Assessment of a new state-dependent dynamic piecewise linear model of thermal generation costs for hydrothermal coordination

Hydrothermal coordination usually leads to large-scale stochastic nonlinear optimization problems, in general solved by sampling approaches as stochastic dual dynamic programming (SDDP). Nonlinear expressions such as thermal generation costs and hydro production are usually represented by convex piecewise linear approximations. Even though dynamic piecewise linear (DPWL) models - which evolve as the problem is being solved - are advantageous as compared to static PWL models (which are computed a priori), its applicability to SDDP-based approaches is hampered by the fact that it is not possible to build a model for all nodes that may be visited during its iterative procedure. As a consequence, we lose the advantage of such DPWL models, which is to approximate the nonlinear expressions only around the regions of optimal operation, which are scenario-dependent. In order to overcome this difficulty, we propose a new state-dependent dynamic piecewise linear model for thermal generation costs, where we build a DPWL for each system state, which are defined as the combination of system energy storage level at a given time step and the inflow scenario of the SDDP solving strategy. We assess the performance of this model for small / medium scale hydrothermal problems.