Adaptive stochastic approach for solving long-term hydrothermal scheduling problems

The long-term hydrothermal scheduling (HTS) is a multi-stage stochastic optimization problem which aims to calculate a decision policy regarding the operation of hydrothermal systems that minimizes the expected costs while taking into account physical and operational constraints of the system. The HTS problem has traditionally been solved by means of stochastic dual dynamic programming (SDDP). Despite its successful utilization for solving large-scale HTS problems, the computation times for solving the HTS problem by means of an SDDP approach may become prohibitive in the context of energy markets (where the HTS model generally appears in the lower level of bilevel equilibrium problems) and also in the context of risk-averse decision making policies. In these contexts, rolling horizon (RH) approaches can provide a good trade-off between optimality and computational effort. The RH approach approximates expected future costs by means of a single forward procedure. Although the RH approach is able to fully explore uncertainties embedded in the set of scenarios, it does not present a mechanism for evaluating the errors in the expected future costs, which may result in some level of cost sub-optimality. In this paper, an adaptive stochastic (AS) approach is proposed for solving multi-stage stochastic optimization problems that enhances the level of optimality of the RH approach. Two HTS models are proposed, involving the adoption of the RH and the AS approaches, respectively. The decision-making policies calculated by these models are compared in terms of the evolution of the expected values for power dispatches, optimality, prices, and reservoir volumes. Numerical results confirm the higher levels of optimality achieved by the proposed AS approach where reduction costs of near 20% were achieved for a portion of the Brazilian system with a total of 48.4 GW, which represents 47.4% of the installed hydraulic capacity of this system, as well as significant improvements in the hydraulic and economic aspects (e.g. prices were reduced around 50% in peak periods for a 10-power plant study) of the HTS problem. A post-optimization simulation procedure conducted to evaluate the quality of the uncertainty modeling within the proposed RH-HTS and AS-HTS models demonstrates that the decisions calculated by both models have proven to be highly robust in withstanding random water inflows.