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Environmental constraints in hydropower systems serve to ensure sustainable use of water resources. Through accurate treatment in hydropower scheduling, one seeks to respect such constraints in the planning phase while optimizing the utilization of hydropower. However, many environmental constraints introduce state-dependencies and even nonconvexities to the scheduling problem, making them challenging to represent in stochastic hydropower scheduling models. This paper describes how the state-dependent maximum discharge constraint, which is widely enforced in the Norwegian hydropower system, can be embedded within the stochastic dual dynamic programming (SDDP) algorithm for hydropower scheduling without compromising computational time. In this work, a combination of constraint relaxation and time-dependent auxiliary lower reservoir volume bounds is applied, and the modeling is verified through computational experiments on two different systems. The results demonstrate that the addition of an auxiliary lower bound on reservoir volume has significant potential for improved system operation, and that a bound based on the minimum accumulated inflow in the constraint period is the most efficient.

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The aim of this paper is to quantify the value of flexible power generation technologies in Northern Europe in 2030, and in particular hydropower with storage. Two scenarios for the European power system in 2030 are presented. The study uses a fundamental hydrothermal power system model for the combined North-and West-European power system. The model gives optimal operation of the system, including operation strategies for individual hydro reservoirs, dispatch of power plants and simulated power prices. The results show power generation, income and realized power prices for a selection of hydropower and gas power plants, as well as wind and solar power. It is demonstrated that the value of flexible power generation increases with increasing shares of variable renewables in the power system, even if the average prices are reduced.

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