Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/7/1866 |
| _version_ | 1797539736803344384 |
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| author | Zahid Javid Ulas Karaagac Ilhan Kocar Ka Wing Chan |
| author_facet | Zahid Javid Ulas Karaagac Ilhan Kocar Ka Wing Chan |
| author_sort | Zahid Javid |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T12:50:05Z |
| format | Article |
| id | doaj.art-2ffdc103d0b64ce2b08984e4ee554a26 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T12:50:05Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-2ffdc103d0b64ce2b08984e4ee554a262023-11-21T13:06:18ZengMDPI AGEnergies1996-10732021-03-01147186610.3390/en14071866Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed ConfigurationsZahid Javid0Ulas Karaagac1Ilhan Kocar2Ka Wing Chan3Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, ChinaDepartment of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, ChinaDepartment of Electrical Engineering, Polytechnique Montreal, Montreal, QC H3T 1J4, CanadaDepartment of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, ChinaThere 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.https://www.mdpi.com/1996-1073/14/7/1866constant power loaddistribution systemdirect load flowgraph theorylow voltage DC gridsmeshed networks |
| spellingShingle | Zahid Javid Ulas Karaagac Ilhan Kocar Ka Wing Chan Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations Energies constant power load distribution system direct load flow graph theory low voltage DC grids meshed networks |
| title | Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations |
| title_full | Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations |
| title_fullStr | Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations |
| title_full_unstemmed | Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations |
| title_short | Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations |
| title_sort | laplacian matrix based power flow formulation for lvdc grids with radial and meshed configurations |
| topic | constant power load distribution system direct load flow graph theory low voltage DC grids meshed networks |
| url | https://www.mdpi.com/1996-1073/14/7/1866 |
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