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

 Publication Type Conference Paper Year of Publication 1999 Authors Beltran, C.; Heredia, F. J. Conference Name 19th IFIP TC7 Conference on System Modelling and Optimization Conference Date 12-16/07/1999 Conference Location Cambridge, U.K. Type of Work Contributed oral presentation Key Words augmented lagrangian relaxation; generalized unit commitment; block coordinated descent method; auxiliary principle problem; research Abstract The 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. Export Tagged XML BibTex

## Generalized Unit Commitment (closed)

Under construction

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

 Publication Type Conference Paper Year of Publication 1998 Authors Beltran, C.; Heredia, F. J. Conference Name IX Congreso Latino-Iberoamericano de Investigación Operativa Conference Date 31-4/08/98 Conference Location Buenos Aires, Argentina Type of Work Contributed oral presentation Key Words augmented lagrangian relaxation; radar subgradient method; generalized unit commitment; research Abstract Augmented 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 Export Tagged XML BibTex

## SLOEGAT Project. Short and Long term Optimization of Energy Generation And Trading (Esprit 22695).

 Publication Type Funded research projects Year of Publication 1996 Authors F.-Javier Heredia Type of participation Full time researcher Duration 12/1996-05/1999 Funding organization European Union, ESPRIT Programme Partners Universidad Politécnica de Catalunya, Iberdrola, Universidad de Aachen, VEW Alemania, SIEMENS Austria Full time researchers 4 (DEIO/UPC) Budget 180.238€ Project code Esprit 22695 Key Words research; nonlinear network flows; side constraints; power systems; transmission network; short-term hydrothermal coordination; long-term hydrothermal coordination project; public; competitive; EU; energy Abstract The 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. URL Click Here Export Tagged XML BibTex

## Planificación óptima de gran dimensión de la produción hidrotérmica de energia eléctrica (TAP99-1075-C02-01).

 Publication Type Funded research projects Year of Publication 2000 Authors F.-Javier Heredia Type of participation Full researcher Duration 01/2000-12/2002 Funding organization Ministerio de Educación y Ciencia / Comisión Interministerial de Ciencia y Tecnologia Partners Departament d'Estadística i Investigació Operativa, Univ. Politècnica de Catalunya Full time researchers 5 Budget 76.785€ Project code TAP99-1075-C02-01 Key Words research; nonlinear network flows; side constraints; power systems; transmission network; short-term hydrothermal coordination; long-term hydrothermal coordination; project; public; competitive; cicyt; energy Export Tagged XML BibTex

## Coordinación hidrotérmica a corto y largo plazo de la generación eléctrica en un mercado competitivo (DPI2002-03330).

 Publication Type Funded research projects Year of Publication 2002 Authors F.-Javier Heredia Type of participation Full time researcher Duration 01/2003 -12/2005 Funding organization Ministerio de Educación y Ciencia Partners Departament d'Estadística i Investigació Operativa / Universitat Politècnica de Catalunya; Unión Fenosa Full time researchers 7 Budget 85.000’00 € Project code DPI2002-03330 Key Words research; dual methods; lagrangian relaxation; unit commitment; power systems; transmission network; radar multiplier; project; public; competitive; micinn; energy Export Tagged XML BibTex

## Planificación de la generación eléctrica a corto y largo plazo en un mercado liberalizado con contratos bilaterales (DPI2005-09117-C02-01).

 Publication Type Funded research projects Year of Publication 2005 Authors F.-Javier Heredia Type of participation Full time researcher Duration 01/2006-12/2008 Funding organization Ministerio de Educación y Ciencia Partners Departament d'Estadística i Investigació Operativa, Universidad Politèctica de Catalunya; Unión Fenosa Full time researchers 5 Budget 289.408'00€ Project code DPI2005-09117-C02-01 Key Words research; stochastic programming; electricity markets; future contracts; bilateral contracts; regulation markets; project; public; competitive; micinn; energy Abstract The 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 URL Click Here Export Tagged XML BibTex

## The radar multiplier method: a two-phase approach for large scale nonlinear combinatorial optimization problems

 Publication Type Conference Paper Year of Publication 2003 Authors Heredia, F. J.; Beltran, C. Conference Name 21th IFIP TC7 Conference on System Modelling and Optimization Pagination 92 Conference Date 21-25/07/2003 Publisher INRIA Conference Location Sophia Antipolis, France Editor J. Cagnol; J.P. Zolesio Type of Work Contributed oral presentation ISBN Number 2-7261-1253-6 Key Words augmented lagrangian relaxation; generalized unit commitment; radar multiplier method; research Export Tagged XML BibTex

## Generalized Unit Commitment

 Publication Type Conference Paper Year of Publication 2004 Authors Heredia, F. J.; Beltran, C. Conference Name Applied Mathematical Programming and Modellization (APMOD 2004) Conference Date 21-23/06/2004 Conference Location Brunel University, Uxbridge, UK. Type of Work Invited oral presentation Key Words augmented lagrangian relaxation; generalized unit commitment; radar multiplier method; research Abstract The 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. Export Tagged XML BibTex

## Short Term Hydrothermal Coordination by Augmented Lagrangean Relaxation: a New Multiplier Updating

 Publication Type Journal Article Year of Publication 1999 Authors Beltran, C.; Heredia, F. J. Journal Title Investigació Operativa Volume 8 Issue 1, 2, 3 Pages 63-75 Journal Date July-Dec. 1999 ISSN Number 1014-8364 Key Words generalized unit commitment; augmented lagrangian relaxation; radar subgradient method; block coordinated descent method; auxiliary principle problem; research; paper URL Click Here Export Tagged XML BibTex