Two-stage robust optimization dispatch for multiple microgrids with electric vehicle loads based on a novel data-driven uncertainty set

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

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Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

Complexity ◽

10.1155/2020/5649821 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Ke Shang ◽

Felix T. S. Chan ◽

Stephen Karungaru ◽

Kenji Terada ◽

Zuren Feng ◽

...

Keyword(s):

Mathematical Programming ◽

Robust Optimization ◽

Comparative Studies ◽

Complex Model ◽

Orienteering Problem ◽

Two Stage ◽

Second Stage ◽

Robust Model ◽

Uncertainty Set

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights.

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Technical Note—Two-Stage Sample Robust Optimization

Operations Research ◽

10.1287/opre.2020.2096 ◽

2021 ◽

Author(s):

Dimitris Bertsimas ◽

Shimrit Shtern ◽

Bradley Sturt

Keyword(s):

Robust Optimization ◽

Approximation Scheme ◽

Optimization Problems ◽

Linear Optimization ◽

Decision Rules ◽

Technical Note ◽

Data Driven ◽

Two Stage ◽

Linear Optimization Problems ◽

Stochastic Linear Optimization

In “Two-Stage Sample Robust Optimization,” Bertsimas, Shtern, and Sturt investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-infinity Wasserstein ambiguity set. Their main result establishes that this approximation scheme is asymptotically optimal for two-stage stochastic linear optimization problems; that is, under mild assumptions, the optimal cost and optimal first-stage decisions obtained by approximating the robust optimization problem converge to those of the underlying stochastic problem as the number of data points grows to infinity. These guarantees notably apply to two-stage stochastic problems that do not have relatively complete recourse, which arise frequently in applications. In this context, the authors show through numerical experiments that the approximation scheme is practically tractable and produces decisions that significantly outperform those obtained from state-of-the-art data-driven alternatives.

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Data-Driven Robust Optimization for Steam Systems in Ethylene Plants under Uncertainty

Processes ◽

10.3390/pr7100744 ◽

2019 ◽

Vol 7 (10) ◽

pp. 744 ◽

Cited By ~ 2

Author(s):

Liang Zhao ◽

Weimin Zhong ◽

Wenli Du

Keyword(s):

Robust Optimization ◽

Dirichlet Process ◽

Programming Model ◽

Operating Cost ◽

Data Driven ◽

Mixed Integer ◽

Ethylene Plant ◽

Uncertainty Set ◽

Quadratic Mixed Integer Programming ◽

Steam System

In an ethylene plant, steam system provides shaft power to compressors and pumps and heats the process streams. Modeling and optimization of a steam system is a powerful tool to bring benefits and save energy for ethylene plants. However, the uncertainty of device efficiencies and the fluctuation of the process demands cause great difficulties to traditional mathematical programming methods, which could result in suboptimal or infeasible solution. The growing data-driven optimization approaches offer new techniques to eliminate uncertainty in the process system engineering community. A data-driven robust optimization (DDRO) methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. A hybrid model of extraction–exhausting steam turbine is developed, and its coefficients are considered as uncertain parameters. A deterministic mixed integer linear programming model of the steam system is formulated based on the model of the components to minimize the operating cost of the ethylene plant. The uncertain parameter set of the proposed model is derived from the historical data, and the Dirichlet process mixture model is employed to capture the features for the construction of the uncertainty set. In combination with the derived uncertainty set, a data-driven conic quadratic mixed-integer programming model is reformulated for the optimization of the steam system under uncertainty. An actual case study is utilized to validate the performance of the proposed DDRO method.

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