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Gaussian Copula Methodology to Model Photovoltaic Generation Uncertainty Correlation in Power Distribution Networks

Author

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  • Harshavardhan Palahalli

    (Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci, 32-20133 Milano, Italy)

  • Paolo Maffezzoni

    (Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci, 32-20133 Milano, Italy)

  • Giambattista Gruosso

    (Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci, 32-20133 Milano, Italy)

Abstract

Deterministic load flow analyses of power grids do not include the uncertain factors that affect the network elements; hence, their predictions can be very unreliable for distribution system operators and for the decision makers who deal with the expansion planning of the power network. Adding uncertain probability parameters in the deterministic load flow is vital to capture the wide variability of the currents and voltages. This is achieved by probabilistic load flow studies. Photovoltaic systems represent a remarkable source of uncertainty in the distribution network. In this study, we used a Gaussian copula to model the uncertainty in correlated photovoltaic generators. Correlations among photovoltaic generators were also included by exploiting the Gaussian copula technique. The large sets of samples generated with a statistical method (Gaussian copula) were used as the inputs for Monte Carlo simulations. The proposed methodologies were tested on two different networks, i.e., the 13 node IEEE test feeder and the non-synthetic European low voltage test network. Node voltage uncertainty and network health, measured by the percentage voltage unbalance factor, were investigated. The importance of including correlations among photovoltaic generators is discussed.

Suggested Citation

  • Harshavardhan Palahalli & Paolo Maffezzoni & Giambattista Gruosso, 2021. "Gaussian Copula Methodology to Model Photovoltaic Generation Uncertainty Correlation in Power Distribution Networks," Energies, MDPI, vol. 14(9), pages 1-16, April.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:9:p:2349-:d:540371
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    References listed on IDEAS

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    1. Prusty, B Rajanarayan & Jena, Debashisha, 2017. "A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 1286-1302.
    2. Kumar, Ravinder & Umanand, L., 2005. "Estimation of global radiation using clearness index model for sizing photovoltaic system," Renewable Energy, Elsevier, vol. 30(15), pages 2221-2233.
    3. Brandon Cortés-Caicedo & Laura Sofía Avellaneda-Gómez & Oscar Danilo Montoya & Lazaro Alvarado-Barrios & Harold R. Chamorro, 2021. "Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems," Energies, MDPI, vol. 14(5), pages 1-35, February.
    4. Zio, Enrico & Piccinelli, Roberta & Delfanti, Maurizio & Olivieri, Valeria & Pozzi, Mauro, 2012. "Application of the load flow and random flow models for the analysis of power transmission networks," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 102-109.
    5. Baljinnyam Sereeter & Kees Vuik & Cees Witteveen, 2017. "Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks," Energies, MDPI, vol. 10(10), pages 1-20, October.
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    Cited by:

    1. Igor Simone Stievano & Riccardo Trinchero, 2023. "Advanced Techniques for the Modeling and Simulation of Energy Networks," Energies, MDPI, vol. 16(5), pages 1-3, February.
    2. Giambattista Gruosso & Luca Daniel & Paolo Maffezzoni, 2022. "Piece-Wise Linear (PWL) Probabilistic Analysis of Power Grid with High Penetration PV Integration," Energies, MDPI, vol. 15(13), pages 1-15, June.

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