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Tight MIP Formulations of the Power-Based Unit Commitment Problem
KTH, School of Electrical Engineering (EES), Electric Power Systems. Universidad Pontificia Comillas.ORCID iD: 0000-0002-6372-6197
(Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, C.N.R., Viale Manzoni 30, 00185 Roma, Italy)
Universidad Pontificia Comillas.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper provides the convex hull description for the basic operation of slow- and quick-startunits in power-based unit commitment (UC) problems. The basic operating constraints that are modeled forboth types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startupand shutdown processes are also modeled, using 3) startup and shutdown power trajectories for slow-startunits, and 4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, powerschedules are used to represent the staircase energy schedule; however, this simplification leads to infeasibleenergy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-basedUC formulation drawing a clear distinction between power and energy. The proposed constraints can be usedas the core of any power-based UC formulation, thus tightening the final mixed-integer programming UCproblem. We provide evidence that dramatic improvements in computational time are obtained by solvingdifferent case studies, for self-UC and network-constrained UC problems.

National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering; Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-151883OAI: oai:DiVA.org:kth-151883DiVA: diva2:748955
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QS 2014

Available from: 2014-09-22 Created: 2014-09-22 Last updated: 2014-09-23Bibliographically 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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