Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems

A.S. Markensteijn, J.E. Romate, C. Vuik

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Coupling single-carrier networks (SCNs) into multi-carrier energy systems (MESs) has recently become more important. Steady-state load flow analysis of energy systems leads to a system of nonlinear equations, which is usually solved using the Newton-Raphson method (NR). Due to various physical scales within a SCN, and between different SCNs in a MES, scaling might be needed to solve the nonlinear system. In single-carrier electrical networks, per unit scaling is commonly used. However, in the gas and heat networks, various ways of scaling or no scaling are used. This paper presents a per unit system and matrix scaling for load flow models for a MES consisting of gas, electricity, and heat. The effect of scaling on NR is analyzed. A small example MES is used to demonstrate the two scaling methods. This paper shows that the per unit system and matrix scaling are equivalent, assuming infinite precision. In finite precision, the example shows that the NR iterations are slightly different for the two scaling methods. For this example, both scaling methods show the same convergence behavior of NR in finite precision.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
Place of PublicationCham
PublisherSpringer Science+Business Media
Number of pages9
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)978-3-030-55873-4
Publication statusPublished - 2021
EventEuropean Numerical Mathematics and Advanced Applications Conference 2019 - Hotel Zuiderduin , Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


ConferenceEuropean Numerical Mathematics and Advanced Applications Conference 2019
Abbreviated titleENUMATH 2019
CityEgmond aan Zee
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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