Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques
Abstract
:1. Introduction
2. Literature Review on Load Uncertainty Forecasting
2.1. Interval Forecasting
2.2. Probability Density Forecasting
3. Basic Theory of the Proposed Methodology
3.1. K-Means Clustering Method
3.2. Deterministic Forecasting Model Based on Salp Swarm Algorithm (SSA)-Least Square Support Vector Machine (LSSVM)
3.3. Kernel Density Estimation Model
4. The Framework of the Proposed Method
5. Empirical Results and Analysis
5.1. Data Sorting and Preprocessing
5.2. K-Means Clustering Results
5.3. SSA-LSSVM Forecasting Results
5.4. Probability Density Forecasting Results
5.5. Results and Discussion
- (1).
- By comparing model 1 and model 2, it can be found that the model optimized by SSA algorithm can significantly improve the interval coverage and reduce the interval average width. This is because the optimized model can effectively find the parameter values in the LSSVM model, avoiding the subjectivity of artificially given parameters, and thus improving the model forecasting performance.
- (2).
- By comparing model 1 and model 3, it can be found that, in comparison with the traditional parameter estimation, the non-parametric estimation method can effectively improve the interval coverage and reduce the interval average width. This is because the traditional parameter estimation method needs to make assumptions about the probability density function in advance when estimating the error distribution of point forecasting. In contrast, the non-parametric estimation method can better reflect the true distribution of the error, and the fitting effect is better.
- (3).
- By comparing model 1 and model 4, it can be found that the two models perform similarly on the interval coverage and interval average width. On the interval average width index, model 1 is slightly better than model 4, but the difference is not obvious, indicating that the selection of the kernel function does not show a greater difference in the improvement of the model forecasting performance relative to the improvement of other parts of the model.
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Unit | N | Max. | Min. | Mean | S.D. | |
---|---|---|---|---|---|---|
Load | GW | 2040 | 163.9060 | 61.4797 | 112.0106 | 23.5318 |
Temperature | °C | 2040 | 33.1 | −3.7 | 14.2171 | 7.5424 |
Humidity | g/m3 | 2040 | 97 | 11 | 50.9137 | 23.6818 |
Wind speed | m/s | 2040 | 8.6 | 0 | 1.8655 | 1.3130 |
Air pressure | kPa | 2040 | 1030.8 | 995.5 | 1015.8346 | 6.3951 |
Rainfall | mm | 2040 | 3.6 | 0 | 0.0153 | 0.1819 |
Air quality level | / | 2040 | 310 | 9 | 61.1656 | 51.2375 |
N | Max. | Min. | Mean | S.D. | |
---|---|---|---|---|---|
Load | 2040 | 1 | 0 | 0.4933 | 0.2297 |
Temperature | 2040 | 1 | 0 | 0.4869 | 0.2050 |
Humidity | 2040 | 1 | 0 | 0.4641 | 0.2754 |
Wind speed | 2040 | 1 | 0 | 0.2169 | 0.1527 |
Air pressure | 2040 | 1 | 0 | 0.5761 | 0.1812 |
Rainfall | 2040 | 1 | 0 | 0.0043 | 0.0505 |
Air quality level | 2040 | 1 | 0 | 0.1733 | 0.1702 |
Confidence Level/% | ||||
---|---|---|---|---|
Non-Holidays | Holidays | Non-Holidays | Holidays | |
80 | 93.33 | 90.28 | 3.5597 | 4.0156 |
85 | 96.67 | 95.83 | 3.812 | 4.2932 |
90 | 100 | 98.61 | 4.7921 | 5.4212 |
Model | Confidence Level/% | ||||
---|---|---|---|---|---|
Non-Holidays | Holidays | Non-Holidays | Holidays | ||
Model 1 | 80 | 93.33 | 90.28 | 3.5597 | 4.0156 |
85 | 96.67 | 95.83 | 3.812 | 4.2932 | |
90 | 100 | 98.61 | 4.7921 | 5.4212 | |
Model 2 | 80 | 88.33 | 86.11 | 3.7352 | 4.4373 |
85 | 94.17 | 91.67 | 4.0689 | 4.7481 | |
90 | 95.83 | 93.06 | 4.9857 | 5.8837 | |
Model 3 | 80 | 87.5 | 83.33 | 4.7498 | 4.9215 |
85 | 91.67 | 86.11 | 4.7838 | 4.9375 | |
90 | 95.83 | 90.28 | 5.5247 | 6.0786 | |
Model 4 | 80 | 95.83 | 90.28 | 3.5172 | 3.8225 |
85 | 95.83 | 94.44 | 3.9034 | 4.6896 | |
90 | 100 | 98.61 | 4.7943 | 5.6759 |
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Li, F.; Zhang, S.; Li, W.; Zhao, W.; Li, B.; Zhao, H. Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques. Sustainability 2019, 11, 6954. https://doi.org/10.3390/su11246954
Li F, Zhang S, Li W, Zhao W, Li B, Zhao H. Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques. Sustainability. 2019; 11(24):6954. https://doi.org/10.3390/su11246954
Chicago/Turabian StyleLi, Fuqiang, Shiying Zhang, Wenxuan Li, Wei Zhao, Bingkang Li, and Huiru Zhao. 2019. "Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques" Sustainability 11, no. 24: 6954. https://doi.org/10.3390/su11246954
APA StyleLi, F., Zhang, S., Li, W., Zhao, W., Li, B., & Zhao, H. (2019). Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques. Sustainability, 11(24), 6954. https://doi.org/10.3390/su11246954