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<p>We study network design problems for nonlinear and nonconvex flow models without controllable elements under &#xa0;load scenario&#xa0; uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, &#xa0;load&#xa0; scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all &#xa0;load scenario&#xa0; uncertainties, if and only if a finite number of worst-case &#xa0;load&#xa0; scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future &#xa0;load&#xa0; fluctuations.</p>

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Adjustable robust nonlinear network design without controllable elements under load scenario uncertainties

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月21日

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  • Johannes Thürauf,
  • Julia Grübel,
  • Martin Schmidt

摘要

We study network design problems for nonlinear and nonconvex flow models without controllable elements under  load scenario  uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many,  load  scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all  load scenario  uncertainties, if and only if a finite number of worst-case  load  scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future  load  fluctuations.