Linearization and Conic Convexification in a Nonlinear Hydrothermal OPF Model

Abstract

This paper proposes linearization and convexification techniques applied to the nonlinear hydrothermal optimal power flow problem with the objective of obtaining a convex and computationally tractable formulation suitable for advanced optimization frameworks. The proposed approach combines a second-order cone relaxation of the electrical network with linear approximations of the hydraulic subsystem, including a unit-level four-dimensional representation of the hydropower production function and a piecewise linear approximation of thermal fuel costs. The formulation is validated on the 24-bus and 118-bus hydrothermal systems adapted from the IEEE Reliability Test System (RTS) and supplemented with operational data from Brazilian hydropower plants. Numerical results show that the convexified model accurately reproduces the nonlinear reference solution, yielding objective function errors below 1% for both systems while significantly reducing computational effort. These results demonstrate the potential of the proposed formulation as an efficient and reliable alternative for large-scale hydrothermal optimization and as a suitable foundation for robust, stochastic, and bilevel optimization models.