**3. Model description**

The proposed model aims at providing a model scheme, for the resilience assessment of EDNs, where all the abovementioned influencing factors could be appropriately considered.

Having recognized that resilience mostly starts with a number of activities that are performed during the normal operational mode of the network such as ordinary management of assets, accurate prediction of the events, and subsequent efficacy in performing preparedness actions rather than only with a "last minute" emergency management; the idea was to realize advanced technological tools enabling CI operators to improve the operational procedures during the normal operation mode while ensuring a continuous monitoring of external scenarios to forecast possible perturbing events, accompanied to some ex ante prediction of the expected impact (in terms of both economic losses and reduction of citizen's well-being) of possible emergency scenarios. With this objective in mind, ENEA has designed and realized a decision support system (DSS), called CIPCast, enabling to provide an operational (24/7) forecast and risk analysis for the CI in a specific area [16]. CIPCast includes a map of CI elements which could be hit and disrupted by predicted natural events (flash floods, snow, landslides, flooding) or occurred events (such as earthquakes). CIPCast allows to estimate:

• The physical impacts induced on EDNs following earthquakes [17] and flooding events

**37**

**Figure 1.**

*Modeling Resilience in Electrical Distribution Networks DOI: http://dx.doi.org/10.5772/intechopen.85917*

the quality of service

the electrical service to the final users.

*The elements considered in the electrical distribution grid model.*

• The impact on service functionality associated with the predicted damage of CI elements (in terms of outage duration and geographical extension), also considering possible perturbation cascades toward other networks and services [29, 30]

accounting for economic losses, reduction of citizen well-being, and impacts on

• The consequences of the predicted outages, according to several metrics

Within CIPCast, the RecSIM simulator represents the basic module for the

This section describes the theoretical model used to represent the topology of a large EDN within RecSIM. **Figure 1** shows the main elements of the proposed model. EDNs are composed of a number of primary substations (PS). Each PS originates one (or more) medium-voltage (MV) line(s) ending into a further PS. The MV line is cut at a certain stage by a switch which decouples the line into two halves, each one supplied by one of the two overlooking PS. Each line connects a number of secondary substations (SS) that, from the technological point of view, can be of one of the following types: "normal," "remotely telecontrolled," "automated," and "frontier" substations (represented, respectively, as white, gray, orange, and purple nodes in **Figure 1**). The "automated" substations are key elements of the network as they are able to perform automatically the isolation and restoration procedures needed to react to failures happening to their downstream substations. "Frontier" substations can be used to restore a portion of a MV line from another MV line. The configuration of the network switches defines the running configuration of the network. The electrical operator attempts to operate the network in order to maintain as much as possible the grid in a so-called normal configuration which is chosen by the operator as being able to allow the optimal operability of the grid (i.e., a good trade-off between robustness and efficiency, with the lowest possible electrical losses).

During a crisis, the electrical operator can change the configuration of the network by operating the switches along the perturbed lines; the operator brings the network into a "contingency" configuration, in order to restore as fast as possible

The model considers, furthermore, the dependencies between the electrical distribution grid supervisory control and data acquisition (SCADA) systems and the telecommunication components providing the telecontrol service. As shown in **Figure 2**, the telecontrolled substations use the communication service provided by the telecommunication (tlc) network components (i.e., the base transceiver

resilience assessment of the EDN, as better described in Section 4.

*Infrastructure Management and Construction*

traffic that might delay repair activities.

earthquakes). CIPCast allows to estimate:

**3. Model description**

appropriately considered.

control and data acquisition (SCADA) system and computes, in output, the power grid performance degradation in terms of the number of electrical users disconnected times the minutes of disconnection. As metrics for characterizing, in a posteriori analysis, the resilience of the power grid is proposed in [24] in terms of outage duration, dependency and interdependency relations, and the existence of energy storages, and a mathematical model for their calculation is proposed and implemented with respect to test cases focusing on recent natural disasters hitting major countries. In [25] the authors adopted the definition of resilience provided by the NIAC [26] that considers robustness, redundancy, and rapid recovery as main resilience features and developed a sequential Monte Carlo-based model for assessing the impact of weather on EDN resilience and applied to transmission networks. Their model considers the impact of human response during weather emergencies through the characterization of the delay required for the restoration of damaged components (due to delay in the development of individual situation awareness in the affected control centers) and the delay in the information sharing between the system agents, namely, the transmission system operators (TSOs) and the repair crews. As a test case, the model was applied to the transmission network considering extreme wind events, and simulation results show the resilience of the network in terms of robustness, redundancy, and response measures. Other past works also included the effects of humans [27], and others consider the dependencies [28] on resilience.

Similar to the approach proposed in [24] but considering the performance of EDN grids in complex urban contexts, RecSIM considers, simultaneously, the influence of different key features that might affect the time required for restoring the functionality of EDNs after extreme events, namely, (1) the degree of dependency with other networks providing essential services; (2) the network topology; (3) the number of repair crews available; (4) the number and functionality of SCADA telecontrol devices; and (5) the conditions of the road network and of the

The proposed model aims at providing a model scheme, for the resilience assessment of EDNs, where all the abovementioned influencing factors could be

Having recognized that resilience mostly starts with a number of activities that are performed during the normal operational mode of the network such as ordinary management of assets, accurate prediction of the events, and subsequent efficacy in performing preparedness actions rather than only with a "last minute" emergency management; the idea was to realize advanced technological tools enabling CI operators to improve the operational procedures during the normal operation mode while ensuring a continuous monitoring of external scenarios to forecast possible perturbing events, accompanied to some ex ante prediction of the expected impact (in terms of both economic losses and reduction of citizen's well-being) of possible emergency scenarios. With this objective in mind, ENEA has designed and realized a decision support system (DSS), called CIPCast, enabling to provide an operational (24/7) forecast and risk analysis for the CI in a specific area [16]. CIPCast includes a map of CI elements which could be hit and disrupted by predicted natural events (flash floods, snow, landslides, flooding) or occurred events (such as

• The physical impacts induced on EDNs following earthquakes [17] and flooding

**36**

events


Within CIPCast, the RecSIM simulator represents the basic module for the resilience assessment of the EDN, as better described in Section 4.

This section describes the theoretical model used to represent the topology of a large EDN within RecSIM. **Figure 1** shows the main elements of the proposed model.

EDNs are composed of a number of primary substations (PS). Each PS originates one (or more) medium-voltage (MV) line(s) ending into a further PS. The MV line is cut at a certain stage by a switch which decouples the line into two halves, each one supplied by one of the two overlooking PS. Each line connects a number of secondary substations (SS) that, from the technological point of view, can be of one of the following types: "normal," "remotely telecontrolled," "automated," and "frontier" substations (represented, respectively, as white, gray, orange, and purple nodes in **Figure 1**). The "automated" substations are key elements of the network as they are able to perform automatically the isolation and restoration procedures needed to react to failures happening to their downstream substations. "Frontier" substations can be used to restore a portion of a MV line from another MV line. The configuration of the network switches defines the running configuration of the network. The electrical operator attempts to operate the network in order to maintain as much as possible the grid in a so-called normal configuration which is chosen by the operator as being able to allow the optimal operability of the grid (i.e., a good trade-off between robustness and efficiency, with the lowest possible electrical losses).

During a crisis, the electrical operator can change the configuration of the network by operating the switches along the perturbed lines; the operator brings the network into a "contingency" configuration, in order to restore as fast as possible the electrical service to the final users.

The model considers, furthermore, the dependencies between the electrical distribution grid supervisory control and data acquisition (SCADA) systems and the telecommunication components providing the telecontrol service. As shown in **Figure 2**, the telecontrolled substations use the communication service provided by the telecommunication (tlc) network components (i.e., the base transceiver

**Figure 1.** *The elements considered in the electrical distribution grid model.*

**Figure 2.** *Electrical distribution grid SCADA system and tlc dependencies.*

**Figure 3.** *Secondary substation (SS) finite state model.*

station—BTS hereafter—of the telecommunication network). In turn, BTS are supplied by the energy provided by the SS of the EDN, thus configuring a dependency loop (no energy on a specific BTS, no telecontrol functionality of this BTS in favor of other SS of the network). In this work, we suppose that BTS do not have power backup, i.e., we will simulate the worst possible case. This implies that if a certain BTS depends on a certain substation SS that is in a damaged (or disconnected) state, that specific BTS will immediately stop functioning.

Each SS can be modeled as a finite state machine as shown in **Figure 3**. In normal conditions, the SS is in the initial "functioning" state. Starting from this state, the secondary substation (SS) can move into two different states:


**39**

*Modeling Resilience in Electrical Distribution Networks DOI: http://dx.doi.org/10.5772/intechopen.85917*

*P*:*F*(*N*,*L*,*t*) → *F*′

the functioning state to the not functioning or the failure states.

**4. Resilience metrics**

referred to as *F*:

such a case

where *F*′

in terms of *kilominutes* (i.e., 103

*<sup>i</sup>* = ∑

∫**<sup>0</sup>**

remains in this state waiting for restoration. The duration of the restoration can be in the range of few minutes (about 3–5 minutes) if the SS can be telecontrolled or much longer (50–55 minutes to few hours) depending on several factors (e.g., time required by emergency crews to reach the faulted substation and to restore it).

Let us assume to have an EDN characterized by its topology, with nodes *N* and links *L* corresponding to electrical stations and electrical lines, respectively. The function representing the *functioning state* for all the elements of the EDN is

*F*(*N*,*L*,*t*) = **0**∀*t* (1)

if all elements *N* and *L* are in a *functioning state* and all telecontrol functionalities are active. Let us now introduce a perturbation function *P* that can change the state of one EDN element from the *functioning state* to one of the other possible states. In

(*N,L,t*) *>* **0** for *t* ∈ [*0,T*] and zero elsewhere. For the sake of simplicity,

we will apply the perturbation *P* only to the electrical secondary station (referred to as SS). Time *T* represents the time when all elements have been repaired and the network comes back to its fully functional state *F(N, L, t) = 0*. A perturbation *P*, in principle, could affect one (or more) electrical station and bring it (or them) from

The damage of a SS consequent to the introduction of *P* produces a sequence of perturbations on the network. These consist in the disconnection of other nodes along the line due to instantaneous opening of protection switches. The damaged nodes are replaced by power generators (PGs) to ensure electrical continuity to the node's customers. The damaged nodes will not be repaired in the time space of the simulation, but their function will be restored through the settlement of PGs. The disconnected nodes, in turn, are reconnected either through a telecontrol operation (if available) or by dispatching technical crews to provide manual reconnection. All such interventions require specific times, which are considered when defining a restoration sequence of interventions. The impact of the perturbation *P* on the EDN is measured using a key performance indicator (KPI) that is currently used by the Italian Energy Authority to estimate the level of service continuity of an EDN. Such KPI is expressed as the number of disconnected customers *ni* of the *i-th* EDN node times the duration *i* of its disconnection. Such a value is expressed

network will result in the disconnection of *m* SS, each one for a time *<sup>j</sup>* ( *j =* **1**,*m*), the overall KPI outage metrics will be measured in terms of *i* that is defined as follows:

> *j*=**1** *m*

For a given perturbation *P*, the integral over the simulated time span of Eq. (3)

represents the perturbed functional state of the grid defined in Eq. (2):

*<sup>T</sup> F*′

(*N*,*L*,*t*) (2)

minutes). Thus, if the damage of the *i-th* SS of the

*nj <sup>j</sup>* (3)

(*N*,*L*,*t*)*dt* = *<sup>i</sup>* (4)

remains in this state waiting for restoration. The duration of the restoration can be in the range of few minutes (about 3–5 minutes) if the SS can be telecontrolled or much longer (50–55 minutes to few hours) depending on several factors (e.g., time required by emergency crews to reach the faulted substation and to restore it).
