# Resilience Quantification of Smart Distribution Networks--A Bird's Eye View Perspective
## 1 Introduction
Within the growing literature on power system resilience [27; 28; 29; 30; 31], utilities are particularly interesting in quantitative assessments of resilience, which propose relevant indicators to guide cost-benefit studies before planning investments. In this context, multi-dimensional characteristics of resilience are a considerable challenge [32; 33; 34]. [PERSON] and [PERSON] [35] tackled technical, organizational, and social dimensions of resilience, while providing an alternative to evaluate the economic dimension by estimation of economic losses. Only the technical dimension of the power network is widely investigated in the literature [36], which reveals the need to examine all other dimensions for a comprehensive analysis of resilience [33; 37; 38]. Technical and organizational dimensions are the most suitable in the case of power grids as they can be applicable at individual system levels, while social and economic dimensions are better suited for community level (interdependent systems), to which resilience studies should converge in the future [38]. Temporal multi-phase resilience quantification is a well-adopted technique that can embed other dimensions by linking them to technical and organizational dimensions through the implementation of enhancement strategies. Unlike [35], most proposed metrics in literature exclude pre-event and post-recovery phases, suggesting that quantification is conducted for a single scenario and not for a sequence of disruptive events, which corroborates the relevance of resilience for HILP disruptions. Work in [39] introduced resilience-based component importance measures centered in the recovery phase; on the one hand by establishing a ranking for load restoration using optimal repair time, and on the other hand, by quantifying the potential loss in optimal system resilience due to a delay in component repair process (computed through resilience reduction worth metric). Likewise, [40] focuses on the recovery stage of resilience, with the goal of comparing different restoration strategies and selecting an appropriate performance measure. Authors in [41] proposed a multi-phase framework to assess the resilience of the UK power transmission network under a windstorm. The framework considered both infrastructural and operational aspects, introducing four simple metrics to describe the degree and speed of degradation, duration of the disruption, and recovery speed. Grid connectivity and operational metrics can jointly describe the whole span of post-event analysis, and be used for planning short-term mitigation and recovery, or long-term hardening [42]. Resilience strategies to minimize system performance loss can be further analyzed under budget constraint by a tri-level planner-attacker-defender model [43], where a planner optimizes long-term transmission network expansion before an attack hits the system. Short-term switching operations are then applied in reaction. Resilience is quantified using customer demand not supplied, which includes both mitigation and recovery capabilities in the system. Many other optimization models and performance measures are adopted in related studies [44; 45]. Given widely stretched power networks, resilience studied at the system level for generation and transmission, does not (or negligibly) include distribution grid components [35; 39; 40; 41; 42; 43]. In 2010, only 15% to 20% of feeders implement distribution automation in the North American grid, one of the most advanced electrical systems [46]. This illustrates that the PDN is the most fragile level of electrical systems due to legacy \"blindness\" and manual operations along with electromechanical components [47], especially with the fact that an estimated 90% of customer outages in the US are related to this part of the system [48].