Risk-averse medium-term hydro optimization considering provision of spinning reserves

Abgottspon, Hubert; Njálsson, Karl; Bucher, Matthias; Andersson, Göran

doi:10.1109/pmaps.2014.6960657

Cited by 23 publications

(19 citation statements)

References 21 publications

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“…In spite of considerable research effort, see e.g. [20], [21], [22], [23], [24], the SDDP method does not easily facilitate nonconvexities. As mentioned previously, nonconvexities arise, for example, when representing the detailed relationship between power output and water discharge [25], and the exact unit commitment of generators [26].…”

Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

“…In [21] McCormick envelopes were applied to regions of the nonconvex function between power, discharge and water head. In [22] Lagrangian relaxation was used to convexify the EFP function, whereas [24] applied locally valid cuts to represent the nonconvex EFP function. All the above methods produce solutions to different forms of relaxations rather than the original problem.…”

Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

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Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Hjelmeland

Zou

Helseth

et al. 2019

IEEE Trans. Sustain. Energy

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Hydropower producers rely on stochastic optimization when scheduling their resources over long periods of time. Due to its computational complexity, the optimization problem is normally cast as a stochastic linear program. In a future power market with more volatile power prices, it becomes increasingly important to capture parts of the hydropower operational characteristics that are not easily linearized, e.g. unit commitment and nonconvex generation curves.Stochastic dual dynamic programming (SDDP) is a stateof-the-art algorithm for long-and medium-term hydropower scheduling with a linear problem formulation. A recently proposed extension of the SDDP method known as stochastic dual dynamic integer programming (SDDiP) has proven convergence also in the nonconvex case. We apply the SDDiP algorithm to the medium-term hydropower scheduling (MTHS) problem and elaborate on how to incorporate stagewise dependent stochastic variables on the right-hand sides and the objective of the optimization problem. Finally, we demonstrate the capability of the SDDiP algorithm on a case study for a Norwegian hydropower producer.The case study demonstrates that it is possible but timeconsuming to solve the MTHS problem to optimality. However, the case study shows that a new type of cut, known as strengthened Benders cut, significantly contributes to closing the optimality gap compared to classical Benders cuts.

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Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Hjelmeland

Zou

Helseth

et al. 2019

IEEE Trans. Sustain. Energy

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“…The reservoir volume is denoted v (in Mm 3 ), the inflow to the reservoir I, and a water balance is presented in (2). Water discharge through the station is modeled using one variable q s (in Mm 3 ) per discharge segment s ∈ S. These segments will be used in decreasing order according to their energy equivalent η s , in MWh/Mm 3 , provided that η s decreases with s. There is an upper bound on generation P max (in MW).…”

Section: Analytical Expressionsmentioning

confidence: 99%

Water values in future power markets

Helseth

Fodstad

2017

2017 IEEE Manchester PowerTech

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In this paper we elaborate on how a hydropower producer's expected marginal value of water (water value) is affected when considering both sales of energy and reserve capacity in a liberalized market setting. We derive analytical expressions for the water value in this market context, and verify these through numerical computations. We find that the water values are more sensitive to changes in the reservoir level when considering sales of both energy and reserve capacity compared to the energy-only case.

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“…A similar approach is adopted by Steeger and Rebennack in [11]. Abgottspon et al [1] introduce a heuristic to add locally valid cuts that enhance a convexified approximation of the value function.…”

Section: Introductionmentioning

confidence: 99%

MIDAS: A mixed integer dynamic approximation scheme

2019

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Mixed Integer Dynamic Approximation Scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description of MIDAS, and prove its almost-sure convergence to an ε-optimal policy when the Bellman functions are known to be continuous, and the sampling process satisfies standard assumptions.

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Risk-averse medium-term hydro optimization considering provision of spinning reserves

Cited by 23 publications

References 21 publications

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Water values in future power markets

MIDAS: A mixed integer dynamic approximation scheme

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