Short-term hydrothermal dispatch with river-level and routing constraints

On the Decision-Hazard Approach for the Stochastic Dual Dynamic Programming Applied to Hydrothermal Operation Planning

“…Consequently, the decision vector at period t includes not only the generation of the second-stage variables at t, but also of the first-stage variables at t + 1. This is done by means of the decision variable g o t+1|t , which stands for the first-stage generation at t + 1 given the conditions at the end of period t, and guaranteed by expression (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The adaptation results in the following:…”

“…From equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23), similarly to the hazard-decision problem, within the augmented-state approach, for a given initial state (v t−1 , g o t|t−1 ), defined by the initial volume in the hydro reservoirs and the dispatch for the first-stage generators set J, it is possible to solve each subproblem determined by the water inflow scenarios w t,ω individually and then obtain the expected value. Therefore, the proposed methodology results in a decision-hazard structure problem that may be solved through a hazard-solution methodology.…”

“…Analogously to (3)(4)(5)(6)(7)(8)(9),π (k) t+1 translates the expected value of the dual variable π of constraint (4-18) at t + 1, iteration k; andγ (k) j,t+1 translates the expected value of the dual variable γ j of constraint (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) for each j ∈ J, represented by expressions (4-25) and (4-26), respectively.…”

“…In Brazil, some of the introduced restrictions are the representation of electrical network transmission losses [13], modeling of hydro generation plants as a function of turbined outflow, spillage and head in the reser- 1. INTRODUCTION 11 voir [14], n − k security criteria [15,16], individual reservoir representation [17], renewable resources intermittent generation, and demand uncertainty [18]. Centralized hydrothermal energy dispatch models have also been studied with great attention.…”

“…Centralized hydrothermal energy dispatch models have also been studied with great attention. Some of these studies include limitations on the gas network [19], CO 2 emission constraints [20], river level and routing restrictions [17], and transmission constraints with non-linear formulation [21]. In general, apart from the main subject referred in each of the mentioned works, other important aspects of the problem are usually disregarded, consequently it is difficult to find a work that properly addresses all of them.…”