Solvability of the power flow problem in DC overhead wire circuit modeling

Jakub Ševčík; Lukáš Adam; Jan Přikryl; Václav Šmídl

Applications of Mathematics (2021)

  • Volume: 66, Issue: 6, page 837-855
  • ISSN: 0862-7940

Abstract

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Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly in situations where the vehicle power demands are too high (during acceleration), the solution of the studied problem may not exist. To deal with such cases, we introduce a numerical method which seeks maximal suppliable power demands for which the solution exists. This corresponds to introducing a scaling parameter to reduce the demanded power. The interpretation of the scaling parameter is the amount of energy which is absent in the system, and which needs to be provided by external sources such as on-board batteries. We propose an efficient two-stage algorithm to find the optimal scaling parameter and the resulting potentials in the overhead wire network. We perform a comparison with a naive approach and present a real-world simulation in the part of the Pilsen city in the Czech Republic. These simulations are performed in the traffic micro-simulator SUMO, a popular open-source traffic simulation platform.

How to cite

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Ševčík, Jakub, et al. "Solvability of the power flow problem in DC overhead wire circuit modeling." Applications of Mathematics 66.6 (2021): 837-855. <http://eudml.org/doc/298015>.

@article{Ševčík2021,
abstract = {Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly in situations where the vehicle power demands are too high (during acceleration), the solution of the studied problem may not exist. To deal with such cases, we introduce a numerical method which seeks maximal suppliable power demands for which the solution exists. This corresponds to introducing a scaling parameter to reduce the demanded power. The interpretation of the scaling parameter is the amount of energy which is absent in the system, and which needs to be provided by external sources such as on-board batteries. We propose an efficient two-stage algorithm to find the optimal scaling parameter and the resulting potentials in the overhead wire network. We perform a comparison with a naive approach and present a real-world simulation in the part of the Pilsen city in the Czech Republic. These simulations are performed in the traffic micro-simulator SUMO, a popular open-source traffic simulation platform.},
author = {Ševčík, Jakub, Adam, Lukáš, Přikryl, Jan, Šmídl, Václav},
journal = {Applications of Mathematics},
keywords = {power flow problem; Newton-Raphson method; solvability; scaling parameter},
language = {eng},
number = {6},
pages = {837-855},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability of the power flow problem in DC overhead wire circuit modeling},
url = {http://eudml.org/doc/298015},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Ševčík, Jakub
AU - Adam, Lukáš
AU - Přikryl, Jan
AU - Šmídl, Václav
TI - Solvability of the power flow problem in DC overhead wire circuit modeling
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 6
SP - 837
EP - 855
AB - Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly in situations where the vehicle power demands are too high (during acceleration), the solution of the studied problem may not exist. To deal with such cases, we introduce a numerical method which seeks maximal suppliable power demands for which the solution exists. This corresponds to introducing a scaling parameter to reduce the demanded power. The interpretation of the scaling parameter is the amount of energy which is absent in the system, and which needs to be provided by external sources such as on-board batteries. We propose an efficient two-stage algorithm to find the optimal scaling parameter and the resulting potentials in the overhead wire network. We perform a comparison with a naive approach and present a real-world simulation in the part of the Pilsen city in the Czech Republic. These simulations are performed in the traffic micro-simulator SUMO, a popular open-source traffic simulation platform.
LA - eng
KW - power flow problem; Newton-Raphson method; solvability; scaling parameter
UR - http://eudml.org/doc/298015
ER -

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