Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

Abstract

One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. In this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on the alternating direction multiplier method, that efficiently handles transmission line outages in N-1 security requirements. Benchmarks on multizonal security-constrained unit commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems with up to 6,515 buses with no convergence or numerical issues. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was partially supported by Laboratory Directed Research and Development funding from Argonne National Laboratory provided by the Director, Office of Science, of the U.S. Department of Energy [Grant DE-AC02-06CH11357]. This work was also partially supported by the U.S. Department of Energy Advanced Grid Modeling Program [Grant DE-OE0000875]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0326 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0326 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .