## 4 Application Example
### Energy Study of the Transformation House
#### 4.2.2 Reduction of Transformer Copper Losses Caused by Imbalance and Distortion Currents  
The losses caused by current imbalances in the transformer are not affected by the operation of the capacitor banks, since these are balanced loads. Likewise, the values of these losses are very small, both working days and holidays (Figures 8 and 9). This is an indication that the loads are slightly unbalanced and, therefore, it will not be necessary to apply any specific action to reduce these losses, whose values will remain at those indicated in Table 7.  
Regarding the phenomenon of distortion, the optimization of the operation of the capacitor banks has an additional beneficial effect, reducing the distortion currents and copper losses.  
Indeed, the distortion of the currents is fundamentally caused by the amplifying effect caused by the capacitive loads. This fact is observed in Figure 13. During periods of low activity of the companies, in which there are high supplies of capacitive reactive power, the currents are highly distorted (Figure 13a), with THD% of 14.58%, while in the times of high activity of the companies, the currents are slightly distorted (Figure 13b), with THD% lower than 3.74%. Under these latter conditions, distortion copper losses have an average value of 5.5 W (Figure 8). In our opinion, this is the maximum value of the losses caused by the distortion of the loads, without the amplifying effect of the capacitors, in periods of low activity for the companies.  
Consequently, the disconnection of the capacitor bank \(Q_{\textit{C2}}\), in the periods of low activity of the companies, gives rise to an additional reduction of the distortion currents and the losses caused by them. Considering that the value of losses due to distortion, without the effect of the capacitors, is the previously indicated 5.5 W every hour, it results in a 50% decrease in energy losses due to distortion currents, indicated in Table 7, for working days, and 75% for holidays. These reductions also extend, with the same percentage, to carbon dioxide emissions (Table 10). These important benefits make the additional installation of harmonic filters unnecessary, in our opinion.  
Figure 13: A-phase voltage and current waveforms registered in the secondary of the transformer in periods of (**a**) small power consumptions and (**b**) high power consumptions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Losses and Emissions**} & \multicolumn{2}{c}{**Savings**} \\ \cline{2-5}  & **Energy Losses** & **CO\({}_{\textbf{2}}\) Emissions** & **Energy Losses** & **CO\({}_{\textbf{2}}\) Emissions** \\  & **(kWh/Year)** & **(kg/Year)** & **(kWh/Year)** & **(kg/Year)** \\ \hline Working days & & & & \\ (251 days/year) & 272.74 & 65.73 & 1050.03 & 253.01 \\ \hline Holidays & & & & \\ (114 days/year) & 2.65 & 0.64 & 1770.05 & 426.57 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Annual energy losses (\(W_{\sigma}^{\prime}\)) and CO\({}_{\textbf{2}}\) emissions caused by reactive currents and savings after optimizing the operation of the capacitor bank \(Q_{\textit{C2}}\).