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

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

doi:10.1007/978-3-030-55874-1_70

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

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

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

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 language	English
Title of host publication	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Editors	Fred J. Vermolen, Cornelis Vuik
Place of Publication	Cham
Publisher	Springer Science+Business Media
Pages	713-721
Number of pages	9
ISBN (Electronic)	978-3-030-55874-1
ISBN (Print)	978-3-030-55873-4
DOIs	https://doi.org/10.1007/978-3-030-55874-1_70
Publication status	Published - 2021
Event	European Numerical Mathematics and Advanced Applications Conference 2019 - Hotel Zuiderduin , Egmond aan Zee, Netherlands Duration: 30 Sep 2019 → 4 Oct 2019 https://www.enumath2019.eu/

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Numerical Mathematics and Advanced Applications Conference 2019
Abbreviated title	ENUMATH 2019
Country/Territory	Netherlands
City	Egmond aan Zee
Period	30/09/19 → 4/10/19
Internet address	https://www.enumath2019.eu/

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

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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Markensteijn, A. S., Romate, J. E., & Vuik, C. (2021). Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems. In F. J. Vermolen, & C. Vuik (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (pp. 713-721). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer Science+Business Media. https://doi.org/10.1007/978-3-030-55874-1_70

Markensteijn, A.S. ; Romate, J.E. ; Vuik, C. / Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems. Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. editor / Fred J. Vermolen ; Cornelis Vuik. Cham : Springer Science+Business Media, 2021. pp. 713-721 (Lecture Notes in Computational Science and Engineering).

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Markensteijn, AS, Romate, JE & Vuik, C 2021, Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems. in FJ Vermolen & C Vuik (eds), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer Science+Business Media, Cham, pp. 713-721, European Numerical Mathematics and Advanced Applications Conference 2019, Egmond aan Zee, Netherlands, 30/09/19. https://doi.org/10.1007/978-3-030-55874-1_70

Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems. / Markensteijn, A.S.; Romate, J.E.; Vuik, C.

Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. ed. / Fred J. Vermolen; Cornelis Vuik. Cham : Springer Science+Business Media, 2021. p. 713-721 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Markensteijn, A.S.

AU - Romate, J.E.

AU - Vuik, C.

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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SN - 978-3-030-55873-4

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BT - Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference

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Markensteijn AS, Romate JE, Vuik C. Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems. In Vermolen FJ, Vuik C, editors, Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Cham: Springer Science+Business Media. 2021. p. 713-721. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-030-55874-1_70

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

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