A time series model for building scenarios trees applied to stochastic optimisation

Abstract

Abstract Given the dependence on hydrologic regimes, the uncertainty in energy planning in Brazil requires adequate and coherent stochastic modelling. The structure used to simulate synthetic series in the current Brazilian Electrical Sector model generates nonlinearity in the model equation via lognormal distribution adopted for the model residuals. This nonlinearity can cause non-convexity problems in calculating the Cost to Go Functions, which are formed by convex polyhedral approximation through piecewise linear functions. Given the above considerations, the stochastic model characteristics used to generate a scenarios tree and its use in optimisation models, this study proposes the development of an alternative methodology for scenario construction. Thus, a new general approach is proposed for constructing trees used in the stochastic optimisation processes. This simulation structure combines the computationally intensive Bootstrap technique and Monte Carlo simulation method. Scenario trees were generated using a time horizon consistent with the long-term hydrothermal dispatch planning. The synthetic series were compared to the historical series through statistical tests, which demonstrated that the developed model was sustainable during the stochastic portion of the experiment. Finally, the tree paths were applied to the Stochastic Dual Dynamic Programming, and various response variables were analysed. Such analysis support the conclusion that the model herein can reproduce structures that are compatible with the current model without nonlinearity in the stochastic model equation and non-convexity in the Cost to Go Functions.