Multi-time Scale Dynamics in Energy-integrated Networks: A Graph Theoretic Analysis

Graph reduction of complex energy‐integrated networks: Process systems applications

“…In this section, we describe briefly the main features of the developed graph reduction framework (for details see the Refs. ).…”

“…However, such an analysis becomes cumbersome as the size of the network increases. To this end, we have proposed a generic and scalable graph‐theoretic framework which can be used to analyze such networks . The developed framework relies on knowledge of the energy flow structure in the network and the orders of magnitude of the different energy flows to generate information on (1) the time scales where each unit evolves, (2) the form of the reduced order models in each time scale, and (3) controlled outputs and potential manipulated inputs available in each time scale.…”

Control structure design for complex energy integrated networks using graph-theoretic methods

“…Noting that the above structural form requires structural information of the network, we can exploit the connectivity information provided by the energy flow graph of the network to construct an equation graph. The energy flow graph is a digraph, wherein nodes represent individual process entities and edges represent energy flows [7].…”

“…To this end, we have proposed a generic, scalable graphtheoretic framework which can be used to analyze such plants. In the first phase of this work, we have developed a graph reduction framework which, starting from an energy flow graph of the network, i) generates subgraphs for each time scale, ii) derives the structural form of the reduced order models in each time scale, and iii) classifies controlled outputs and potential manipulated inputs according to the time scale they act [7], [8].…”

Graph-theoretic Analysis of Complex Energy Integrated Networks

“…In the case of such complex networks, the rigorous analysis using singular perturbations, is in principle possible, but can be cumbersome. To this end, we have developed a graph-theory based analysis framework for complex networks which mimics the approach based on singular perturbations and provides a scalable reduction for large networks (Jogwar et al, 2011;Heo et al, 2012).…”