Computationally Efficient Analysis of Energy Distribution Networks using Finite Volume Method and Interpolatory Model Order Reduction

Abstract

Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this paper, we performed discretization on the underlying partial differential equations of a pipeline and identified the complete network model for the gas, water and power distribution network. The discretized network model can be represented in a unified state-space form, that is, a specific matrix vector form for a set of differential-algebraic equations (DAEs). Due to the size and complexity of these models, their simulation can be computationally expensive. To address this issue, we applied model order reduction to the original unified mathematical model, constructing a reduced-order model that approximates the behavior of the original model with minimal computational cost. Specifically, we utilize the tangential iterative rational Krylov algorithm (tIRKA) which ensure that the interpolation condition of the linear part of the original and the reduced nonlinear unified models are interpolating along the predefined tangent directions. A specific scenario of the energy network is simulated with and without model order reduction and the behaviour is observed in terms of its performance.