## 7 Conclusions
\begin{array}{c}\lambda_{i,k}=f_{k}\left[\left(1-\rho_{A,j}\right)+\rho_{A, j}\left(\left(1-\rho_{A,tsc}\right)+\rho_{A,tsc}\left(1-\rho_{A,msc}\right) \right)\right]\\ U_{i,k}=f_{k}\,\left[\begin{array}{c}\left(1-\rho_{A,j}\right)\left(t_{ST}+ t_{AV,tsc}\right)+\\ \left(1-\rho_{A,tsc}\right)\left(t_{S,msc}+t_{AV,msc}-t_{AV,tsc}\right)+\\ \left(1-\rho_{A,msc}\right)\left(t_{R,k}-t_{ST}-t_{S,msc}-t_{AV,msc}\right) \end{array}\right]\end{array} , \tag{15}\]  
where \(t_{AV,tsc}\) is the DGs' time to be available in island _tsc_, this is created by telecontrolled sectionalizer _tsc_ opening. _A9. Scenario I (e.g., i = 30, k = 18, CBS j = 8, tsc = 4, and msc = 17 in Figure 1):_  
Considering a network where islanding operation is not permitted, the following equations must be applied:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,\left(t_{ST}+t_{S,msc}\right)\end{array} ; \tag{16}\]  
otherwise, when islanding operation is permitted:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\left[\left(1-\rho_{A,j}\right)+\rho_{A, j}\left(1-\rho_{A,tsc}\right)\right]\\ U_{i,k}=f_{k}\left[\left(1-\rho_{A,j}\right)\left(t_{ST}+t_{AV,tsc}\right)+ \left(1-\rho_{A,tsc}\right)\left(t_{S,msc}-t_{AV,tsc}\right)\right]\end{array} . \tag{17}\]  
_A10. Scenario J (e.g., i = 30, k = 22, j = 8, and tsc = 21, or i = 30, k = 24, j = 8, tsc = 21, and msc = 23 in Figure 1):_Considering a network where islanding operation is not permitted, the following equations must be applied:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,t_{ST}\end{array} ; \tag{118}\]  
otherwise, when islanding operation is permitted:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,\left(1-\rho_{A,j}\right)\,t_{ST}\end{array} . \tag{119}\]  
_A11. Scenario K (e.g., for i = 30, k = 14, tsc = 13, or i = 30, k = 16, tsc = 13, and msc = 15 in Figure 1):_  
Considering networks in which islanding operation is either permitted or not permitted, the following equations must be applied:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,t_{ST}\end{array} . \tag{120}\]  
_A12. Scenario L (sub-scenario L1, e.g., for i = 30, k = 11, and tsc = 12- or -sub-scenario L2, e.g., for i = 30, k = 9, tsc = 12, and mcs = 10 in Figure 1)_  
Considering a network where islanding operation is not permitted, the following formulas must be applied in both sub-scenarios:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,t_{R,k}\end{array} ; \tag{121}\]  
otherwise, when islanding operation is permitted and sub-scenario L1 is considered:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\left[t_{ST}+t_{AV,tsc}\,\,+\,\left(1-\rho_{A,tsc}\right)\,\left(t _{R,k}-t_{ST}-t_{AV,tsc}\right)\right]\end{array} , \tag{122}\]  
or, if sub-scenario L2 is considered:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,\,\left[\begin{array}{c}t_{ST}+t_{AV,tsc}+\\ \left(1-\rho_{A,tsc}\right)\,\left(t_{S,msc}+t_{AV,msc}-t_{AV,tsc}\right)+\\ \left(1-\rho_{A,msc}\right)\,\left(t_{R,k}-t_{ST}-t_{S,msc}-t_{AV,msc}\right) \end{array}\right]\end{array} . \tag{123}\]  
_A13. Scenario M (e.g., i = 30, k = 26, tsc = 12, and msc = 25 in Figure 1):_  
Considering a network where islanding operation is not permitted, the following formulas must be applied:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,\,\left(t_{ST}+t_{S,msc}\right)\end{array} ; \tag{124}\]  
otherwise, when islanding operation is permitted:  
\[ \begin{array}{c}\lambda_{i,k}=f_{k}\\ U_{i,k}=f_{k}\,\,\left(t_{ST}+t_{S,msc}\right)\end{array} . \tag{125}\]