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

An Efficient Optimal Energy Flow Model for Integrated Energy Systems Based on Energy Circuit Modeling in the Frequency Domain