Stochastic Optimization of Electricity Portfolios: Scenario Tree Modeling and Risk Management

2010 ◽  
pp. 405-432 ◽  
Author(s):  
Andreas Eichhorn ◽  
Holger Heitsch ◽  
Werner Römisch
Keyword(s):  
Risk Management ◽  
Stochastic Optimization ◽  
Scenario Tree ◽  
Tree Modeling

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

scholarly journals New Developments in Uncertainty: Linking Risk Management, Reliability, Statistics and Stochastic Optimization

2014 ◽  
Author(s):  
Stan Uryasev ◽  
Tyrrel R. Rockafellar
Keyword(s):  
Risk Management ◽  
Stochastic Optimization ◽  
New Developments

scholarly journals Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

2017 ◽  
Vol 143 (12) ◽  
pp. 04017073 ◽  
Author(s):  
Sara Séguin ◽  
Charles Audet ◽  
Pascal Côté
Keyword(s):  
Scenario Tree ◽  
Short Term ◽  
Operations Planning ◽  
Tree Modeling

A multi-stage stochastic optimization model for energy systems planning and risk management

2016 ◽  
Vol 110 ◽  
pp. 49-56 ◽  
Author(s):  
Emilio L. Cano ◽  
Javier M. Moguerza ◽  
Antonio Alonso-Ayuso
Keyword(s):  
Risk Management ◽  
Stochastic Optimization ◽  
Optimization Model ◽  
Energy Systems ◽  
Systems Planning ◽  
Multi Stage

scholarly journals Stochastic scenario generation: An empirical approach

2018 ◽  
Author(s):  
A. D. Oliveira ◽  
T. P. Filomena
Keyword(s):  
Monte Carlo ◽  
Stochastic Optimization ◽  
Random Sampling ◽  
Sampling Method ◽  
Empirical Approach ◽  
Scenario Tree ◽  
Scenario Generation ◽  
Distinctive Features

We briefly discuss the differences among several methods to generate a scenario tree for stochastic optimization. First, the Monte Carlo Random sampling is presented, followed by the Fitting of the First Two Moments sampling, and lastly the Michaud sampling. Literature results are reviewed, taking into account distinctive features of each kind of methodology. According to the literature results, it is fundamental to consider the problem’s unique characteristics to make the more appropriate choice on sampling method.  

Robust Stochastic Optimization Made Easy with RSOME

2020 ◽  
Vol 66 (8) ◽  
pp. 3329-3339 ◽  
Author(s):  
Zhi Chen ◽  
Melvyn Sim ◽  
Peng Xiong
Keyword(s):  
Robust Optimization ◽  
Stochastic Optimization ◽  
Linear Optimization ◽  
Mixture Distribution ◽  
Scenario Tree ◽  
Distributionally Robust Optimization ◽  
Clustering And Classification ◽  
Stochastic Linear Optimization ◽  
Distributionally Robust ◽  
Generalized Moments

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.

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