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@PHDTHESIS{Lemkens:464551,
author = {Lemkens, Stephan},
othercontributors = {Koster, Arie M. C. A. and Triesch, Eberhard},
title = {{S}tructural {P}roperties of {L}inearized {P}ower {F}lows
and {P}ower {G}rid {D}esign},
school = {Aachen, Techn. Hochsch.},
type = {Dissertation},
address = {Aachen},
publisher = {Publikationsserver der RWTH Aachen University},
reportid = {RWTH-2015-01361},
pages = {VII, 254 S. : Ill., graph. Darst., Kt.},
year = {2015},
note = {Aachen, Techn. Hochsch., Diss., 2015},
abstract = {In this thesis we linearize the power flow and power grid
design problem and analyze the mathematical properties of
these problems. We introduce a linearization which takes
care of some of the drawbacks of the well-established DC
formulation. The DC formulation is an approximation of the
nonlinear power flow equations, useful for deriving an
approximation of the active power flow. Our new
linearization, called AC-linear, is based on Taylor
expansion of the nonlinear formulation and yields
information on active and reactive flows. We show that it is
a generalization of the often used DC formulation. Our main
contribution is the thorough analysis of the newly
introduced AC-linear formulation. We show the existence of
combinatorial structures in the problem, which involve the
class of bispanning graphs. The first part concludes with a
computational comparison of the quality of the two discussed
linearizations. We are able to show, that the AC-linear
formulation is superior to the DC one when interested in
active and reactive flow information. The second part of
this work considers the impact of the new linearization on
the power grid design problem. We therefore study the
computational complexity of various power grid design
problems and show that a special formulation of the DC
problem can be considered as a partition problem without the
involvement of power flow equations. We show that this does
no longer hold for the generalized formulation. As the set
of feasible power grid designs is given by a polytope, we
thoroughly study its structure for both formulations. We
then give an in depth analysis of a special case of the DC
power grid design polytope, where the polytope's dimension
is easily determinable. We are able to derive facets for the
polytope, utilizing results of both the connected-subgraph
and the knapsack polytope. We then perform a computational
study in order to determine the tractability of the two
linearizations on modern integer programming solvers. While
the DC model significantly outperforms the AC-linear one,
its computed designs do not allow for a feasible AC power
flow. We show that the designs derived by using the
AC-linear formulation are superior with regards to this
property. Thus the newly introduced formulation allows for a
more accurate approximation of the power grid design
problem.},
cin = {113320 / 110000},
ddc = {510},
cid = {$I:(DE-82)113320_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
urn = {urn:nbn:de:hbz:82-rwth-2015-013612},
url = {https://publications.rwth-aachen.de/record/464551},
}
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