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Laplacian matrix-based power flow formulation for LVDC grids with radial and meshed configurations

Zahid Javid, Ulas Karaagac, Ilhan Kocar and Ka Wing Chan

Article (2021)

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Abstract

There is an increasing interest in low voltage direct current (LVDC) distribution grids due to advancements in power electronics enabling efficient and economical electrical networks in the DC paradigm. Power flow equations in LVDC grids are non-linear and non-convex due to the presence of constant power nodes. Depending on the implementation, power flow equations may lead to more than one solution and unrealistic solutions; therefore, the uniqueness of the solution should not be taken for granted. This paper proposes a new power flow solver based on a graph theory for LVDC grids having radial or meshed configurations. The solver provides a unique solution. Two test feeders composed of 33 nodes and 69 nodes are considered to validate the effectiveness of the proposed method. The proposed method is compared with a fixed-point methodology called direct load flow (DLF) having a mathematical formulation equivalent to a backward forward sweep (BFS) class of solvers in the case of radial distribution networks but that can handle meshed networks more easily thanks to the use of connectivity matrices. In addition, the convergence and uniqueness of the solution is demonstrated using a Banach fixed-point theorem. The performance of the proposed method is tested for different loading conditions. The results show that the proposed method is robust and has fast convergence characteristics even with high loading conditions. All simulations are carried out in MATLAB 2020b software.

Uncontrolled Keywords

constant power load; distribution system; direct load flow; graph theory; low voltage DC grids; meshed networks; power flow; radial networks; distributed generation

Subjects: 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering
2500 Electrical and electronic engineering > 2501 Power systems
2500 Electrical and electronic engineering > 2506 Electronic circuits and devices
2700 Information technology > 2714 Mathematics of computing
Department: Department of Electrical Engineering
Funders: The Hong Kong Polytechnic University - Department of Electrical Engineering - Start-up Fund Research Project
Grant number: 1-ZVLU
PolyPublie URL: https://publications.polymtl.ca/9384/
Journal Title: Energies (vol. 14, no. 7)
Publisher: MDPI
DOI: 10.3390/en14071866
Official URL: https://doi.org/10.3390/en14071866
Date Deposited: 16 Aug 2023 12:15
Last Modified: 08 Apr 2024 22:07
Cite in APA 7: Javid, Z., Karaagac, U., Kocar, I., & Chan, K. W. (2021). Laplacian matrix-based power flow formulation for LVDC grids with radial and meshed configurations. Energies, 14(7), 21 pages. https://doi.org/10.3390/en14071866

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