Multi-horizon Modeling in Hydro Power Planning

Abgottspon, Hubert; Andersson, Göran

doi:10.1016/j.egypro.2015.12.351

Cited by 17 publications

(6 citation statements)

References 11 publications

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“…Since the suboptimality decreases with the exact horizon length, we would choose the longest T 1 that allows Algorithm 1 to converge in the allotted time. For the hydro application here, the allotted time would typically be on the order of one hour, as in [3].…”

Section: B Solution Of Nonlinear and Split-horizon Problemsmentioning

confidence: 99%

“…We typically wish to operate long-term storage devices in response to underlying energy demand or supply patterns that Several methods have been proposed to tackle nonlinear seasonal storage problems. Many involve approximating the nonlinear dynamics through modeling simplifications and heuristic methods such as timescale separation [3]. Specifically for hydro optimization, a fundamental difficulty is the presence of nonlinear head effects when converting between stored water and electrical energy.…”

Section: Introductionmentioning

confidence: 99%

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Two-Stage Dual Dynamic Programming With Application to Nonlinear Hydro Scheduling

Flamm

Eichler

Warrington

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the remainder of the horizon is modeled using a linear relaxation. As this approximate problem may still be too large to solve directly, we present a Benders decomposition-based solution algorithm that iterates between solving the nonlinear and linear parts of the horizon. This extends the Dual Dynamic Programming approach commonly employed for optimization of linearized hydro power systems. We prove that the proposed algorithm converges after a finite number of iterations, even when the nonlinear initial stage problems are solved inexactly. We also bound the suboptimality of the split-horizon method with respect to the original nonlinear problem, in terms of the properties of a map between the linear and nonlinear stateinput trajectories. We then apply this method to a case study concerning a multiple reservoir hydro system, approximating the nonlinear head effects in the second stage using McCormick envelopes. We demonstrate that near-optimal solutions can be obtained in a shrinking horizon setting when the full nonlinear model is used for only a short initial section of the horizon. For this example, the approach is shown to be more practical than both conventional dynamic programming and a multi-cell McCormick envelope approximation from literature.

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Section: B Solution Of Nonlinear and Split-horizon Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Stage Dual Dynamic Programming With Application to Nonlinear Hydro Scheduling

Flamm

Eichler

Warrington

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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“…On the other hand, cyclic storage formulation would keep the same stored energy at the period's start and end. In hydro power planning, multi-time horizon approaches have already been used but not modelled by MILP (Abgottspon and Andersson 2016;Beltrán et al 2021;Flamm et al 2018a;Bordin et al 2021;Flamm et al 2018b;Ming et al 2021;Parvez et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Time series aggregation for energy system design: review and extension of modelling seasonal storages

et al. 2022

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Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, “Time series aggregation for energy system design: Modeling seasonal storage”, has developed a seasonal storage model to address this issue. Simultaneously, the paper “Optimal design of multi-energy systems with seasonal storage” has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.

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“…Other papers in the literature considering aspects related to handling both time scales in one model are given by [31] who include short-term variations in a strategic model for the Norvegian meat industry, [33] analyze strategic investment decisions in liquefied natural gas transport and discuss the impact of using a stochastic model at the operational level showing that also operational flexibility is important in order to cope with short-term variations and has a significant impact on profitability. In [1,2] the multi-horizon modeling approach has been applied to a complex pumped storage hydro power plant in a liberalized market environment in or-der to give decision support for its scheduling. In [28] the authors analyze the short-term uncertainty in long-term energy system models considering a wind power case-study in Denmark and in [29] they consider the impact of policy actions and future energy prices on the cost-optimal development of the energy system in Norway and Sweden.…”

Section: Introductionmentioning

confidence: 99%

Bounds in multi-horizon stochastic programs

2019

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In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in [16] relevant in many industry-life applications tipically involving strategic and operational decisions on two different time scales.After providing three general mathematical formulations of a multi-horizon stochastic program, we extend the definition of the traditional Expected Value problem and Wait-and-See problem from stochastic programming in a multihorizon framework. New measures are introduced allowing to quantify the importance of the uncertainty at both strategic and operational levels. Relations among the solution approaches are then determined and chain of inequalities provided. Numerical experiments based on an energy planning application are finally presented.

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Multi-horizon Modeling in Hydro Power Planning

Cited by 17 publications

References 11 publications

Two-Stage Dual Dynamic Programming With Application to Nonlinear Hydro Scheduling

Two-Stage Dual Dynamic Programming With Application to Nonlinear Hydro Scheduling

Time series aggregation for energy system design: review and extension of modelling seasonal storages

Bounds in multi-horizon stochastic programs

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