## 4 Application Example
### Energy Study of the Transformation House
#### 4.2.3 Replacing the Actual Transformer with a More Efficient One, with Less Power  
The nominal values of the copper and core losses of efficient distribution transformers are indicated in Table 11. It is observed that the core losses of the transformers are smaller in the transformers of lower nominal power. This fact could justify the replacement of transformers with others of lower-rated power. However, it can also be seen in Table 11 that the short-circuit resistance (\(r_{cc}\)) evolves in the opposite direction, so the load losses will increase if lower-power transformers are used, since the currents maintain their value. For this reason, in the event of replacing the actual transformer with another of lower power, the most suitable replacement transformer must be the one whose total losses, obtained as the sum of the copper losses and the core losses, have the lowest value. The comparison of the energy loss values in the copper of the 1600 kVA Ormazabal transformer (\(W_{c}^{(1)}\)), indicated in Table 12, and is measured by the Fluke 435 Series II instrument according to the equation:  
\[W_{c}^{(1)}=W_{ca}+W_{cr}+W_{cu}+W_{ch} \tag{12}\]  
denotes the impact of optimizing the operation of capacitor banks. The copper energy lost in the 1600 kVA Ormazabal transformer, with the optimized operation of the capacitors (\(W_{c}^{(2)}\)), is obtained as the sum of the losses due to the active currents (\(W_{ca}\)), to the reactive currents (\(W_{cr}^{\prime}\), Table 9), to the unbalanced currents (\(W_{cu}\), Table 7) and the distortion currents (\(W_{ch}^{\prime}\), Table 10), determined after the optimization of the operation of the capacitors, i.e. :  
\[W_{c}^{(2)}=W_{ca}+W_{cr}^{\prime}+W_{cu}+W_{ch}^{\prime} \tag{13}\]  
The copper losses for efficient transformers (\(W_{c}^{(3)}\)) have been calculated based on the following expression:  
\[W_{c}^{(3)}=W_{c}^{(2)}\;\frac{r_{cc}^{\prime}}{r_{cc}} \tag{14}\]  
where \(r_{cc}\) is the short-circuit resistance of the 1600 kVA Ormazabal transformer (Table 4) and \(r_{cc}^{\prime}\) is the short-circuit resistance of the analyzed efficient transformers (Table 11). The total losses of each transformer have been obtained by adding their copper losses (\(W_{c}^{(1)}\), \(W_{c}^{(2)}\) or \(W_{c}^{(3)}\)) to the core losses of each transformer (Tables 4 and 11). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type of Day**} & \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) & 34.685 & 8.36 & 34.685 & 8.36 \\ \hline Holidays (114) & 13.93 & 3.345 & 41.59 & 10.035 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Annual energy losses (\(W_{ch}^{\prime}\)) and CO\({}_{\textbf{2}}\) emissions caused by distorted currents and savings after the optimization in the operation of the capacitor bank \(Q_{c2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Power (kVA)**} & \multirow{2}{*}{**Copper Losses (W)**} & \multirow{2}{*}{**Core Losses (W)**} & **Short-Circuit** \\  & & & **Resistance (\(\Omega\))** \\ \hline
1600 & 12,000 & 1080 & 0.000826447 \\ \hline
1000 & 7600 & 693 & 0.00134064 \\ \hline
800 & 6000 & 585 & 0.001653704 \\ \hline
630 & 4600 & 450 & 0.00204438 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Nominal features of 24 kV efficient distribution transformers according to Commission Regulation (EU) No 548/2014. The values of carbon dioxide emissions (Table 13) have been determined by multiplying the total energy lost for each transformation and operation of the capacitor banks, indicated in Table 12, by the emissions factor for the year 2019, in Spain, 0.241 kg CO\({}_{2}\)/kWh.