Hydrothermal coordination of large-scale multi-area power systems is a challenging problem from both mathematical and computational perspectives. In this study, a mathematical formulation of long and medium-term problem that accounts for nonlinear hydropower production functions with variable head and efficiency, a direct-current interconnection power flow model with nonlinear transmission losses and explicit network representation of Kirchhoff's current and voltage laws, in addition to support for multiple power balance equations, representing blocks of peak and off-peak hours as different load levels per stage, is considered. In order to efficiently solve this problem, a primal-dual nonlinear interior-point method with line search filter and inexact search direction computations will be used as means of overcoming the difficulties that arise from the continuous non-convexity introduced by the non-linearity of the constraints space. Additionally, the use of decomposition and warm-start algorithms will also be investigated in order to increase computational efficiency. This long and medium-term model will be coupled with a short-term hydrothermal dispatch and unit commitment model solved by interior-point semi-definite programming. Very large-scale numerical case studies with over 5,000 buses and 4,000 branches, and more than 120 hydro and 140 thermal plants, will be tested in applications to the Brazilian power system official data. The results will be compared to the coupled stochastic dual dynamic programming and linear optimization models for interconnected areas currently in use by the system operator for operation planning and calculation of weekly intra-area uniform marginal pricing.
News published in Agência FAPESP Newsletter about the scholarship: