# An Algorithm for Estimation of SF\({}_{6}\) Leakage on Power Substation Assets
## 2 Stages of the Algorithm
### Information Entry  
The information of the existing assets is provided by the workbook user. This stage of the algorithm is strictly descriptive. The workbook includes a spreadsheet to insert the data. The necessary fields to produce the charts are: substation and module id, year of commissioning, SF\({}_{6}\) initial mass, rate voltage and weight of injected SF\({}_{6}\) mass along with the corresponding dates.  
Model for Estimation of SF\({}_{6}\) Leakage  
The model selection was defined by the available information sources and the level of complexity. In a first approach, field monitoring measurements on the equipment were taken into account. For this, it was assumed that gas pressure or density measurements would be available for the fleet equipment, so gas behavior models such as one based on density [18], Van der Waals, or Beattie-Bridgeman models could be implemented [6; 19]. However, those models assume that changes in density and/or pressure are due only to gas leaks in the equipment and require data that may be difficult to obtain. If such a model could be interesting for realtime monitoring, its consolidation over long-time data makes it appropriate not for a quick estimation of historic leakage but for fast projection for future projects.  
A second approach taken into consideration was to use the information provided by the manufacturer about the nominal leakage rate of each asset. Again, very particular and organized information would be required, such as hard to find historical data, which should not be a problem for new projects.  
Considering the drawbacks of the first two approaches, a simple linear model was chosen, which depends only on easy to obtain information. Although the flexibility of the model decreases for the sake of simplicity, the parameters of the model can be changed according to the needs of the user, so different scenarios can be easily visualized. The model assumes a constant SF\({}_{6}\) leakage averaged rate per year, which summarizes the combined effect of all assets in all conditions during the lifetime of the project, as observed in previous leakage analyses [6; 16; 20]. The general model equation is shown below:  
\[m_{SF_{6}}=m_{0}\cdot F_{p}\cdot(t-t_{0}) \tag{1}\]  
where  
* \(m_{SF_{6}}\): leaked SF\({}_{6}\) mass in kg;
* \(m_{0}\): initial SF\({}_{6}\) mass in the asset in kg;
* \(F_{p}\): reference leak rate in % kg/year;
* \(t\): year for which the leak is estimated; and
* \(t_{0}\): year of asset commissioning.  
There is an additional parameter named \(L_{col}\), used to model end-of-life leakages, which considers the emissions related to the handling of the gas for disposal or recycling [21]. This parameter affects only the estimation for the final year \(t_{end}\) as shown below:  
\[m_{SF_{6}}(t_{end})=m_{0}\cdot F_{p}\cdot(t_{end}-t_{0})+m_{0}\cdot L_{col}. \tag{2}\]  
Additionally, economic impact parameters are used to make an estimation of SF\({}_{6}\) leakage equivalent cost. The model used is presented:  
\[m_{CO_{2}-eq}=m_{SF_{6}}\cdot GWP_{SF_{6}} \tag{3}\]  
\[CA=m_{CO_{2}-eq}\cdot CO_{2-cost} \tag{4}\]  
where* \(m_{CO_{2}-eq}\): mass of equivalent CO\({}_{2}\) in kg;
* \(GWP_{\mathrm{SF}_{6}}\): Global Warming Potential of SF\({}_{6}\);
* \(CA\): cost of environmental impact; and
* \(CO_{2-cost}\): cost of CO\({}_{2}\) emission per ton.  
The parameters of time and initial mass of the assets depend on the project to be analyzed. All the values used in equations 1 to 3 can be edited by the workbook user. In the next section the algorithm is used with real data and selected parameter values are further explained.