An Islanding Model for Preventing Wide-Area Blackouts and the Issue of Local Solutions of the Optimal Power Flow Problem

Research output: ThesisDoctoral Thesis


Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow problem (OPF). This is an old and well-known nonconvex optimization problem in power system. The existence of local solutions of OPF has been a question of interest for decades. Both local and global solution techniques have been put forward to solve OPF problem but without any documented cases of local solutions. We have produced test cases of power networks with local solutions and have collected these test cases in a publicly available online archive (, which can be used now by researchers and practitioners to test the robustness of their solution techniques. Also a new nonlinear relaxation of OPF is presented and it is shown that this relaxation in practice gives tight lower bounds of the global solution of OPF. The second problem considered is how to split a network into islands so as to prevent cascading blackouts over wide areas. A mixed integer linear programming (MILP) model for islanding of power system is presented. In recent years, islanding of power networks is attracting attention, because of the increasing occurrence and risk of blackouts. Our
proposed approach is quite flexible and incorporates line switching and load shedding. We also give the motivation behind the islanding operation and test our model on variety of test cases. The islanding model uses DC model of power flow equations. We give some of the shortcomings of this model and later improve this model by using piecewise linear approximation of nonlinear terms. The improved model yields good feasible results very quickly and numerical results on large networks show the promising performance of this model.
Original languageEnglish
Awarding Institution
  • University of Edinburgh
  • Mckinnon, Kenneth , Supervisor, External person
  • Grothey, Andreas, Supervisor, External person
Place of PublicationEdinburgh
Publication statusPublished - 1 Jul 2014


  • optimal power flow
  • power systems modelling
  • islanding model
  • blackout prevention


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