# Operational Resilience Metrics for Complex Inter-Dependent Electrical Networks
## 1 Introduction
In this work, the performance of the EDN system is defined through a contingency indicator commonly used as a key performance indicator (KPI) to estimate the level of service continuity of an EDN that is the _customers minutes of interruption_ (_CMI_) index [19]. For each electrical substation impacted by a disturbance, the indicator is equal to the number of disconnected customers \(d\) supplied by electrical substation times the time duration \(\tau\) of its disconnection expressed in terms of _kilomitutes_ (i.e., \(10^{3}\) min). The CMI indicator is suitable to measure the performances of large and complex networks where, in general, it is very difficult--if not impossible--to obtain the detailed electrical model needed to compute detailed electrical quantities as power delivered and the power flows used in other quantitative resilience assessment frameworks [20]. Indeed, the proposed quantitative resilience assessment model is a simulation-based approach that considers different factors/system properties that have a strong influence on the electrical distribution network performances; the factors are:  
1. _EDN-robustness_ of main components. The robustness of the EDN components has to do with their ability to withstand stress while sustaining limited or no damage. The structural hardening or in any case structural suitability of the main power delivery components, such as individual substations, transmission lines and distribution feeders, is a common approach to decrease vulnerability, i.e., their propensity to sustain damage if stressed, and enhance electric power system robustness. The magnitude of the loss of functionality at the time of the shock, i.e., \(mQoS(t1)\) of Figure 2 mainly depends on the robustness of main EDN components;
2. _EDN topology_. The topology of the network has a significant impact on its robustness and functionality. For the EDN, the term topology encompasses both the graph structure of the network and the position of the switches along the distribution lines. Both the properties have an impact in determining the overall resilient response of the network ([21] and references therein);
3. _Tele-controlled devices_. A large fraction of CI elements along the distribution network is tele-controlled, i.e., their control could be remotely performed by using telecommunication systems. Among them, \"automatic\" CI elements allow for a rapid decoupling of the faulted branch from the rest of the line. The lower the number of such units, the weaker the remote controllability of the system and the longer the required restoration time;
4. _EDN-Telecommunication dependencies_. The topology of the EDN-Telco interconnection, to discover how perturbation spreads on the different networks and which feedback should be expected;
5. _Efficiency of remote-controlled devices_. This can be achieved by redundant connections to telecommunication networks or private (and more secure) proprietary, wired communication networks;
6. _Efficiency of restoration procedures_. This can be achieved, for instance, by decreasing the time required to carry out the different restoration actions including tele-controlled and manual actions;
7. _Number of available technical crews_. The amount of technical resources available on the field when manual interventions on CI elements are required can lower the time of the intervention. This work describes the resilience assessment results of a large EDN (the Rome metropolitan EDN) obtained with RecSIM, a tool developed within the projects RoMA(\"Resilience enhancement Of a Metropolitan Area\", Italian project) and CIPRNet (\"Critical Infrastructures Preparedness and Resilience Research Network\", EU FP7 project) in collaboration with Areti SpA, the electrical distribution operator of the metropolitan area of Rome.