The Optimal Transmission Switching deals with changing the transmission = network topology in order to improve voltage profiles, increase transfer ca= pacity, and reduce the market power of some market participants. The topolo= gy is changed, primarily by the deliberate outage of some specific transmis= sion lines. Further, one may also consider, the use of phase shifters (whic= h change the angle difference between two adjacent buses) and other Flexibl= e Alternating Current Transmission System (FACTS) devices (which can, among= others, increase/decrease the impedance of two adjacent buses). The change= in topology can be done by one or combination of the following actions:

- Deliberate outage of some specific transmission lines
- Adding phase shifters (these devices can change the angle difference be= tween two connected buses)
- Adding Flexible Alternating Current Transmission System (FACTS) devices= (these devices can increase/decrease the impedance of two connected buses = in the system)
- Adding reactive series impedance (these devices can increase the impeda= nce of two connected buses in the system)

**References**

1- R. P. O'Neill, R. Baldick, U. Helman, M. H. Rothkopf and W. Stewart, = "Dispatchable transmission in RTO markets," in IEEE Transactions on Po= wer Systems, vol. 20, no. 1, pp. 171-179, Feb. 2005.

2- N-1 DCOPF formulation: Hedman, Kory W., et al. "Optimal transmission = switching with contingency analysis." Power Systems, IEEE Transactions on 2= 4.3 (2009): 1577-1586.

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 ef=
ficiency 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 an=
d financial transmission rights (FTR) and Flexible Alternating Current Tran=
smission System (FACTS) devices. The unit commitment problem constrained by=
transmission system is solved in [10]. Much of this early modelling work h=
as been performed using linear programming (LP) approximations of the alter=
nating-current power flow and can be applied to large-scale transmission sy=
stems. An alternative LP formulation has been studied by [9].

In or=
der to capture the complexity of the alternating-current transmission, a va=
riety of non-linear models have been suggested. [14] proposes an SOCP relax=
ation and [15] extends it. [16] have experimented with the sparse variant o=
f the method of moments for two formulations, lift-and-branch-and-bound usi=
ng SDP relaxations, and certain piece-wise linearisations. [12,17] studies =
a variety of heuristics based on non-linear optimisation. Generally, conver=
gent methods considering the line-use decision within the alternating curre=
nt 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-an= d-bound-and-cut. Often, modest instances considering either piece-wis= e linearisations or uncertainty, can be solved exactly using the general-pu= rpose software. Decompositions, such as Benders decomposition, Lagrangian r= elaxation, 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 limitation=
s of the general-purpose non-linear programming optimisation software. =
; [16] surveys three convergent approaches, based on piece-wise linearisati=
on 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 clos=
ely related, although the uncertainty is often modelled differently. Note a=
lso one would often [11] like to expand the network knowing that one can pe=
rform switching later. **

PowerTools (http://hhijazi.github.io/PowerTools/) is = a mathematical programming library for Power Systems optimization. PowerToo= ls is an open source c++ mathematical modeling platform linking to state-of= -the-art optimization solvers. It implements problems such as Optimal Power= Flow, and Optimal Transmission Switching, while benefiting from cutting-ed= ge research results. These include smart on/off constraints modeling, effic= ient bound propagation, domain-specific cut generation techniques and tight= convexification procedures providing global optimality guarantees. PowerTo= ols is still under active development, future versions will include Gas exp= ansion and Unit Commitment models, decomposition methods, multi-threading, = and support to additional solvers such as Cplex, Bonmin and others. Note th= at PowerTools is already used by another open-source project for Smart Grid= simulation: http://nicta.github.io/SmartGridToolbox/

[1] H. Glavitsch, =E2=80=9CState of the art review: switching as&n=
bsp; means of control in the power system,=E2=80=9D Inter=
national Journal Electric Power Energy Systems, vol, 7(2): 92-100, 1985. **[2] A. A. Mazi, B. F. Wollenberg, and M. H. Hesse, =E2=80=9CCorrective co=
ntrol of power system flows by line and bus-bar switching,=E2=80=9D IEEE Tr=
ans. Power Syst., vol. 1(3): 258-264, 1986. [3] R. P. O'Neill, R. Baldi=
ck, U. Helman, M. H. Rothkopf and W. Stewart, "Dispatchable transmission in=
RTO markets," in IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 1=
71-179, Feb. 2005.[4] Hedman, Kory W., et al. "Optimal transmission swi=
tching with contingency analysis." Power Systems, IEEE Transactions on 24.3=
(2009): 1577-1586.**

**MIP (CPLEX):**

[5] E. B. Fisher, R. P. O'Neill and M.=
C. Ferris, "Optimal Transmission Switching," in IEEE Transactions on Power=
Systems, vol. 23, no. 3, pp. 1346-1355, Aug. 2008.

[6] W. Hedman, S. S=
. Oren, and R. P. O=E2=80=99Neill, =E2=80=9COptimal transmission switching:=
economic efficiency and market implications,=E2=80=9D Journal of Regulator=
y Economics, vol. 40, no. 2, pp. 111-140, Oct. 2011.

[7] W. Hedman, M. =
C. Ferris, R. P. O=E2=80=99Neill, E. B. Fisher, and S. S. Oren, =E2=80=9CCo=
-optimization of generation unit commitment and transmission switching with=
N-1 reliability,=E2=80=9D IEEE Transactions on Power Systems, vol. 25, no.=
2, pp. 1052-1063, May 2010.

[8] M. Sahraei-Ardakani and K. W. Hedman, =
"A Fast LP Approach for Enhanced Utilization of Variable Impedance Based FA=
CTS Devices," IEEE Transactions on Power Systems , vol.PP, no.99, pp.1-10** [9] B. Kocuk. H. Jeon, S. S. Dey, J. Linderoth, J. Luedtke, and A. X. Su=
n, =E2=80=9CA Cycle-Based Formulation and Valid Inequalities for DC Power T=
ransmission Problems with Switching,=E2=80=9D Operations Research, vol. 64(=
4): 922-938, 2016.**

**Decomposition Methods:**

[10] Villumsen, Jonas Christ=
offer, and Andy B. Philpott. "Column generation for transmission switching =
of electricity networks with unit commitment." Lecture Notes in Engineering=
and Computer Science 2189 (2011): 1440-1443.

[11] Villumsen, Jonas Chr=
istoffer, Geir Bronmo, and Andy B. Philpott. "Line capacity expansion and t=
ransmission switching in power systems with large-scale wind power." Power =
Systems, IEEE Transactions on 28.2 (2013): 731-739.

**MINLP**:

[12] F. Capitanescu and L. Wehenkel, "An AC OPF-based heuristic algorith=
m for optimal transmission switching," Power Systems Computation Conference=
(PSCC), 2014, Wroclaw, 2014, pp. 1-6. doi: 10.1109/PSCC.2014.7038445

[=
13] C. Coffrin, H. L. Hijazi, K. Lehmann, P. Van Hentenryck, "Primal and du=
al bounds for optimal transmission switching." Power Systems Computation Co=
nference (PSCC), 2014. IEEE, 2014.

[14] R. A. Jabr, "Optimization of AC=
Transmission System Planning," IEEE Transactions on Power Systems, vol. 28=
(3), 2013.

[15] B. Kocuk, S. S. Dey, X. A. Sun, "New Formulation and St=
rong MISOCP Relaxations for AC Optimal Transmission Switching Problem, https://arxiv.org/pdf/1510.02064.pdf, 2016

[16] J. Marec=
ek, M. Mevissen, J. C. Villumsen, =E2=80=9CMINLP in transmission expansion =
planning.=E2=80=9D 2016 Power Systems Computation Conference (PSCC). IEEE, =
2016.

[17] M. Sahraei-Ardakani, A. Korad, K. W. Hedman, P. Lipka, S. Or=
en, =E2=80=9CPerformance of AC and DC based transmission switching heuristi=
cs on a large-scale Polish system=E2=80=9C, 2014 IEEE PES General Meeting| =
Conference & Exposition, 1-5, 2014.

**Grid Resiliency**

smartwire: http://www.smartwire=
s.com/

They are using plexus to find the optimal location of the imp=
edance in the system using LPs

Software:

- PowerTools by Hijazi: http://hhijazi.github.io/PowerTools/

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>

Dr Fabrizio Lacalandra, QuanTek