## 4 Practical Application
### Calculation of the ZSCC Compensator  
The unbalanced reactive powers that are caused by line-to-neutral voltages and zero-sequence currents in the load are given by:  
\[Q_{2n}^{2L0}=V_{2n}I_{zL0}\ \sin(\alpha_{2n}-\beta_{zL0})\]  
For \(z=\{a,b,c\}\), their values are as follows:  
\[Q_{an}^{zL0}=-126.253\ \text{var}\ Q_{bn}^{bL0}=5262.245\ \text{var}\ Q_{cn}^{zL0}=-4511.18\ \text{var}\]  
Substituting these values in Equation (25), \(X_{aW(25)}\), \(X_{bW(25)}\) and \(X_{cW(25)}\) were obtained as follows:  
\[X_{aW(25)}=211.325\ \Omega\ X_{aW(25)}=211.325e^{\beta 0.00}\ \Omega\] \[X_{bW(25)}=-5.473\ \Omega\ \overline{X_{bW(25)}}=5.473e^{-\beta 0.00}\ \Omega\] \[X_{cW(25)}=4.215\ \Omega\ \overline{X_{cW(25)}}=4.215e^{\beta 0.00}\ \Omega\]  
Using Equation (28), we determined the zero sequence current \(I_{\underline{2W0(25)}}\) given by:  
\[I_{aW0(25)}=I_{bW0(25)}=I_{cW0(25)}=29.648e^{-\beta 10.423}\ \text{A}\]  
Comparing these values with those shown in Table 2, it is observed that this zero-sequence current does not coincide with the zero-sequence current of the load with the opposite sign. This is because the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Phases** & \multicolumn{2}{c}{\(V_{zm+}\) **(V)**} & \multicolumn{2}{c}{\(V_{zm-}\) **(V)**} & \multicolumn{2}{c}{\(V_{zm0}\) **(V)**} \\ \hline \(z\) & **Mod.** & **Ang.** & **Mod.** & **Ang.** & **Mod.** & **Ang.** \\ \hline a & 212.891 & \(-\)5.014 & 42.094 & 136.859 & 50.671 & \(-\)11.585 \\ b & 212.891 & \(-\)125.014 & 42.094 & \(-\)103.141 & 50.671 & \(-\)11.585 \\ c & 212.891 & 114.986 & 42.094 & 16.859 & 50.671 & \(-\)11.585 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Positive-, negative-, and zero-sequence voltages. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Phases** & \multicolumn{2}{c}{\(I_{z+}\) **(A)**} & \multicolumn{2}{c}{\(I_{z}\)**- **(A)**} & \multicolumn{2}{c}{\(I_{z0}\) **(A)**} \\ \hline \(z\) & **Mod.** & **Ang.** & **Mod.** & **Ang.** & **Mod.** & **Ang.** \\ \hline a & 40.979 & \(-\)36.959 & 25.938 & 111.747 & 23.141 & 178.647 \\ b & 40.979 & \(-\)156.959 & 25.938 & \(-\)128.253 & 23.141 & 178.647 \\ c & 40.979 & 83.041 & 25.938 & \(-\)8.253 & 23.141 & 178.647 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Positive-, negative-, and zero-sequence line currents. line-to-neutral voltages are not offset \(\pm 120\) degrees from each other, as indicated in Section 3.2. Thus, considering Equation (27), the phasor of deviation of the zero-sequence current \(\underline{f_{\text{W0}}}\) is given by:  
\[\underline{f_{\text{W0}}}=0.771+\text{j0.123}\]  
Substituting \(\underline{f_{\text{W0}}}\) in Equation (37), \(\underline{f_{\text{W+}}}\) and \(\underline{f_{\text{W-}}}\) are given by:  
\[\underline{f_{\text{W+}}}=\underline{f_{\text{W-}}}=0.827-\text{j0.227}\]  
Therefore, considering Equations (38)-(40), the currents consumed by the ZSCC compensator are as follows:  
\[\underline{I_{\text{aW}}}=9.61e^{\text{j00.00}}\text{ A }\underline{I_{\text{bW}}}=32.889e^{- \text{j20.00}}\text{ A }\underline{I_{\text{cW}}}=38.497e^{\text{j0.00}}\text{ A}\]  
Table 3 shows currents \(\underline{I_{\text{aW}}}\), \(\underline{I_{\text{bW}}}\) and \(\underline{I_{\text{cW}}}\) in sequence values. Positive- and negative-sequence currents are necessary in subsequent sections to calculate SVC and NSCC compensators. As expected, the zero-sequence current is equal to the zero-sequence current of the load with the opposite sign.