radar subgradient method
Fri, 12/31/2010 - 18:11 — admin
Wed, 12/29/2010 - 16:48 — admin
| Publication Type | Thesis |
| Year of Publication | 2001 |
| Authors | Cesar Beltran |
| Academic Department | Dept. of Statistics and Operations Research. Prof. F.-Javier Heredia, advisor. |
| Number of Pages | 147 |
| University | Universitat Politècnica de Catalunya |
| City | Barcelona |
| Degree | PhD Thesis |
| Key Words | research; radar multiplier; generalised unit commitment; teaching |
| Abstract | This operations research thesis should be situated in the field of the power generation industry. The general objective of this work is to efficiently solve the Generalized Unit Commitment (GUC) problem by means of specialized software. The GUC problem generalizes the Unit Commitment (UC) problem by simultane-ously solving the associated Optimal Power Flow (OPF) problem. There are many approaches to solve the UC and OPF problems separately, but approaches to solve them jointly, i.e. to solve the GUC problem, are quite scarce. One of these GUC solving approaches is due to professors Batut and Renaud, whose methodology has been taken as a starting point for the methodology presented herein.
This thesis report is structured as follows. Chapter 1 describes the state of the art of the UC and GUC problems. The formulation of the classical short-term power planning problems related to the GUC problem, namely the economic dispatching problem, the OPF problem, and the UC problem, are reviewed. Special attention is paid to the UC literature and to the traditional methods for solving the UC problem. In chapter 2 we extend the OPF model developed by professors Heredia and Nabona to obtain our GUC model. The variables used and the modelling of the thermal, hydraulic and transmission systems are introduced, as is the objective function. Chapter 3 deals with the Variable Duplication (VD) method, which is used to decompose the GUC problem as an alternative to the Classical Lagrangian Relaxation (CLR) method. Furthermore, in chapter 3 dual bounds provided by the VDmethod or by the CLR methods are theoretically compared.
Throughout chapters 4, 5, and 6 our solution methodology, the Radar Multiplier (RM) method, is designed and tested. Three independent matters are studied: first, the auxiliary problem principle method, used by Batut and Renaud to treat the inseparable augmented Lagrangian, is compared with the block coordinate descent method from both theoretical and practical points of view. Second, the Radar Sub- gradient (RS) method, a new Lagrange multiplier updating method, is proposed and computationally compared with the classical subgradient method. And third, we study the local character of the optimizers computed by the Augmented Lagrangian Relaxation (ALR) method when solving the GUC problem. A heuristic to improve the local ALR optimizers is designed and tested.
Chapter 7 is devoted to our computational implementation of the RM method, the MACH code. First, the design of MACH is reviewed brie y and then its performance is tested by solving real-life large-scale UC and GUC instances. Solutions computed using our VD formulation of the GUC problem are partially primal feasible since they do not necessarily fulfill the spinning reserve constraints. In chapter 8 we study how to modify this GUC formulation with the aim of obtaining full primal feasible solutions. A successful test based on a simple UC problem is reported. The conclusions, contributions of the thesis, and proposed further research can be found in chapter 9.
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Fri, 03/16/2007 - 23:59 — admin
Fri, 03/16/2007 - 16:43 — admin
| Publication Type | Journal Article |
| Year of Publication | 2005 |
| Authors | Beltran C.; F.-Javier Heredia |
| Journal Title | Journal of Optimization Theory and Applications |
| Volume | 125 |
| Issue | 1 |
| Pages | 19 |
| Start Page | 1 |
| ISSN Number | 0022-3239 |
| Key Words | lagrangian relaxation; generalized unit commitment; radar subgradient method; research; paper |
| Abstract | One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of steplengths. In this paper, the radar subgradient method, a heuristic method designed to compute a tuning-free subgradient steplength, is geometrically motivated and algebraically deduced. The unit commitment problem, which arises in the electrical engineering field, is used to compare the performance of the subgradient method with the new radar subgradient method. |
| URL | Click Here |
| DOI | 10.1007/s10957-004-1708-4 |
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