## 4 Application Example
### Energy Study of the Transformation House
#### 4.2.1 Optimization of the Operation of the Capacitor Banks  
We have already indicated above that there are two banks of three-phase capacitors, fixed, connected to the secondary of the transformation center transformer. The first, \(Q_{c1}=3\times 25\) kVAR is located in the transformation center itself. The existence of the second bank of capacitors, \(Q_{c2}=3\times 100\) kVAR, was deduced after analyzing the registered powers.  
The operation of the capacitor banks \(Q_{c1}\) and \(Q_{c2}\) is only efficient in the periods of greatest activity of the companies, in which the reactive power supplies are considerably reduced (Figure 2) and the power factor of the transformer is close to 1 (Figure 10). However, in periods of low activity, whether on working days or holidays, the capacitor banks supply large amounts of reactive power to the mains (Figures 4 and 5), with factors of capacitive power being very small, less than 0.3 capacitive (Figure 10).  
The environmental and economic consequences of reactive power in the inefficient operation of the transformer are observed in Tables 5 and 6, respectively. To reduce their impact, it is necessary to optimize the operation of the capacitor banks. For this, it is proposed:  
1. Maintain the operation of the first capacitor bank (\(Q_{c1}\)), without disconnection, at any time of the day, every day of the year, both working days and holidays;
2. Connect the second capacitor bank (\(Q_{c2}\)) only between 7:00 a.m. and 8:00 p.m. on working days, keeping it disconnected for the rest of the hours on working days and all hours on holidays. This solution can be applied, in a very economical way, by incorporating a switch with a programmable timer in this capacitor bank.  
The energy effects of the limitation of the period of operation of the capacitor bank \(Q_{c2}\) are:  
Figure 10: Transformer power factor on (a) working days and (b) holidays. (Positive values indicate inductive PF, whereas negative values signify capacitive PF).  
1. A significant decrease in the reactive power supplied, with very short capacitive periods, which are compensated by the inductive periods on working days and holidays (Figure 11), reaching power factors very close to unity (Table 8);  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type of Day**} & \multirow{2}{*}{**Power Factor**} & **Total Reactive** & **Penalized** & **Annual** \\  & & **Consumptions** & **Capacitive** & **Penalization** \\  & & **Per Day**, \(W_{q}\) & **Energy \(W_{q}\)** & **Penalization** \\  & & **(kvar-h)** & **(kvar-h/day)** & **(**kvar-h/day**)** \\ \hline Working days & 0.99773 (ind) & 394.51 & 0 & 0 \\ \hline Holidays & 0.99998 (cap) & 6.7998 & 0 & 0 \\ \hline \hline \end{tabular} (2) The high reduction of transformer copper losses caused by reactive currents, especially on holidays (Figure 12), which, compared to those indicated in Table 5, represent energy savings of 2820 kWh/year and 679.58 kg/year, in CO2 emissions (Table 9).  
\end{table}
Table 8: Power factor and reactive energies each day and annual penalizations resulting from applying the above actions on the second capacitor bank (\(Q_{c2}\)).  
Figure 11: Transformer reactive powers, in kVAR, after applying actions for optimizing the operation of capacitor bank \(Q_{c2}\): (a) working days, and (b) holidays.