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

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.