Forecasting Photovoltaic Power Generation with a Stacking Ensemble Model
Abstract
:1. Introduction
- An ensemble stacking model (Stack-ETR) was developed that can be utilized as a baseline model for one-day-ahead PV power output forecasts, utilizing metrological data without heavy hyperparameter tuning.
- A performance evaluation of the proposed Stack-ETR was conducted on three different actual Malaysian PV systems over four years (2018 to 2021).
- In addition, the proposed model was compared with existing models and works to highlight the superiority of the proposed model.
2. Methodology
2.1. The Machine Learning Models
2.1.1. Bagging Ensemble Model
Random Forest Regressor (RFR)
Extra Trees Regressor (ETR)
2.1.2. Boosting Ensemble Model
Extreme Gradient Boosting (XGBoost)
Adaptive Boosting (AdaBoost)
2.1.3. Stack Generalization
Model Name | Base Learners | Meta-Learner |
---|---|---|
Stack-RFR | ETR, XGBoost, AdaBoost | RFR |
Stack-ETR | RFR, XGBoost, AdaBoost | ETR |
Stack-XGBoost | RFR, ETR, AdaBoost | XGBoost |
Stack-AdaBoost | RFR, ETR, XGBoost | AdaBoost |
2.2. Performance Metrics Utilized to Assess the Model’s Effectiveness
2.3. Data Preparation and Partitioning
2.4. A Summary of the Grid-Connected PV Systems Utilized for Forecasting
3. Results and Discussions
3.1. Evaluation of Stack-ETR for Forecasting Thin-Film PV System Output Power
3.2. Evaluation of Stack-ETR for Forecasting Monocrystalline PV System Output Power
3.3. Evaluation of Stack-ETR for Forecasting Polycrystalline PV System Output Power
3.4. Discussion
3.5. Comparative Studies
4. Conclusions
- For all investigated PV systems, the proposed Stack-ETR model consistently outperformed earlier models in varied climates, showing that the proposed model is superior and acceptable. Consequently, extending the model’s predictions to other regions is simple.
- Due to its efficacy in forecasting daily PV output power, Stack-ETR could potentially be applied to other studies, such as global horizontal irradiance, electricity consumption, and wind speed and power.
- A real-time evaluation of the proposed model’s performance and practical applicability to building energy management systems would also be interesting.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
Acronyms | |
PV | Photovoltaic |
RFR | Random Forest Regressor |
XGBoost | Extreme Gradient Boosting |
AdaBoost | Adaptive Boosting |
ETR | Extra Trees Regressor |
TF | Thin-Film |
MC | Monocrystalline |
PC | Polycrystalline |
CO2 | Carbon Dioxide |
ML | Machine learning |
AR | Auto-Regression |
ARMA | Auto-Regressive Moving Average |
ARMAX | Autoregressive Moving Average with Exogenous Variable |
LR | Linear Regression |
RF | Random Forest |
GBRT | Gradient Boosting Regression Trees |
RNN | Recurrent Neural Network |
ANN | Artificial Neural Network |
PEARL | Power Electronics and Renewable Energy Research Laboratory |
LSTM | Long Short-Term Memory |
DT | Decision Trees |
DTR | Decision Trees Regression |
OOB | Out-of-Bag |
CART | Classification and Regression Trees |
ELM | Extreme Learning Machine |
RMSE | Root Mean Square Error |
MSE | Mean Square Error |
R2 | Coefficient of Determination |
MAE | Mean Absolute Error |
SEDA | Sustainable Energy Development Authority |
Nomenclature | |
Actual Values | |
Forecasted Values | |
Average of the Actual | |
The Collected Data | |
The Normalized Collected Data | |
μ | The Mean Value |
σ | Standard Deviation |
H | Dataset’s Size |
Value of Each Datapoint in the Dataset | |
Actual Data Forecasted |
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Ref | Model | Input Variables | Horizon | PV Module | Dataset Duration | Target | ||
---|---|---|---|---|---|---|---|---|
MC | PC | TF | ||||||
[29] | Stacking-GBDT | Light intensity, wind speed and direction, weather temperature, PV module temperature, transfer efficiency | Ultra-short-term (5 min ahead) | Not mentioned | 4 years | PV power output | ||
[32] | XGBoost-DNN | Temperature, pressure, wind speed and direction, relative humidity, month number, clear sky index, time | Short-term (1 h ahead) | Not included | 10 years | Solar irradiance | ||
[33] | RNN-LSTM | Time, solar irradiance, wind speed, ambient temperature, PV module temperature, actual output power | Short-term (1 h ahead) | ✓ | ✓ | ✓ | 4 years | PV power output |
[34] | ELM | Solar irradiance, wind speed, ambient temperature, PV module temperature, actual output power | Short-term (1 day ahead and 1 h ahead) | ✓ | ✓ | ✓ | 1 year | PV power output |
[31] | LSTM-RNN | Actual output power | Short-term (1 h ahead) | Not mentioned | 1 year | PV power output | ||
[35] | LSTM | Actual output power and sky images | Ultra-short-term (1, 2, 5, 10 min ahead) | Not mentioned | Not mentioned | PV power output | ||
[36] | DPNN | Temperature, wind speed and direction, relative humidity, sky condition, time, solar irradiance, sea level pressure | Short-term (1-9 h ahead) | ✓ | ✕ | ✕ | 2 weeks | PV power output |
[37] | DSE-XGB | Hour, day, month, previous day, same-time historical PV generation, previous 15 min, previous hour, solar irradiance, relative humidity, temperature | Ultra-short and short-term (15 min and 1 h ahead) | ✓ | ✕ | ✕ | 3 years | PV power output |
Proposed Research | Stacking-ETR | Time, solar irradiance, wind speed, ambient temperature, PV module temperature, actual output power | Short-term (1 day ahead) | ✓ | ✓ | ✓ | 4 years | PV power output |
Model | Thin-Film | |||
---|---|---|---|---|
MSE (Wh/m2) | RMSE (Wh/m2) | MAE (Wh/m2) | R2 | |
RFR | 1967.3 | 44.35 | 33.26 | 0.9949 |
XGB | 2013.01 | 44.87 | 33.64 | 0.9947 |
DTR | 3038.29 | 55.12 | 41.01 | 0.9921 |
ADA | 2622.19 | 51.21 | 38.33 | 0.9931 |
ETR | 2395.43 | 48.94 | 36.38 | 0.9937 |
Stack-RFR | 1826.15 | 42.73 | 31.63 | 0.9952 |
Stack-ETR | 1365.16 | 36.95 | 25.87 | 0.9964 |
Stack-ADA | 1755.79 | 41.9 | 30.88 | 0.9954 |
Stack-XGB | 1575.48 | 39.69 | 28.8 | 0.9959 |
Model | Monocrystalline | |||
---|---|---|---|---|
MSE (Wh/m2) | RMSE (Wh/m2) | MAE (Wh/m2) | R2 | |
RFR | 939.12 | 30.65 | 23.68 | 0.9711 |
XGB | 1038.73 | 32.23 | 25.09 | 0.968 |
DTR | 1933.63 | 43.97 | 33.04 | 0.9405 |
ADA | 1213.94 | 34.84 | 30.1 | 0.9627 |
ETR | 950.04 | 30.82 | 24.93 | 0.9708 |
Stack-RFR | 414.43 | 20.36 | 14.38 | 0.9872 |
Stack-ETR | 339.6 | 18.43 | 13.16 | 0.9896 |
Stack-ADA | 375.01 | 19.37 | 13.74 | 0.9885 |
Stack-XGB | 383.74 | 19.59 | 13.91 | 0.9882 |
Model | Polycrystalline | |||
---|---|---|---|---|
MSE (Wh/m2) | RSME (Wh/m2) | MAE (Wh/m2) | R2 | |
RFR | 1518.1 | 38.96 | 27.57 | 0.9898 |
XGB | 1163.5 | 34.11 | 23.37 | 0.9922 |
DTR | 1340.41 | 36.61 | 27.85 | 0.991 |
ADA | 1261.89 | 35.52 | 27.05 | 0.9915 |
ETR | 1027.2 | 32.05 | 24.53 | 0.9931 |
Stack-RFR | 619.92 | 24.9 | 17.39 | 0.9958 |
Stack-ETR | 533.33 | 23.09 | 14.5 | 0.9964 |
Stack-ADA | 604.05 | 24.58 | 16.76 | 0.9959 |
Stack-XGB | 574.4 | 23.97 | 15.8 | 0.9961 |
Predicting Method | Year | Ref. | RMSE (Wh/m2) | MAE (Wh/m2) |
---|---|---|---|---|
Stack-ETR (TF) | - | Present Study | 37.37 | 23.36 |
Stack-ETR (MC) | 13.95 | 8.79 | ||
Stack-ETR (PC) | 20.41 | 12.24 | ||
Stack-GBDT | 2022 | [29] | 47.7826 | 106.0726 |
RNN-LSTM (TF) | 2022 | [33] | 39.2 | - |
RNN-LSTM (MC) | 19.78 | - | ||
RNN-LSTM (PC) | 26.85 | - | ||
XGBoost-DNN | 2021 | [32] | 51.35 | - |
DPNN | 2020 | [36] | 52.8 | - |
Kmeans-AE-CNN-LSTM | 2020 | [52] | 45.11 | - |
LSTM-RNN | 2019 | [31] | 82.15 | - |
LSTM | 2018 | [35] | 139.3 | - |
ELM (TF) | 2018 | [34] | 90.41 | - |
ELM (MC) | 59.93 | - | ||
ELM (PC) | 54.96 | - |
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Abdellatif, A.; Mubarak, H.; Ahmad, S.; Ahmed, T.; Shafiullah, G.M.; Hammoudeh, A.; Abdellatef, H.; Rahman, M.M.; Gheni, H.M. Forecasting Photovoltaic Power Generation with a Stacking Ensemble Model. Sustainability 2022, 14, 11083. https://doi.org/10.3390/su141711083
Abdellatif A, Mubarak H, Ahmad S, Ahmed T, Shafiullah GM, Hammoudeh A, Abdellatef H, Rahman MM, Gheni HM. Forecasting Photovoltaic Power Generation with a Stacking Ensemble Model. Sustainability. 2022; 14(17):11083. https://doi.org/10.3390/su141711083
Chicago/Turabian StyleAbdellatif, Abdallah, Hamza Mubarak, Shameem Ahmad, Tofael Ahmed, G. M. Shafiullah, Ahmad Hammoudeh, Hamdan Abdellatef, M. M. Rahman, and Hassan Muwafaq Gheni. 2022. "Forecasting Photovoltaic Power Generation with a Stacking Ensemble Model" Sustainability 14, no. 17: 11083. https://doi.org/10.3390/su141711083