## 7 Conclusions  
This paper proposes a procedure for compensation by passive compensators formed by reactive elements (coils and/or capacitors), to compensate for the positive-sequence reactive power, and the unbalanced powers caused by the negative-sequence currents. Unlike most other methods, the proposed method is valid for systems that are fed with unbalanced voltages, and does not require the characteristics and values of the loads connected to the bus or measurement point. It is enough to know the line-to-line voltages and line currents to design the compensators that compensate for these inefficient powers. Although it has been assumed that the network is of infinite power, it can be observed that the compensator adapts to the fixed voltages on the bus. These voltages and currents at the measuring point can be measured with any traditional measuring device. It has been confirmed that when the system is fed with balanced voltages, the positive-sequence reactive and unbalanced powers represent two different phenomena that occur in the transfer of energy from the network to the bus load. These phenomena can be compensated with two independent compensators. It has also been shown that when the voltages are unbalanced, the compensators are not independent of each other, and the two phenomena indicated are compensated between the two compensators. These compensators can be connected in star or delta. They can also be unified into a single compensator that compensates for both phenomena, coupling them into a single delta connection. The equations that have been presented are simple, and their application is immediate. Therefore, the objective of this study is fulfilled, that is, the efficiency in the transfer of electrical energy from the network to the charges through the bus should be as efficient as possible, by eliminating negative-sequence currents and positive-sequence reactive currents. With this, the streams of lines delivered by the network to the system form a symmetrical system of positive sequence. To facilitate the application of the method, a case study was analyzed based on a three-phase unbalanced three-wire linear system connected to an infinite power network with unbalanced voltages. Conceptualization, P.A.B., R.M. and J.M.D. ; Methodology, P.A.B., R.M.-M., J.M.D. and R.M. ; Validation, P.A.B., R.M.-M. and R.M. ; Formal Analysis, P.A.B. and R.M.-M.; Investigation, P.A.B., R.M.-M., J.M.D. and R.M. ; Resources, P.A.B. and R.M.-M.; Data Curation, P.A.B. and R.M.-M.; Writing-Original Draft \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Phase** & \(P_{z+}^{-}\) & \(Q_{z+}^{-}\) & \(P_{z-}^{+}\) & \(Q_{z-}^{+}\) \\ \hline
**Condition** & **z** & **(VA)** & **(VA)** & **(VA)** & **(VA)** \\ \hline  & a & \(-4697.32\) & \(267.65\) & \(-259.04\) & \(411.58\) \\ Before compensation & b & \(2116.87\) & \(-4201.82\) & \(485.96\) & \(18.55\) \\  & c & \(2580.45\) & \(3934.17\) & \(-226.92\) & \(-430.13\) \\ \hline  & a & \(0\) & \(0\) & \(11.20\) & \(391.36\) \\ After compensation & b & \(0\) & \(0\) & \(333.33\) & \(-205.38\) \\  & c & \(0\) & \(0\) & \(-344.53\) & \(-185.98\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Powers caused by voltages and currents of different sequence. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(S_{+}\) & \(S_{-}\) & \(S_{+}^{-}\) & \(S_{-}^{+}\) & \(S_{T}\) \\ \hline
**Condition** & **(VA)** & **(VA)** & **(VA)** & **(VA)** & **(VA)** \\ \hline Before compensation & \(8278.64\) & \(2487.45\) & \(14114.81\) & \(1458.94\) & \(16615.64\) \\ After compensation & \(6664.96\) & \(0\) & \(0\) & \(1174.56\) & \(6767.66\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Apparent powers in symmetric components and apparent power of Buchholz. Preparation, J.M.D. and R.M. ; Writing-Review & Editing, R.M.-M., J.M.D. and R.M. ; Visualization, P.A.B. and R.M.-M.; Supervision, J.M.D., R.M. and M.J.R. ; Project Administration, J.M.D. All authors have read and agreed to the published version of the manuscript.