Hydro unit commitment and loading problem for day-ahead operation planning problem Erlon Cristian Finardi, Murilo Reolon Scuzziato ⇑ LabPlan/UFSC, Electrical Systems Planning Research Laboratory, Federal University of Santa Catarina, Campus Universitário, CP 476, CEP 88040-900, Florianópolis, SC, Brazil article info Article history: Received 31 October 2011 Received in revised form 18 June 2012 Accepted 5 July 2012 Available online 9 August 2012 Keywords: Hydro unit commitment and loading problem Hydropower function Lagrangian relaxation Inexact Augmented Lagrangian abstract We describe a new model for the hydro unit commitment and loading (HUCL) problem that has been developed to be used as a support tool for day-ahead operation in the Brazilian system. The objective is to determine the optimal unit commitment and generation schedules for cascaded plants with multiple units and a head-dependent hydropower model. In this paper, we propose a new mathematical model for the hydropower function where the mechanical and electrical losses in the turbine-generator are included. We model the HUCL problem as a nonlinear mixed 0–1 programming problem and solve it with a strategy that includes a two-phase approach based on dual decomposition. The computational tool allows the model to effectively schedule hydro units for the problem in the Brazilian regulatory frame- work. Application of the approach is demonstrated by determining a 24-time step HUCL schedule for four cascaded plants with 4170 MW of installed capacity. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Brazil has a modern electricity industry that depends heavily on hydropower. Its power system has the largest capacity for water storage in the world and one of largest transmission networks, gi- ven the long distances between hydro plants and consumers. In the Brazilian regulatory framework, an Independent System Opera- tor (ISO) performs the system operation scheduling, and it conducts studies extending from the long/medium-term to short-term prob- lems. This hierarchical approach is basically divided into three com- putational levels: (i) long-term planning, which covers ten years with monthly time-steps [1,2]; (ii) medium-term planning over a two-month horizon with weekly time-steps [3]; and (iii) short- term optimization, which produces plant schedules for a day ahead [4–6]. In step (iii), the ISO performs every day a week-ahead study to produce a day-ahead schedule for all plants to meet the system load at minimum cost. However, the huge number of reservoirs pre- cludes the ISO from precisely taking into account the complex mod- elling associated with the hydro units. 1 More specifically, in step (iii), the hydro units are modelled by a piecewise linear function, and the hydro unit commitment constraints are not taken into ac- count [7]. Therefore, an intrinsic nonlinear mixed-discrete modelling [8] is replaced by a linear continuous one. As a result of the centralized dispatch aforementioned, each hy- dro power plant receives an hourly generation target for the day- ahead. As a consequence, the generation distribution among the generating units in the cascaded is a local decision. This task is de- fined in this paper as the hydro unit commitment and loading (HUCL) problem, which searches for the most economical sched- ules. In the Brazilian case, the most economical schedule is related to the efficient use of water and to minimize startups and shut- downs of hydro generating units as well. If any unit is committed to generate at an inefficient operating point, there is waste of water, which could be saved by more efficient generation. This sit- uation is particularly critical during drought periods. For instance, in Brazil, in the last energy rationing, in 2001, the regulatory authority launched a project aiming to incentive hydro plants to produce more with less water. Furthermore, it is worth pointing out that all generating units need to comply with technical param- eters of efficiency declared to the regulatory authority, which is empowered to audit the performance of such generators. From the point of view of hydro conversion efficiency, it is nec- essary to simulate all possible scenarios with respect the number of hydro generating units in operation throughout the day in an at- tempt to find a better combination of units depending on the var- iation of the load. However, frequent unit switches reduce service life and increase maintenance costs [9]. Thus, the HUCL problem is formulated in a way that will minimize the startup/shutdown costs of the generating units in addition to the discharged outflow. In real-life cascaded head-dependent hydro plants, a large num- ber of variables are involved in this problem and most of them are integer, which are related to startup and shutdown decisions. Thus, 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.07.023 ⇑ Corresponding author. Tel.: +55 48 3721 9731; fax: +55 48 3721 7538. E-mail address: muriloscz@gmail.com (M. Reolon Scuzziato). 1 The Brazilian ISO manages a mix of approximately 650 hydro units distributed in 170 plants, which are dispatched in 32 cascades. At the end of 2010, the hydro installed capacity in Brazil was nearly 85,000 MW. 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