# Resilience Quantification of Smart Distribution Networks--A Bird's Eye View Perspective
## 4 Resilience Quantification Objectives  
Four broad classes of resilience metrics are generally adopted: (i) average performance metrics, (ii) integrated multi-phase metrics, (iii) time-dependent metrics, and (iv) probability-based metrics [118]. In the case of a HILP event, probability distributions are often not available, whereas the other three classes depend on the measure of performance in the network. Thus, a reasonable statement is that an ideal evaluation of resilience may consist of a complete tracking of the time-dependent performance function P(t). This way, network operators can have the value of performance at any instant for the complete event duration. However, despite the apparent dependence of P(t) in time, performance function does not necessarily change with time if it is not for the extreme event which hits the system. In other words, performance function depends on many parameters including hazard intensity, system preparedness, resilience strategies in hand, and priority decisions made, all of which cause network state to change. This sends back the problem of resilience multi-dimensionality, which makes developing closed form derivation for resilience function challenging and hitherto out of reach. Performance-based methods try to include all previously mentioned parameters and additional ones into a temporal curve describing the performance evolution of the network. It can be said that many resilience features are embedded in a performance curve as shown in Figure 3, because the construction of such a graph takes into consideration all factors intervening during a catastrophic contingency. A salient advantage of such an approach is to have the temporal follow-up of network state which allows decision-makers to be in a best-informed posture. Four main phases can be distinguished, among which some can be further detailed into sub-phases:  
* Anticipation phase (phase I): Represents the time period before the event occurrence, when performance is at its nominal level. Monitoring information, impact projections, and historical data when available are used for prediction studies, and all possible defensive measures are implemented. This serves particularly in the case of multi-hazard management where risks and vulnerabilities to each event are investigated. For single hazard resilience analysis which is the most relevant in the case of HILP event, this phase is not considered and a post-event resilience study is adopted. However, this also refers to the period of normal operation where reliability and risk management for recurrent failures can be conducted, which participates in system resilience, because a resilient system needs to be first as reliable and low-risk as possible. In addition, security measures for protecting the system and preparing it to withstand malicious behaviors are implemented at this stage [96]. * Mitigation phase (phase II): Once an extreme event hits the network, reliance is on system robustness, reactivity, and absorption to minimize the effect on services and infrastructure. Adding to some preparation policies that could be anticipated, many dynamic actions can be implemented to reduce the aftermath, like distribution automation actions, load shedding, and monitoring actions in power distribution networks or customer prioritization in telecom networks. These actions can withstand performance degradation that is in place, or serve to coordinate between entities in order to achieve an accurate assessment of consequences and prepare next crisis management steps. * Recovery phase (phase III): Unlike short-timed low impact incidents where maintenance actions are achieved relatively fast, in major events, recovery actions can require anywhere between several weeks to months [119]. The main reason is that, given the safety of emergency crews and logistic constraints, restoration is conducted carefully and waits for the reduction in hazard intensity, or more generally identification of restoration windows.