## 5 Conclusions  
Electrical systems with unbalanced loads and voltages give rise to inefficient currents: negative-sequence currents, zero-sequence currents, and positive-sequence reactive currents. This produces inefficient powers, which causes an increase in the total apparent power that the generator or network must supply in the bus. In this work, a three-phase four-wire system connected to an infinite short-circuit power network with unbalanced voltages and unbalanced currents was considered. A methodology for compensating zero-sequence currents through the parallel connection of a compensating circuit (ZSCC) was developed. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{\(I_{a}\) **(A)**} & \multicolumn{2}{c}{\(I_{b}\) **(A)**} & \multicolumn{2}{c}{\(I_{c}\) **(A)**} \\ \cline{2-7}  & **Mod.** & **Ang.** & **Mod.** & **Ang.** & **Mod.** & **Ang.** \\ \hline Proposed method & 33.996 & \(-5.014\) & 33.996 & \(-125.014\) & 33.996 & 114.986 \\ Classical method & 36.438 & 7.389 & 37.814 & \(-115.626\) & 29.150 & 49.677 \\ Leon [19] & 39.527 & \(-4.442\) & 43.804 & \(-102.403\) & 11.226 & 91.381 \\ Pana [23] & 37.212 & \(-0.121\) & 32.645 & \(-101.964\) & 28.015 & 78.780 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the proposed method with other existing methods. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{\(I_{a}\) **(A)**} & \multicolumn{2}{c}{\(I_{b}\) **(A)**} & \multicolumn{2}{c}{\(I_{c}\) **(A)**} \\ \cline{2-7}  & **Mod.** & **Ang.** & **Mod.** & **Ang.** & **Mod.** & **Ang.** \\ \hline Proposed method & 33.910 & 0 & 33.910 & \(-120\) & 33.910 & 120 \\ Classical method & 33.910 & 0 & 33.910 & \(-120\) & 33.910 & 120 \\ [PERSON] [19] & 33.910 & 0 & 33.910 & \(-120\) & 33.910 & 120 \\ [PERSON] [23] & 33.910 & 0 & 33.910 & \(-120\) & 33.910 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of the proposed method with other methods with unbalanced voltages. This compensator is formed by reactances. A simple analytical equation is provided to determine these elements. This ensures that the network does not provide a zero sequence current in the bus. That is, no current will flow through the neutral wire. With this compensator (ZSCC), together with those developed by the authors in a previous work for three-wire systems, the negative sequence current compensator (NSCC), and the positive sequence reactive current compensator (SVC), we have formulated a procedure for the total compensation of inefficient currents produced by the unbalanced load. This achieves maximum efficiency in the transfer of electrical energy between the network and the downstream load of the bus. It becomes clear that the active power consumed by the load remains constant, while the reactive power has a null value. The value of Buchholz's total apparent power is greatly diminished in the bus. Only the inefficiencies due to the negative- and zero-sequence voltages that are not compensable efficiently (since they are inherent in the network) will remain. This is achieved without knowledge of the nature and characteristics of the load, only of the voltages and currents measured in the bus. The proposed equations can be used with active or hybrid filters in order to overcome the inconvenience of passive filters. These are only useful in installations with a fairly stationary consumption which need a staggering of the compensation reactances just like the current SVC. Finally, a case study is developed and compared with three of the methods analyzed to show the simplicity of the application of the proposed compensation methodology. The results obtained in each step and the final result are analyzed. This shows that the classic models or the capacitors-based model are not intended to work correctly in three-phase four-wire systems with unbalanced voltages. On the other hand, the model proposed in this article does respond correctly.