Linear-Gompertz Model-Based Regression of Photovoltaic Power Generation by Satellite Imagery-Based Solar Irradiance
2.1. Solar Irradiance Data
2.2. PV Power Generation Data
3.1. Regression Model
3.1.1. Gompertz Function
3.1.2. Linear-Gompertz Conjoint Function
3.2. Evaluation of Regression
4. Results and Discussions
4.1. Comparison of the Regression Models
4.2. Gompertz Model Coefficients
4.3. Validation of the Model
- The Linear-Gompertz model successfully expressed the sigmoidal characteristics of the PV system performance countrywide as a single function of GHI, which is the simplest regression form adequate for machine learning needed to develop a forecasting model. The nonphysical trend of the Gompertz model in the low GHI range was fixed by combining a linear equation having the same slope at the conjoint point. The fitness of the Linear-Gompertz regression was R2 = 0.85, and the nRMSE of normalized power output ratio was 0.09.
- The three Gompertz coefficients A, B, and C were calculated by year, by season, and by province, and it was found that they had normal distributions and equivariances, meaning that the Gompertz coefficients were the general parameters for the entire country. Moreover, the Gompertz coefficient of the growth rate C showed a strong correlation (R2 = 0.53) with the capacity factor of the PV power plant. Therefore, it was possible to derive the capacity factor equation as a function of A, B, and C, that showed a fitness of R2 = 0.88.
- In order to use the Linear-Gompertz model to obtain South Korea’s general PV performance curve for PV power forecasting, it will be necessary to increase the fitness of the model to over R2 > 0.9 by including significant environmental variables such as ambient temperature. Future research will consist of securing long-term PV power output data and analyzing the aging effect of the PV panel to correct the degradation effect. In addition, the accuracy of the Linear-Gompertz model will be improved by calculating and applying the POA, the primary input variable, instead of GHI. To that end, the solar irradiance decomposition algorithm should be improved in the UASIBS-KIER model, and verification and compensation steps using actual measurement data should be implemented in advance.
- Because the solar irradiance in most regions of South Korea is less than 1300 W/m2, an additional verification of the conditions of high solar irradiance is needed to apply this result to regions with high solar irradiance. In addition, since PV power generation is significantly influenced by climate conditions, there will be some differences compared to regions in which the climate zone is completely different from that of South Korea. However, South Korea has four distinct seasons and a wide temperature distribution ranging from −15 °C to +35 °C throughout the year. Thus, the effect of climate conditions on PV power generation is relatively significant, which means the prediction error that occurred when the present regression model was applied to other climate zone is expected to be smaller in a relative sense.
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|Province||Sampling||PV Plants (>50 kWp)||Total No. of PV Plants|
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Vilanova, A.; Kim, B.-Y.; Kim, C.K.; Kim, H.-G. Linear-Gompertz Model-Based Regression of Photovoltaic Power Generation by Satellite Imagery-Based Solar Irradiance. Energies 2020, 13, 781. https://doi.org/10.3390/en13040781
Vilanova A, Kim B-Y, Kim CK, Kim H-G. Linear-Gompertz Model-Based Regression of Photovoltaic Power Generation by Satellite Imagery-Based Solar Irradiance. Energies. 2020; 13(4):781. https://doi.org/10.3390/en13040781Chicago/Turabian Style
Vilanova, Alba, Bo-Young Kim, Chang Ki Kim, and Hyun-Goo Kim. 2020. "Linear-Gompertz Model-Based Regression of Photovoltaic Power Generation by Satellite Imagery-Based Solar Irradiance" Energies 13, no. 4: 781. https://doi.org/10.3390/en13040781