Integrated Two-Stage Benders Decomposition and Dual Dynamic Programming for Hydrothermal-Wind Planning With Intra-Stage Cost Functions

The continuous increase of renewable energy sources (RES) brings challenges to electric power system planning, since RES effects must be considered in both short-term dispatch and mid/long-term planning (MLTP). In the latter, immediate or intra-stage cost functions (ICF or ISCF) have been proposed in the literature to provide thermal generation costs for each weekly/monthly stage, to address the uncertainty and high variability of RES without explicitly discretizing the stage in hourly steps. This work proposes a combined two-stage Benders decomposition and dual dynamic programming (DDP) approach to improve the construction and consideration of such ISCF for the MLTP problem. In this case, a set of subproblems considering hourly aspects as load curve, RES intermittency and peak capacity of hydro-generation are iteratively solved in the DDP master problem of each stage, for several scenarios of RES generation profiles, along DDP iterations. Since the discretization points of the ISCF are obtained on demand, this approach yields more accurate ISCF functions, specially in multi-area systems. The methodology is validated for both a tutorial case and a case based on data from the large-scale Brazilian system, where more realistic mid-term policies are obtained when compared to current approaches, with a reduced number of subproblems.