## 4 Practical Application
### Star-Connected SVC Compensator Calculation  
The unbalanced factor \(\delta_{-}\) is given by:  
\[\delta_{-}=\frac{V_{-}}{V_{+}}=0.1977\]  
The reactive powers \(Q_{xL+}\) and \(Q_{xL-}\) in the load are determined by the following expressions:  
\[Q_{xL+}=V_{2n+}I_{2L+}\sin(\alpha_{2n+}-\beta_{xL+})=\ Q_{dL+}=Q_{bl+}=Q_{cl+}\]  
\[Q_{xL-}=V_{2n-}I_{2L-}\sin(\alpha_{2n-}-\beta_{xL-})=\ Q_{dL-}=Q_{bl-}=Q_{cl-}\]  
If we substitute the values of Tables 1 and 2 in the above expressions, we obtain:  
\[Q_{dL+}=Q_{bl+}=Q_{cl+}=4615.876\ \text{var}\]  
\[Q_{dL-}=Q_{bl-}=Q_{cl-}=463.353\ \text{var}\]  
The reactive powers \(Q_{2W+}\) and \(Q_{2W-}\) in the ZSCC are determined by the following expressions:  
\[Q_{2W+}=V_{2n+}I_{2W+}\sin(\alpha_{2n+}-\beta_{2W+})=\ Q_{dW+}=Q_{bW+}=Q_{cW+}\]  
\[Q_{2W-}=V_{2n-}I_{2W-}\sin(\alpha_{2n-}-\beta_{2W-})=\ Q_{dW-}=Q_{bW-}=Q_{cW-}\]  
If we substitute the values of Tables 2 and 4 in the above expressions, we obtain:  
\[Q_{aW+}=Q_{bW+}=Q_{cW+}=-457.297\ \text{var}.\]  
\[Q_{aW-}=Q_{bW-}=Q_{cW-}=-203.135\ \text{var}.\]  
Equation (44) determines the positive-sequence reactive power, which the SVC compensator consumes, and its value is as follows:  
\[Q_{2P+}=\frac{(463.353-203.135)-(4615.876-457.297)}{1-0.1977^{2}}=-4056.968 \ \text{var}.\]  
Considering \(Q_{2P+}\) in Equation (43), the reactances that the SVC compensator must have are determined by:  
\[X_{P}=X_{aP}=X_{bP}=X_{cP}=\frac{212.891^{2}}{-4056.968}=-11.172\ \Omega.\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(P\) & \(Q\) & \(P_{+}\) & \(Q_{+}\) & \(P_{-}\) & \(Q_{-}\) & \(P_{0}\) & \(Q_{0}\) \\ \hline
**Compen.** & **(W)** & **(var)** & **(W)** & **(var)** & **(W)** & **(var)** & **(W)** & **(var)** \\ \hline Before & 21,712.50 & 15826.50 & 22,208.37 & 13,847.63 & 2965.86 & 1390.06 & \(-\)3461.73 & 624.81 \\ After & 21,712.50 & 13256.39 & 16,753.88 & 12,475.74 & 4958.62 & 780.65 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of powers, before and after including the ZSCC compensator.  
Therefore, \(\underline{X_{P}}=11.172e^{-\gamma 90.00}\ \Omega\).  
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 SVC compensator:  
\[\underline{I_{aP}}=16.26e^{\gamma 93.211}\ \text{A}\ \underline{I_{bP}}=22.597e^{-j 31.453}\ \text{A}\ \underline{I_{cP}}=18.986e^{-j166.40}\ \text{A}\]  
Therefore, the new line currents supplied by the network in the bus after including the ZSCC and SVC compensators are determined by:  
\[\begin{array}{l}\underline{I_{a}}+\underline{I_{aW}}+\underline{I_{aP}}=25.859e^{-\bar{5}.014}\ \text{A}\\ \underline{I_{b}}+\underline{I_{bW}}+\underline{I_{bP}}=64.678e^{-j125.014} \ \text{A}\\ \underline{I_{c}}+\underline{I_{cW}}+\underline{I_{cP}}=43.084e^{j114.986} \ \text{A}\end{array}\]  
Table 6 shows these currents expressed in symmetric components.  
Considering Equation (2), the total apparent power of Buchholz that supplies the network in the bus is given by:  
\[S_{T}=3\sqrt{\left(212.891^{2}+42.094^{2}+50.67^{2}\right)\ \left(26.237^{2}+39.341^{2}+0. 00^{2}\right)}=31613.58\ \text{VA}\]  
Comparing this value of \(S_{T}\) with the previous values, it is observed that its value continues to decrease.