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Mathematics, Vol. 12, Pages 1543: A Fluid Dynamic Approach to Model and Optimize Energy Flows in Networked Systems
Mathematics doi: 10.3390/math12101543
Authors: Massimo de de Falco Luigi Rarità Alfredo Vaccaro
In this paper, attention is focused on the analysis and optimization of energy flows in networked systems via a fluid-dynamic approach. Considering the real case of an energy hub, the proposed model deals with conservation laws on arcs and linear programming problems at nodes. Optimization of the energy flows is accomplished by considering a cost functional, which estimates a term proportional to the kinetic energy of the overall system in consideration. As the real optimization issue deals with an integral formulation for which precise solutions have to be studied through variational methods, a decentralized approach is considered. First, the functional is optimized for a simple network having a unique node, with an incoming arc and two outgoing ones. The optimization deals with distribution coefficients, and explicit solutions are found. Then, global optimization is obtained via the local optimal parameters at the various nodes of the real system. The obtained results prove the correctness of the proposed approach and show the evident advantages of optimization procedures dealing with variational approaches.
