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<p>Microgrids play a vital role in modern energy systems by integrating renewable energy sources and distributed energy resources (DERs) to enhance efficiency, reliability, and sustainability. However, maintaining power quality in such environments is challenging due to harmonics, nonlinear loads, and transient disturbances. Harmonic estimation is essential for stable microgrid operation. Conventional least mean squares (LMS) algorithms, though widely used, often underperform in dynamic and nonlinear conditions. This study explores fractional-order LMS (FLMS) algorithms, which leverage memory effects and fractional derivatives to improve adaptability and convergence. Four FLMS variants are investigated: Weyl’s (WFLMS), Riemann–Liouville (RFLMS), Chen’s (CFLMS), and Atangana–Baleanu (AB-FLMS). A generalized adaptive filtering framework is presented, and each variant is evaluated under various disturbances such as notches, sags, swells, and interharmonics. Simulation results show that AB-FLMS achieves the best performance in terms of convergence speed, steady-state error, and robustness to noise. Convergence analysis, statistical confidence evaluation, and practical implementation on a 60.8&#xa0;kW rooftop grid-connected PV microgrid further demonstrate the superior estimation accuracy of AB-FLMS under real-world conditions. The Mittag–Leffler kernel used in AB-FLMS contributes to smoother weight updates and accelerated convergence by balancing memory depth and noise resilience. These findings support its suitability for real-time power quality monitoring and adaptive harmonic estimation in renewable-integrated microgrids.</p>

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Fractional adaptive filtering algorithms for harmonic estimation in renewable energy integrated microgrid

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Siddhanta Pani,
  • Umamani Subudhi

摘要

Microgrids play a vital role in modern energy systems by integrating renewable energy sources and distributed energy resources (DERs) to enhance efficiency, reliability, and sustainability. However, maintaining power quality in such environments is challenging due to harmonics, nonlinear loads, and transient disturbances. Harmonic estimation is essential for stable microgrid operation. Conventional least mean squares (LMS) algorithms, though widely used, often underperform in dynamic and nonlinear conditions. This study explores fractional-order LMS (FLMS) algorithms, which leverage memory effects and fractional derivatives to improve adaptability and convergence. Four FLMS variants are investigated: Weyl’s (WFLMS), Riemann–Liouville (RFLMS), Chen’s (CFLMS), and Atangana–Baleanu (AB-FLMS). A generalized adaptive filtering framework is presented, and each variant is evaluated under various disturbances such as notches, sags, swells, and interharmonics. Simulation results show that AB-FLMS achieves the best performance in terms of convergence speed, steady-state error, and robustness to noise. Convergence analysis, statistical confidence evaluation, and practical implementation on a 60.8 kW rooftop grid-connected PV microgrid further demonstrate the superior estimation accuracy of AB-FLMS under real-world conditions. The Mittag–Leffler kernel used in AB-FLMS contributes to smoother weight updates and accelerated convergence by balancing memory depth and noise resilience. These findings support its suitability for real-time power quality monitoring and adaptive harmonic estimation in renewable-integrated microgrids.