## 4 Practical Application
### Star-Connected NSCC Compensator Calculation  
The values of \(Q_{zF+}^{-}\) are determined by the following expressions:  
\[Q_{zF+}^{-}=V_{zn+}I_{zF-}\sin(\alpha_{zn+}-\beta_{zF-})\]  
If we substitute the values of Tables 1 and 6 in the above expressions, we obtain:  
\[Q_{aF+}^{-}=-5565.414\qquad Q_{bF+}^{-}=-2637.477\qquad Q_{cF+}^{-}=8202.891\]  
Substituting the values of \(\underline{I_{zF-}}\) and \(Q_{zF+}^{-}\) in Equation (45), the values of \(X_{zF}\) are given by:  
\[X_{aF}=-2\frac{-5565.414}{39.341^{2}}=7.192\ \Omega\ \ \ \ \ \ \underline{X_{aF}}=7.192e^{\gamma 90.00}\ \Omega\]  
\[X_{bF}=-2\frac{-2637.477}{39.341^{2}}=3.408\ \Omega\ \ \ \ \ \ \ \underline{X_{bF}}=3.408e^{\gamma 90.00}\ \Omega\]  
\[X_{cF}=-2\frac{8202.891}{39.341^{2}}=-10.60\ \Omega\ \ \ \ \ \ \underline{X_{cF}}=10.60e^{-\gamma 90.00}\ \Omega\]  
Therefore, \(X_{aF}\) is a capacitor, \(X_{bF}\) is a coil, and \(X_{cF}\) is a capacitor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Phases** & \multicolumn{2}{c}{\(\mathbf{I_{z+}}\) **(A)**} & \multicolumn{2}{c}{\(\mathbf{I_{z-}}\) **(A)**} & \multicolumn{2}{c}{\(\mathbf{I_{z0}}\) **(A)**} \\ \hline \(z\) & **Mod.** & **Ang.** & **Mod.** & **Ang.** & **Mod.** & **Ang.** \\ \hline a & 26.237 & \(-6.057\) & 39.341 & 133.341 & 0.00 & 0.00 \\ b & 26.237 & \(-126.057\) & 39.341 & \(-106.659\) & 0.00 & 0.00 \\ c & 26.237 & 113.943 & 39.341 & 13.341 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Positive-, negative-, and zero-sequence line currents in the bus after ZSCC and SVC collocation. Considering the line-to-line voltages \(V_{zz}\), where \(zz=\{ab,bc,ca\}\), and applying the mesh currents method, we determined the currents consumed by the NSCC compensator:  
\[\underline{I_{aF}}=45.163e^{-\
icefrac{{1}}{{39.644}}}\text{ A }\underline{I_{bF}}=31.884e^{ \
icefrac{{76.923}}{{23}}}\text{ A }\underline{I_{cF}}=42.051e^{-\
icefrac{{1}}{{176.944}}}\text{ A}\]  
Therefore, the new line currents supplied by the network in the bus after including the ZSCC, SVC, and NSCC compensators are determined by:  
\[ \begin{array}{l}\underline{I_{a}}+\underline{I_{aW}}+\underline{I_{aP}}+ \underline{I_{aF}}=33.996e^{-\
icefrac{{7.014}}{{5.014}}}\text{ A}\\ \underline{I_{b}}+\underline{I_{bW}}+\underline{I_{bP}}+\underline{I_{bF}}=33. 996e^{-\
icefrac{{7125.014}}{{25.014}}}\text{ A}\\ \underline{I_{c}}+\underline{I_{cW}}+\underline{I_{cP}}+\underline{I_{cF}}=33. 996e^{\
icefrac{{7114.986}}{{5.014}}}\text{ A}\end{array} \]  
Figure 10 displays the waveform of the line currents in each phase obtained from the simulation after include compensation. It is observed that after compensation we obtained a system of balanced line currents. These same results can be obtained by joining the SVC and NSCC compensators in delta connection according to Figure 7. Using the star-delta transformations, the reactance values of the compensator \"NSCC + SVC\" were obtained as follows:  
\[\begin{array}{l}X_{abC}=11.011\text{ }\Omega\text{ }\text  
Considering Equation (2), the total apparent power of Buchholz that supplies the network in the bus is given by:  
\[S_{T}=3\sqrt{\left(212.891^{2}+42.094^{2}+50.67^{2}\right)\,\left(34.996^{2}+0.0 0^{2}+0.00^{2}\right)}=22728.17\,\text{VA}\]  
If we compare the final value of \(S_{T}\) with the previous values, it is observed that the total apparent power is practically equal to the total active power and the positive-sequence active power. This small difference is due to the negative- and zero-sequence voltages that are imposed by the infinite short-circuit power network. Table 8 compares the results of the line currents that have been obtained from our proposal with other existing methods and that have been cited in this work. It is observed that the line currents that circulate in the bus or PCC after compensation, are only balanced when the proposed compensation method is used. In addition, it can be seen that these currents are in phase with the positive-sequence voltage (see Table 1). This implies that its sum is zero.