An efficient optimal energy flow model for integrated energy systems based on energy circuit modeling in the frequency domain

With more energy networks being interconnected to form integrated energy systems (IESs), the optimal energy flow (OEF) problem has drawn increasing attention. Extant studies on OEF models mostly utilize the finite difference method (FDM) to address partial-differential-equation (PDE) constraints related to the dynamics in natural gas networks (NGNs) and district heating networks (DHNs). However, this time-domain approach suffers from a heavy computational burden with regard to achieving high finite-difference accuracy. In this paper, a novel OEF model that formulates NGN and DHN constraints in the frequency domain and corresponding model compaction techniques for efficient solving are contributed. First, an energy circuit method (ECM) that algebraizes the PDEs of NGNs and DHNs in the frequency domain is introduced. Then, an ECM-based OEF model is formulated, which contains fewer variables and constraints than an FDM-based OEF model and thereby yields better solving efficiency. Finally, variable space projection is employed to remove implicit variables, by which another constraint generation algorithm is enabled to remove redundant constraints. These two techniques further compact the OEF model and bring about a second improvement in solving efficiency. Numerical tests on actual systems indicate the final OEF model reduces variables and constraints by more than 95% and improves the solving efficiency by more than 10 times. In conclusion, the proposed OEF model and solving techniques well meet the optimization needs of large-scale IESs.