Impact of Modelling Details on the Generation Function for a Norwegian Hydropower Producer

Hjelmeland, Martin N.; Helseth, Arild; Korpås, Magnus

doi:10.1088/1742-6596/1042/1/012010

Cited by 4 publications

(11 citation statements)

References 8 publications

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“…The work carried out in this paper is based on earlier work on developing improved methods to solve the MTHS problem, as in [7,16]. The main contributions are:…”

Section: Contributionsmentioning

confidence: 99%

“…Similar behavior might also be imposed by environmental constraints, such as minimum discharge limits for certain periods of the year. While operating at low power outputs, the linear optimization model will observe a higher power output than what is physically feasible and thus overestimate the system's potential profit, as discussed in [7,16]. This overestimation can be avoided by more accurate modeling of the generation function.…”

Section: Generation Functionmentioning

confidence: 99%

“…Therefore, one must make a trade-off between accurate problem formulation and computation time. To tackle this, we base our implementation on the generation function presented in [16]. Several authors have investigated how to include variable head in the hydropower scheduling problem.…”

Section: Generation Functionmentioning

confidence: 99%

“…The objective function (16) consists of the present profit function, f t , and the EFP function φ i t . The problem is constrained by the set X t and the copy constraint Equation (18) as described in [6] together with the copy variable z t .…”

Section: Dp Formulationmentioning

confidence: 99%

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Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

2019

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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.

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“…The work carried out in this paper is based on earlier work on developing improved methods to solve the MTHS problem, as in [7,16]. The main contributions are:…”

Section: Contributionsmentioning

confidence: 99%

Section: Generation Functionmentioning

confidence: 99%

Section: Generation Functionmentioning

confidence: 99%

Section: Dp Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

2019

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show abstract

“…While operating at low power outputs, the linear optimization model will observe a higher power output than what is physically feasible and thus overestimate the system's potential profit, as discussed in [7,16]. This overestimation can be avoided by more accurate modelling of the generation function.…”

Section: Generation Functionmentioning

confidence: 99%

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

Hjelmeland¹,

Helseth²,

Korpås³

2018

Preprint

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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 other markets than just the energy market. To capture this added potential the hydropower system should be modeled with a higher level of details. 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 provide 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.

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Optimal price-based scheduling of a pumped-storage hydropower plant considering environmental constraints

Alic,

Schäffer,

Toffolon

et al. 2023

Energy Syst

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The paper proposes a novel medium-term scheduling model for a hydropower system composed by a pumped storage hydropower plant connected to a traditional hydropower plant subject to three types of environmental constraints; these deal with the maximum water abstraction from the reservoir thought the turbines and through the pump for energy production, the minimum environmental water flow and the ramping capabilities of water volumes inside the system's reservoirs. The scheduling problem is formulated for a planning horizon of 1 year with weekly decision stages. The methodology to determine the optimal operation of the plant is based on a stochastic dynamic programming algorithm which allows for an accurate representation of the uncertainties associated to the water inflows and energy prices. Moreover, it facilitates the handling of the non-convex characteristic of the statedependent constraint on maximum water abstraction from the reservoir. The model is applied to the case of a real hydropower system based on a cascaded watercourse with two conventional hydropower plants in south of Norway to assess the economic benefits of having a pumping unit and the technical impact of the above-mentioned environmental constraints. Furthermore, this work proposes a methodology to analyze the optimal operation of the hydropower system, computed for different temporal resolutions, in order to investigate the techno-economic impact of the constraints involving dependencies on the states of the system, the different environmental constraints and other seasonal effects on the accuracy and the applicability of mediumterm scheduling models. Further case studies assess the computational burden and the precision of the results when adopting a finer discretization of the state variables of the dynamic-programming-based methodology. KeywordsPumped storage hydropower plant • Optimal hydropower scheduling • Environmental constraints • Electricity markets • Stochastic dynamic programming Abbreviations BC Base Case FS Forward Simulation Extended author information available on the last page of the article Optimal price-based scheduling of a pumped-storage hydropower… Upper extreme for the water segment s in hydropower plant h, for N discretization points [Mm 3 ] _ s h,N Lower extreme for the water segment s in hydropower plant h, for N discretization points [Mm 3 ]

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Impact of Modelling Details on the Generation Function for a Norwegian Hydropower Producer

Cited by 4 publications

References 8 publications

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

Optimal price-based scheduling of a pumped-storage hydropower plant considering environmental constraints

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