Scenario Reduction Techniques in Stochastic Programming

Römisch, Werner

doi:10.1007/978-3-642-04944-6_1

Cited by 43 publications

(44 citation statements)

References 23 publications

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“…It is anticipated that implementing formal scenario reduction techniques may become necessary in solving the more challenging multistage problems. 186,[198][199][200][201][202] On a more conceptual level, although the focus of this review is on mathematical programming technique for single-site water network synthesis problems, it can also benefit from concepts in 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 related sub-areas within the domain (and vice-versa). For example, work on hybrid mathematical programming and water pinch analysis techniques 21-22, 24, 69 have shown that the latter (i.e., pinch) can enhance a formulation and reduce model size as well as be exploited in devising solution strategies.…”

mentioning

confidence: 99%

Optimization of Water Network Synthesis for Single-Site and Continuous Processes: Milestones, Challenges, and Future Directions

Khor

Chachuat

Shah

2014

Ind. Eng. Chem. Res.

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9 10Increasing water demand in the process and its allied industries coupled with global water stress 11 and scarcity has underlined the importance of water as a crucial resource and elevated a need for 12 widespread adoption of water reuse and recycle. This paper provides a state-of-the-art review of 13 the area of water network synthesis focusing on single-site continuous process problems since its 14 inception in the 1980s. The survey centers around model-based optimization or mathematical 15 programming methods for water network synthesis and covers key findings from the water pinch 16 analysis technique, which are often essential in enhancing model formulations. Major modeling 17 and computational challenges are discussed that explore the issues of nonconvexity, nonlinearity, 18 and uncertainty inherent in

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mentioning

confidence: 99%

Optimization of Water Network Synthesis for Single-Site and Continuous Processes: Milestones, Challenges, and Future Directions

Khor

Chachuat

Shah

2014

Ind. Eng. Chem. Res.

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“…Since for low values of , D attains a large value, in order to handle the emerging computational complexity issues, we have performed scenario reduction. Our scenario reduction method is based on the concept of probability distance and follows the lines of the methodology in [33], using the Chebyshev distance to determine the similarity of two scenarios. According to this methodology, the reduced set of scenarios lies close in probability distance to the initial set including all scenarios.…”

Section: H Determination Of the Number Of Scenariosmentioning

confidence: 99%

Dispatching Stochastic Heterogeneous Resources Accounting for Grid and Battery Losses

Stai

Reyes-Chamorro

Sossan

et al. 2018

IEEE Trans. Smart Grid

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Abstract-We compute an optimal day-ahead dispatch plan for distribution networks with stochastic resources and batteries, while accounting for grid and battery losses. We formulate and solve a scenario-based AC Optimal Power Flow (OPF), which is by construction non-convex. We explain why the existing relaxation methods do not apply and we propose a novel iterative scheme, Corrected DistFlow (CoDistFlow), to solve the scenariobased AC OPF problem in radial networks. It uses a modified branch flow model for radial networks with angle relaxation that accounts for line shunt capacitances. At each step, it solves a convex problem based on a modified DistFlow OPF with correction terms for line losses and node voltages. Then, it updates the correction terms using the results of a full load flow. We prove that under a mild condition, a fixed point of CoDistFlow provides an exact solution to the full AC power flow equations. We propose treating battery losses similarly to grid losses by using a single-port electrical equivalent instead of battery efficiencies. We evaluate the performance of the proposed scheme in a simple and real electrical networks. We conclude that grid and battery losses affect the feasibility of the dayahead dispatch plan and show how CoDistFlow can handle them correctly.Index Terms-Dispatch plan; day-ahead; optimal power flow; grid losses; battery models; NOMENCLATURE PCCPoint of Common Coupling.Index of bus at the top and bottom of line l respectively.Parameters per line l r l Direct sequence longitudinal resistance.Direct sequence shunt susceptance.

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“…To overcome this problem, many well-known scenario reduction methods have been put forward [36][37][38][39][40]. Römisch, et al [37] reviewed available scenario reduction techniques and discussed the related open problems.…”

Section: Wind Power Scenario Reduction Strategymentioning

confidence: 99%

“…Römisch, et al [37] reviewed available scenario reduction techniques and discussed the related open problems. This paper chooses the Kantorovich distance method [27,39], and sets to minimize the Kantorovich distance between the initial scenario and the removed scenario as the reduction objective.…”

Section: Wind Power Scenario Reduction Strategymentioning

confidence: 99%

An Optimization Model for Large–Scale Wind Power Grid Connection Considering Demand Response and Energy Storage Systems

Tan

et al. 2014

Energies

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Abstract:To reduce the influence of wind power output uncertainty on power system stability, demand response (DRPs) and energy storage systems (ESSs) are introduced while solving scheduling optimization problems. To simulate wind power scenarios, this paper uses Latin Hypercube Sampling (LHS) to generate the initial scenario set and constructs a scenario reduction strategy based on Kantorovich distance. Since DRPs and ESSs can influence the distribution of demand load, this paper constructs a joint scheduling optimization model for wind power, ESSs and DRPs under the objective of minimizing total coal cost, and constraints of power demand and supply balance, users' demand elasticity, thermal units' startup-shutdown, thermal units' output power climbing and wind power backup service. To analyze the influences of ESSs and DRPs on system wind power consumption capacity, example simulation is made in a 10 thermal units system with a 1000 MW wind farm and 400 MW energy storage systems under four simulation scenarios. The simulation results show that the introduction of DRPs and ESSs could promote system wind power consumption capacity with significantly economic and environment benefits, OPEN ACCESSEnergies 2014, 7 7283 which include less coal consumption and less pollutant emission; and the optimization effect reaches the optimum when DRPs and ESSs are both introduced.

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Scenario Reduction Techniques in Stochastic Programming

Cited by 43 publications

References 23 publications

Optimization of Water Network Synthesis for Single-Site and Continuous Processes: Milestones, Challenges, and Future Directions

Optimization of Water Network Synthesis for Single-Site and Continuous Processes: Milestones, Challenges, and Future Directions

Dispatching Stochastic Heterogeneous Resources Accounting for Grid and Battery Losses

An Optimization Model for Large–Scale Wind Power Grid Connection Considering Demand Response and Energy Storage Systems

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