and the physical damage of the building. In these cases, it is possible that the structure is significantly damaged and that the component is fully operational, as none of the equipment is damaged. Conversely, it is possible for the structure to be unaffected and the component has lost its function due to the damage of the equipment. Damage of infrastructure edges (a cable, for instance) can be assessed quantitatively in terms of a damage rate DR, a deterministic estimate of the number of damages that a cable is expected to experience per unit of length (usually per kilometer).