A Homotopy-Based Approach to Solve the Power Flow Problem in Islanded Microgrid with Droop-Controlled Distributed Generation Units

Alisson Lima-Silva, Francisco Damasceno Freitas () and Luis Filomeno de Jesus Fernandes
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Alisson Lima-Silva: University of Brasilia, Department of Electrical Engineering, Brasilia 70910-900, Brazil
Francisco Damasceno Freitas: University of Brasilia, Department of Electrical Engineering, Brasilia 70910-900, Brazil
Luis Filomeno de Jesus Fernandes: University of Brasilia, Faculdade do Gama—FGA, Brasilia 70910-900, Brazil

Energies, 2023, vol. 16, issue 14, 1-19

Abstract: This paper proposes a homotopy-based approach to solve the power flow problem (PFP) in islanded microgrid networks with droop-controlled distributed generation (DG) units. The technique is based on modifying an “easy” problem solution that evolves with the computation of intermediate results to the PFP solution of interest. These intermediate results require the solution of nonlinear equations through Newton–Raphson (NR) method. In favor of convergence, the intermediate solutions are close to each other, strengthening the convergence qualities of the technique for the solution of interest. The DG units are modeled with operational power limits and three types of droop-control strategies, while the loads are both magnitude voltage- and frequency-dependent. To evaluate the method performance, simulations are performed considering the proposed and classical NR methods, both departing from a flat start estimation. Tests are carried out in three test systems. Different load and DG unit scenarios are implemented for a 6-, 38-, and 69-bus test system. A base case is studied for all systems, while for the two larger models, a loading factor is used to simulate the load augmenting up to the maximum value. The results demonstrated that for the largest-size model system, only the homotopy-based approach could solve the PFP for stringent requirements such as the diversification of the load profile and hard loading operation point.

Keywords: homotopy; Newton–Raphson method; distributed generation; energy management; islanded microgrid; distributed energy resources (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: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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