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Augmented Lagrangean Relaxation and Decomposition Applied to the Short-Term Hydrothermal Coordination Problem

Mon, 10/29/2007 - 18:36 — admin
Publication TypeConference Paper
Year of Publication1999
AuthorsBeltran, C.; Heredia, F. J.
Conference Name19th IFIP TC7 Conference on System Modelling and Optimization
Conference Date12-16/07/1999
Conference LocationCambridge, U.K.
Type of WorkContributed oral presentation
Key Wordsaugmented lagrangian relaxation; generalized unit commitment; block coordinated descent method; auxiliary principle problem; research
AbstractThe problem dealt with is called the Short-Term Hydrothermal Coordination (SHTC) problem. The objective of this problem is the optimization of electrical production and distribution, considering a short-term planning horizon (from one day to one week). Hydraulic and thermal plants must be coordinated in order to satisfy the customer demand of electricity at the minimum cost and with a reliable service. The model for the STHC problem presented here considers the thermal system, the hydraulic system and the distribution network. Nowadays the Lagrangean Relaxation (LR) method is the most widespread procedure to solve the STHC problem. The initial Classical Lagrangean Relaxation (CLR) method was improved by the Augmented Lagrangean Relaxation (ALR) method, although recent advances in the multiplier updating for the CLR method (cutting plane, bundle methods, etc.) have brought this classical method back into fashion. Two main advantages of the ALR method over the CLR method: (1) the ALR method allows us to obtain a saddle-point even in cases where the CLR method presents a duality gap. The solution of the STHC problem by the CLR method usually yields an infeasible primal solution $x_k$ due to the duality gap, whereas in the ALR method a solution of the dual problem provides a feasible primal solution. (2) The second advantage is that, using the CLR method, the differentiability of the dual function cannot be ensured and therefore nondifferentiable methods must be applied in the CLR method. This difficulty can be overcome if an augmented Lagrangean is used, since the dual function $q_c$ is differentiable for an appropriate c. Thus, the multipliers can be updated using ``large steps''. The main weakness of the ALR method is that the quadratic terms introduced by the augmented Lagrangean are not separable. If we want to solve the STHC problem by decomposition, some methods, such as the Auxiliary Problem Principle, or, as in our case, the Block Coordinate Descent method, must be used. However, the CLR method gives a separable Lagrangean. The starting point is the paper by Batut and Renaud [1] and therefore we use Variable Duplication plus the Augmented Lagrangean Relaxation (ALR) method. The method used by Batut and Renaud is improved theoretically and practically. From the theoretical point of view, the conservative Auxiliary Problem Principle is replaced by the Block Coordinate Descent Method that shows to be faster. From the practical point of view, an effective software package designed to solve the Optimum Short-Term Hydrothermal Coordination Problem, is incorporated in order to speed up the whole algorithm. Several medium to large scale instances of this problem have been solved showing the applicability of the proposed procedure.
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Generalized Unit Commitment (closed)

Mon, 10/29/2007 - 16:21 — admin

Under construction

Short-Term Hydrothermal Coordination by Augmented Lagrangean Relaxation: a new Multiplier Updating

Sun, 10/28/2007 - 18:21 — admin
Publication TypeConference Paper
Year of Publication1998
AuthorsBeltran, C.; Heredia, F. J.
Conference NameIX Congreso Latino-Iberoamericano de Investigación Operativa
Conference Date31-4/08/98
Conference LocationBuenos Aires, Argentina
Type of WorkContributed oral presentation
Key Wordsaugmented lagrangian relaxation; radar subgradient method; generalized unit commitment; research
AbstractAugmented Lagrangean Relaxation Method (ALRM) is one of the most powerfull technique to solve the Short­Term Hydrothermal Coordination Problem (STHC Problem ). A crucial step when using the ALR Method is the multipliers updating. In this paper we present an efficient new multiplier updating procedure: the Gradient Method with Radar Step. The method has been successfully tested solving large ­scale exemples of the STHC Problem
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SLOEGAT Project. Short and Long term Optimization of Energy Generation And Trading (Esprit 22695).

Thu, 10/25/2007 - 00:30 — admin
Publication TypeFunded research projects
Year of Publication1996
AuthorsF.-Javier Heredia
Type of participationFull time researcher
Duration12/1996-05/1999
Funding organizationEuropean Union, ESPRIT Programme
PartnersUniversidad Politécnica de Catalunya, Iberdrola, Universidad de Aachen, VEW Alemania, SIEMENS Austria
Full time researchers4 (DEIO/UPC)
Budget180.238€
Project codeEsprit 22695
Key Wordsresearch; nonlinear network flows; side constraints; power systems; transmission network; short-term hydrothermal coordination; long-term hydrothermal coordination project; public; competitive; EU; energy
AbstractThe project aims to develop, implement and test, on a high performance computing platform, a software system to simulate and optimise the energy generation and trading coordination planning process in large electricity generating systems, both in the short (1 day-1 week) and medium to long term (one-two years). Special consideration will be given to this process to the growing importance of the energy trading problem in a deregulated market.
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Planificación óptima de gran dimensión de la produción hidrotérmica de energia eléctrica (TAP99-1075-C02-01).

Thu, 10/25/2007 - 00:19 — admin
Publication TypeFunded research projects
Year of Publication2000
AuthorsF.-Javier Heredia
Type of participationFull researcher
Duration01/2000-12/2002
Funding organizationMinisterio de Educación y Ciencia / Comisión Interministerial de Ciencia y Tecnologia
PartnersDepartament d'Estadística i Investigació Operativa, Univ. Politècnica de Catalunya
Full time researchers5
Budget76.785€
Project codeTAP99-1075-C02-01
Key Wordsresearch; nonlinear network flows; side constraints; power systems; transmission network; short-term hydrothermal coordination; long-term hydrothermal coordination; project; public; competitive; cicyt; energy
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Coordinación hidrotérmica a corto y largo plazo de la generación eléctrica en un mercado competitivo (DPI2002-03330).

Wed, 10/24/2007 - 23:53 — admin
Publication TypeFunded research projects
Year of Publication2002
AuthorsF.-Javier Heredia
Type of participationFull time researcher
Duration01/2003 -12/2005
Funding organizationMinisterio de Educación y Ciencia
PartnersDepartament d'Estadística i Investigació Operativa / Universitat Politècnica de Catalunya; Unión Fenosa
Full time researchers7
Budget85.000’00 €
Project codeDPI2002-03330
Key Wordsresearch; dual methods; lagrangian relaxation; unit commitment; power systems; transmission network; radar multiplier; project; public; competitive; micinn; energy
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Planificación de la generación eléctrica a corto y largo plazo en un mercado liberalizado con contratos bilaterales (DPI2005-09117-C02-01).

Wed, 10/24/2007 - 23:39 — admin
Publication TypeFunded research projects
Year of Publication2005
AuthorsF.-Javier Heredia
Type of participationFull time researcher
Duration01/2006-12/2008
Funding organizationMinisterio de Educación y Ciencia
PartnersDepartament d'Estadística i Investigació Operativa, Universidad Politèctica de Catalunya; Unión Fenosa
Full time researchers5
Budget289.408'00€
Project codeDPI2005-09117-C02-01
Key Wordsresearch; stochastic programming; electricity markets; future contracts; bilateral contracts; regulation markets; project; public; competitive; micinn; energy
AbstractThe project aims at two new features: the simultaneous consideration of bidding power to the liberalized market and of bilateral contracts (between a generation company and a consumer client), given the future elimination of the current regulations discouraging bilateral contracts, and the developement of optimization procedures more efficient than those employed now to solve these problems. This higher efficiency will allow a more accurate modeling and solving larger real problems in reasonable CPU time. In this project, both modeling languages and commercially available solvers in the one hand, and our own optimization algorithms in the other are employed. The algorithms to be developed include the use of: interior-point methods, global optimization, column-generation methods, and Lagrangian relaxation procedures employing dual methods
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The radar multiplier method: a two-phase approach for large scale nonlinear combinatorial optimization problems

Mon, 10/15/2007 - 17:38 — admin
Publication TypeConference Paper
Year of Publication2003
AuthorsHeredia, F. J.; Beltran, C.
Conference Name 21th IFIP TC7 Conference on System Modelling and Optimization
Pagination92
Conference Date21-25/07/2003
PublisherINRIA
Conference LocationSophia Antipolis, France
EditorJ. Cagnol; J.P. Zolesio
Type of WorkContributed oral presentation
ISBN Number2-7261-1253-6
Key Wordsaugmented lagrangian relaxation; generalized unit commitment; radar multiplier method; research
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Generalized Unit Commitment

Mon, 10/15/2007 - 12:22 — admin
Publication TypeConference Paper
Year of Publication2004
AuthorsHeredia, F. J.; Beltran, C.
Conference NameApplied Mathematical Programming and Modellization (APMOD 2004)
Conference Date21-23/06/2004
Conference LocationBrunel University, Uxbridge, UK.
Type of WorkInvited oral presentation
Key Wordsaugmented lagrangian relaxation; generalized unit commitment; radar multiplier method; research
AbstractThe Generalized Unit Commitment problem (GUC) extends the unit commitment problem by adding the transmission network. A full-network modelization of the GUC problem is presented. In this model, all non-binary variables of the problem can be represented as flows of the so called Hydro-Thermal-Transmission Network (HTTN), including those representing incremental and decremental spinning reserve. The result is a large scale nonlinear mixed optimization problem that is solved with the Radar Multiplier method, a novel two-phase dual technique based on augmented Lagrangian relaxation and variable duplication. The computational implementation of the proposed model and method, both in FORTRAN and AMPL, are described. The numerical solution of several instances of the GUC problem will be presented and discussed, showing the capability of the model and solution technique to cope with real-world instances of the GUC problem.
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