# Resilience Quantification of Smart Distribution Networks--A Bird's Eye View Perspective
## 5 Literature Review
### Power Distribution Network
#### 5.2.5 Metrics Computation  
As said before, performance assessment is an enabler for resilience quantification. Performance can include network topological characteristics and human factors, but it is mostly associated with service operational aspects defined in various ways: number of disconnected users [122; 127; 129; 134], probability of lines failure [123], power from the main grid [123], power from distribution generation [123], supplied/connected load [124; 126; 128; 130; 131; 135; 136] (or equivalently load shedding [122; 123; 126; 127; 132; 133]), critical supplied load [124; 131], total customer-hours of outages [127], total customer energy not served [122; 125; 127], outage duration [129; 130; 134], number of outages [129], loss of voltage and frequency regulation [133], load control and islanding [133], probability of source availability and penalty [137], total forecasted load [138], and current flow [139]. A straightforward approach suggests considering displayed performance indicators as resilience metrics [122; 127; 128; 129; 132; 131; 122] or proposes a justified empirical formula [136] that concocks performance into resilience. The dominant technique is to build a representation of performance (e.g., time curve) and use it to extract indicators, as in [122] where an index of resilience is proposed by tracking the number of LV customers not served. This results in a time-dependent index which can be used in different phases illustrated in Figure 3. With the same dynamic, [138] introduces an index calculated periodically as the ratio between the level of priority (or critical) load and total load. Moreover, authors in [124] propose to compute multiple phase-specific indices for vulnerability, degradation, and restoration efficiency, all from a timely curve of supplied load. This is then supplemented with a resilience index, which covers the whole event horizon. The same tendency is observed in [128] where the load expected maximum loss, interruption rate, restoration rate, and the recovery rate are evaluated. In relation to this, works in [131; 139] present fewer details on phase, but still offer the possibility to distinguish, in a broad sense, between survivability and restoration. A novel approach is highlighted in [135], where the percentage of loss load is proposed as a resilience metric, explicitly distinguishing in its terms loss of load in each single resilience phase. However, unlike the above phases fine-grained analyses of resilience, studies in [126; 130; 133; 134] opt for embedding the entire resilience information in a single metric, based on the inverse of power loss during an extreme typhoon event in [126], the ratio between up-time and event time in [130], loss percentage in [133], and combination of average loss and recovery time in [134]. This offers the advantage to be more attractive for DSOs as the framework is simple and less cumbersome, but it should be handled carefully to not miss tradeoffs that exist in resilience assessment. A good example is illustrated in [130], where resilience is calculated as the ratio between up-time and total event time. Attention was given to emphasize that this measure is defined for a single node, embodying another kind of granularity different from the one offered by multiple metrics for different phases. [PERSON] et al. [125], extend a risk-based metric, value-at-risk (VaR) which calculates the maximum loss expected over a given time period and give a specified degree of confidence. The proposal is conditional VaR (CVaR), defined to calculate the expected resilience loss due to probabilistic threat events, conditioned on the events being HILP. This bridges traditional risk management and all-phases resilience study. Topological characteristics are considered in [131] in the form of node degree. [PERSON] et al.