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%.

As we move towards electrical networks with a growing presence of renewable generation, the representation of the electrical components becomes more important. In hydro-dominated power systems, modelling the forbidden zones of hydro plants becomes increasingly challenging as the number of plants increases. Such zones are ranges of generation that either should be avoided or are altogether unreachable. However, because representing the forbidden zones introduces a substantial computational burden, hydrothermal unit-commitment problems (HTUC) for large systems are usually formulated ignoring the forbidden zones. Nonetheless, this simplification may demand adjustments to the solution of the HTUC, because the generation of the hydro stations may fall in forbidden zones. In practice, the adjustments are usually performed based on the experience of system operators and, then, can be far from an optimal correction. In this paper, we study the impact of explicitly representing the hydro-generation forbidden zones in a large-scale system with more than 7000 buses, 10,000 lines, and 700 hydro units. Our findings show that the simplified model that is current used can deviate significantly from the model with forbidden zones, both in terms of the generation of hydro plants, as well as the generation of thermal plants and the system marginal costs.

The long-term generation scheduling (LTGS) problem aims to build an operating policy over a multi-year planning horizon, correlating thermal generation and deficit costs with water storage. The LTGS is modeled as a linear multistage stochastic program, whose state-of-art solution is the stochastic dual dynamic programming (SDDP). One critical challenge is to represent the time-dependency of river inflows accurately. Despite recent advances, modeling simplifications are needed to allow the LTGS computational tractability via SDDP since it is necessary to increase the state space to include the time-dependent variables properly. Thus, most works simplify the hydro production function (HPF) to represent the inflows in detail to overcome this negative aspect. However, the literature lacks this trade-off, i.e., finding a balance between stochastic inflow modeling and HPF representation. Thus, this paper proposes an alternative approach to analyzing this trade-off, using the inflow aggregation and run-of-the-river energy inflow instead of individual inflow in SDDP. The proposed approach drastically reduces the number of state variables in SDDP, allowing a detailed HPF representation in the LTGS. We employ a one-sided confidence interval for expected cost estimation to show that our approach provides better performance than the individualized inflows. The analysis is performed in several large-scale computational instances using a power system with 53 geographically widespread hydro plants. The numerical results demonstrate that inflow aggregation provides, on average, a 4 % reduction on the operating cost, whereas for the run-of-the-river inflow energy, the reduction is, on average, 2 %. INDEX TERMS Inflow modeling, hydro production function, the long-term generation scheduling problem, stochastic dual dynamic programming, run-of-the-river inflow energy.