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A Stochastic Optimal Power Flow Problem With Stability Constraints - Part II: The Optimization Problem

Perninge, Magnus LU and Hamon, Camille (2013) In IEEE Transactions on Power Systems 28(2). p.1849-1857
Abstract
Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on lineflows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint surfaces with secondorder approximations in parameter space. Then we refine... (More)
Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on lineflows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint surfaces with secondorder approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this, the second part of the paper, we look at how CornishFisher expansion combined with a method of excluding sets that are counted twice, can be used to estimate the probability of violating the stability constraints. We then show in a numerical example how this leads to an efficient solution method for the stochastic optimal power flow problem. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Power Systems
volume
28
issue
2
pages
1849 - 1857
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • WOS:000322139300130
  • Scopus:84886388808
ISSN
0885-8950
DOI
10.1109/TPWRS.2012.2226761
language
English
LU publication?
yes
id
df69c756-82bb-45df-983c-64b3ed8bfc75 (old id 4076468)
date added to LUP
2013-10-09 09:22:24
date last changed
2016-11-13 04:27:37
@misc{df69c756-82bb-45df-983c-64b3ed8bfc75,
  abstract     = {Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on lineflows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint surfaces with secondorder approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this, the second part of the paper, we look at how CornishFisher expansion combined with a method of excluding sets that are counted twice, can be used to estimate the probability of violating the stability constraints. We then show in a numerical example how this leads to an efficient solution method for the stochastic optimal power flow problem.},
  author       = {Perninge, Magnus and Hamon, Camille},
  issn         = {0885-8950},
  language     = {eng},
  number       = {2},
  pages        = {1849--1857},
  publisher    = {ARRAY(0xacc7c28)},
  series       = {IEEE Transactions on Power Systems},
  title        = {A Stochastic Optimal Power Flow Problem With Stability Constraints - Part II: The Optimization Problem},
  url          = {http://dx.doi.org/10.1109/TPWRS.2012.2226761},
  volume       = {28},
  year         = {2013},
}