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A discrete time-varying grey Fourier model with fractional order terms for electricity consumption forecast

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  • Liu, Xiaomei
  • Li, Sihan
  • Gao, Meina

Abstract

Accurate electricity consumption forecast plays an important role in managing and operating a country’s power system and is a challenging task due to the data exhibiting the mixture characteristics of trend, periodicity and randomness. To accurately describe the dynamic changes of seasonal fluctuations of electricity consumption, a novel discrete time-varying grey Fourier model with fractional order terms is proposed by coupling Fourier functions with fractional order time-varying terms, as the grey action, to fit the amplitude variations hidden in seasonal pattern and improve the fitting and forecasting accuracy. Moreover, the mechanism and properties of the proposed model are discussed. Then the optimal fractional order is determined by the Dingo Optimization Algorithm (DOA) and the optimal Fourier order is selected by the hold-out method to enhance the robustness of the model. Subsequently, the results of designed experiments based on Monte-Carlo method testify the validity of the Fourier order selection method and the proposed model. Finally, this model is applied to predict the monthly residential electricity consumption of China from 2015 to 2022. The results indicate that the proposed model captures the dynamic amplitude variations of the time series and has better prediction performances than other benchmark grey prediction models and non-grey prediction models.

Suggested Citation

  • Liu, Xiaomei & Li, Sihan & Gao, Meina, 2024. "A discrete time-varying grey Fourier model with fractional order terms for electricity consumption forecast," Energy, Elsevier, vol. 296(C).
    • Handle: RePEc:eee:energy:v:296:y:2024:i:c:s0360544224008375
    DOI: 10.1016/j.energy.2024.131065
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    as
    1. Das, Utpal Kumar & Tey, Kok Soon & Seyedmahmoudian, Mehdi & Mekhilef, Saad & Idris, Moh Yamani Idna & Van Deventer, Willem & Horan, Bend & Stojcevski, Alex, 2018. "Forecasting of photovoltaic power generation and model optimization: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 912-928.
    2. Hernán Peraza-Vázquez & Adrián F. Peña-Delgado & Gustavo Echavarría-Castillo & Ana Beatriz Morales-Cepeda & Jonás Velasco-Álvarez & Fernando Ruiz-Perez, 2021. "A Bio-Inspired Method for Engineering Design Optimization Inspired by Dingoes Hunting Strategies," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-19, September.
    3. Wang, Zheng-Xin & Li, Qin & Pei, Ling-Ling, 2018. "A seasonal GM(1,1) model for forecasting the electricity consumption of the primary economic sectors," Energy, Elsevier, vol. 154(C), pages 522-534.
    4. Garcia-Rendon, John & Rey Londoño, Felipe & Arango Restrepo, Luis José & Bohorquez Correa, Santiago, 2023. "Sectoral analysis of electricity consumption during the COVID-19 pandemic: Evidence for unregulated and regulated markets in Colombia," Energy, Elsevier, vol. 268(C).
    5. Tang, Tao & Jiang, Weiheng & Zhang, Hui & Nie, Jiangtian & Xiong, Zehui & Wu, Xiaogang & Feng, Wenjiang, 2022. "GM(1,1) based improved seasonal index model for monthly electricity consumption forecasting," Energy, Elsevier, vol. 252(C).
    6. Wu, Wen-Ze & Pang, Haodan & Zheng, Chengli & Xie, Wanli & Liu, Chong, 2021. "Predictive analysis of quarterly electricity consumption via a novel seasonal fractional nonhomogeneous discrete grey model: A case of Hubei in China," Energy, Elsevier, vol. 229(C).
    7. Vu, D.H. & Muttaqi, K.M. & Agalgaonkar, A.P., 2015. "A variance inflation factor and backward elimination based robust regression model for forecasting monthly electricity demand using climatic variables," Applied Energy, Elsevier, vol. 140(C), pages 385-394.
    8. Kaytez, Fazil, 2020. "A hybrid approach based on autoregressive integrated moving average and least-square support vector machine for long-term forecasting of net electricity consumption," Energy, Elsevier, vol. 197(C).
    9. Meira, Erick & Cyrino Oliveira, Fernando Luiz & de Menezes, Lilian M., 2021. "Point and interval forecasting of electricity supply via pruned ensembles," Energy, Elsevier, vol. 232(C).
    10. Zhou, Weijie & Wu, Xiaoli & Ding, Song & Pan, Jiao, 2020. "Application of a novel discrete grey model for forecasting natural gas consumption: A case study of Jiangsu Province in China," Energy, Elsevier, vol. 200(C).
    11. Sen, Parag & Roy, Mousumi & Pal, Parimal, 2016. "Application of ARIMA for forecasting energy consumption and GHG emission: A case study of an Indian pig iron manufacturing organization," Energy, Elsevier, vol. 116(P1), pages 1031-1038.
    12. Du, Pei & Guo, Ju'e & Sun, Shaolong & Wang, Shouyang & Wu, Jing, 2022. "A novel two-stage seasonal grey model for residential electricity consumption forecasting," Energy, Elsevier, vol. 258(C).
    13. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    14. Bilgili, Mehmet & Pinar, Engin, 2023. "Gross electricity consumption forecasting using LSTM and SARIMA approaches: A case study of Türkiye," Energy, Elsevier, vol. 284(C).
    15. Chen, Hai-Bao & Pei, Ling-Ling & Zhao, Yu-Feng, 2021. "Forecasting seasonal variations in electricity consumption and electricity usage efficiency of industrial sectors using a grey modeling approach," Energy, Elsevier, vol. 222(C).
    16. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    17. Carmona-Benítez, Rafael Bernardo & Nieto, María Rosa, 2020. "SARIMA damp trend grey forecasting model for airline industry," Journal of Air Transport Management, Elsevier, vol. 82(C).
    18. Du, Pei & Wang, Jianzhou & Yang, Wendong & Niu, Tong, 2018. "Multi-step ahead forecasting in electrical power system using a hybrid forecasting system," Renewable Energy, Elsevier, vol. 122(C), pages 533-550.
    19. Ghimire, Sujan & Nguyen-Huy, Thong & AL-Musaylh, Mohanad S. & Deo, Ravinesh C. & Casillas-Pérez, David & Salcedo-Sanz, Sancho, 2023. "A novel approach based on integration of convolutional neural networks and echo state network for daily electricity demand prediction," Energy, Elsevier, vol. 275(C).
    20. Wang, Xiaolei & Xie, Naiming & Yang, Lu, 2022. "A flexible grey Fourier model based on integral matching for forecasting seasonal PM2.5 time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    21. Munkhammar, Joakim & van der Meer, Dennis & Widén, Joakim, 2021. "Very short term load forecasting of residential electricity consumption using the Markov-chain mixture distribution (MCM) model," Applied Energy, Elsevier, vol. 282(PA).
    22. de Oliveira, Erick Meira & Cyrino Oliveira, Fernando Luiz, 2018. "Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods," Energy, Elsevier, vol. 144(C), pages 776-788.
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