Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations

Zahid Javid, Ulas Karaagac, Ilhan Kocar and Ka Wing Chan
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Zahid Javid: Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
Ulas Karaagac: Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
Ilhan Kocar: Department of Electrical Engineering, Polytechnique Montreal, Montreal, QC H3T 1J4, Canada
Ka Wing Chan: Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

Energies, 2021, vol. 14, issue 7, 1-21

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.

Keywords: constant power load; distribution system; direct load flow; graph theory; low voltage DC grids; meshed networks; power flow; radial networks; distributed generation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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