Dealing with Negative Inflows in the Long-Term Hydrothermal Scheduling Problem

Abstract

The long-term hydrothermal scheduling (LTHS) problem seeks to obtain an operational policy that optimizes water resource management. The most employed strategy to obtain such a policy is stochastic dual dynamic programming (SDDP). The primary source of uncertainty in predominant hydropower systems is the reservoirs inflow, usually a linear time series model (TSM) based on the order-p periodic autoregressive [PAR(p)] model. Although the linear PAR(p) can represent the seasonality and autocorrelation of the inflow datasets, negative inflows may appear during SDDP iterations, leading to water balance infeasibilities in the LTHS problem. Different from other works, the focus of this paper is not avoiding negative inflows but instead dealing with the negative values that cause infeasibilities. Hence, three strategies are discussed: (i) inclusion of a slack variable penalized in the objective function, (ii) negative inflow truncation to zero, and (iii) optimal inflow truncation, among which the latter is a novel approach. The strategies are compared individually and combined. Methodological conditions and evidence of the algorithm convergence are presented. Out-of-sample simulations show that the choice of negative inflow strategy significantly impacts the performance of the resultant operational policy. The combination of strategy (i) and (iii) reduces the expected operation cost by 15%.

A Novel Hybrid Approach for Hydrothermal Scheduling Using Mathematical and Metaheuristic Search Methods

“…Hence this ϑ-constraint method considers ramp constraints in thermal constraints to obtain a feasible working region in the thermal unit without uncertainty. The essential thermal constraints in HTS with the consideration of ramp constraints are given in equations (3)(4)(5)(6)(7)(8)(9)(10).…”

“…Forecasted water inflows are assumed to be constant across the whole time range. The Vmin for three reservoirs are 131ℎ𝑚 3 , 84 ℎ𝑚 3 and 403 ℎ𝑚 3 . The Vmax for three reservoirs are 246 ℎ𝑚 3 , 133 ℎ𝑚 3 and 280 ℎ𝑚 3 .…”

“…The Vmin for three reservoirs are 131ℎ𝑚 3 , 84 ℎ𝑚 3 and 403 ℎ𝑚 3 . The Vmax for three reservoirs are 246 ℎ𝑚 3 , 133 ℎ𝑚 3 and 280 ℎ𝑚 3 . For thermal power plants, the essential inputs include the generation capacity, fuel costs, operating constraints (min/max output, startup/shutdown times, ramping rates), emission constraints, and the current state of the power plant, all of which play a critical role in optimizing power generation.…”