Modeling and forecasting of electricity energy consumption using an optimized Stacking ensemble machine learning model based on particle swarm optimization

Document Type : Original Article

Authors

1 PhD Candidate, Department of Energy Conversion, Faculty of 1 M.Sc. Student in Energy Systems Engineering, Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran

2 Master of Business Administration, Department of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran

3 Assistant Professor, Department of Renewable Energy Engineering, Faculty of Energy Engineering, Shahid Beheshti University, Tehran, Iran

10.22059/ses.2026.412276.1222

Abstract

In this study, a data-driven framework is developed to model  and forecast electricity energy consumption (EEC) in countries with diverse economic, social, and climate characteristics. Five input variables including population (POP), gross domestic product (GDP), energy imports (IMP), energy exports (EXP), and annual average air temperature (TEMP) are used to model EEC. Annual data from 1991 to 2020 are employed for training and evaluation. Four machine learning algorithms, namely ANN, Ridge, Stack, and Stack-PSO, are implemented and assessed using MSE, MAE, R2, and MAPE. The results show that while the standalone ANN and Ridge models achieve acceptable accuracy, they exhibit lower stability and weaker generalization compared with ensemble-based approaches. The Stack model, constructed by combining the outputs of ANN and Ridge, yields noticeable improvements across the error metrics. The results demonstrated that the Stack-PSO model consistently outperformed the other models across the majority of cases. The R2 values for this model ranged from 0.974 to 0.997 across the surveyed countries. The lowest MSE was recorded for China at 0.00015, while for Iran, the Stack-PSO model achieved an MSE of 0.00042 and an R2 of 0.996. Furthermore, the lowest MAPE was observed in the United States at 2.5%, underscoring the high precision of the proposed model in minimizing forecasting errors. Subsequently, the superior model was employed to forecast electrical energy consumption up to the 2035 horizon. The findings indicate a generally increasing consumption trend in most countries; however, growth intensity varied significantly, with some cases exhibiting a moderate growth pattern or approaching relative stability.

Keywords

Main Subjects

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Journal of sustainable Energy Systems
Volume 5, Issue 3
July 2026
Pages 579-600

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