On the frequency variation in load-flow calculations for islanded alternating current microgrids

Matthias Molénat, Jean Mahseredjian, Nasim Rashidirad and Antoine Lesage-Landry

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 247-256

Abstract: Load-flow analyses of islanded microgrids often assume constant line admittances evaluated at the grid’s nominal frequency. This paper investigates errors introduced by this assumption and leverages the versatile modified-augmented nodal-analysis (MANA) formulation to propose new algorithms to account for the frequency variation in line admittances in load-flow calculations. The proposed algorithms, namely MANA-Y(ω), BD1-MANA-Y(ω), BD2-MANA-Y(ω), and their hybrid versions, are tested and compared to MANA on a 25-bus microgrid and a 906-bus grid. Simulations under varying loading conditions demonstrate the advantages of the proposed approach in terms of solution accuracy, particularly for loadability assessments. For the 25-bus case, the voltage magnitude accuracy improves by up to 5%, and the MANA-Y(ω) is particularly effective near the system’s maximum loadability point, enabling convergence up to 13% beyond the MANA-estimated limit. Under moderate loadability conditions, the block-dishonest Newton–Raphson method BD2-MANA-Y(ω) emerges as the most computationally efficient among the proposed methods. For the 906-bus grid under critical loading, its computation time is 25% faster than the full MANA-Y(ω) method, while maintaining comparable accuracy.

Keywords: Modified-augmented nodal-analysis (MANA) formulation; Islanded grid; Microgrid; Droop-controlled generators; Multiphase load-flow; Newton–Raphson method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:247-256

DOI: 10.1016/j.matcom.2025.09.007

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