# Resilience Quantification of Smart Distribution Networks--A Bird's Eye View Perspective
## 3 Taxonomy of Resilience Evaluation Methods
### Performance Calculation
#### 3.2.1 System Model Method  
The study of power distribution or telecommunication networks requires, as with other critical infrastructure, modeling the system with all its internal and external characteristics [79; 90]. Two broad families of modeling are usually embraced for performance evaluation: analytical models, and simulation-based models [61]. Analytical models rely on mathematical concepts like graph theory, percolation theory, worst-case analysis, Markov chains (or processes), and statistics [91; 92; 93; 94] to represent the structure and behavior in any network and interactions therein. Theoretical analyzes can also be used for the threat, fragility, and recovery characterization process. Then, rigorous formulation is conducted using multiple mathematical tools.  
Simulation-based models basically have the same objective of system representation analytical models, but with the intent to have less abstraction and more fidelity to real networks. To do so, simulators are developed [95; 96; 97], based on the analytical approaches, however with many practical considerations which are usually too complex and not tractable by mathematical formulation. Thus, it is quite common to use simulation-based models as a validation method for the solution obtained by analytical analysis [79].  
A deeper look at the modeling techniques explained above shows that both are comprised of four distinguishable sub-models [35]. Note that this further granularity allows, in some cases, hybrid analytical-simulation models, as each sub-model is constructed analytically or by simulation, independently from the others. These sub-models are:  
* Contingency model: describes hazard profile, which is expressed in terms of characterizing parameters. An example would be to have a statistical profile that gives the probability distribution of wind intensities [41] or meteorological data to calculate the amount of ice accreted on conductors and overhead lines during an ice disaster [91]. Another widely considered example is cyber (or cyber/physical) attack scenarios [98; 99]. In some cases, there is deep uncertainty about the threat, then worst-case analysis [100; 101] and less conservative approaches like robust optimization [43] are the most suitable to model such events.  
* Component fragility model: represents the sensitivity of system components to a threat. This goes hand in hand with the contingency models, as fragility curves or other ways of representation are developed with respect to event profiles [41; 91].
* Restoration model: complements previous contingency and fragility models in order to yield threat impact quantification [102]. Focus is in recovery times which can be estimated using mathematical programming, fuzzy logic, statistical methods, specialist expertise, random distributions, or even heuristic approaches in some cases [28; 103].
* Network functional model: functional models in use range in complexity from pure topological approaches to physics-based models of AC power flows [104]. They describe system infrastructure, topology, services, and all related dynamic interactions. This is present in all system models and constitutes their core element, because it replicates the structure and all functions found in real networks as much as possible. Examples include percolation theory and complex networks [92], graph theory analysis [21; 105], power flow [14; 41], agent-based information traffic flow [106], and many simulation software that emulate network behavior [82; 96].