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Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines

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  • Marcolino Díaz-Araujo

    (División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, México)

  • Aurelio Medina

    (División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, México)

  • Rafael Cisneros-Magaña

    (División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, México)

  • Amner Ramírez

    (Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Zapopan 45019, México)

Abstract

This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among other issues, of microgrids with PV sources. The results are successfully validated through direct comparison against those obtained with the PSCAD/EMTDC simulator, widely accepted by the power industry.

Suggested Citation

  • Marcolino Díaz-Araujo & Aurelio Medina & Rafael Cisneros-Magaña & Amner Ramírez, 2018. "Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines," Energies, MDPI, vol. 11(8), pages 1-16, August.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:8:p:2096-:d:163389
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    References listed on IDEAS

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    Cited by:

    1. Marcolino Humberto Díaz-Araujo & Aurelio Medina-Rios & Manuel Madrigal-Martínez & Luis Arthur Cleary-Balderas, 2019. "Analysis of Grid-Connected Photovoltaic Generation Systems in the Harmonic Domain," Energies, MDPI, vol. 12(24), pages 1-14, December.
    2. Kewei Cai & Belema Prince Alalibo & Wenping Cao & Zheng Liu & Zhiqiang Wang & Guofeng Li, 2018. "Hybrid Approach for Detecting and Classifying Power Quality Disturbances Based on the Variational Mode Decomposition and Deep Stochastic Configuration Network," Energies, MDPI, vol. 11(11), pages 1-18, November.

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