# Quantification of the Benefits for Power System of Resilience Boosting Measures
## 5 Case Studies
### Calculating the Return Periods of OHL Outages due to Wind and Wet Snow Loads (PL1)  
This long term planning application of the methodology consists in evaluating the RP of outages of the OHLs due to combined wind and wet snow actions. The example refers to the HV and EHV lines of GRID 2 model. The extreme values of wet snow loads and wind loads are derived from Std En. 50341-2-13 for area 1 (that is the North of Italy) [39]. From Figure 4a it can be noticed that the minimum RP is 29 years. For all the lines, the weakest sub-component (i.e., the one with lowest RP) is the support composed by the cross-arms and the body. Figure 4b shows the OHLs of the region with different colors representing decreasing values of return period of outage (from longer RPs in white to shorter RPs in magenta). In particular, the colormap in the following figure indicates: RP in the interval [0, 30] years with magenta color, RP in the interval (30, 50) years with red color, RP in the interval (50, 100) years with yellow color, RP in the interval (100, 300) years with cyan color, RP in the interval (300, Inf) years with white color. The knowledge of the RPs of component outages is a fundamental element to compute the long term resilience indicators such as EENS (Expected Energy Not Served). Comparing the Return Periods of Component Outages due to Pollution for Different Vulnerabilities of Insulators (PL2)  
This subsection presents an application of the methodology in long term planning in order to assess the return periods of outages of grid components due to pollution for different vulnerabilities of component insulators. In particular, the most important stress variable for \"pollution\" threat is the Salt Deposit Density (SDD) in mg/cm\({}^{2}\) even though also NSDD affects the vulnerability of the insulators to flashover. Thus, in the tests to demonstrate the effectiveness in applying the general methodology, only the map of SDD will be taken into account. The most vulnerable components are the insulator chains which are prone to flashover under polluted environments. In the present paper the authors adopt a voltage withstanding capability model for each insulator chain given by a three parameter Weibull distribution truncated for SDDs lower than a minimum value \(\gamma_{0}\), as suggested in [40]. This distribution is characterized by the 50% flashover SDD \(\gamma_{50}\) and parameters \(n\), \(c\) and \(\alpha\). Figure 4: (a) List of overhead lines (OHLs) with increasing RPs—EN 50341 indications for extreme values distribution, (b) Georeferenced map of OHLs with colors indicating increasing values of return periods (from magenta to white)—extreme values evaluated via Std EN 50341-2-13. The available maps provide the georeferenced distribution of the maximum values (over a two-year measurement campaign) of the SDD (Salt Deposit Density), in mg/cm\({}^{2}\), on the same type of insulators in the whole Italian peninsula in UTM coordinates. The measurements have been conducted on anti-salt glass insulators. The TSO guidelines indicate that in case of area with very heavy pollution (like Sardinia) then the minimum specific creepage length expressed in mm per kVrms maximum voltage at the terminals of the insulator chain should be included between 53 and 61 mm/kV: higher values of SCL are not advisable [30] and other measures should be deployed (such as special types/coverings for insulators, frequent cleaning of insulators). \[A\times\gamma^{\alpha}=SCL \tag{7}\]  
Equation (7) describes the relationship between SDD and the flashover voltage U [40]. Parameters A and \(\alpha\) are derived from lab tests and depend on the specific type of insulator. Examples of values for parameters A and \(\alpha\) can be found in [40] for some typologies of insulators. Considering a value of SCL for 50% flashover equal to 54 mm/kV, and A = 54.4 and \(\alpha\) = 0.22 as reported in [40], then the value of SDD which corresponds to the 50% probability of flashover reported in Equation (8).