## 4 Application Example
### Energy Study of the Transformation House
Figure 7: Transformer power losses in holidays due to (a) active currents (\(P_{ca}\)); (b) reactive currents with capacitors (\(P_{cr}^{\prime}\)) and (c) reactive currents without capacitors (\(P_{cr}\)). From the values of the powers and losses in the copper measured in the secondary of the transformer, an inefficient operation of the same is observed, whose cause is, mainly, in the inadequate operation of the non-variable capacitor banks, used for the compensation of the reactive power. These devices are responsible for high values of capacitive reactive power in periods of low activity in companies (Figures 4 and 5). Consequently:  
1. There are significant copper losses in the transformer, caused by the reactive compensation equipment, which give rise to significant CO\({}_{2}\) emissions. This fact can be seen in the energy losses on holidays in Table 5. The energy losses due to reactive currents on holidays amount to 1772.7 kWh/year. This value has been obtained by multiplying the losses caused by the reactive currents, each day (15.55 kWh, calculated based on the values in Figure 6), by 114 holidays in a one-year period, between September 2020 and August 2021. If the capacitor banks had not been connected, the reactive losses would have been only 113.92 kWh, on holidays (at a rate of only 0.9993 kWh/day). Likewise, CO\({}_{2}\) emissions, on holidays, are 427.21 kg each year compared to only 27,454 kg/year that would be produced without the capacitor banks. The CO\({}_{2}\) emissions indicated in Table 5 have been determined based on the 0.241 kg CO\({}_{2}\)/kWh ratio, obtained from Red Electrica Espanola, in 2019 [34]. Figure 8: Transformer power losses, in working days, caused by (a) unbalanced currents (\(P_{cu}\)) and (b) distorted currents (\(P_{ch}\)). Figure 9: Transformer power losses, during holidays, caused by (a) unbalanced currents (\(P_{cu}\)) and (b) distorted currents (\(P_{ch}\)). On the contrary, during the hours of greatest activity on working days, the capacitor banks work properly and achieve significant savings in losses and CO2 emissions (Table 5). 2. There are high economic penalties for capacitive reactive consumptions, after the Circular 3/2020 of the National Commission of Markets and Competition of Spain was introduced. (Table 6). In accordance with what is indicated in Section 2, not all the capacitive reactive energy (\(W_{q}\)), recorded each day in kVAr-h, is penalized, but only the net value (\(\Delta W_{q}\)) that results from discounting the inductive reactive energy in the penalty periods and indicated in Table 6, for working days and holidays. Penalties for the capacitive reactive energy (\(RCAP\)) have been calculated based on Equations (3) and (4), for a period of one year, between September 2020 and August 2021. This period includes 251 business days and 114 holidays. 3. Copper losses and CO2 emissions caused by unbalanced and distortion currents in the transformer windings are much lower than those due to reactive currents. These energy losses have been obtained by adding the values of copper losses indicated in Figures 8 and 9, for each hour of the working days and holidays, and multiplying the resulting values by 251 working days and 114 holidays (Table 7). The carbon dioxide emissions, indicated in Table 7, have been calculated by multiplying the energy losses by 0.241 kg CO2/kWh [34]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Penalization for Capacitive Energy**} \\ \cline{2-5}
**Type of Day** & **Penalization** & **Measured Capacitive** & **Penalized Capacitive** & **Annual** \\  & **Period** & **Energy, \(W_{q}\)** & **Energy, \(AW_{q}\)** & **Energy, \(AW_{q}\)** & **Penalization** \\  & & **(kvar-h/day)** & **(kvar-h/day)** & **(kvar-h/day)** & **(kvar-h/day)** \\ \hline Working days (251) & 0–8 h & 1511.17 & 324.53 & 4072.93 \\ \hline Holidays (114) & 24 h & 7249.43 & 7032.61 & 40,085.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Measured and penalized capacitive energies each day and annual penalizations.