# An Algorithm for Estimation of SF\({}_{6}\) Leakage on Power Substation Assets
## 4 Discussion  
The algorithm was designed to achieve simplicity and clarity. However, it was evaluated to understand its limitations and discuss future work. Table 4 compares the results of the linear model estimation, given by Equation (1), applied to data of the current fleet against the available reports of SF\({}_{6}\) leakage, without considering the end-of-life emissions.  
Note that a positive error means that the prediction was above the injected mass. That is an indication of better than expected performance regarding gas leakage in the equipment. Negative errors underestimate the leakage. However, reasons for the high error values can be explained and help understand limitations of the algorithm.  
Asset 2082 from substation VE, which has the maximum relative error, is a Crompton Greaves SF\({}_{6}\) gas insulated circuit breaker. According to the technical brochure, the equipment has a guaranteed maximum leakage rate of less than 1% per year [26]. The model estimation with a \(F_{p}\) parameter value of 1% is 0.4 kg of leaked gas, with a corresponding relative error of \(-28.6\%\). This reduction in the prediction error applies to another 31 assets.  
Asset 2082 from substation FO is an ABB HPL145/25C1 circuit breaker installed in 1991, with 0.42 kg of SF\({}_{6}\) injected in 2013 and 1 kg in 2017. This behavior may indicate an inadequate top-up operation in 2013, which led to higher leaks since then. Another influential aspect is the technology available when the circuit breaker was manufactured,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Substation**} & \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{**SF\({}_{6}\) Injected**} & \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Relative Error**} \\  & & **[kg]** & **Prediction [kg]** & **\%** \\ \hline FO & 2082 & 1.42 & 0.65 & \(-54.23\) \\ UM & 2062 & 0.4 & 0.18 & \(-55.00\) \\ FO & 2042 & 1.05 & 0.725 & \(-30.95\) \\ MU & 2012 & 0.55 & 0.324 & \(-41.09\) \\ AU & 2052 & 0.95 & 0.6 & \(-36.84\) \\ TU & 3062 & 2.06 & 1.68 & \(-18.45\) \\ UM & 2032 & 0.8 & 0.66 & \(-17.50\) \\ VE & 2082 & 0.56 & 0.2 & \(-64.29\) \\ LG & 2032 & 0.7 & 0.68 & \(-2.86\) \\ TZ & 2012 & 0.88 & 0.8 & \(-9.09\) \\ NO & 3122 & 0.8 & 0.95 & \(18.75\) \\ AJ & 2012 & 0.5 & 0.68 & \(36.00\) \\ CO & 2042 & 0.32 & 0.16 & \(-50.00\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of model results against historical data.  
Figure 5: Estimation of SF\({}_{6}\) leakage for a new project according to the parameters given in Table 2.  
as found in [16] where the largest emissions came from the oldest equipment. It is relevant to consider that 142 out of the 410 assets have over 25 years of service.  
In addition to the reasons previously mentioned, other factors can be considered to explain high error values:  
* Leak rate error: for this specific implementation of the algorithm, an average leak rate of 0.5% was used. However, assets with a longer operating time or lower quality may have higher leak rates, while newer higher building quality assets may suffer less leakage. To solve this problem, as was seen with asset 2082 from substation VE, catalog data could be used instead of average leakage rate.
* Important leaks during the recharging process: the model developed does not take into account leaks that may occur during maintenance of the asset, which can result in a significant mass of gas that is not injected. Manufacturers usually recommend good practices, such as those exposed in [6], for the recharging process to avoid SF6 leakage.
* Damaged equipment: although the estimation in the algorithm itself is not designed to be compared with historical data, an exaggerated deviation from the model estimation may indicate damages in an asset. Along with the record of top-ups, this kind of result offers the opportunity to anticipate failures and to take proper actions early in order to analyze the situation in more detail and start preventive maintenance.