Hierarchical Network Partitioning for Solution of Potential-Driven, Steady-State Nonlinear Network Flow Equations

TL;DR

This paper introduces a hierarchical network partitioning method to efficiently solve large potential-driven steady-state nonlinear network flow equations, improving convergence reliability over traditional methods.

Contribution

The paper presents a novel hierarchical partitioning algorithm that decomposes large nonlinear network flow problems into smaller, more manageable sub-systems for solution.

Findings

Enables solution of large nonlinear network equations via smaller sub-systems.

Improves convergence guarantees compared to existing methods.

Applicable to large-scale engineering networks like pipelines.

Abstract

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends on the network topology and in general there is no numerical algorithm that offers guaranteed convergence to the solution (assuming a solution exists). Some methods offer guarantees in cases where the network topology satisfies certain assumptions, but these methods fail for larger networks. On the other hand, the Newton-Raphson algorithm offers a convergence guarantee if the starting point lies close to the (unknown) solution. It would be advantageous to compute the solution of the large nonlinear system through the solution of smaller nonlinear sub-systems wherein the solution algorithms (Newton-Raphson or otherwise) are more likely to succeed. This article proposes and describes such a procedure, an hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.