# 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)
\[\gamma_{50}=\left({{SCL}/{A}}\right)^{(\
icefrac{{1}}{{\alpha}})}=\left({54 /54.4}\right)^{(\
icefrac{{1}}{{\alpha}})}=1.05\;\text{mg/cm}^{2} \tag{8}\]  
Assuming a maximum value for SCL equal to 61 mm/kV leads to a \(\gamma_{50}\) = (SCL/A)\({}^{(1/\alpha)}\) = (61/54.4) = 1.68 mg/cm\({}^{2}\). In a similar way, for heavy pollution the estimated SDD value for 50% probability of flashover is 0.381 mg/cm\({}^{2}\). In particular, a sensitivity analysis is performed on the 50% flashover SDD by considering the values 0.381, 1.05 and 1.68 mg/cm\({}^{2}\) for all the insulators of the island. The other parameters \(n\) and \(c\) of the Weibull distribution remain the same and equal to the following value derived from [40]: \(n\) = 2.6 and \(c\) = 0.084. The minimum value \(\gamma_{0}\) of SDD which do not cause flashover depends on \(n\), \(c\), \(\gamma_{50}\) and \(\alpha\): with the parameters analyzed for the present study the ratio \(\gamma_{0}\)/\(\gamma_{50}\) is equal to 0.349. It is worth noticing that all the mentioned parameters depend on the type and configuration of the insulator. In real world practice, specific solutions are studied for the grid portion and reasonable return periods are assured also using specific countermeasures such as silicone coverings. This study only intends to demonstrate the benefit to resilience which can be achieved by replacing the insulators with specific performances with higher performance insulators. Specifically, simulation case PL2 compares the response to the same extreme values of pollution for insulators with three different design choices: heavy, very heavy and exceptional. Figure 5 compares the profile of return periods for OHLs (considering RPs lower than 150 years) for the three sub-cases considered. Figure 6 compares the profile of return periods for other grid components (considering RPs lower than 150 years) for the three sub-cases considered. In case of insulators designed for heavy pollution, it can be noticed that the RPs for lines and other components are generally higher than in the previous case, even though the RP values can still be too low in specific regions. In particular 207 components (other than OHLs) out of 1159 still show a RP lower than 10 years, only 57 components show a RP between 50 and 150 years. An area where still low RPs for OHLs and other components are detected corresponds to two portions of the Sardinian grid where pollution induced disturbances have recently taken place (extreme events of September 2001 and October 2014). In case of insulators designed for very heavy pollution, it can be noticed that fewer components (5 components) show a RP lower than 10 years: the areas with relatively low RPs are the North Western area and still the Southern area which underwent a series of pollution induced line trippings during the 2001 blackout of Sardinia. Figure 5: Profile of return periods (RPs) for OHLs in case of insulators design for (**a**) heavy pollution, (**b**) very heavy pollution, and (**c**) exceptional pollution. Figure 6: Profile of RPs for grid components (other than OHLs) in case of insulators design for (a) heavy pollution, (b) very heavy pollution, and (c) exceptional pollution. In case of insulators designed for exceptional pollution, it is worth noting that all components have a RP higher than 30 years (the lowest RP is equal to 30.1 years) and that only ten lines at 132 kV have a RP lower than 10 years (with a minimum RP higher than 2 years). The area where the OHLs present the lowest RPs is still the Southern area mentioned for the previous subcases. The components with RPs lower than 50 years are identified in the South East part of Sardinian system. This means also that a very conservative design of insulators considering the maximum advisable SCL for very heavy pollution conditions allows to limit and not to eliminate completely flashover problems: In real operation, additional measures (special silicone coverings, frequent cleaning of insulators, etc.)