The Optimal Transmission Switching deals with changing the transmission network topology in order to improve voltage profiles, increase transfer capacity, and reduce the market power of some market participants. The topology is changed, primarily by the deliberate outage of some specific transmission lines. Further, one may also consider, the use of phase shifters (which change the angle difference between two adjacent buses) and other Flexible Alternating Current Transmission System (FACTS) devices (which can, among others, increase/decrease the impedance of two adjacent buses).
The idea of topology dispatch has been studied for several decades [1,2,3,4], although it has gained much attention recently thanks to [4, 5], who have demonstrated how it can provide the electricity market with greater efficiency and competition. This idea was further developed in [6,7,8,11] by not only considering the normal operation but also the N-1 contingencies and financial transmission rights (FTR) and Flexible Alternating Current Transmission System (FACTS) devices. The unit commitment problem constrained by transmission system is solved in . Much of this early modelling work has been performed using linear programming (LP) approximations of the alternating-current power flow and can be applied to large-scale transmission systems. An alternative LP formulation has been studied by .
In order to capture the complexity of the alternating-current transmission, a variety of non-linear models have been suggested.  proposes an SOCP relaxation and  extends it.  have experimented with the sparse variant of the method of moments for two formulations, lift-and-branch-and-bound using SDP relaxations, and certain piece-wise linearisations. [12,17] studies a variety of heuristics based on non-linear optimisation. Generally, convergent methods considering the line-use decision within the alternating current model [14,15,16] have turned out to be challenging.
For mixed-integer linear-programming (MILP) models, there has been much recent progress in general-purpose optimisation software based on branch-and-bound-and-cut. Often, modest instances considering either piece-wise linearisations or uncertainty, can be solved exactly using the general-purpose software. Decompositions, such as Benders decomposition, Lagrangian relaxation, or column generation [10,11] are frequently used beyond that.
For mixed-integer non-linear programming (MINLP) models, the methods are an active area of research [12,13,14,15,16,17], considering the limitations of the general-purpose non-linear programming optimisation software.  surveys three convergent approaches, based on piece-wise linearisation of certain higher-dimensional surfaces, based on the method of moments, and based on combining lifting and branching. The preliminary conclusion is that the combining lifting and branching may be the most promising.
See also Transmission expansion planning, which is structurally very closely related, although the uncertainty is often modelled differently. Note also one would often  like to expand the network knowing that one can perform switching later.
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Jakub Marecek, IBM