Graph-Based Modeling and Decomposition of Energy Infrastructures

Nonlinear optimization problems are found at the heart of real-time operations critical infrastructures. These computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these as graph-structured problems, and illustrate how their structure can be exploited level (for parallelizing function/derivative computations) solver linear algebra operations). Specifically, we present a restricted additive Schwarz scheme enables flexible decomposition graph structures within an interior-point algorithm. The proposed approach is implemented general-purpose nonlinear programming call MadNLP.jl; this Julia-based interfaced to graph-based package Plasmo.jl. efficiency framework demonstrated via arising in transient gas network multi-period AC optimal power flow. show our accelerates solution (compared off-the-shelf tools) by over 300%; specifically, times reduced from 72.36 sec 23.84 for problem 515.81 149.45 flow problem.