Abstract
We propose a model for medium-term hydropower scheduling (MTHS) with variable head and uncertainty in inflow, reserve capacity, and energy price. With an increase of intermittent energy sources in the generation mix, it is expected that a flexible hydropower producer can obtain added profits by participating in markets other than just the energy market. To capture this added potential, the hydropower system should be modeled with a higher level of detail. In this context, we apply an algorithm based on stochastic dual dynamic programming (SDDP) to solve the nonconvex MTHS problem and show that the use of strengthened Benders (SB) cuts to represent the expected future profit (EFP) function provides accurate scheduling results for slightly nonconvex problems. A method to visualize the EFP function in a dynamic programming setting is provided, serving as a useful tool for a priori inspection of the EFP shape and its nonconvexity.
Highlights
Increasing rates of renewable energy generation are resulting in a higher demand for flexible power units to balance the power system and to deliver ramping capacity
We investigate how improvements in the stochastic dual dynamic programming (SDDP) algorithm, derived from the stochastic dual dynamic integer programming (SDDiP) algorithm [6], can be used to improve the medium-term hydropower scheduling (MTHS) problem under uncertainty
The MTHS problem was first solved with uncertainty of inflow, reserve capacity, and energy price
Summary
Increasing rates of renewable energy generation are resulting in a higher demand for flexible power units to balance the power system and to deliver ramping capacity. Except [10], which proposed a novel approach that uses step functions to model a nonconvex EFP function, they all rely on solving some relaxation of the original problem This is the case for the SB cuts applied in this work. For the MTHS problem, a hybrid stochastic dynamic programming (SDP)-SDDP method is currently the state-of-the-art in the Nordic power system. This method was developed in the late 1990s and uses a discrete Markov chain to describe the price uncertainty and an autoregressive model to describe the inflow to the reservoirs [5,12]. The representation of nonconcave generation functions that are dependent on discharge and water head by concave regions
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