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A Stochastic Optimal Power Flow Problem With Stability Constraints-Part II: The Optimization Problem
KTH, School of Electrical Engineering (EES), Electric Power Systems.
KTH, School of Electrical Engineering (EES), Electric Power Systems.ORCID iD: 0000-0002-4173-1390
2013 (English)In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 2, 1849-1857 p.Article in journal (Refereed) Published
Abstract [en]

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 line flows 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 second-order 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 Cornish-Fisher 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.

Place, publisher, year, edition, pages
2013. Vol. 28, no 2, 1849-1857 p.
Keyword [en]
Hopf bifurcation, saddle-node bifurcation, stochastic optimal power flow, switching loadability limit
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-129640DOI: 10.1109/TPWRS.2012.2226761ISI: 000322139300130Scopus ID: 2-s2.0-84886388808OAI: oai:DiVA.org:kth-129640DiVA: diva2:653147
Funder
StandUp
Note

QC 20150623

Available from: 2013-10-03 Created: 2013-10-03 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Probabilistic security management for power system operations with large amounts of wind power
Open this publication in new window or tab >>Probabilistic security management for power system operations with large amounts of wind power
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Power systems are critical infrastructures for the society. They are therefore planned and operated to provide a reliable eletricity delivery. The set of tools and methods to do so are gathered under security management and are designed to ensure that all operating constraints are fulfilled at all times.

During the past decade, raising awareness about issues such as climate change, depletion of fossil fuels and energy security has triggered large investments in wind power. The limited predictability of wind power, in the form of forecast errors, pose a number of challenges for integrating wind power in power systems. This limited predictability increases the uncertainty already existing in power systems in the form of random occurrences of contingencies and load forecast errors. It is widely acknowledged that this added uncertainty due to wind power and other variable renewable energy sources will require new tools for security management as the penetration levels of these energy sources become significant.

In this thesis, a set of tools for security management under uncertainty is developed. The key novelty in the proposed tools is that they build upon probabilistic descriptions, in terms of distribution functions, of the uncertainty. By considering the distribution functions of the uncertainty, the proposed tools can consider all possible future operating conditions captured in the probabilistic forecasts, as well as the likeliness of these operating conditions. By contrast, today's tools are based on the deterministic N-1 criterion that only considers one future operating condition and disregards its likelihood.

Given a list of contingencies selected by the system operator and probabilitistic forecasts for the load and wind power, an operating risk is defined in this thesis as the sum of the probabilities of the pre- and post-contingency violations of the operating constraints, weighted by the probability of occurrence of the contingencies.

For security assessment, this thesis proposes efficient Monte-Carlo methods to estimate the operating risk. Importance sampling is used to substantially reduce the computational time. In addition, sample-free analytical approximations are developed to quickly estimate the operating risk. For security enhancement, the analytical approximations are further embedded in an optimization problem that aims at obtaining the cheapest generation re-dispatch that ensures that the operating risk remains below a certain threshold. The proposed tools build upon approximations, developed in this thesis, of the stable feasible domain where all operating constraints are fulfilled.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xvi, 144 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2015:018
Keyword
Power systems, wind power, probabilistic security management, chance-constrained optimal power flow, monte-carlo, importance sampling
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-166398 (URN)978-91-7595-547-6 (ISBN)
Public defence
2015-05-29, E3, Lindstedtsvägen 3, KTH, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20150508

Available from: 2015-05-08 Created: 2015-05-08 Last updated: 2015-05-08Bibliographically approved

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