Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression
Abstract
:Featured Application
Abstract
1. Introduction
2. The Proposed Logistic Functions Based on Quantile Regression
2.1. Logistic Functions
2.2. Quantile Regression
2.3. Logistic Functions Based Quantile Regression
2.4. Parameter Optimization Algorithms
2.4.1. Particle Swarm Optimization
2.4.2. Whale Optimization Algorithm
2.4.3. Adam Optimization Algorithm
3. WTPC Modelling with the Proposed QRLF
3.1. Outlier Filtering
- Preliminary data processing
- 2.
- Power curve fitting
- 3.
- Threshold setting
- 4.
- Outlier filtering
3.2. WTPC Modelling with the Proposed QRLF
4. Case Study
4.1. Data Sources
4.2. Evaluation Metrics
4.2.1. Deterministic Evaluation Metrics
4.2.2. Probabilistic Evaluation Metrics
4.3. Experimental Results
4.3.1. Results for Parameter Selection and Optimization
4.3.2. Results for Outlier Filtering
4.3.3. Results for WTPC Modelling
4.4. Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ANFIS | Adaptive Neural-fuzzy Inference Systems |
CI | Confidence interval |
CSI | Cubic Spline Interpolation |
GP | Gaussian process |
KNN | K-Nearest Neighbors |
LF | Logistic function |
MAPE | Mean absolute percentage error |
nPL | n-parameter logistic function |
NRMSE | Normalized root mean square error |
PICP | Prediction intervals coverage probability |
PINAW | Prediction intervals normalized average width |
PR | Polynomial Regression |
PSO | Particle swarm optimization |
QR | Quantile regression |
QRLF | Quantile regression based on logistic function |
QRNN | Quantile regression neural network |
RVM | Relevance vector machine |
SVM | Support Vector Machine |
WF | Wind farm |
WOA | Whale optimization algorithm |
WTPC | Wind turbine power curve |
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Parameter Name | Value | Attribute |
---|---|---|
Operation mode | 32 (Normal) | State parameters |
Power generation | [0.01Prated, 1.05Prated] | Operation parameters |
Wind speed | [vcut-in, vcut-out] | |
Rotor speed | [6 r/min, 12 r/min] | |
Pitch angle | [0°, 20°] |
Attributes | WF1 | WF2 | WF3 |
---|---|---|---|
Hub height | 80 m | 84 m | 90 m |
Rotor diameter | 108 m | 111 m | 171 m |
Rated power | 2 MW | 2 MW | 5 MW |
Rated wind speed | 9.5 m/s | 12 m/s | 10.9 m/s |
Cut-in wind speed | 3 m/s | 3 m/s | 3 m/s |
Fitting Method | Optimization Algorithm | WT02 | WT08 | WT10 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
MAPE | NRMSE | NC90% | MAPE | NRMSE | NCα | MAPE | NRMSE | NC90% | ||
4P-QRLF | PSO | 18.89% | 2.04% | 0.53 | 9.12% | 1.77% | 0.51 | 10.30% | 1.94% | 0.44 |
WOA | 19.10% | 1.98% | 0.62 | 9.31% | 1.81% | 0.47 | 9.90% | 1.49% | 0.46 | |
Adam | 38.50% | 2.40% | 0.72 | 22.25% | 2.37% | 0.49 | 20.99% | 2.33% | 0.57 | |
5P-QRLF | PSO | 12.57% | 1.52% | 0.44 | 7.42% | 1.49% | 0.39 | 7.00% | 1.37% | 0.38 |
WOA | 9.92% | 1.92% | 0.57 | 7.31% | 1.61% | 0.43 | 8.23% | 1.56% | 0.41 | |
Adam | 27.85% | 1.96% | 0.77 | 9.09% | 1.81% | 0.45 | 12.44% | 1.86% | 0.51 |
Algorithm | Control Parameters |
---|---|
PSO | particle number = 20; inertia weight (ω) = 0.8; acceleration constants (c1, c2) = 2 |
WOA | search agent number (whales papulation) = 40 |
Adam | exponential decay rates (γ1, γ2) = 0.9; learning rate = 0.0002 |
Wind Farm | Methods | MAPE | NRMSE | PICP90% | PINAW90% | NC90% |
---|---|---|---|---|---|---|
WF1 (2 MW) | 5PL | 6.26% | 1.68% | N/A | N/A | N/A |
RVM | 5.73% | 1.62% | 0.91 | 0.46 | 0.49 | |
QRNN | 7.93% | 1.83% | 0.83 | 0.31 | 0.38 | |
QRLF | 5.95% | 1.65% | 0.82 | 0.27 | 0.29 | |
WF2 (2 MW) | 5PL | 11.44% | 2.21% | N/A | N/A | N/A |
RVM | 9.12% | 2.19% | 0.90 | 0.81 | 0.89 | |
QRNN | 15.88% | 2.34% | 0.79 | 0.43 | 0.54 | |
QRLF | 9.28% | 2.19% | 0.91 | 0.36 | 0.39 | |
WF3 (5 MW) | 5PL | 10.28% | 1.72% | N/A | N/A | N/A |
RVM | 8.05% | 1.65% | 0.88 | 0.61 | 0.69 | |
QRNN | 13.99% | 2.49% | 0.61 | 0.39 | 0.67 | |
QRLF | 8.84% | 1.72% | 0.93 | 0.39 | 0.42 |
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Jing, B.; Qian, Z.; Zareipour, H.; Pei, Y.; Wang, A. Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression. Appl. Sci. 2021, 11, 3048. https://doi.org/10.3390/app11073048
Jing B, Qian Z, Zareipour H, Pei Y, Wang A. Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression. Applied Sciences. 2021; 11(7):3048. https://doi.org/10.3390/app11073048
Chicago/Turabian StyleJing, Bo, Zheng Qian, Hamidreza Zareipour, Yan Pei, and Anqi Wang. 2021. "Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression" Applied Sciences 11, no. 7: 3048. https://doi.org/10.3390/app11073048
APA StyleJing, B., Qian, Z., Zareipour, H., Pei, Y., & Wang, A. (2021). Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression. Applied Sciences, 11(7), 3048. https://doi.org/10.3390/app11073048