## 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 |
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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 |

Pages | 713-721 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-030-55874-1 |

ISBN (Print) | 978-3-030-55873-4 |

DOIs | |

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 |
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Volume | 139 |

ISSN (Print) | 1439-7358 |

ISSN (Electronic) | 2197-7100 |

### Conference

Conference | European Numerical Mathematics and Advanced Applications Conference 2019 |
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Abbreviated title | ENUMATH 2019 |

Country | Netherlands |

City | Egmond aan Zee |

Period | 30/09/19 → 4/10/19 |

Internet address |