Long-Term Total Load Forecasting using a Functional Regression Model

doi:10.15266/KEREA.2024.33.4.315

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2024 Vol.33, Issue 4 Next Page

Research Paper

Long-Term Total Load Forecasting using a Functional Regression Model 함수회귀 모형을 이용한 중장기 부하곡선 예측: 신학림*‧김창식**‧최용옥***
Haklim Shin*, Chang Sik Kim**, and Yongok Choi***; *성균관대학교 경제학과 박사과정, 제1저자(e-mail: haklim.shin@gmail.com)
**성균관대학교 경제학과 교수, 교신저자(e-mail: skimcs@skku.edu)
***중앙대학교 경제학과 부교수, 공동저자(e-mail: choiyongok@cau.ac.kr)

*PhD Program, Department of Economics, Sungkyunkwan University, First author (e-mail: haklim.shin@gmail.com)
**Professor, Department of Economics, Sungkyunkwan University, Corresponding author (e-mail: skimcs@skku.edu)
***Associate Professor, School of Economics, Chung-Ang University, Coauthor (e-mail: choiyongok@cau.ac.kr)

31 December 2024. pp. 315-341

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Abstract

We propose a model for long-term forecasting of the daily total load curve, which represents the hourly total demand in South Korea. In this study, the daily load curve is assumed to be influenced by both deterministic factors--such as trends, temperature, and special days--and probabilistic factors, which account for time-dependent dynamic variations that cannot be explained by deterministic components. The deterministic factors are estimated on an hourly basis, reflecting their time-varying nature. Meanwhile, the dynamic variations in the total load curve, driven by probabilistic factors, are modeled using a functional autoregression estimation methodology. One-year rolling forecasting results demonstrate an average MAPE (Mean Absolute Percentage Error) of 2%, highlighting the robust performance of our proposed methodology.

Keywords

Long-term forecasting electricity load curve

Functional autoregression

Functional principal component analysis

본 연구에서는 우리나라 전체의 시간별 수요에 상응하는 총부하(Total Load) 곡선을 예측하는 방법론을 제시한다. 먼저 일별 총부하 곡선을 추세, 기온, 특수일 등과 같이 확정적 요소와 확정적 요소로 설명되지 않는 시간대별 동적 변동을 나타내는 확률적인 요소로 구분하고, 이들을 각각 모형화하여 예측한다. 확정적 요소는 각각의 요인별 효과를 시간대별로 추정하되 각 요인의 효과가 시간에 따라 변동할 수 있는 시간 변동성을 함께 고려하였다. 확률적인 요소를 결정하는 부하곡선의 동적 변동은 함수 주성분 분석(functional principal component analysis, FPCA)을 활용한 함수자기회귀(functional autoregression, FAR) 모형을 이용하여 분석하고 예측하였다. 본 연구에서 제시된 모형으로 365일 동안의 예측실험을 한 결과, 예측된 일별 부하곡선의 평균 절대 백분율 오차(mean absolute percentage error, MAPE)는 약 2% 내외로 안정적으로 나타남을 확인하였다.

키워드

중장기 부하곡선 예측

함수자기회귀모형

함수 주성분 분석

References

윤용기‧최용옥, “C-Lasso를 이용한 도시가스 수요의 특수일 변동석 분석”, 「에너지경제 연구」, 제21권 제1호, 2022, pp. 1~22.
Bashir, T., H. Chen, M. F. Tahir, and L. Zhang, “Short Term Electricity Load Forecasting Using Hybrid Prophet-LSTM Model Optimized by BPNN,” Energy Reports, Vol. 8, 2022, pp. 1678~1686.10.1016/j.egyr.2021.12.067
Bosq, D., “Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes,” in Nonparametric Functional Estimation and Related Topics, 1991, pp. 509~529.10.1007/978-94-011-3222-0_38
Chang, Y., Y. Choi, C. S. Kim, J. I. Miller, and J. Y. Park, “Common Trends and Country-Specific Heterogeneities in Long-Run World Energy Consumption,” Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington, CAEPR Working Papers, 2024-001 Classification-1, 2024.10.2139/ssrn.4687908
Chang, Y., Y. Choi, C. S. Kim, J. I. Miller, and J. Y. Park, “Forecasting Regional Long-run Energy Demand: A Functional Coefficient Panel Approach,” Energy Economics, Vol. 96, 2021.10.1016/j.eneco.2021.105117
Chang, Y., C. S. Kim, J. I. Miller, J. Y. Park, and S. Park, “A New Approach to Modeling the Effects of Temperature Fluctuations on Monthly Electricity Demand,” Energy Economics, Vol. 60, 2016, pp. 206~216.10.1016/j.eneco.2016.09.016
Chen, Y., T. Koch, X. Xu, and K. G. Lim, “A Review Study of Functional Autoregressive Models with Application to Energy Forecasting,” Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 13, No. 3, 2020.10.1002/wics.1525
Engle, R. F., C. W. Granger, and J. J. Hallman, “Merging Short-and Long-run Forecasts: An Application of Seasonal Cointegration to Monthly Electricity Sales Forecasting,” Journal of Econometrics, Vol. 40, No. 1, 1989, pp. 45~62.10.1016/0304-4076(89)90029-8
Henley, A., and J. Peirson, “Residential Energy Demand and the Interaction of Price and Temperature: British Experimental Evidence,” Energy Economics, Vol. 20, No. 2, 1998, pp. 157~171.10.1016/S0140-9883(97)00025-X
Kuster, C., Y. Rezgui, and M. Mourshed, “Electrical Load Forecasting Models: A Critical Systematic Review,” Sustainable Cities and Society, Vol. 35, 2017, pp. 257~270.10.1016/j.scs.2017.08.009
Li, Q., and J. S. Racine, Nonparametric Econometrics: Theory and Practice, Princeton, Princeton University Press, 2007.
Lindberg, K. B., P. Seljom, H. Madsen, D. Fischer, and M. Korpås, “Long-Term Electricity Load Forecasting: Current and Future Trends,” Utilities Policy, Vol. 58, 2019, pp. 102~119.10.1016/j.jup.2019.04.001
Mas, A., “Weak Convergence in the Functional Autoregressive Model,” Journal of Multivariate Analysis, Vol. 98, No. 6, 2007, pp. 1231~1261.10.1016/j.jmva.2006.05.010
Moral-Carcedo, J., and J. Vicens-Otero, “Modelling the Non-linear Response of Spanish Electricity Demand to Temperature Variations,” Energy Economics, Vol. 27, No. 3, 2005, pp. 477~494.10.1016/j.eneco.2005.01.003
Pardo, A., V. Meneu, and E. Valor, “Temperature and Seasonality Influences on Spanish Electricity Load,” Energy Economics, Vol. 24, No. 1, 2002, pp. 55~70.10.1016/S0140-9883(01)00082-2
Rafi, S. H., N. A. Masood, S. R. Deeba, and E. Hossain, “A Short-Term Load Forecasting Method Using Integrated CNN and LSTM Network,” IEEE Access, Vol. 9, 2021, pp. 32436~32448.10.1109/ACCESS.2021.3060654
Valor, E., V. Meneu, and V. Caselles, “Daily Air Temperature and Electricity Load in Spain,” Journal of Applied Meteorology, Vol. 40, 2001, pp. 1413~1421.10.1175/1520-0450(2001)040<1413:DATAEL>2.0.CO;2
Yildiz, B., J. I. Bilbao, and A. B. Sproul, “A Review and Analysis of Regression and Machine Learning Models on Commercial Building Electricity Load Forecasting,” Renewable and Sustainable Energy Reviews, Vol. 73, 2017, pp. 1104~1122.10.1016/j.rser.2017.02.023

Information

Publisher :Environmental and Resource Economics Review
Publisher(Ko) :자원 · 환경경제연구
Journal Title :자원·환경경제연구
Journal Title(Ko) :Environmental and Resource Economics Review
Volume : 33
No :4
Pages :315-341
DOI :https://doi.org/10.15266/KEREA.2024.33.4.315

[1] 윤용기‧최용옥, “C-Lasso를 이용한 도시가스 수요의 특수일 변동석 분석”, 「에너지경제 연구」, 제21권 제1호, 2022, pp. 1~22.

[2] Bashir, T., H. Chen, M. F. Tahir, and L. Zhang, “Short Term Electricity Load Forecasting Using Hybrid Prophet-LSTM Model Optimized by BPNN,” Energy Reports, Vol. 8, 2022, pp. 1678~1686.10.1016/j.egyr.2021.12.067

[3] Bosq, D., “Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes,” in Nonparametric Functional Estimation and Related Topics, 1991, pp. 509~529.10.1007/978-94-011-3222-0_38

[4] Chang, Y., Y. Choi, C. S. Kim, J. I. Miller, and J. Y. Park, “Common Trends and Country-Specific Heterogeneities in Long-Run World Energy Consumption,” Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington, CAEPR Working Papers, 2024-001 Classification-1, 2024.10.2139/ssrn.4687908

[5] Chang, Y., Y. Choi, C. S. Kim, J. I. Miller, and J. Y. Park, “Forecasting Regional Long-run Energy Demand: A Functional Coefficient Panel Approach,” Energy Economics, Vol. 96, 2021.10.1016/j.eneco.2021.105117

[6] Chang, Y., C. S. Kim, J. I. Miller, J. Y. Park, and S. Park, “A New Approach to Modeling the Effects of Temperature Fluctuations on Monthly Electricity Demand,” Energy Economics, Vol. 60, 2016, pp. 206~216.10.1016/j.eneco.2016.09.016

[7] Chen, Y., T. Koch, X. Xu, and K. G. Lim, “A Review Study of Functional Autoregressive Models with Application to Energy Forecasting,” Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 13, No. 3, 2020.10.1002/wics.1525

[8] Engle, R. F., C. W. Granger, and J. J. Hallman, “Merging Short-and Long-run Forecasts: An Application of Seasonal Cointegration to Monthly Electricity Sales Forecasting,” Journal of Econometrics, Vol. 40, No. 1, 1989, pp. 45~62.10.1016/0304-4076(89)90029-8

[9] Henley, A., and J. Peirson, “Residential Energy Demand and the Interaction of Price and Temperature: British Experimental Evidence,” Energy Economics, Vol. 20, No. 2, 1998, pp. 157~171.10.1016/S0140-9883(97)00025-X

[10] Kuster, C., Y. Rezgui, and M. Mourshed, “Electrical Load Forecasting Models: A Critical Systematic Review,” Sustainable Cities and Society, Vol. 35, 2017, pp. 257~270.10.1016/j.scs.2017.08.009

[11] Li, Q., and J. S. Racine, Nonparametric Econometrics: Theory and Practice, Princeton, Princeton University Press, 2007.

[12] Lindberg, K. B., P. Seljom, H. Madsen, D. Fischer, and M. Korpås, “Long-Term Electricity Load Forecasting: Current and Future Trends,” Utilities Policy, Vol. 58, 2019, pp. 102~119.10.1016/j.jup.2019.04.001

[13] Mas, A., “Weak Convergence in the Functional Autoregressive Model,” Journal of Multivariate Analysis, Vol. 98, No. 6, 2007, pp. 1231~1261.10.1016/j.jmva.2006.05.010

[14] Moral-Carcedo, J., and J. Vicens-Otero, “Modelling the Non-linear Response of Spanish Electricity Demand to Temperature Variations,” Energy Economics, Vol. 27, No. 3, 2005, pp. 477~494.10.1016/j.eneco.2005.01.003

[15] Pardo, A., V. Meneu, and E. Valor, “Temperature and Seasonality Influences on Spanish Electricity Load,” Energy Economics, Vol. 24, No. 1, 2002, pp. 55~70.10.1016/S0140-9883(01)00082-2

[16] Rafi, S. H., N. A. Masood, S. R. Deeba, and E. Hossain, “A Short-Term Load Forecasting Method Using Integrated CNN and LSTM Network,” IEEE Access, Vol. 9, 2021, pp. 32436~32448.10.1109/ACCESS.2021.3060654

[17] Valor, E., V. Meneu, and V. Caselles, “Daily Air Temperature and Electricity Load in Spain,” Journal of Applied Meteorology, Vol. 40, 2001, pp. 1413~1421.10.1175/1520-0450(2001)040<1413:DATAEL>2.0.CO;2

[18] Yildiz, B., J. I. Bilbao, and A. B. Sproul, “A Review and Analysis of Regression and Machine Learning Models on Commercial Building Electricity Load Forecasting,” Renewable and Sustainable Energy Reviews, Vol. 73, 2017, pp. 1104~1122.10.1016/j.rser.2017.02.023

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