**7. Conclusions**

*Infrastructure Management and Construction*

ferent stations. Over *nh*

*black = heuristic scheme).*

**Figure 6.**

along the same medium tension line).

, and *R(h)* = 1.78 × 10<sup>−</sup><sup>2</sup>

(among the manifold of possible damaged network states) those states where one or more SS are simultaneously damaged, in agreement with the rate of faults of the dif-

*Comparison of the D() distribution values for the N − 1 and N − 2 unbiased scheme simulation resulting from the simulation via the heuristic scheme (red = unbiased (N − 2), purple = unbiased (N − 1), and* 

Carlo sampling, of which 1163 were constituted by a single damaged SS; 296 with 2 damaged SS; 49 with 3 damaged SS; 5 with 4 damaged SS; and 2 with 5 damaged SS. **Figure 6** summarizes all the results obtained thanks to the simulations by using the (*N* **−** 1) and the (*N* **−** 2) *unbiased* scheme and the *heuristic* perturbation scheme. In all simulations (both for the *unbiased* and for the *heuristic* schemes), the same number of technical crews *C* available for the service restoration has been assumed (*C* = 2). The three curves, however, derive from simulations scheme which have produced different amounts of crisis scenarios whose impacts have been measured through Eq. (3). In fact, for the *unbiased* (*N* **−** 1) simulation, a number of crisis scenarios *n* equal to the number of nodes *N* have been produced (*n(N* **<sup>−</sup>** *1)* = *N* = 13,618). In the case of the unbiased (*N* **−** 2) simulation, a number of crisis scenarios *n(N* **<sup>−</sup>** *2)* = 271,581 have been produced (this number corresponds to the total number of double faults occurring

For the heuristic perturbation scenario, the number of cases was, in turn, *nh* = 1515 as previously stated. The most relevant feature of the three distributions must be observed in the impact dimension. The perturbations produced by using an unbiased (*N* − 2) scheme produce very large effects, as they tend to involve a large number of SS, which impose a sequence of interventions (with the provided number of technical crews *k* available, not all SS could be simultaneously repaired). The estimate of the corresponding *R(1)*, *R(2)*, and *R(h)* [through the use of Eq. (6)] appropriately renormalized all the distributions. Application of Eq. (6) to the three different distribution functions provides the following values: *R(1)* = 2.17 × 10<sup>−</sup><sup>2</sup>

. It is interesting, in turn, to notice that crises produced by the *heuristic* scheme (i.e., involving SS which have shown a large propensity to fault), although in some cases involving more than a SS produces impacts which, even in the largest cases, are of the same dimension of those produced by worst cases in the (*N* − 1) unbiased simulation. This is probably due to the fact that more vulnerable SS are located

= 1515 damaged configurations were obtained with the Monte

,

**44**

*R(2)* = 7.60 × 10<sup>−</sup><sup>3</sup>

The work presented in this chapter that built a great amount of work done on the same topic [18, 19] presents the RecSIM system and its relevant capabilities to represent and simulate real urban system and in particular problems related to the reconfiguration of electric distribution systems following faults. In particular two major achievements are highlighted, one related to the possibility to account for a number of issues, which have not been appropriately considered in the resilience assessment process in the existing literature, and the second concerning the viability of implementing RecSIM (and its scalability) to large, real EDN. In particular reference has been made in the paper to the case study of Rome city that has a quite large distribution network containing more than 13,500 electrical substations.

As for the general achievements in the area of the models for estimating resilience of EDN, a novel, computable scheme has been identified, on which the RecSIM engine, described in the paper, is based on. The RecSIM model considers different factors encompassing all the phases of risk management, including the technological properties of the network, the fault management procedures, and the network interdependency with the telecontrol network. In many cases of previous works on the same topic (recalled in Section 2), the resilience estimates have been done by using models which considered just the electrical response of the network, thus disregarding the topological and technological features of the network, as well as the management skills and procedures, and the external and environmental constraints. The EDN management model behind the RecSIM tool, in turn, is able to reconstruct the impact of a crisis by considering all the abovementioned factors (recalled in Section 4) which play a critical role in determining the overall systemic resilience of the EDN. Moreover, the possibility of relating the resilience to the distribution of impacts generated by a range of possible perturbations, described in this chapter, provides a further improvement to the prosed approach. Many different perturbation schemes could be therefore investigated, and a resilience score, more suitable for to the user's requirements, can be therefore assessed. Last but not the least, this scheme could also be prone to be modified by varying the outage impact metrics. Whereas in this work the outage impact Γ was assessed in terms of the KPI adopted by the Italian regulatory agency [Eq. (3)], it can be expressed by considering further metrics, able to account, for instance, the economic losses or the level of wealth reduction caused to the citizens [19].

As from the analysis of the data resulting from the case study analyzed, i.e., the Rome city EDN, the profile of the impact distribution functions resulting from the different simulations made on the basis of the *unbiased* and the *heuristic* schemes has revealed two main results.

Firstly, the *unbiased* (*N* − 2) scheme provides the worst-case scenario. The simultaneous damage of two SS residing along the same medium-voltage line, produces (as expected) impacts of a significant severity since several other SS are involved.

In this case, the model would be able to help the detection of the most impacting causes and to validate the possible improvements which could be introduced by acting on specific issues (i.e., by increasing the quantity of telecontrolled SS along the lines and/or by increasing the number of technical crews available and/or by improving the telecontrol strategy). This information would be particularly useful for electrical operators for the planning of new activities for enhancing resilience.

Secondly, the *heuristic* scheme, where SS are damaged according to their effective rate of fault (as measured and reported by the electrical operator), provides a resilience score which is slightly lower than the one resulting from the (*N* − 1) unbiased scheme. As previously discussed, this could be the result of the correct management of the operators which has "segregated" more vulnerable assets along the lines whose disruptions cause less relevant impacts on services. The RecSIM tool, in this respect, could be useful for assessing which should be the correct way for further improving this score by selecting the substations (among those which have produced the crisis scenarios accounted for in the simulations) whose robustness improvement could further reduce the impact and thus increase the resilience score. Moreover, the tool can be used within more general framework as, for example, the emergency management support tool CIPCast-ES [16] which allows to explore a realistic earthquake event occurring in an urban area by predicting disruptions on buildings and critical infrastructure and by designing a reliable scenario, accounting for road obstruction due to building collapse, to be used to design an efficient contingency plan.

In conclusion, the RecSIM model, being able to gather into a unique scheme several EDN features, can provide a reliable tool for the analysis of large and complex infrastructures. This is going to be exploited in Italy through the establishment of a competence center for risk analysis and forecast of critical infrastructure called EISAC. it (*European Infrastructure Simulation and Analysis Centre Italian node* [31]) which will deliver competences and services to support operators and public authorities committed to the protection and the emergency management of critical infrastructure.
