The power systems are usually subject to disturbances which may lead to = loss of synchronization between groups of generators and possibly blackouts= . The system islanding refers to the condition in which some areas of the t= ransmission or distribution system are disconnected from the main grid howe= ver the power supply continues in that region by local generating facilitie= s. It may automatically happen after some transmission lines are tripped by= local relays [1] to isolate the faulted region. The role of system operato= r is to optimally maintain the balance between the generation and demand in= each island. The main idea is to reduce the total amount of load shedding = to maintain such a balance and avoiding the blackout. There are two types o= f islanding namely intentional and unplanned islanding as follows:

It is done to determine optimal splitting points (or called splitting st= rategies) to split the entire interconnected transmission network into isla= nds ensuring generation/load balance and satisfaction of transmission capac= ity constraints when islanding operation of system is unavoidable [1]. It i= s considered as an emergency response for isolating failures that might pro= pagate and lead to major disturbances [2].

[1] Kai Sun, Da-Zhong Zheng and Qiang Lu, "Splitting strategies for isla= nding operation of large-scale power systems using OBDD-based methods," in&= nbsp;IEEE Transactions on Power Systems, vol. 18, no. 2, pp. 912-923, May 2= 003.

[2]. Pahwa, Sakshi, et al. "Optim= al intentional islanding to enhance the robustness of power grid networks."= Physica A: Statistical Mechanics and its Applications 392.17 (20= 13): 3741-3754.

Model: **DC-based islanding + AC-load shedding**

Class: MILP

Software: CPLEX + PSAT

[3] Trodden, P. A., et al. "MILP = formulation for controlled islanding of power networks." International Jour= nal of Electrical Power & Energy Systems 45.1 (2013): 501-508.

[4] Fan, Neng, et al. "A mixed integer programming approach for optimal = power grid intentional islanding." Energy Systems 3.1 (2012): 77-= 93.

[5] Trodden, P. A., et al. "MILP formulation for controlled islanding of= power networks." International Journal of Electrical Power & Ener= gy Systems 45.1 (2013): 501-508.

Model: **Piecewise linear AC islanding**

Class: MILP

Software: CPLEX

[6] Trodden, P. A., Bukhsh W. A.,= Grothey A., McKinnon K. I. M. (2014): Optimization-based islanding of powe= r networks using piecewise linear AC power flow. Power Systems, IEEE Transa= ctions, 29, 1212-1220.

This is an unplanned condition which should be avoided [7]. The islandin= g detection techniques are applied to reduce the risk of this event. This p= henomena is due to line tripping, equipment failure, human errors and so on= [8].

[7] M. A. Farhan and K. Shanti Swarup, "Mathematical morphology-based is= landing detection for distributed generation," in IET Generation, Tran= smission & Distribution, vol. 10, no. 2, pp. 518-525, 2 4 2016.

[8] Li, Canbing, et al. "A review of islanding detection methods for mic= rogrid."Renewable and Sustainable Energy Reviews 35 (2014): 211-220.

The optimal network restoration is called to a class of actions taken by= network operator to bring back the power system into its normal condition = following a complete or partial collapse. Intentional system islanding can = one of these actions.

Model: Robust restoration approach

Class: MIQCP

Software: CPLEX

[9] K. Chen, W. Wu, B. Zhang and H. Sun, "Robust Restoration Decision-Ma= king Model for Distribution Networks Based on Information Gap Decision Theo= ry," in IEEE Transactions on Smart Grid, vol. 6, no. 2, pp. 587-597, March = 2015.

Class: MILP

Software: IBM ILOG CPLEX 12.5

[10] X. Chen; W. Wu; B. Zhang, "Robust Restoration Method for Active Dis= tribution Networks," in IEEE Transactions on Power Systems , vol.= PP, no.99, pp.1-11

Mixed integer second-order cone programming problem

Modelled in AMPL

Software: CPLEX

[11] R. Romero, J. F. Franco, F. B. Le=C3=A3o, M. J. Rider and E. S. de = Souza, "A New Mathematical Model for the Restoration Problem in Balanced Ra= dial Distribution Systems," in IEEE Transactions on Power Systems, vol= . 31, no. 2, pp. 1259-1268, March 2016.

A greedy algorithm

[12] Y. Xu, C. C. Liu, K. P. Schneider and D. T. Ton, "Placement of Remo= te-Controlled Switches to Enhance Distribution System Restoration Capabilit= y," in IEEE Transactions on Power Systems, vol. 31, no. 2, pp. 1139-11= 50, March 2016.

[13] L. Sun et al., "Optimisation model for power system restoratio= n with support from electric vehicles employing battery swapping," in = IET Generation, Transmission & Distribution, vol. 10, no. 3, pp. 771-77= 9, 2 18 2016.

Dr Jakub Marecek, IBM

Dr Cedric Josz, Laboratory for Analysis and Architecture of Systems LAAS= CNRS

Dr Martin Mevissen, IBM

Dr Bissan Ghaddar, University of Waterloo

Dr Alireza Soroudi, University College Dublin<= /p>