Гибридная модель EMD-двухветвевой MLP с многоцелевой оптимизацацией NSGA-II для прогнозирования нагрузки на сутки вперёд

В работе рассматривается задача суточного многократного прогнозирования электрической нагрузки при дискретизации 15 минут (24 ч, 96 шагов), где нелинейность, нестационарность и многомасштабное смешение осложняют точное долгогоризонтное предсказание. Предлагается схема EMD-двухветвевой MLP с покомпонентным моделированием и калиброванным слиянием. В частности, эмпирическая модовая декомпозиция (EMD) применяется для разложения ряда нагрузки и последующей реконструкции в высокочастотную (HFC) и низкочастотную (LFC) компоненты; для HFC и LFC обучаются две прямые многовыходные MLP-модели с корреляционным отбором признаков (Пирсон), а для компенсации смещения реконструкции используется глобальное аффинное слияние (Global Affine) в качестве пост-калибровки. Многоцелевая оптимизация гиперпараметров выполняется алгоритмом NSGA-II (Optuna) путём совместной минимизации валидационных ошибок ветвей HFC и LFC. Эксперименты на наборе UCI ElectricityLoadDiagrams (MT_232, 2012-2013) с температурными рядами IPMA (Лиссабон) показывают, что EMD_MLP достигает RMSE/MAE/sMAPE = 8.567/5.434/7.546, снижая RMSE на 16,6 % и 19,5 % по сравнению с MLP и LSTM; вариант с NSGA-II дополнительно улучшает результаты до 8.363/5.377/7.503 и обеспечивает более стабильный профиль ошибки по горизонту. Предложенный метод формирует надёжные высокочастотные суточные траектории нагрузки для задач оперативного планирования, включая unit commitment, резервирование и рыночные операции.

1. Kondaiah V., Saravanan B., Sanjeevikumar P. et al. A review on short‐term load forecasting models for micro‐grid application // The Journal of Engineering. – 2022; 2022(7):665-689. Doi: 10.1049/tje2.12151

2. Akhtar S., Shahzad S., Zaheer A. et al. Short-Term Load Forecasting Models: A Review of Challenges, Progress, and the Road Ahead // Energies. – 2023; 16(10):4060. Doi: 10.3390/en16104060

3. Hu Y., Ye C., Ding Y. et al. Short-term load forecasting utilizing wavelet transform and time series considering accuracy feedback // Int Trans Electr Energy Syst. – 2020. Doi: 10.1002/2050-7038.12455.

4. Eren Y., Küçükdemiral İ. A comprehensive review on deep learning approaches for short-term load forecasting // Renewable and Sustainable Energy Reviews. – 2024(189); Part B:114031 Doi: 10.1016/j.rser.2023.114031.

5. Torkzadeh R., Mirzaei A., Mirjalili M. et al. Medium term load forecasting in distribution systems based on multi linear regression & principal component analysis: A novel approach. 2014 19th Conference on Electrical Power Distribution Networks (EPDC). – 2014: 66-70. Doi: 10.1109/EPDC.2014.6867500.

6. Pandey A., Sahay K., Tripathi M. et al. Short-term load forecasting of UPPCL using ANN. 2014 6th IEEE Power India International Conference (PIICON). – 2014: 1-6. Doi: 10.1109/POWERI.2014.7117741.

7. Aguilar E., Antonio N. Short-Term Electricity Load Forecasting with Machine Learning // Information. – 2021; 12(2):50. Doi:10.3390/info12020050

8. Nury H., Hasan K., Alam B. Comparative study of wavelet-ARIMA and wavelet-ANN models for temperature time series data in northeastern Bangladesh // Journal of King Saud University-Science. – 2017; 29(1): 47-61. Doi: 10.1016/j.jksus.2015.12.002

9. Rodrigues F., Pereira F. Beyond Expectation: Deep Joint Mean and Quantile Regression for Spatiotemporal Problems. Transactions on Neural Networks and Learning Systems // IEEE, 2020, 31(12):5377-5389. Doi: 10.1109/TNNLS.2020.2966745.

10. Liu Y., Zhao J., Liu J. et al. Regional midterm electricity demand forecasting based on economic, weather, holiday, and events factors. IEEJ Transactions on Electrical and Electronic Engineering. – 2020; 15(2):225-234. Doi: 10.1002/tee.23049

11. Sun G., Jiang C., Wang X. et al. Short‐term building load forecast based on a data‐mining feature selection and LSTM‐RNN method // IEEJ Transactions on Electrical and Electronic Engineering. – 2020; 15(7):1002-1010. Doi: 10.1002/tee.23144

12. Kong W., Dong Y., Jia Y. et al. Short-Term Residential Load Forecasting Based on LSTM Recurrent Neural Network. Transactions on Smart Grid // IEEE. – 2019; 10(1):841-851. Doi: 10.1109/TSG.2017.2753802.

13. Yang L., Wu H., Ding M. et al. Short-term load forecasting in renewable energy grid based on bi-directional long short-term memory network considering feature selection // Automation of Electric Power Systems. – 2021; 45(3):166-173. Doi: 10.7500/AEPS20200202002

14. Morais S., Aquila G., de Faria, D. et al. Short-term load forecasting using neural networks and global climate models: An application to a large-scale electrical power system // Applied Energy. – 2023; 348:121439. Doi: 10.1016/j.apenergy.2023.121439.

15. Ahranjani K., Beiraghi M., Ghanizadeh R. Short time load forecasting for Urmia city using the novel CNN-LTSM deep learning structure // Electr Eng. – 2025; 107:1253-1264. Doi: 10.1007/s00202-024-02361-4

16. Shuang R., Kai Y., Jicai S. et al. Short-term Power Load Forecasting Based on CNN-BiGRU-Attention // J. Electr. Eng. – 2024; 19:344-350. Doi: 10.11985/2024.01.037

17. Mounir N., Ouadi H, Jrhilifa I. Short-term electric load forecasting using an EMD-BI-LSTM approach for smart grid energy management system // Energy and Buildings. – 2023; 288:113022. Doi: 10.1016/j.enbuild.2023.113022.

18. Zhou Y., Su Z., Gao K. et al. A short-term electricity load forecasting method integrating empirical modal decomposition with SAM-LSTM // Frontiers in Energy Research. – 2024; 12:1423692. Doi: 10.3389/fenrg.2024.1423692.

19. Su Z., Zeng J., Liu J. A Short-Term Power Load Forecasting Approach Based on EMD-SSA-LSTM // Journal of Physics: Conference Series. – 2024; 2774-012005. Doi: 10.1088/1742-6596/2774/1/012005.

20. Lotfipoor A., Patidar S., Jenkins P. Deep neural network with empirical mode decomposition and Bayesian optimisation for residential load forecasting // Expert Systems with Applications. – 2024; 237: Part A, 121355. Doi: 10.1016/j.eswa.2023.121355.

21. Alberg D., Last M. Short-term load forecasting in smart meters with sliding window-based ARIMA algorithms // Vietnam J Comput Sci. – 2018; 5:241-249. Doi: 10.1007/s40595-018-0119-7

22. Zheng Z., Chen H., Luo X. A Kalman filter-based bottom-up approach for household short-term load forecast // Applied Energy. – 2019; 250:882-894. Doi: 10.1016/j.apenergy.2019.05.102

23. Wang Y., Sun S., Chen X. et al. Short-term load forecasting of industrial customers based on SVMD and XGBoost // International journal of electrical power & energy systems. – 2021; 129:106830. Doi: 10.1016/j.ijepes.2021.106830

24. Zhang L., Jánošík D. Enhanced short-term load forecasting with hybrid machine learning models: CatBoost and XGBoost approaches // Expert systems with applications. – 2024; 241:122686. Doi: 10.1016/j.eswa.2023.122686

25. Li K., Huang W., Hu G. et al. Ultra-short term power load forecasting based on CEEMDAN-SE and LSTM neural network // Energy and Buildings. – 2023; 279:112666. Doi: 10.1016/j.enbuild.2022.112666

26. Ran P., Dong K., Liu X. et al. Short-term load forecasting based on CEEMDAN and Transformer // Electric power systems research. – 2023; 214: part A, 108885. Doi: 10.1016/j.epsr.2022.108885

27. Luo H., Zhang H., Wang J. Ensemble power load forecasting based on competitive-inhibition selection strategy and deep learning // Sustainable energy technologies and assessments. 2022, 51: 101940. Doi: 10.1016/j.seta.2021.101940

28. Cui J., Kuang W., Geng K. et al. Advanced Short-Term Load Forecasting with XGBoost-RF Feature Selection and CNN-GRU // Processes. – 2024; 12(11):2466. Doi: 10.3390/pr12112466

29. Asiri M., Aldehim G., Alotaibi F. et al. Short-Term Load Forecasting in Smart Grids Using Hybrid Deep Learning in IEEE Access. – 2024; 12:23504-23513. Doi: 10.1109/ACCESS.2024.3358182.

30. Trindade A. ElectricityLoadDiagrams20112014. UCI Machine Learning Repository [Data set]. – 2015. https://doi.org/10.24432/C58C86.

31. IPMA, n. d. Long data series (Séries longas): Lisboa/Geofísico station (daily Tmin, Tmean, Tmax) [Data set]. Instituto Português do Mar e da Atmosfera. Accessed 12 Feb 2026. https://www.ipma.pt/en/oclima/series.longas/?loc=Lisboa%2FGeof%C3%ADsico&type=raw&utm_source=chatgpt.com

32. Al-Bossly A. Metaheuristic Optimization with Deep Learning Enabled Smart Grid Stability Prediction // Computers, Materials & Continua. – 2023; 75(3):6395-6408. Doi:10.32604/cmc.2023.028433

33. Huang E., Shen Z., Long R. et al. The empirical model decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis // Proceedings of the Royal Society of London Series A: mathematical, physical and engineering sciences. – 1998; 454(1971): 903-995. Doi: 10.1098/rspa.1998.0193

34. Yin C., Wei N., Wu J. et al. An Empirical Mode Decomposition-Based Hybrid Model for Sub-Hourly Load Forecasting // Energies. – 2024; 17(2):307. Doi: 10.3390/en17020307

35. Tian F., Fan X., Wang R. et al. A power forecasting method for ultra-short-term photovoltaic power generation using transformer model // Math. Probl. Eng. – 2022 (2022). Doi: 10.1155/2022/9421400

36. Roy S., Mehera R., Pal K. et al. Hyperparameter optimization for deep neural network models: a comprehensive study on methods and techniques // Innovations Syst Softw Eng. – 2025; 21:789-800. Doi: 10.1007/s11334-023-00540-3.

37. Deb K., Pratap A., Agarwal S. et al. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation. – 2002; 6:182-197. Doi: 10.1109/4235.996017

38. Ibrahim M., Harkouss F., Biwole P. et al. Multi-objective hyperparameter optimization of artificial neural network in emulating building energy simulation // Energy and Buildings. 2025; 337:115643. Doi: 10.1016/j.enbuild.2025.115643

39. Nti K., Teimeh M., Nyarko-Boateng O. et al. Electricity load forecasting: a systematic review // Journal of Electrical Systems and Inf Technol. – 2020; 7(13). Doi: 10.1186/s43067-020-00021-8.

40. Makridakis S., Spiliotis E., Assimakopoulos V. The M4 Competition: Results, findings, conclusion and way forward // International Journal of Forecasting. – 2018; 34(4):802-808. Doi: 10.1016/j.ijforecast.2018.06.001