## 7 Conclusions  
This paper has presented an analytical formulation to assess distribution system reliability in networks where intentional islanding is permitted by regulation, and all circuit breakers and some sectionalizers are telecontrolled. The considered protection scheme exploits a delayed operation of the circuit breakers to perform logic selectivity. During the delay, a centralized control system  
Figure 8: PoA variation with duration of islanding operation in island 32.  
receives information about the fault current direction from the circuit breakers detecting the fault, and sends an opening authorization to the circuit breakers that have to be opened. Typically, the delay is around 100 ms, and the smart communications subsystems enabling this protection scheme play a fundamental role in the behavior of the whole network. The main wireless and wired telecommunications technologies have been considered and compared, highlighting their installation and maintenance costs, and their appropriateness to the specific case of allowing the DMS to manage faults in order to guarantee safety and respect the maximum delay requirements. The formulation proposed for computing the adequacy of island generation is based on a Markov chain that models the ratio between load and generation in order to represent the fluctuation during islanding of load and green-energy generators. The results have shown that network reliability indices are overestimated when the aforementioned fluctuations occurring during intentional islanding are neglected. Moreover, the overestimation of SAIFI improvement is greater than for SAIDI. This work was partially supported by \"Programma Operativo Nazionale: Ricerca & Competitivita 2007-2013\" within the project \"PON04a2_E--SINERGEREN--RES NOVAE--Smart Energy Master per il governor energetico del territorio\". This work was also partially supported by the University of Catania within the project \"Study on the interdependence of the electrical network and the _Information and Communications Technology_ infrastructure in Smart Grid scenarios\" (FIR 2014). All authors contributed equally to this work. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} DNO & Distribution network operator \\ LP & Load point \\ DG, RDG, CDG & Distributed generator, renewable-based DG, \\  & and conventional DG, respectively \\ CB, CBS & Circuit breaker and CB with a sectionalizer installed \\  & at the same branch, respectively \\ PS & Primary substation \\ DMS & Distribution management system \\ SCS & Smart communications subsystems \\ SG & Smart grid \\ \(i,k,r,c,j,l\) & Identifier of LP, branch, RDG, CDG, island, and power level, respectively \\ PoA, \(\rho_{A,j}\) & Probability of Adequacy, PoA, of island \(j\) \\ \(L_{j},R_{j},C_{j}\) & Number of LPs, RDGs, and CDGs, respectively, in island \(j\) \\ \(\pi^{(D)}_{r,l}\) & Occurrence probability of power level \(l\) in the load model of LP \(i\) \\ \(\pi^{(RG)}_{r,l},\pi^{(CG)}_{c,l}\) & Occurrence probability of power level \(l\) in the generation model of RDG \(r\) \\  & and CDG \(c\), respectively \\ \(N^{l}_{r},N^{G}_{r}\) & Number of power levels in the LP \(i\) and RDG \(r\) models, respectively \\ \(M_{j}\) & Number of working points at which island \(j\) can operate, obtained by combining LPs and DGs models \\ \(D^{E}_{j,m},G^{E}_{j,m}\) & Equivalent load and generation, respectively, in island \(j\) when the \(m\)-th \\  & combination occurs \\ \(R_{j,m}\) & Percentage of load supplied by the local generation when the \(m\)-th \\  & combination occurs \\ \(D^{E,RQ}_{j}(p)\) & Equivalent power demand, before quantization, in island \(j\) at the time slot \(p\) \\ \(D^{E}_{j}(p)\) & Markov process of the quantized equivalent power demand \\  & in island \(j\) at time \(p\) \\ \(RG^{E}_{j}(p)\) & Markov process of the quantized equivalent renewable \\  & generation in island \(j\) at time \(p\) \\ \end{tabular}