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Application of Chance Constrained Optimization to Gas Networks

  • We consider optimization problems with a joint probabilistic constraint under normally distributed uncertain parameters. The parametric constraints are replaced by one constraint stating that the probability of being feasible shall exceed or be equal to a prescribed threshold. In order to apply the concept to gas network optimization under uncertain boundary flows, which corresponds to the demand of customers, we derive an analytic gradient formula. The integral corresponding to the probability can be parameterized by spherical radial decomposition. For this parameterization gradient formulas are known under convexity assumptions of the parametric constraints in the parameter. For the application in gas networks that we have in mind, the convexity assumption of the parametric constraints is not satisfied. Therefore, we weaken it to convexity of the region of feasible parameters for a fixed optimization variable. We proceed to show that the assumptions needed for the gradient formula are met in the gas network optimization problem on a tree. For the numerical implementation we propose a multilevel sampling algorithm that uses a coarse approximation of the chance constraint to generate a warm start for the expensive approximation with fine sampling. The numerical results illustrate that this approach significantly reduces the computation time.

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Author:David Wintergerst
Document Type:Preprint
Language:English
Date of Publication (online):2017/11/08
Date of first Publication:2017/08/29
Release Date:2017/08/29
Tag:chance constraint; gas networks; isothermal Euler equations; multilevel; spherical radial decomposition
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:C03