Dealing with Multiple Water Uses and Infeasibilities in Complex Hydrothermal System Optimization

Severe droughts, water-use conflicts, and minimum outflow requirements have caused infeasibilities in modeling large-scale complex hydrothermal systems. This paper presents and discusses a new formulation of objective function and constraints to better represent multiple water uses and deal with infeasibilities in the HIDROTERM model, a nonlinear programming (NLP) model developed to optimize the operation of the Brazilian interconnected hydrothermal system. The system is one of the largest in the world. In the last 10 years, approximately 72% of electricity consumed in Brazil has been supplied by hydropower plants, but with increasing shares from thermal, wind, and, more recently, solar power generation. Because of hydrological changes in recent years and the additional operational constraints imposed by environmental agencies, the use of models for decision making, such as HIDROTERM, frequently encounters the problem of infeasibility. To avoid this problem, a new objective function is proposed in HIDROTERM that incorporates economic penalties when the preset requirements are not met. Based on economic considerations, some hard constraints are removed from the constraint set and added to the objective function as penalty terms. These constraints are tightly linked with multiple water uses, including environmental protection, flood control, consumptive uses, and navigation purposes. The proposed change in the objective function and constraints avoids the problem of infeasibilities and makes it possible to apply the model to extreme conditions. Additionally, this formulation helps identify and minimize the risk, duration, and intensity of unavoidable non-compliance occurrences related to multiple water uses.

The presented new version of the HIDROTERM model can be used to study and support decision making in the management and operation of large-scale hydrothermal systems. These systems can be formed by a set of hydraulically connected individual hydropower plants and reservoirs, located within a set of electrically connected subsystems. Each subsystem contains demands and other power plants, including thermal, wind, nuclear, and solar plants, and exchanges. The model has been developed with continued improvements since 2008 and applied to large systems such as the Brazilian Interconnected Power System (BIPS) with over 150 reservoirs. A graphical user interface is provided. The objective function is to minimize the total costs of additional thermal dispatch and exchanges, as well as avoid or minimize deficits in energy supply in subsystems, minimum releases, consumptive uses, and minimum storages in reservoirs. The decision variables are the power and nonpower releases for each hydropower plant and the thermal dispatches and exchanges for each subsystem. Some typical applications include (1) monthly planning operation of the system, considering a planning horizon from 3 to 5 years; (2) diagnostic studies about reliability and resilience of existing systems, processing the same system configuration to a set of different hydrological or energy demand scenarios; (3) impact analysis of changes in operational rules and constraints related to multiple uses of water; and (4) planning and evaluation of expansion alternatives. The model can be applied to a complete hydrothermal system or subsets of it, including subsystems, basins, cascades, or a single hydropower plant.