Computationally Efficient Analysis of Energy Distribution Networks using Finite Volume Method and Interpolatory Model Order Reduction
Saleha Kiran, Farhan Hussain, Mian Ilyas Ahmad
TL;DR
The paper addresses the computational challenge of simulating large energy distribution networks by formulating gas, water, and power networks within a unified nonlinear descriptor framework $E\dot{x}(t)=Ax(t)+Bu(t)+G(x,u)y(t)=Cx(t)$ and applying a tangential IRKA-based model order reduction that retains the polynomial part via $D_r$. The reduced model $E_r\dot{x}_r(t)=A_r x_r(t)+B_r u(t)+G_r(x_r,u)\tilde{y}(t)=C_r x_r(t)$ interpolates the linear transfer functions along predefined tangent directions while preserving nonlinear dynamics, enabling significant online speedups. The method is demonstrated on a gas-network test case discretized by finite-volume and finite-difference schemes, comparing full-order and reduced-order simulations and showing preserved pressure and mass-flow behavior with reduced computation time. This approach offers scalable, accurate, real-time capable simulations for integrated energy distribution systems, supporting design, control, and optimization tasks.
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.