A Log-Logistic Predictor for Power Generation in Photovoltaic Systems
Abstract
:1. Introduction
1.1. Impact of Soiling on Power Generation in Photovoltaic Systems
1.2. Related Work
1.3. Statistical Methodology for Soiling Estimation
2. Materials and Methods
2.1. Estimation of Accumulated Particle Mass
- M is the accumulated mass in the time interval (g/);
- t is the time interval in seconds;
- v is the particulate deposition speed (g/m);
- C is the particulate concentration in the environment (g/);
- is the PV module angle;
- 10−2.5 is the index of the particles from 10 μm to 2.5 μm;
- 2.5 is the index of particles less than 2.5 μm.
2.2. Dataset and Statistical Modeling
2.3. Nonlinear Mixed-Effects Model
3. Results and Discussion
3.1. Fitted Model
3.2. Model Validation
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AIC | Akaike information criterion |
ANN | Artificial neural network |
AWS | Amazon Web Services |
BIC | Bayesian information criterion |
BNN | Bayesian neural network |
CI | Cleanness index |
CNN | Convolutional neural network |
FAMEZ | Faculty of Veterinary Medicine and Animal Science |
MENA | Middle East and North Africa |
MLR | Multilinear regression |
MPPT | Maximum power point tracker |
MSE | Mean squared error |
NLME | Nonlinear mixed-effects |
p-Si | Polycrystalline silicon |
PV | Photovoltaic |
PM1.0 | Particles less than 1.0 μm in diameter |
PM2.5 | Particles less than 2.5 μm in diameter |
PM4.0 | Particles less than 4.0 μm in diameter |
PM10.0 | Particles less than 10.0 μm in diameter |
PRM | Polynomial regression model |
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Variable | Measurements | ||||||
---|---|---|---|---|---|---|---|
Min. | 1st Q. | Median | Average | S. Deviation | 3rd Q. | Max. | |
Power | 2.77 | 997.19 | 3616.73 | 3858.56 | 2882.368 | 6528.59 | 8475.12 |
Irradiance | 0.10 | 118.60 | 420.40 | 470.50 | 362.37 | 799.30 | 1197.20 |
Temperature | 19.15 | 27.63 | 31.36 | 30.80 | 4.67649 | 34.71 | 39.34 |
Accumulated Mass | 0.1387 | 0.1971 | 0.2599 | 0.2768 | 0.08948 | 0.3720 | 0.3920 |
Variable | Variable | ||
---|---|---|---|
Irradiance | Temperature | Accumulated Mass | |
Irradiance | 1 | 0.6754 | −0.2226 |
Temperature | 0.6754 | 1 | −0.5231 |
Accumulated Mass | −0.2226 | −0.5231 | 1 |
Criteria | Model | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
MSE | 0.0037 | 0.3334 | 0.2181 | 0.2998 | 0.2338 | 0.2056 | 0.218 | 0.2119 | 0.1889 | 0.0007 |
AIC | −4495.575 | 2834.605 | 2245.463 | 2730.587 | 2351.410 | 2191.774 | 2248.816 | 2234.820 | 2090.743 | −15,395.292 |
BIC | −4474.002 | 2856.177 | 2272.429 | 2757.554 | 2378.466 | 2229.527 | 2286.569 | 2272.573 | 2144.675 | −15,325.179 |
Parameter | Estimate | Std. Error | DF | t-Value | p-Value |
---|---|---|---|---|---|
6.7092 | 0.2823 | 1598 | 23.7691 | 0.0000 | |
0.6577 | 0.0210 | 1598 | 31.3600 | 0.0000 | |
0.0696 | 0.0383 | 1598 | 1.8162 | 0.0695 | |
4.9754 | 0.2696 | 1598 | 18.4537 | 0.0000 | |
−0.4143 | 0.0162 | 1598 | −25.6015 | 0.0000 | |
0.1148 | 0.0549 | 1598 | 2.0936 | 0.0365 | |
0.0009 | 0.0001 | 1598 | 9.4311 | 0.0000 |
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Souza, G.; Santos, R.; Saraiva, E. A Log-Logistic Predictor for Power Generation in Photovoltaic Systems. Energies 2022, 15, 5973. https://doi.org/10.3390/en15165973
Souza G, Santos R, Saraiva E. A Log-Logistic Predictor for Power Generation in Photovoltaic Systems. Energies. 2022; 15(16):5973. https://doi.org/10.3390/en15165973
Chicago/Turabian StyleSouza, Guilherme, Ricardo Santos, and Erlandson Saraiva. 2022. "A Log-Logistic Predictor for Power Generation in Photovoltaic Systems" Energies 15, no. 16: 5973. https://doi.org/10.3390/en15165973