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

Srinivasan, Shriram; Sundar, Kaarthik

doi:10.1109/lcsys.2025.3533383

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

Journal Article · Thu Jan 23 00:00:00 EST 2025 · IEEE Control Systems Letters

DOI:https://doi.org/10.1109/lcsys.2025.3533383· OSTI ID:2530362

^[1]; ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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. Here, this letter proposes and describes such a procedure, a hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2530362

Report Number(s):: LA-UR--24-31207

Journal Information:: IEEE Control Systems Letters, Journal Name: IEEE Control Systems Letters Vol. 8; ISSN 2475-1456

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

References (14)

Modeling and optimization of steady flow of natural gas and hydrogen mixtures in pipeline networks Kazi, Saif R.; Sundar, Kaarthik; Srinivasan, Shriram International Journal of Hydrogen Energy, Vol. 54 https://doi.org/10.1016/j.ijhydene.2023.12.054	journal	February 2024
A Reduction Technique for Natural Gas Transmission Network Optimization Problems Ríos-Mercado, Roger Z.; Wu, Suming; Scott, L. Ridgway Annals of Operations Research, Vol. 117, Issue 1/4, p. 217-234 https://doi.org/10.1023/A:1021529709006	journal	January 2002
Structural characterisation for the synthesis of large‐scale combined electric–gas networks Birchfield, Adam B.; Abu‐Khalifa, Yousef IET Energy Systems Integration, Vol. 6, Issue S1 https://doi.org/10.1049/esi2.12170	journal	September 2024
On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks Srinivasan, Shriram; Panda, Nishant; Sundar, Kaarthik IEEE Control Systems Letters, Vol. 8 https://doi.org/10.1109/LCSYS.2024.3394317	journal	January 2024
Solving the natural gas flow problem using semidefinite program relaxation Ojha, Abhi; Kekatos, Vassilis; Baldick, Ross 2017 IEEE Power & Energy Society General Meeting https://doi.org/10.1109/PESGM.2017.8273748	conference	July 2017
Optimal Scheduling of Water Distribution Systems Singh, Manish K.; Kekatos, Vassilis IEEE Transactions on Control of Network Systems, Vol. 7, Issue 2 https://doi.org/10.1109/TCNS.2019.2939651	journal	June 2020
Natural Gas Flow Solvers Using Convex Relaxation Singh, Manish Kumar; Kekatos, Vassilis IEEE Transactions on Control of Network Systems, Vol. 7, Issue 3 https://doi.org/10.1109/TCNS.2020.2972593	journal	September 2020
On the Flow Problem in Water Distribution Networks: Uniqueness and Solvers Singh, Manish Kumar; Kekatos, Vassilis IEEE Transactions on Control of Network Systems, Vol. 8, Issue 1 https://doi.org/10.1109/TCNS.2020.3029150	journal	March 2021
Numerical Solution of the Steady-State Network Flow Equations for a Nonideal Gas Srinivasan, Shriram; Sundar, Kaarthik; Gyrya, Vitaliy IEEE Transactions on Control of Network Systems, Vol. 10, Issue 3 https://doi.org/10.1109/TCNS.2022.3232524	journal	September 2023
On the Newton–Kantorovich Theorem Ciarlet, Philippe G.; Mardare, Cristinel Analysis and Applications, Vol. 10, Issue 03 https://doi.org/10.1142/S0219530512500121	journal	July 2012
Graph Theory Harary, Frank https://doi.org/10.21236/AD0705364	report	November 1969
Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver Singh, Manish K.; Kekatos, Vassilis 2019 American Control Conference (ACC) https://doi.org/10.23919/ACC.2019.8814704	conference	July 2019
Exploring Network Structure, Dynamics, and Function using NetworkX Hagberg, Aric A.; Schult, Daniel A.; Swart, Pieter J. Proceedings of the Python in Science Conference https://doi.org/10.25080/tcwv9851	conference	June 2008
GasLib—A Library of Gas Network Instances Schmidt, Martin; Aßmann, Denis; Burlacu, Robert Data, Vol. 2, Issue 4 https://doi.org/10.3390/data2040040	journal	December 2017

Similar Records

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Journal Article · Mon Dec 26 19:00:00 EST 2022 · IEEE Transactions on Control of Network Systems · OSTI ID:1969233

On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks

Journal Article · Thu Apr 25 20:00:00 EDT 2024 · IEEE Control Systems Letters · OSTI ID:2477796

A method for identifying weak nodes in nonconvergent load flows

Journal Article · Mon May 01 00:00:00 EDT 1989 · IEEE Trans. Power Syst.; (United States) · OSTI ID:6261675

Related Subjects

42 ENGINEERING
fluid flow systems
network analysis and control
networked control systems

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

Citation Formats

References (14)

Similar Records

Related Subjects