IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i7p1727-d341596.html
   My bibliography  Save this article

Probabilistic Load Flow Approach Considering Dependencies of Wind Speed, Solar Irradiance, Electrical Load and Energy Exchange with a Joint Probability Distribution Model

Author

Listed:
  • Marie-Louise Kloubert

    (TransnetBW GmbH, 70173 Stuttgart, Germany)

Abstract

The modelling of stochastic feed-ins and demands becomes essential for transmission grid operation and planning due to the extension of renewable energy sources (RES). Neglecting the correlation between uncertain variables and/or oversimplifying the distribution through the assumption of Normal distributions leads to the inaccurate determination of future network states. Therefore, the uncertainties need to be accurately modelled in order to be used in a probabilistic load flow approach. This paper analyses the characteristics of wind speed and solar irradiance for different locations throughout countries and models the dependencies between them. In addition, the total electrical load and the energy exchange between neighbouring countries are analysed. All of these uncertainties are modelled together in a high-dimensional joint probability distribution using pair-copula constructions. The model is applied to generate samples and determine the probability of extreme events, e.g. high RES production and low demand. The probability for rather high load (>65 GW) and low RES production with wind speed less than 3 m/s and solar irradiance less than 100 W m ² at 90% of all stations is e.g. 0.064%. In addition, the model is integrated in a probabilistic load flow approach in order to analyse the German transmission grid for a future scenario of the year 2025. With the copula, samples are generated as an input for the Monte Carlo simulation approach. The approach enables the assessment of planned HVDC lines. When considering the HVDC lines, the load on the AC lines can be significantly reduced.

Suggested Citation

  • Marie-Louise Kloubert, 2020. "Probabilistic Load Flow Approach Considering Dependencies of Wind Speed, Solar Irradiance, Electrical Load and Energy Exchange with a Joint Probability Distribution Model," Energies, MDPI, vol. 13(7), pages 1-15, April.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:7:p:1727-:d:341596
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/7/1727/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/13/7/1727/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cadini, F. & Zio, E. & Petrescu, C.A., 2010. "Optimal expansion of an existing electrical power transmission network by multi-objective genetic algorithms," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 173-181.
    2. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    3. Brechmann, Eike Christian & Schepsmeier, Ulf, 2013. "Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i03).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohamed El-Hendawi & Zhanle Wang & Raman Paranjape & Shea Pederson & Darcy Kozoriz & James Fick, 2022. "Electric Vehicle Charging Model in the Urban Residential Sector," Energies, MDPI, vol. 15(13), pages 1-21, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beatrice D. Simo-Kengne & Kofi A. Ababio & Jules Mba & Ur Koumba, 2018. "Behavioral portfolio selection and optimization: an application to international stocks," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 32(3), pages 311-328, August.
    2. Salaheddine El Adlouni, 2018. "Quantile regression C-vine copula model for spatial extremes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(1), pages 299-317, October.
    3. Wu Zening & He Chentao & Huiliang Wang & Qian Zhang, 2020. "Reservoir Inflow Synchronization Analysis for Four Reservoirs on a Mainstream and its Tributaries in Flood Season Based on a Multivariate Copula Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(9), pages 2753-2770, July.
    4. Maziar Sahamkhadam & Andreas Stephan, 2019. "Portfolio optimization based on forecasting models using vine copulas: An empirical assessment for the financial crisis," Papers 1912.10328, arXiv.org.
    5. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    6. Nagler Thomas & Czado Claudia & Schellhase Christian, 2017. "Nonparametric estimation of simplified vine copula models: comparison of methods," Dependence Modeling, De Gruyter, vol. 5(1), pages 99-120, January.
    7. Brechmann, Eike & Czado, Claudia & Paterlini, Sandra, 2014. "Flexible dependence modeling of operational risk losses and its impact on total capital requirements," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 271-285.
    8. Li, Haihe & Wang, Pan & Huang, Xiaoyu & Zhang, Zheng & Zhou, Changcong & Yue, Zhufeng, 2021. "Vine copula-based parametric sensitivity analysis of failure probability-based importance measure in the presence of multidimensional dependencies," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    10. Wang, Fan & Li, Heng & Dong, Chao, 2021. "Understanding near-miss count data on construction sites using greedy D-vine copula marginal regression," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    11. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    12. Cooke, R.M. & Kurowicka, D. & Wilson, K., 2015. "Sampling, conditionalizing, counting, merging, searching regular vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 4-18.
    13. Müller, Dominik & Czado, Claudia, 2019. "Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 211-232.
    14. Chemkha, Rahma & BenSaïda, Ahmed & Ghorbel, Ahmed, 2021. "Connectedness between cryptocurrencies and foreign exchange markets: Implication for risk management," Journal of Multinational Financial Management, Elsevier, vol. 59(C).
    15. Fernandez, Viviana, 2017. "Some facts on the platinum-group elements," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 333-347.
    16. Eling, Martin & Jung, Kwangmin, 2018. "Copula approaches for modeling cross-sectional dependence of data breach losses," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 167-180.
    17. Erhardt, Tobias Michael & Czado, Claudia & Schepsmeier, Ulf, 2015. "Spatial composite likelihood inference using local C-vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 74-88.
    18. Niemierko, Rochus & Töppel, Jannick & Tränkler, Timm, 2019. "A D-vine copula quantile regression approach for the prediction of residential heating energy consumption based on historical data," Applied Energy, Elsevier, vol. 233, pages 691-708.
    19. Guillaume Arnould & Catherine Bruneau & Zhun Peng, 2015. "Liquidity and Equity Short term fragility: Stress-tests for the European banking system," Post-Print halshs-01254729, HAL.
    20. Vahidin Jeleskovic & Mirko Meloni & Zahid Irshad Younas, 2020. "Cryptocurrencies: A Copula Based Approach for Asymmetric Risk Marginal Allocations," MAGKS Papers on Economics 202034, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:7:p:1727-:d:341596. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.