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Unit Commitment: Computational Performance, System Representation and Wind Uncertainty Management
KTH, School of Electrical Engineering (EES), Electric Power Systems. Universidad Pontificia Comillas.ORCID iD: 0000-0002-6372-6197
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: urn:nbn:se:kth:diva-152155ISBN: 978-84-697-1230-6 (print)OAI: oai:DiVA.org:kth-152155DiVA: diva2:749131
Public defence
2014-10-08, Sala de vistas, Alberto Aguilera 23, Comillas Pontifical University, Madrid, 13:30 (English)
Opponent
Supervisors
Funder
StandUp
Note

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
List of papers
1. Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment
Open this publication in new window or tab >>Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment
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.

National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-139310 (URN)10.1109/TPWRS.2012.2222938 (DOI)000322139300073 ()2-s2.0-84886442362 (Scopus ID)
Funder
StandUp
Note

QC 20140326

Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
2. An MIP Formulation for Joint Market-Clearing of Energy and Reserves Based on Ramp Scheduling
Open this publication in new window or tab >>An MIP Formulation for Joint Market-Clearing of Energy and Reserves Based on Ramp Scheduling
2014 (English)In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 29, no 1, 476-488 p.Article in journal (Refereed) Published
Abstract [en]

The day-ahead unit-commitment (UC)-based market-clearing (MC) is widely acknowledged to be the most economically efficient mechanism for scheduling resources in power systems. In conventional UC problems, power schedules are used to represent the staircase energy schedule. However, the realizability of this schedule cannot be guaranteed due to the violation of ramping limits, and hence conventional UC formulations do not manage the flexibility of generating units efficiently. This paper provides a UC-based MC formulation, drawing a clear distinction between power and energy. Demand and generation are modeled as hourly piecewise-linear functions representing their instantaneous power trajectories. The schedule of generating unit output is no longer a staircase function, but a smoother function that respects all ramp constraints. The formulation represents in detail the operating reserves (online and offline), their time deployment limits (e.g., 15 min), their potential substitution, and their limits according to the actual ramp schedule. Startup and shutdown power trajectories are also modeled, and thus a more efficient energy and reserves schedule is obtained. The model is formulated as a mixed-integer programming (MIP) problem, and was tested with a 10-unit and 100-unit system in which its computational performance was compared with a traditional UC formulation.

National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-139314 (URN)10.1109/TPWRS.2013.2259601 (DOI)000329035000054 ()2-s2.0-84891555130 (Scopus ID)
Funder
StandUp
Note

QC 20140331

Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
3. Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem
Open this publication in new window or tab >>Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem
2013 (English)In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 4, 4897-4908 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.

National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-139308 (URN)10.1109/TPWRS.2013.2251373 (DOI)000326184100146 ()2-s2.0-84886085924 (Scopus ID)
Funder
StandUp
Note

QC 20140328

Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
4. A Tight MIP Formulation of the Unit Commitment Problemwith Start-up and Shut-down Constraints
Open this publication in new window or tab >>A Tight MIP Formulation of the Unit Commitment Problemwith Start-up and Shut-down Constraints
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper provides the convex hull description for the following basic operating con-straints of a single thermal generation unit in Unit Commitment (UC) problems: 1)generation limits, 2) startup and shutdown capabilities, and 3) minimum up and downtimes. Although the model does not consider some crucial constraints, such as ramping,the proposed constraints can be used as the core of any UC formulation, thus tighteningthe final UC model. We provide evidence that dramatic improvements in computationaltime are obtained by solving a self-UC problem for different case studies.

Keyword
Unit Commitment (UC), Mixed-Integer Programming (MIP), Facet/Convex hull description.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering; Mathematics
Identifiers
urn:nbn:se:kth:diva-151832 (URN)
Funder
StandUp
Note

QS 2014

Available from: 2014-09-22 Created: 2014-09-22 Last updated: 2014-09-23Bibliographically approved
5. Tight MIP Formulations of the Power-Based Unit Commitment Problem
Open this publication in new window or tab >>Tight MIP Formulations of the Power-Based Unit Commitment Problem
(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:nbn:se:kth:diva-151883 (URN)
Funder
StandUp
Note

QS 2014

Available from: 2014-09-22 Created: 2014-09-22 Last updated: 2014-09-23Bibliographically approved
6. Robustified Reserve Modelling for Wind PowerIntegration in Ramp-Based Unit Commitment
Open this publication in new window or tab >>Robustified Reserve Modelling for Wind PowerIntegration in Ramp-Based Unit Commitment
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper proposes a “robustified” network-constrained Unit Commitment (UC) formulation as an altern-ative to the robust and stochastic UC formulations under windgeneration uncertainty. The formulation draws a clear distinctionbetween power-capacity and ramp-capability reserves to deal withwind production uncertainty. These power and ramp require-ments can be obtained from wind forecast information. The modelis formulated under the ramp-based scheduling approach, whichschedules power-trajectories instead of the traditional energy-blocks and takes into account the inherent startup and shutdownpower trajectories of thermal units. These characteristics allowa correct representation of unit’s ramp schedule which definetheir ramp availability for reserves. The proposed formulationsignificantly decreases operation costs if compared to traditionaldeterministic and stochastic UC formulations while simultan-eously lowering the computational burden. The operation costcomparison is made through 5-min economic dispatch simulationunder hundreds of out-of-sample wind generation scenarios.

Keyword
Mixed-integer programming, operating reserves, ramp scheduling, robustified formulation, unit commitment.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-151963 (URN)
Funder
StandUp
Note

QS 2014

Available from: 2014-09-22 Created: 2014-09-22 Last updated: 2015-04-28Bibliographically approved

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