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Energies 2018, 11(8), 2096; https://doi.org/10.3390/en11082096

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

1
División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, México
2
Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Zapopan 45019, México
*
Author to whom correspondence should be addressed.
Received: 14 June 2018 / Revised: 7 July 2018 / Accepted: 17 July 2018 / Published: 13 August 2018
(This article belongs to the Section Sustainable Energy)
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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. View Full-Text
Keywords: time domain; photovoltaic energy sources; periodic steady state; limit cycle; numerical differentiation method; cubic splines time domain; photovoltaic energy sources; periodic steady state; limit cycle; numerical differentiation method; cubic splines
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Díaz-Araujo, M.; Medina, A.; Cisneros-Magaña, R.; Ramírez, A. Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines. Energies 2018, 11, 2096.

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