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Probabilistic security management for power system operations with large amounts of wind power
KTH, School of Electrical Engineering (EES), Electric Power Systems.ORCID iD: 0000-0002-4173-1390
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 [en]
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: urn:nbn:se:kth:diva-166398ISBN: 978-91-7595-547-6 (print)OAI: oai:DiVA.org:kth-166398DiVA: diva2:810806
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
List of papers
1. A Stochastic Optimal Power Flow Problem With Stability Constraints-Part I: Approximating the Stability Boundary
Open this publication in new window or tab >>A Stochastic Optimal Power Flow Problem With Stability Constraints-Part I: Approximating the Stability Boundary
2013 (English)In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 2, 1839-1848 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 line flows have been used as security 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 boundaries 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 first part of the paper, we derive second-order approximations of stability boundaries in parameter space. In the second part, the approximations will be used to solve a stochastic optimal power flow problem.

Keyword
Hopf bifurcation, saddle-node bifurcation, stability boundary, stochastic optimal power flow (SOPF), switching loadability limit
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-129639 (URN)10.1109/TPWRS.2012.2226760 (DOI)000322139300129 ()2-s2.0-84886423924 (Scopus ID)
Funder
StandUp
Note

QC 20150623

Available from: 2013-10-03 Created: 2013-10-03 Last updated: 2017-12-06Bibliographically approved
2. A Stochastic Optimal Power Flow Problem With Stability Constraints-Part II: The Optimization Problem
Open this publication in new window or tab >>A Stochastic Optimal Power Flow Problem With Stability Constraints-Part II: The Optimization Problem
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.

Keyword
Hopf bifurcation, saddle-node bifurcation, stochastic optimal power flow, switching loadability limit
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-129640 (URN)10.1109/TPWRS.2012.2226761 (DOI)000322139300130 ()2-s2.0-84886388808 (Scopus ID)
Funder
StandUp
Note

QC 20150623

Available from: 2013-10-03 Created: 2013-10-03 Last updated: 2017-12-06Bibliographically approved
3. Applying stochastic optimal power flow to power systems with large amounts of wind power and detailed stability limits
Open this publication in new window or tab >>Applying stochastic optimal power flow to power systems with large amounts of wind power and detailed stability limits
2013 (English)In: Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid (IREP), 2013 IREP Symposium, 2013Conference paper, Published paper (Refereed)
Abstract [en]

Increasing wind power penetration levels bring about new challenges for power systems operation and planning, because wind power forecast errors increase the uncertainty faced by the different actors. One specific problem is generation re-dispatch during the operation period, a problem in which the system operator seeks the cheapest way of re-dispatching generators while maintaining an acceptable level of system security. Stochastic optimal power flows are re-dispatch algorithms which account for the uncertainty in the optimization problem itself. In this article, an existing stochastic optimal power flow (SOPF) formulation is extended to include the case of non-Gaussian distributed forecast errors. This is an important case when considering wind power, since it has been shown that wind power forecast errors are in general not normally distributed. Approximations are necessary for solving this SOPF formulation. The method is illustrated in a small power system in which the accuracy of these approximations is also assessed for different probability distributions of the load and wind power.

Keyword
power generation dispatch, generation redispatch, power systems, power systems operation, stochastic optimal power flow, system security, wind power forecast errors
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-138437 (URN)10.1109/IREP.2013.6629407 (DOI)2-s2.0-84890489957 (Scopus ID)978-147990199-9 (ISBN)
Conference
2013 IREP Symposium on Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid
Funder
StandUp
Note

QC 20140129

Available from: 2013-12-19 Created: 2013-12-19 Last updated: 2015-05-08Bibliographically approved
4. The value of using chance-constrained optimal power flows for generation re-dispatch under uncertainty with detailed security constraints
Open this publication in new window or tab >>The value of using chance-constrained optimal power flows for generation re-dispatch under uncertainty with detailed security constraints
2013 (English)In: 2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), IEEE Computer Society, 2013, 6837148- p.Conference paper, Published paper (Refereed)
Abstract [en]

The uncertainty faced in the operation of power systems increases as larger amounts of intermittent sources, such as wind and solar power, are being installed. Traditionally, an optimal generation re-dispatch is obtained by solving security-constrained optimal power flows (SCOPF). The resulting system operation is then optimal for given values of the uncertain parameters. New methods have been developed to consider the uncertainty directly in the generation re-dispatch optimization problem. Chance-constrained optimal power flows (CCOPF) are such methods. In this paper, SCOPF and CCOPF are compared and the benefits of using CCOPF for power systems operation under uncertainty are discussed. The discussion is illustrated by a case study in the IEEE 39 bus system, in which the generation re-dispatch obtained by CCOPF is shown to always be cheaper than that obtained by SCOPF.

Place, publisher, year, edition, pages
IEEE Computer Society, 2013
Series
Asia-Pacific Power and Energy Engineering Conference, APPEEC, ISSN 2157-4839
Keyword
Electric load flow, Electric power systems, Optimization, Solar energy, Generation re-dispatch, Operation of power system, Optimal power flows, Optimization problems, Power systems operation, Security-constrained optimal power flow, Uncertain parameters, Wind and solar power
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-140521 (URN)10.1109/APPEEC.2013.6837148 (DOI)2-s2.0-84903973841 (Scopus ID)978-147992522-3 (ISBN)
Conference
2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference, APPEEC 2013; Kowloon; Hong Kong; 8 December 2013 through 11 December 2013
Funder
StandUp
Note

QC 20140128

Available from: 2014-01-24 Created: 2014-01-24 Last updated: 2015-05-08Bibliographically approved
5. A computational framework for risk-based power systems operations under uncertainty. Part I: Theory
Open this publication in new window or tab >>A computational framework for risk-based power systems operations under uncertainty. Part I: Theory
2015 (English)In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 119, 45-53 p.Article in journal (Refereed) Published
Abstract [en]

With larger penetrations of wind power, the uncertainty increases in power systems operations. The wind power forecast errors must be accounted for by adapting existing operating tools or designing new ones. A switch from the deterministic framework used today to a probabilistic one has been advocated. This two-part paper presents a framework for risk-based operations of power systems. This framework builds on the operating risk defined as the probability of the system to be outside the stable operation domain, given probabilistic forecasts for the uncertainty (load and wind power generation levels) and outage rates of chosen elements of the system (generators and transmission lines). This operating risk can be seen as a probabilistic formulation of the N - 1 criterion. The stable operation domain is defined by voltage-stability limits, small-signal stability limits, thermal stability limits and other operating limits. In Part I of the paper, a previous method for estimating the operating risk is extended by using a new model for the joint distribution of the uncertainty. This new model allows for a decrease in computation time of the method, which allows for the use of later and more up-to-date forecasts. In Part II, the accuracy and the computation requirements of the method using this new model will be analyzed and compared to the previously used model for the uncertainty. The method developed in this paper is able to tackle the two challenges associated with risk-based real-time operations: accurately estimating very low operating risks and doing so in a very limited amount of time.

Keyword
Wind power, Stochastic optimal power flow, Risk-limiting dispatch, Chance-constrained optimal power flow, Edgeworth expansions, Risk-based method
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-159967 (URN)10.1016/j.epsr.2014.09.008 (DOI)000347756700006 ()2-s2.0-84907495082 (Scopus ID)
Note

QC 20150306

Available from: 2015-03-06 Created: 2015-02-12 Last updated: 2017-12-04Bibliographically approved
6. A computational framework for risk-based power system operations under uncertainty. Part II: Case studies
Open this publication in new window or tab >>A computational framework for risk-based power system operations under uncertainty. Part II: Case studies
2015 (English)In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 119, 66-75 p.Article in journal (Refereed) Published
Abstract [en]

With larger penetrations of wind power, the uncertainty increases in power systems operations. The wind power forecast errors must be accounted for by adapting existing operating tools or designing new ones. A switch from the deterministic framework used today to a probabilistic one has been advocated. This two-part paper presents a framework for risk-based operations of power systems. This framework builds on the operating risk defined as the probability of the system to be outside the stable operation domain, given probabilistic forecasts for the uncertainty, load and wind power generation levels. This operating risk can be seen as a probabilistic formulation of the N - 1 criterion. In Part I, the definition of the operating risk and a method to estimate it were presented. A new way of modeling the uncertain wind power injections was presented. In Part II of the paper, the method's accuracy and computational requirements are assessed for both models. It is shown that the new model for wind power introduced in Part I significantly decreases the computation time of the method, which allows for the use of later and more accurate forecasts. The method developed in this paper is able to tackle the two challenges associated with risk-based real-time operations: accurately estimating very low operating risks and doing so in a very limited amount of time.

Keyword
Wind power, Stochastic optimal power flow, Risk-limiting dispatch, Chance-constrained optimal power flow, Edgeworth expansions, Risk-based methods
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-159968 (URN)10.1016/j.epsr.2014.09.007 (DOI)000347756700008 ()2-s2.0-84907487450 (Scopus ID)
Note

QC 20150306

Available from: 2015-03-06 Created: 2015-02-12 Last updated: 2017-12-04Bibliographically approved
7. Efficient importance sampling technique for estimating operating risks in power systems with large amounts of wind power
Open this publication in new window or tab >>Efficient importance sampling technique for estimating operating risks in power systems with large amounts of wind power
2014 (English)In: Proceedings of the 13th International Workshop on Large-scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Power Plants / [ed] Uta Betancourt, Thomas Ackermann, Energynautics GmbH, 2014Conference paper, Published paper (Refereed)
Abstract [en]

Uncertainties faced by operators of power systems are expected to increase with increasing amounts of wind power. This paper presents a method to design efficient importance sampling estimators to estimate the operating risk by Monte-Carlo simulations given the joint probability distribution describing the wind power and load forecasts. The operating risk is defined as the probability of violating stability and / or operating constraints. The method relies on an exisiting framework for rare-event simulations but takes into account the peculiarities of power systems. In case studies, it is shown that the number of Monte-Carlo runs needed to achieve a certain accuracy on the estimator can be reduced by up to three orders of magnitude.

Place, publisher, year, edition, pages
Energynautics GmbH, 2014
Keyword
Wind power, Importance sampling, Rare-event simulation, Monte-Carlo
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-166265 (URN)978-3-98 13870-9-4 (ISBN)
Conference
13th Wind Integration Workshop,22 - 24 October 2013 | London, UK
Note

QC 20150507

Available from: 2015-05-06 Created: 2015-05-06 Last updated: 2015-05-08Bibliographically approved
8. An Importance Sampling Technique for Probabilistic Security Assessment In Power Systems with Large Amounts of Wind Power
Open this publication in new window or tab >>An Importance Sampling Technique for Probabilistic Security Assessment In Power Systems with Large Amounts of Wind Power
2016 (English)In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 131, 11-18 p.Article in journal (Refereed) Published
Abstract [en]

Larger amounts of variable renewable energy sources bring about larger amounts of uncertainty in the form of forecast errors. When taking operational and planning decisions under uncertainty, a trade-off between risk and costs must be made. Today's deterministic operational tools, such as N-1-based methods, cannot directly account for the underlying risk due to uncertainties. Instead, several definitions of operating risks, which are probabilistic indicators, have been proposed in the literature. Estimating these risks require estimating very low probabilities of violations of operating constraints. Crude Monte-Carlo simulations are very computationally demanding for estimating very low probabilities. In this paper, an importance sampling technique from mathematical finance is adapted to estimate very low operating risks in power systems given probabilistic forecasts for the wind power and the load. Case studies in the IEEE 39 and 118 bus systems show a decrease in computational demand of two to three orders of magnitude.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Importance sampling, Monte-Carlo simulations, N-1 criterion, Risk-based operation, Stability boundary, Wind power
National Category
Energy Systems
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-166394 (URN)10.1016/j.epsr.2015.09.016 (DOI)2-s2.0-84944351188 (Scopus ID)
Note

Updated from Manuscript to Article. QC 20160126

Available from: 2015-05-08 Created: 2015-05-08 Last updated: 2017-12-04Bibliographically approved

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
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  • en-GB
  • en-US
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  • nn-NO
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