Optimization of Large-Scale Hydropower System Operations

Published: 1/21/2018

The Brazilian hydropower system is one of the largest in the world, boasting a total of 75 hydropower plants with nearly 70,000 MW of installed capacity. The network covers eight basins and includes storage reservoirs and run-of-river plants. A system of such a large scale requires careful planning and oversight, and consequently, a monthly optimization model was developed to help aid the management and operations of the system. The two major challenges faced in modeling the system include its size and nonlinearity. The operational objective was to maximize the potential energy system. The optimization methods explored include linear programming, quadratic programming, dynamic programming, nonlinear programming, mixed integer programming, interior points method, and non-gradient-based search algorithms. SISOPT, the newest optimization model developed, is a multi-objective and optimization ensemble that combines linear programming, nonlinear programming, and successive linear programming models.

Nonlinear programming provides a physically based foundation for the model, as it offers a general form that may be supplemented by other methods. Nonlinear programming is also deemed the most accurate programming method due to its lack of approximations (though an initial policy is required). It is for these reasons, that with the recent improvement in computing power, nonlinear programming has become a popular technique for solving large-scale water resource optimization problems. The Brazilian hydropower system model nonlinear program considers a total of six objectives. These objectives include minimizing the loss of stored potential energy, minimizing storage deviation from targets, maximizing total energy production, minimizing spilled energy, minimizing energy complementation, and maximizing the profit derived from secondary energy. The objective functions were developed using the Wiegting coefficients and constraints and an initial estimate of a solution that was provided by a linear programming model.

To linearize the nonlinear program, a fixed value for nonlinear energy production was used. The average value of the energy production function was selected for this case as there was historical data available through long-term operational records. The nonlinear constraints were also transformed into equivalent linear constraints. As stated above, the solution from the modified linear program offers an accurate initial policy for the nonlinear program.

Successive linear programming is the third and final model used in the SISOPT ensemble. This model was used to solve the initial nonlinear problem but through a sequence of localized linear programs. This yields a result that is similar to that of the nonlinear program. The two main advantages of successive linear program algorithms over nonlinear programs include lower computational time and storage, and their ability to be solved by standard linear programs.

Several linear and nonlinear solvers have been identified for use with the programs developed for the Brazilian hydropower system. The notable ones include MINOS, MINOS LP, EMNET, PCx, and FORTRAN (conjunctively with Excel and Visual Basics). Three case studies were used to test the validity of the programs developed. The first case study was aimed at comparing the different linear programming solvers and found that, while MINOS LP was efficient for small-scale problems, PCx was the most efficient in solving large-scale problems. The second case study was set to test the validity of the model application to large-scale systems. The results demonstrate that there is very little difference between linear programming, nonlinear programming and successive linear programming methods in terms of maximizing the total production. While the nonlinear programming model remains the most accurate of the three, the linear program may be used to explore design parameters for feasibility studies. The third and final case study was used to compare the model with historical records. The historical operational records were assessed using the mean inflow forecast as an input. The upper bound inflow forecast was found using the perfect forecast, which assumes no forecasting errors. This case study demonstrated that a roughly four percent increase in power production can be reached using the model. The results were promising across the board and showed similar performance benefits in energy complementation and reservoir storage. While percentage-wise the benefits appear marginal, when applied to a large-scale real-world problem such as the Brazilian hydropower system, the results become substantial.