**2. Related work**

All definitions of resilience point to quantify a *dynamic, adaptive property of a system* (or of a *system of systems*) expressing its ability to withstand perturbations and to recover, rapidly and effectively, to equilibrium condition as similar as possible to that prior to perturbation [6–9]. When dealing with a technological system, the property of being "adaptive" inevitably leads to think of a number of factors

**35**

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

influencing the way the system might adapt other than its mere technological qualities (such as robustness, technological update of the components, etc.): these factors might include risk awareness and preparedness, to ordinary and emergency management capabilities, in general to management skills which must support the technological and the design quality of the network. Moreover, in the case of a *system of systems*, the resilience of a system also depends on the degree of resilience of the other systems whose services should be available for the recovery process and on the level of dependency that is between them. The nowadays emphasis on the resilience property of technological systems is a direct symptom of the increased awareness that networks' functional dependency is one of the major issues that must be considered for improving CI protection and, as such, should be always appropriately considered when dealing with modeling and simulation activities of these systems. In particular, in Europe different resilience assessment and management methods as well as new approaches and guidelines are proposed within interesting EU projects. The project SMR [10] proposes the guidelines and system dynamic modeling and simulation techniques to increase the resilience of cities, whereas the IMPROVER project [11] is more focused on CI. The project DARWIN [12] is focused on improving responses to expected and unexpected crises affecting critical societal structures during natural disasters (e.g., flooding, earthquakes) and man-made disasters (e.g., cyberattacks). To achieve this, DARWIN developed resilience management guidelines aimed at critical infrastructure managers, crisis and emergency response managers, service providers, first responders, and policy makers. Other interesting EU project results can be found in [13–15]. The main objective of these projects is the proposal of European Resilience Management Guideline (ERMG) frameworks to drive decision and policy makers, local governments, and CI operators toward more resilient cities, societies, and infrastructures. ENEA has proposed CIPCast a framework for the resilience evaluation of a specific area that is compliant with the general guidelines proposed, for example, in [10]. CIPCast allows geographical information system, GIS-based risk assessment, and situational awareness through the continuous acquisition of different kinds of data from the field (e.g., weather forecast, infrastructure network status). Furthermore, CIPCast allows the assessment of the impacts and consequences of possible damage scenarios due to the prediction of natural hazards (such as heavy rain, flash floods, earthquakes) on the infrastructure networks and services and on the affected communities [17, 18]. The present work describes RecSIM [19], a specific module of CIPCast allowing the operational resilience assessment of electrical distribution grids. Indeed, there is an increasing demand for resilience framework assessment of power grids due to the fact that electrical power grids are recognized as critical lifelines that have to cope with different threads including extreme natural disasters and man-made attacks [20–25]. An extensive review of the existing metric system and evaluation methodologies, as well as a quantitative framework for power resilience evaluation, is presented in [9] where a classification and review of the different approaches proposed in literature are provided. Firstly, the proposed resilience evaluation approaches can be classified as qualitative methods and quantitative methods. Qualitative methods, thorough general picture of the system, provide guidelines for long-term energy policy making. In contrast, quantitative methods are often based on the quantification of system performances. The different methods can be further classified as simulation-based [20], analytical-based [21], and methods based on statistical analysis and historic outage data [22]. According to this classification, RecSIM can be classified as a quantitativesimulation-based approach. In particular, RecSIM takes in input a damage scenario (i.e., the set of electrical grid components in failure), the resource available to face the crisis in terms of crews available, and the functioning status of the supervisory

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

*Infrastructure Management and Construction*

able resources rapidly and effectively [6].

traffic congestion [1].

EDNs.

unique system.

**2. Related work**

following earthquakes was seen to range from few hours to months (being more frequently in the range from 1 to 4 days) depending on the repair capabilities (e.g., availability of man power, machinery, and spare material) and on the level of access to damaged facilities, possibly delayed by damages to the road network and/or by

As far as adverse meteorological conditions are concerned, both the transmission and distribution systems have been adversely affected by water bomb causing flooding, extreme snowfall or windstorm, and overheating [1]. As an example, highvoltage overhead lines might be subjected to failure due to ice sleeves on conductors during snowfalls; medium-voltage overhead lines might be subjected to failure due to fall of trees during windstorms, while overheating can cause catastrophic failure of underground cables [4, 5]. As an example, a clamorous case occurred in Auckland, New Zealand, in 1998 that involved the failure of four major underground cables due to overheating in the summer period. The failure of the underground cables kicked off a 5-week-long power outage across the central city and caused an estimated longterm economic impact equivalent to 0.1–0.3% New Zealand's gross domestic product. From the few facts mentioned above, it is clear that additional commitment and investments would be worthwhile, if not needed, to foster the resilience of the

EDN resilience can be pursued steadily before, during, and after crisis situations

by putting in place, in an integrated and balanced way, various actions aimed at increasing the *robustness* of the network components; the *redundancy* of the system; the *resourcefulness*, i.e., availability of resources (such as backup systems, human and material resources); and the *readiness*, i.e., the promptness and efficiency to recover the service functionality after a crisis event by managing and deploying the avail-

The works presented in this paper focuses on the resilience enhancement *after crisis events*, with particular emphasis on the factors that might increase the *readiness*. A further aspect examined by this work is the interdependency of EDNs with other critical infrastructures (CIs) and the implication that this has on the resilience of EDNs. EDNs are, in fact, essential for the functionality of other services such as water, telecommunications (tlc), roads, and other public services; on the other hand, EDNs depend on other critical infrastructures to deliver their service. In particular, EDNs are highly dependent on telecommunication that provides telecontrol functionality to EDN, to such an extent that it is fair to assume that electrical and telecommunication networks do represent a unique, connected *system of systems* whose control, protection, and management should be performed as if it was a

The paper is organized as follows. Section 2 presents relevant works related to existing methods for the resilience assessment of EDNs. Section 3 contains a description of the abstract model representing the topology and the constitutive elements of a large EDN. Section 4 identifies metrics for assessing the resilience of EDNs in terms of induced service impacts after different kinds of perturbations. Finally, Section 6 presents the implementation on the case study of Rome, Italy.

All definitions of resilience point to quantify a *dynamic, adaptive property of a system* (or of a *system of systems*) expressing its ability to withstand perturbations and to recover, rapidly and effectively, to equilibrium condition as similar as possible to that prior to perturbation [6–9]. When dealing with a technological system, the property of being "adaptive" inevitably leads to think of a number of factors

**34**

influencing the way the system might adapt other than its mere technological qualities (such as robustness, technological update of the components, etc.): these factors might include risk awareness and preparedness, to ordinary and emergency management capabilities, in general to management skills which must support the technological and the design quality of the network. Moreover, in the case of a *system of systems*, the resilience of a system also depends on the degree of resilience of the other systems whose services should be available for the recovery process and on the level of dependency that is between them. The nowadays emphasis on the resilience property of technological systems is a direct symptom of the increased awareness that networks' functional dependency is one of the major issues that must be considered for improving CI protection and, as such, should be always appropriately considered when dealing with modeling and simulation activities of these systems. In particular, in Europe different resilience assessment and management methods as well as new approaches and guidelines are proposed within interesting EU projects. The project SMR [10] proposes the guidelines and system dynamic modeling and simulation techniques to increase the resilience of cities, whereas the IMPROVER project [11] is more focused on CI. The project DARWIN [12] is focused on improving responses to expected and unexpected crises affecting critical societal structures during natural disasters (e.g., flooding, earthquakes) and man-made disasters (e.g., cyberattacks). To achieve this, DARWIN developed resilience management guidelines aimed at critical infrastructure managers, crisis and emergency response managers, service providers, first responders, and policy makers. Other interesting EU project results can be found in [13–15]. The main objective of these projects is the proposal of European Resilience Management Guideline (ERMG) frameworks to drive decision and policy makers, local governments, and CI operators toward more resilient cities, societies, and infrastructures. ENEA has proposed CIPCast a framework for the resilience evaluation of a specific area that is compliant with the general guidelines proposed, for example, in [10]. CIPCast allows geographical information system, GIS-based risk assessment, and situational awareness through the continuous acquisition of different kinds of data from the field (e.g., weather forecast, infrastructure network status). Furthermore, CIPCast allows the assessment of the impacts and consequences of possible damage scenarios due to the prediction of natural hazards (such as heavy rain, flash floods, earthquakes) on the infrastructure networks and services and on the affected communities [17, 18]. The present work describes RecSIM [19], a specific module of CIPCast allowing the operational resilience assessment of electrical distribution grids. Indeed, there is an increasing demand for resilience framework assessment of power grids due to the fact that electrical power grids are recognized as critical lifelines that have to cope with different threads including extreme natural disasters and man-made attacks [20–25]. An extensive review of the existing metric system and evaluation methodologies, as well as a quantitative framework for power resilience evaluation, is presented in [9] where a classification and review of the different approaches proposed in literature are provided. Firstly, the proposed resilience evaluation approaches can be classified as qualitative methods and quantitative methods. Qualitative methods, thorough general picture of the system, provide guidelines for long-term energy policy making. In contrast, quantitative methods are often based on the quantification of system performances. The different methods can be further classified as simulation-based [20], analytical-based [21], and methods based on statistical analysis and historic outage data [22]. According to this classification, RecSIM can be classified as a quantitativesimulation-based approach. In particular, RecSIM takes in input a damage scenario (i.e., the set of electrical grid components in failure), the resource available to face the crisis in terms of crews available, and the functioning status of the supervisory

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 traffic that might delay repair activities.
