Collaborative Research: Distributionally Robust Quadratic Optimization and Its Applications to Power Systems

University Of Arizona, Tucson AZ

Investigators

Abstract

This collaborative project aims to develop new distributionally robust quadratic optimization models and methodologies to seamlessly integrate highly uncertain renewable energy into power systems, thereby providing society with cleaner, more reliable, and cost-effective energy solutions. Distributionally robust optimization (DRO) has emerged as a leading framework for optimizing under uncertainty, which can ensure the satisfaction of specified requirements even under adverse distributions of random parameters. Despite its advantages, applying DRO to nonlinear optimization problems under uncertainty remains challenging due to their inherent complexity. Nonlinearity is prevalent across various critical real-world applications in the US economy, beyond just power systems. This collaborative project will bridge this pressing gap by formulating new DRO models tailored to the unique characteristics of power systems and developing computationally efficient approaches to solve DRO problems with quadratic constraints. The project aims to deliver practical solutions that benefit all stakeholders and end-user communities. Its broader impacts include: (i) integrating research and education at the University of Arizona (UArizona) and the University of Illinois Urbana-Champaign (UIUC) by involving undergraduate students in hands-on research, connecting results with practical applications to inspire STEM careers; (ii) enhancing graduate-level education at UArizona and UIUC with contemporary case studies; and (iii) facilitating technology transfer to other societally important industries in the US economy, such as finance and transportation, where effective management of high uncertainty is crucial. This project will utilize distributionally robust optimization to address two critical decision-making challenges in uncertain power systems: (1) alternating current optimal power flow, and (2) power-system generation planning and operations, both of which are inherently formulated as quadratically constrained quadratic programming (QCQP) problems. The research objectives and tasks include: (1) developing new conic reformulations for distributionally robust QCQP problems; (2) designing efficient algorithms that exploit the special structure of these conic reformulations; and (3) adapting and applying these solutions to effectively address key optimization challenges in uncertain, large-scale power systems. These advancements aim to significantly enhance the computational efficiency and practical applicability of DRO solutions in real-world operational settings. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.