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Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment
KTH, School of Electrical Engineering (EES), Electric Power Systems. Universidad Pontificia Comillas.ORCID iD: 0000-0002-6372-6197
Universidad Pontificia Comillas.
Universidad Pontificia Comillas.
2013 (English)In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 2, 1288-1296 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a mixed-integer linear programming (MILP) formulation of start-up (SU) and shut-down (SD) power trajectories of thermal units. Multiple SU power-trajectories and costs are modeled according to how long the unit has been offline. The proposed formulation significantly reduces the computational burden in comparison with others commonly found in the literature. This is because the formulation is 1) tighter, i.e., the relaxed solution is nearer to the optimal integer solution; and 2) more compact, i.e., it needs fewer constraints, variables and nonzero elements in the constraint matrix. For illustration, the self-unit commitment problem faced by a thermal unit is employed. We provide computational results comparing the proposed formulation with others found in the literature.

Place, publisher, year, edition, pages
2013. Vol. 28, no 2, 1288-1296 p.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-139310DOI: 10.1109/TPWRS.2012.2222938ISI: 000322139300073Scopus ID: 2-s2.0-84886442362OAI: oai:DiVA.org:kth-139310DiVA: diva2:684602
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QC 20140326

Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Unit Commitment: Computational Performance, System Representation and Wind Uncertainty Management
Open this publication in new window or tab >>Unit Commitment: Computational Performance, System Representation and Wind Uncertainty Management
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited.

This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: 

  • Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility.
  • UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space.
  • Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations.
  • To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.
Place, publisher, year, edition, pages
Madrid, Spain: Comillas Pontifical University, 2014. ix, 104 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2014:041
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering; Mathematics
Identifiers
urn:nbn:se:kth:diva-152155 (URN)978-84-697-1230-6 (ISBN)
Public defence
2014-10-08, Sala de vistas, Alberto Aguilera 23, Comillas Pontifical University, Madrid, 13:30 (English)
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The Doctoral Degrees issued upon completion of the programme are issued by Comillas Pontifical University, Delft University of Technology and KTH Royal Institute of Technology. The invested degrees are official in Spain, the Netherlands and Sweden, respectively. QC 20140923

Available from: 2014-09-23 Created: 2014-09-23 Last updated: 2014-09-23Bibliographically approved

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