# An Algorithm for Estimation of SF\({}_{6}\) Leakage on Power Substation Assets
## 3 Results of Algorithm Applied to Real Data  
The algorithm was validated using data from the current fleet provided by ENELCODENSA, the DSO with the largest coverage in Colombia [22].  
In this particular case, the Information Entry stage used the information of 410 SF\({}_{6}\)-containing assets. Table 1 shows a portion of the provided assets data and exemplifies the structure of information that is entered in the current fleet data section of this stage.  
Table 2 shows an example of parameters that can be used in the model for the estimation section of the algorithm's first stage in order to estimate SF\({}_{6}\) leakage. However, users may choose different values according to their needs.  
The \(m_{0}\) parameter was arbitrarily picked. The reference leak rate, \(F_{p}\), is the most important parameter, as it defines completely the rate of growth of the gas leakage in the proposed model; 0.5% is the maximum relative leakage rate per year permitted for SF\({}_{6}\) in closed pressure systems according to IEC 62271-1:2017 standard [23]. The \(L_{col}\) parameter selected is the best guess according to [21].  
The \(GWPS_{F_{6}}\) parameter is taken from the European regulation No 517/2014 on fluorinated greenhouse gases [7]. However, a different value may be used based on other sources, as it could actually be 23,500 according to [24]. The cost per ton of CO\({}_{2}\) needs to be adjusted to carbon markets or internal corporate considerations.  
According to the Carbon Pricing Dashboard from The World Bank, in order to meet the goals of the Paris Agreement, for the power sector the carbon prices need to be in the range of USD 24-39/tCO\({}_{2}\)e by 2020 [25]. EUR 23/t is slightly above that lower bound.  
The results of the data handling stage are shown in Table 3, where data is grouped by substation and rate voltage to sum the total SF\({}_{6}\) initial and injected mass values.  
The charts generated in stage 2 are shown in Figures 2-5. Note that said charts correspond not only to the partial data shown in previous tables but to the full 410 assets. Figures 2 and 3 show the generated charts with the distribution of SF\({}_{6}\) mass as explained in Section 2.3.1. Figure 4 displays SF\({}_{6}\) leakage per year and per substation. Figure 5 exhibits the result of process described in Section 2.3.3, with the parameter values shown in Table 2. In Figures 2-4, the category labeled as other groups data has lower values to allow the correct visualization of results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Substation**} & \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Year of Comm.**} & **Rate Voltage** & **SF\({}_{6}\) Initial** & **SF\({}_{6}\) Injected** \\  & & & **[kV]** & **Mass [kg]** & **Mass [kg]** \\ \hline VE & 2012 & 2008 & 115 & 8 & NA & NA \\ VE & 2032 & 2008 & 115 & 8 & NA & NA \\ VE & 2042 & 2006 & 115 & 8 & NA & NA \\ VE & 2062 & 2008 & 115 & 8 & NA & NA \\ VE & 2072 & 1986 & 115 & 4 & NA & NA \\ VE & 2082 & 2008 & 115 & 8 & 0.56 & 30 August 2012 \\ VE & 2092 & 2008 & 115 & 12 & NA & NA \\ VE & 2102 & 2008 & 115 & 12 & NA & NA \\ \hline \hline \end{tabular}
\end{table}
Table 1: Current fleet data example.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(m_{0}\) & 10 kg \\ \(F_{p}\) & 0.5\% kg/year \\ \(t_{end}\) & 35 years \\ \(L_{col}\) & 10\% \\ \(GWPS_{F_{6}}\) & 22,800 \\ \(CO_{2-cost}\) & 23 EUR/t \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters used for the estimation of SF\({}_{6}\) leakage in a new project.  
Figure 4: Historical analysis of SF\({}_{6}\) top-ups in ENEL-CODENSA assets.  
Figure 3: Distribution of SF\({}_{6}\) mass based on ENEL-CODENSA assets data.  
Figure 2: Distribution of SF\({}_{6}\) mass based on ENEL-CODENSA assets data.