# Resilience Quantification of Smart Distribution Networks--A Bird's Eye View Perspective
## 1 Introduction  
Current information and communication technologies (ICTs) have achieved a high degree of penetration in all critical infrastructure (CI) systems, owing to the ever-increasing capabilities of their services in terms of coverage, throughput capacity, latency, scalability, and privacy [1, 2, 3, 4]. In power systems, the massive introduction of telecommunication devices accelerated the shift toward smart grids (SGs) [5] that come with a whole new package of functionalities such as automated control, smart sensing and metering, high-power converters, and modern energy management techniques based on the optimization of demand, energy, and network availability [6]. The high-performance smart grid allows thereby for the insertion of new applications in the network like distributed generation, Industrial Internet of Things (IIOT), and electrical vehicles [7]. This comes, however at the expense of increased complexity, which brings new vulnerabilities and broadens the attack surface [8]. Recent extreme events of natural disasters, cyber-attacks, and man-made errors which we refer to as HILP events, have shown that SGs are susceptible to strong disruptions given the large-scale networks they represent, and the attendant interdependencies [9]. Some recent examples are the power disruptions in the US in 2017, caused by hurricanes and wildfires [10], which caused a cumulative damage of $306.2 billion, affecting a total of47 million people--nearly 15 percent of the nation's population. For instance, at the peak of hurricane Irma, more than 6.7 million electrical customers were without power [11], and hurricane Maria severely damaged the Puerto Rico power grid leaving 1.5 million people out of power [12]. China's severe ice storm in 2008 resulted in the service disruption of 2000 power substations and 8500 towers leading to power interruptions in 13 provinces and 170 cities [13], and over 4 million customers went on power outage for over seven days during the Great East Japan Earthquake in 2011 [14]. During the Ukraine power grid cyber-attack in 2015, 30 power substations were turned off, and hundreds of thousands of people were without electricity for a period from 1 to 6 h [15; 16]. Events like these reveal the need for strategies that are able to cope with such harsh impacts, especially given that the capacity to operate resiliently against attacks and natural disasters is one of the multiple smart grid attributes [17]. Resilience is defined as the ability to \"anticipate, absorb, adapt to and/or rapidly recover from a disruptive event\" [18]. In line with this definition, the U.S. Presidential Policy Directives-21(PPD-21) introduces resilience as \"the ability to prepare for and adapt to changing conditions and withstand and recover rapidly from disruptions\" [19]. This same directive involves the \"fail safe\" paradigm in system engineering through recommendations for cyber-physical security, while highlighting the shift toward \"safe-to-fail\" paradigm brought by cyber-physical resilience. Many conceptual frameworks are proposed for understanding and evaluating resilience, where the time dimension is very important, as various facets (anticipation, absorption, robustness, survivability, mitigation, flexibility, adaptability, restoration, and recovery) are linked to different temporal phases that describe system performance during an extreme event [20; 21; 22; 23; 24; 25]. Resilience moves from traditional risk assessment, which relies on probabilistic analysis of likely failures, toward dealing with unexpected events, requiring mitigation and healing strategies. The main difference is that risk assessment aims to achieve situational awareness and diagnosis, while resilience moves one step further by incorporating reactive actions against the contingency and launching restoration operations, which maintain the functionality of most critical loads and/or make them rapidly recoverable [26].