Optimization of Large-Scale Hydropower System Operations
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Optimization of Large-Scale Hydropower System Operations Mario T. L. Barros1; Frank T-C. Tsai2; Shu-li Yang3; Joao E. G. Lopes4; and William W-G. Yeh, Hon.M.ASCE5 Abstract: A practical monthly optimization model, called SISOPT, is developed for the management and operations of the Brazilian hydropower system. The system, one of the largest in the world, consists of 75 hydropower plants with an installed capacity of 69,375 MW, producing 92% of the nation’s electrical power. The system size and nonlinearity pose a real challenge to the modelers. The basic model is formulated in nonlinear programming ͑NLP͒. The NLP model is the most general formulation and provides a foundation for analysis by other methods. The formulated NLP model was first linearized by two different linearization techniques and solved by linear programming ͑LP͒. A comparative analysis was made of the results obtained from the linearized and the NLP models. The results show that the simplest linearized model ͑referred to as the LP model͒ without iteration is suitable for planning purposes. For example, the LP model could be used in system capacity expansion studies or to explore various design parameters in connection with feasibility studies, where details in storage variation are not as important as the power production. With a good initial policy provided by the LP model, the successive linear programming ͑SLP͒ model produced excellent results with fast convergence. The NLP model, the most complex and accurate model in the suite, is particularly suited for setting up guidelines for real-time operations using inflow forecast with frequent updating. The performance of the NLP model was checked against the historical operational records, and the comparison yields indica- tions of superior performance. DOI: 10.1061/͑ASCE͒0733-9496͑2003͒129:3͑178͒ CE Database subject headings: Optimization models; Brazil; Hydroelectric powerplants. Introduction ber of reservoirs responsible increases to only 17. This shows that the Brazilian hydropower system is composed of a few very large Brazil is replete with natural water resources and its hydropower storage reservoirs and many medium- and small-sized hydro- system, one of the largest in the world, has an installed capacity power plants. Presently, the system is operated in an integrated of 69,375 MW producing 92% of the nation’s electrical power. fashion. A firm established by the Brazilian Federal Government, The system consists of 75 hydropower plants and a combination the National System Operator ͑ONS͒, is in charge of the opera- of storage reservoirs and run-of-river plants. The network covers tions. ONS defines the monthly, weekly, and daily operational the following eight basins in Brazil: ͑1͒ North ͑Amazon͒; ͑2͒ rules. The main operational objective is to maximize the potential South Atlantic; ͑3͒ Tocantins; ͑4͒ Sao Francisco; ͑5͒ Southeast energy of the system. The Brazilian energy commerce is in the Atlantic; ͑6͒ Parana; ͑7͒ Uruguay; and ͑8͒ South Atlantic. Fig. 1 process of changing. In 1998, ONS assigned the power contracts shows the spatial distribution of the hydropower plants. Five hy- for the subsequent 5 years ͑1999–2003͒. A set of models ͑optimi- dropower plants are responsible for producing 50% of the Natural zation and simulation͒ was used to define the energy that each Inflow Energy ͑NIE͒: ͑1͒ Itaipu Dam ͑14,000 MW͒; ͑2͒ Tucurui reservoir must produce during this period. After the year 2003, Dam ͑4,241 MW͒; ͑3͒ Xingo Dam ͑3,000 MW͒; ͑4͒ Paulo the energy commerce in Brazil will be partially controlled by a Afonso/Moxoto Dam ͑4,285 MW͒; and ͑5͒ Ilha Solteira/Tres Ir- free market. For the first time, excess energy ͑amount of energy ͑ ͒ maos Dam 4,252 MW . If considering 75% of the NIE, the num- over the contract level͒ will be available to the free market. In the future, the market will be completely free, but ONS intends to 1Associate Professor, Dept. of Hydraulic and Sanitary Engineering, preserve the benefits of integrated operations. For a system such Univ. of Sao Paulo, Sao Paulo, Brazil. E-mail: [email protected] as the Brazilian one, it will be very important to have an optimi- 2 Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, zation model to plan the operations in advance to support the UCLA, Los Angeles, CA 90095. E-mail: [email protected] management in their decision making. It is also important to point 3Formerly, Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, UCLA, Los Angeles, CA 90095. E-mail: out that a small improvement in operations for a system of such yangគ[email protected] size translates into enormous economic benefits. 4Graduate Student, Dept. of Hydraulic and Sanitary Engineering, Optimization techniques have become increasingly important Univ. of Sao Paulo, Sao Paulo, Brazil. E-mail: [email protected] over the last three decades in the management and operations of 5Professor and Chair, Dept. of Civil and Environmental Engineering, complex reservoir systems. Yeh ͑1985͒, Simonovic ͑1992͒, Wurbs UCLA, Los Angeles, CA 90095. E-mail: [email protected] ͑1993, 1996͒, ReVelle ͑1997͒, and Momoh et al. ͑1999a,b͒ have Note. Discussion open until October 1, 2003. Separate discussions provided an extensive literature review and evaluation of various must be submitted for individual papers. To extend the closing date by optimization methods and their corresponding models. The com- one month, a written request must be filed with the ASCE Managing plexities of a multipurpose, multireservoir system generally re- Editor. The manuscript for this paper was submitted for review and pos- sible publication on December 5, 2001; approved on August 23, 2002. quire that release decisions be made by an optimization or simu- This paper is part of the Journal of Water Resources Planning and lation model. Most of the optimization models are based on some Management, Vol. 129, No. 3, May 1, 2003. ©ASCE, ISSN 0733-9496/ type of mathematical programming technique. In general, the 2003/3-178–188/$18.00. available optimization methods include the following algorithms: 178 / JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / MAY/JUNE 2003 Nonlinear Programming „NLP… Model The basic model is formulated in terms of NLP, which offers the most general formulation and provides a foundation for analysis by other methods ͑Yeh 1985͒. With the drastic advancement in computing power and the development of effective nonlinear solvers in recent years, NLP has become a viable tool in solving large-scale water resources optimization problems ͑Peng and Buras 2000͒. The NLP model proposed herein is designed in such a way that it can be applied to many practical situations. Addi- tionally, it can be easily incorporated into a decision support sys- tem that allows the user to update data, execute the model, and view the results graphically. Traditionally, a reservoir system is designed for multiple pur- poses. There are several ways to solve a multiobjective optimiza- tion problem. Yeh and Becker ͑1982͒ used the constraint method to generate the trade-off curves among the five objectives consid- ered for the California Central Valley Project. Can and Houck ͑1984͒ applied preemptive goal programming to the real-time op- eration of a multipurpose, multireservoir system. Their approach circumvents the need to assign penalty functions, but it does re- Fig. 1. Spatial distribution of hydropower plants quire that the system be highly redundant and that the solution be nonunique so that objectives can be satisfied sequentially. Loga- nathan and Bhattacharya ͑1990͒ outlined five goal-programming schemes and formulated the reservoir operation problem involv- ing multiobjectives as a multiobjective linear program. Ko et al. 1. Linear programming ͑LP͒, including network flow models, ͑1992͒ made a comparative evaluation of several multiobjective ͑ ͒ 2. Quadratic programming QP , optimization methods in connection with reservoir management ͑ ͒ 3. Dynamic programming DP , and operations. They concluded that the constrained method ͑also ͑ ͒ 4. Nonlinear programming NLP , referred to as the ⑀-constrained method͒ was most suitable for ͑ ͒ 5. Mixed integer programming MIP , generating the tradeoffs among the competing objectives. Eschen- ͑ ͒ 6. Interior point methods IP , and bach et al. ͑2001͒ developed a multiobjective, preemptive linear 7. Nongradient-based search algorithms. goal-programming model for reservoir operation and applied it to The choice of methods depends on the characteristics of the the Tennessee Valley Authority network. Another way is to com- system being considered, on the availability of data, and on the bine the various objectives by the weighting method or by treat- objectives and constraints specified. Braga et al. ͑1998͒ devel- ing some of the objectives as constraints. oped a model for optimizing the Brazilian hydropower system For the Brazilian hydropower system, the proposed NLP based on the LP-DP method of Becker and Yeh ͑1974͒. Their model considers the following six objectives: ͑1͒ minimizing the model optimizes the operation month by month, and the LP-DP loss of the stored potential energy; ͑2͒ minimizing storage devia- decomposition may lead to a near-sighted solution if the monthly tions from targets; ͑3͒ maximizing total energy production; ͑4͒ ending storage condition is not properly specified. Barros et al. minimizing spilled energy; ͑5͒ minimizing energy complementa- ͑2001͒ developed an NLP model to optimize the energy produc- tion; and ͑6͒ maximizing the profit derived from secondary en- tion of the Paranapanema subsystem, which consists of three stor- ergy. Note that certain combinations of the objectives are neither age reservoirs and five run-of-river plants ͑Fig. 1, Nodes 32–39͒. desirable nor feasible. We now quantify each of the six objectives Their model considers the entire planning horizon and involves considered in the NLP model. no decomposition. Preliminary results show that NLP is a viable 1. Objective 1 minimizes the loss of the stored potential energy approach.