# A Genetic Algorithm Approach as a Self-Learning and Optimization Tool for PV Power Simulation and Digital Twinning

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{mod}). In contrast, due to costs, such measured data is scarce within small-scale and household PV systems.

- Offer a very accurate GA approach to learn and optimize unknown basic parameters of a PV system based on measured PV power data.
- Show the impact different data set sizes have on digital twinning.
- Create a precise digital twin of a PV system using either all-sky or clear-sky conditions as training data for now-casting purposes.

## 2. Previous Work

#### 2.1. Machine Learning and Optimization in the PV Modelling Domain

#### 2.2. Evaluation Metrics

## 3. Methodology and Data

#### 3.1. Methods

#### 3.1.1. PV System Simulation

#### Irradiance Transposition Mode, Albedo, and AOI Effect

#### DC Power

#### AC Power

#### 3.1.2. PV System Parameters Optimization

- The initialization step creates a vector of different PV plants configurations (members), assigning random values (also known as population) based on the initial value to be optimized (initial parameters), with a randomness percentage defined beforehand. The PV power configuration can differ from several elements or only one.
- In the fitness scoring step, every single PV plant configuration of the population is compared with the monitoring data, evaluated, and a score is assigned based on the loss function defined.
- In the fit selection step, some PV plant configurations of the population are stochastically selected based on their scores; the higher the score, the higher the probability to be selected and passed to the next population.
- In the crossover step, some pairs of PV plant configurations resulting from the fit selection step are selected stochastically and their parameters are randomly combined. Hence, new PV plant configurations are added to the new population.
- In the mutation step, some parameters of the PV plant configurations are mutated due to a mutation probability assigned randomly to each parameter of every PV power plant configuration of the next generation.
- Finally, the next population is repopulated based on the parameters of the best PV plant configuration of the current population. The process stops when the stop criteria have been met; the stop criteria is defined in detail further in this section.

#### Irradiance Transposition Mode, Albedo, and AOI Effect

#### DC Power

_{p}. Second, use cross validation optimization (we evaluate every set of three parameters) to select the best fit for the three parameters from the Heydenreich et al. model, and GA optimization can be used to learn the temperature coefficient.

#### AC Power

_{p}nominal power PV system. Based on the Schmidt and Sauer model, we minimized the deviation between simulated PV power AC and normalized measured PV power using GA. PV power AC is calculated using the parameters optimized beforehand with 1% cabling losses assumed.

#### 3.1.3. Clear-Sky Detection

- We used a Python function called detect_clearsky, available in PVLib library [38], to compare the statistical clear-sky curve based on measured PV power, with actual measured PV power. Hence, we were able to identify the clear-sky-like periods in the time series data set. It is important to mention that the parameters of the Python function were tuned by trial and error based on the input data, as suggested by [18].

#### 3.2. Data Used in This Article

#### 3.2.1. Weather Data

#### 3.2.2. PV Power Measured Data

#### 3.2.3. Initial Parameters

- Nominal power = 1 kW
_{p} - Tilt angle = 25°
- Azimuth angle = 180° (south oriented)
- Albedo = 0.2
- Temperature coefficient = −0.43%/°C
- DC to AC ratio = 1

## 4. Results and Discussion

_{p}.

_{p}and −16.90 W/kW

_{p}, respectively. Only daytime values are considered in both examples.

#### 4.1. PV System Parametrization

_{p}, which is equal to −18% of the reported installed capacity. Figure 7b shows less variability in general, with an MAPD of 10.69% for the worst-case scenario using a training data set of 90 days before. It shows that, it is possible to achieve a mean deviation of less than 10% of the reported installed capacity using clear-sky-like periods as training data.

_{p}, when a loss factor of 0.8%/year for the nominal power is considered.

#### 4.2. Digital Twin Now-Casting

_{p}and 1.53 W/kW

_{p}is feasible. Using the GA proposed here, based on satellite-derived weather data, we can now-cast the PV power of a PV system with higher accuracy than previous publications with a MAPD lower than 6%, without evident seasonal effects. MAPD values above 10% have been reported for previous publications by [4,5,6,7,8].

#### 4.3. Limitations

#### 4.4. Future Directions

## 5. Conclusions

_{p}have been estimated for the digital twin now-casting accuracy of the GA approach of this work.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- International Energy Agency. Trends in Photovoltaic Applications; Technical Report No. IEA PVPS T1-36; International Energy Agency: Paris, France, 2019. [Google Scholar]
- Wood Mackenzie. Ami Global Forecast 2019–2024; Technical Report No. H1 2019; Wood Mackenzie: Edinburgh, UK, 2020. [Google Scholar]
- Mellit, A.; Kalogirou, S.A. Artificial intelligence techniques for photovoltaic applications: A review. Prog. Energy Combust. Sci.
**2008**, 34, 574–632. [Google Scholar] [CrossRef] - Ding, M.; Wang, L.; Bi, R. An ANN-based approach for forecasting the power output of photovoltaic system. Proc. Environ. Sci.
**2011**, 11, 1308–1315. [Google Scholar] [CrossRef][Green Version] - Mandal, P.; Madhira, S.T.S.; Haque, A.U.; Meng, J.; Pineda, R.L. Forecasting power output of solar photovoltaic system using wavelet transform and artificial intelligence techniques. Proc. Comput. Sci.
**2012**, 12, 332–337. [Google Scholar] [CrossRef][Green Version] - Ibrahim, I.A.; Mohamed, A.; Khatib, T. Modeling of photovoltaic array using random forests technique. In Proceedings of the IEEE Conference on Energy Conversion, Johor Bahru, Malaysia, 19–20 October 2015. [Google Scholar]
- Landelius, T.; Andersson, S.; Abrahamsson, R. Modelling and forecasting PV production in the absence of behind-the-meter measurements. Prog. Photovolt Res. Appl.
**2019**, 27, 990–998. [Google Scholar] [CrossRef][Green Version] - Monteiro, C.; Fernandez-Jimenez, L.A.; Ramirez-Rosado, I.J.; Muñoz-Jimenez, A.; Lara-Santillan, P.M. Short-term forecasting models for photovoltaic plants: Analytical vs. soft-computing techniques. Math. Probl. Eng.
**2013**, 2013, 767284. [Google Scholar] [CrossRef][Green Version] - Yona, A.; Senjyu, T.; Saber, A.Y.; Funabashi, T.; Sekine, H.; Kim, C.H. Application of neural network to 24-hour-ahead generating power forecasting for PV system. In Proceedings of the 2008 IEEE Power and Energy Society General Meeting, Pittsburgh, PA, USA, 20–24 July 2008. [Google Scholar]
- Da Silva Fonseca, J.G.; Oozeki, T.; Takashima, T.; Koshimizu, G.; Uchida, Y.; Ogimoto, K. Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan. Prog. Photovolt: Res. Appl.
**2012**, 20, 874–882. [Google Scholar] [CrossRef] - Dolara, A.; Grimaccia, F.; Leva, S.; Mussetta, M.; Ogliari, E. A physical hybrid artificial neural network for short term forecasting of pv plant power output. Energies
**2015**, 8, 1138. [Google Scholar] [CrossRef][Green Version] - Muhsen, D.H.; Ghazali, A.B.; Khatib, T.; Abed, I.A. A comparative study of evolutionary algorithms and adapting control parameters for estimating the parameters of a single-diode photovoltaic module’s model. Renew. Energy
**2016**, 96, 377–389. [Google Scholar] [CrossRef] - Ma, J.; Bi, Z.; Ting, T.O.; Hao, S.; Hao, W. Comparative performance on photovoltaic model parameter identification via bio-inspired algorithms. Sol. Energy
**2016**, 132, 606–616. [Google Scholar] [CrossRef] - Kichou, S.; Silvestre, S.; Guglielminotti, L.; Mora-López, L.; Muñoz-Cerón, E. Comparison of two PV array models for the simulation of PV systems using five different algorithms for the parameters identification. Renew. Energy
**2016**, 99, 270–279. [Google Scholar] [CrossRef] - Bastidas-Rodriguez, J.D.; Petrone, G.; Ramos-Paja, C.A.; Spagnuolo, G. A genetic algorithm for identifying the single diode model parameters of a photovoltaic panel. Math. Comput. Simul.
**2017**, 131, 38–54. [Google Scholar] [CrossRef] - Ismail, M.S.; Moghavvemi, M.; Mahlia, T.M.I. Characterization of PV panel and global optimization of its model parameters using genetic algorithm. Energy Convers. Manag.
**2013**, 73, 10–25. [Google Scholar] [CrossRef] - Saint-Drenan, Y.M.; Bofinger, S.; Fritz, R.; Vogt, S.; Good, G.H.; Dobschinski, J. An empirical approach to parameterizing photovoltaic plants for power forecasting and simulation. Sol. Energy
**2015**, 120, 479–493. [Google Scholar] [CrossRef][Green Version] - Killinger, S.; Engerer, N.; Müller, B. QCPV: A quality control algorithm for distributed photovoltaic array power output. Sol. Energy
**2017**, 143, 120–131. [Google Scholar] [CrossRef] - Mason, K.; Reno, M.J.; Blakely, L.; Vejdan, S.; Grijalva, S. A deep neural network approach for behind-the-meter residential PV size, tilt and azimuth estimation. Sol. Energy
**2020**, 196, 260–269. [Google Scholar] [CrossRef] - Müller, B.; Hardt, L.; Armbruster, A.; Kiefer, K.; Reise, C. Yield predictions for photovoltaic power plants: Empirical validation, recent advances and remaining uncertainties. Prog. Photovolt Res. Appl.
**2016**, 24, 570–583. [Google Scholar] [CrossRef] - Dirnberger, D.; Müller, B.; Reise, C. PV module energy rating: Opportunities and limitations. Prog. Photovolt Res. Appl.
**2015**, 23, 1754–1770. [Google Scholar] [CrossRef] - Perez, R.; Ineichen, P.; Seals, R.; Michalsky, J.; Stewart, R. Modeling daylight availability and irradiance components from direct and global irradiance. Sol. Energy
**1990**, 44, 271–289. [Google Scholar] [CrossRef][Green Version] - Klucher, T.M. Evaluation of models to predict insolation on tilted surfaces. Sol. Energy
**1979**, 23, 111–114. [Google Scholar] [CrossRef] - Hay, J.E. Calculation of monthly mean solar radiation for horizontal and inclined surfaces. Sol. Energy
**1979**, 23, 301–307. [Google Scholar] [CrossRef] - Gueymard, C. An anisotropic solar irradiance model for tilted surfaces and its comparison with selected engineering algorithms. Sol. Energy
**1987**, 38, 367–386. [Google Scholar] [CrossRef] - Martín, N.; Ruiz, J.M. A new model for PV modules angular losses under field conditions. Int. J. Sol. Energy
**2002**, 22, 19–31. [Google Scholar] [CrossRef] - Heydenreich, W.; Müller, B.; Reise, C. Describing the world with three parameters: A new approach to PV module power modelling. In Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, Spain, 1–5 September 2008; pp. 2786–2789. [Google Scholar]
- Müller, B.; Kräling, U.; Heydenreich, W.; Reise, C.; Kiefer, K. Simulation of irradiation and temperature dependent efficiency of thin film and crystalline silicon modules based on different parameterization. In Proceedings of the 5th World Conference on Photovoltaic Energy Conversion, Valencia, Spain, 6–10 September 2010; pp. 4240–4243. [Google Scholar]
- Müller, B.; Heydenreich, W.; Kiefer, K.; Reise, C. More Insights from the monitoring of real world PV power plants—A comparison of measured to predicted performance of PV systems. In Proceedings of the 24th European Photovoltaic Solar Energy Conference, Hamburg, Germany, 21–25 September 2009; pp. 3888–3892. [Google Scholar]
- Müller, B.; Reise, C.; Heydenreich, W.; Kiefer, K. Are Yield Certificates Reliable? A Comparison to Monitored Real World Results. In Proceedings of the 22nd European Photovoltaic Solar Energy Conference and Exhibition, Milano, Italy, 3–7 September 2007. [Google Scholar]
- Schmidt, H.; Sauer, D. Wechselrichter-wirkungsgrade—Praxisgerechte modellierung und abschätzung. Sonnenenergie
**1994**, 1996, 154. [Google Scholar] - Holland, J.H. Adaptation in Natural and Artificial Systems. An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; University of Michigan Press: Ann Arbor, MI, USA, 1975; ISBN 0472084607. [Google Scholar]
- Lorenz, E.; Hurka, J.; Heinemann, D.; Beyer, H.G. Irradiance Forecasting for the Power Prediction of Grid-Connected Photovoltaic Systems. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2009**, 2, 2–10. [Google Scholar] [CrossRef] - Lonij, V.P.A.; Jayadevan, V.T.; Brooks, A.E.; Rodriguez, J.J.; Koch, K.; Leuthold, M.; Cronin, A.D. Forecasts of PV power output using power measurements of 80 residential PV installs. In Proceedings of the 2012 38th IEEE Photovoltaic Specialists Conference, Austin, TX, USA, 3–8 June 2012. [Google Scholar]
- Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods
**2020**, 17, 261–272. [Google Scholar] [CrossRef][Green Version] - Reno, M.J.; Hansen, C.W. Identification of periods of clear sky irradiance in time series of GHI measurements. Renew. Energy
**2016**, 90, 520–531. [Google Scholar] [CrossRef][Green Version] - Stein, J.S.; Hansen, C.W.; Reno, M.J. Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis; Technical Report No. 2012–2389; Sandia National Labaratories: Albuquerque, NM, USA, 2012. [Google Scholar]
- Holmgren, W.; Calama-Consulting; Lorenzo, T.; Hansen, C.; Mikofski, M.; Krien, U.; Bmu; DaCoEx; Driesse, A.; Konstant_t; et al. Pvlib/Pvlib-Python, v0.7.1; Zenodo; 2020. [Google Scholar]
- Suri, M.; Cebecauer, T.; Skoczek, A. SolarGIS: Solar data and online applications for PV planning and performance assessment. In Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, Germany, 5–9 September 2011; pp. 3930–3934. [Google Scholar]
- Louwen, A.; de Waal, A.C.; Schropp, R.E.I.; Faaij, A.P.C.; van Sark, W.G.J.H.M. Comprehensive characterisation and analysis of PV module performance under real operating conditions. Prog. Photovolt Res. Appl.
**2017**, 25, 218–232. [Google Scholar] [CrossRef] - Ernst, M.; Thomson, A.; Haedrich, I.; Blakers, A. Comparison of Ground-based and Satellite-based Irradiance Data for Photovoltaic Yield Estimation. Energy Proc.
**2016**, 92, 546–553. [Google Scholar] [CrossRef][Green Version] - Dürr, B.; Zelenka, A. Deriving surface global irradiance over the Alpine region from METEOSAT Second Generation data by supplementing the HELIOSAT method. Int. J. Remote Sens.
**2009**, 30, 5821–5841. [Google Scholar] [CrossRef] - Jordan, D.C.; Kurtz, S.R.; VanSant, K.; Newmiller, J. Compendium of photovoltaic degradation rates. Prog. Photovolt Res. Appl.
**2016**, 24, 978–989. [Google Scholar] [CrossRef] - Kiefer, K.; Farnung, B.; Müller, B.; Reinartz, K.; Rauschen, I.; Klünter, C. Degradation in PV power plants: Theory and practice. In Proceedings of the 36th European Photovoltaic Solar Energy Conference and Exhibition, Marseille, France, 9–13 September 2018; pp. 1331–1335. [Google Scholar]
- Liu, B.Y.H.; Jordan, R.C. The long-term average performance of flat-plate solar-energy collectors. Sol. Energy
**1963**, 7, 53–74. [Google Scholar] [CrossRef] - Ineichen, P.; Guisan, O.; Perez, R. Ground-reflected radiation and albedo. Sol. Energy
**1990**, 44, 207–214. [Google Scholar] [CrossRef][Green Version] - Ineichen, P.; Perez, R.; Seals, R. The importance of correct albedo determination for adequately modeling energy received by tilted surfaces. Sol. Energy
**1987**, 39, 301–305. [Google Scholar] [CrossRef][Green Version] - Iqbal, M. Ground Albedo: An Introduction to Solar Radiation; Elsevier: Amsterdam, The Netherlands, 1983; pp. 281–293. ISBN 9780123737502. [Google Scholar]

**Figure 1.**General methodology for the Photovoltaic (PV) system parameters optimization. Small dotted lines represent the interactions between the software blocks. Large dotted lines represent measured PV power data as input. Continuous lines represent additional data required as input, namely meteorological data.

**Figure 4.**Heydenreich et al. model fitted curves of 107 different Fraunhofer CalLab measurement results for module efficiency at different irradiance levels.

**Figure 5.**Monthly distribution of clear-sky moments from a PV system located in south-west Germany in the year 2017.

**Figure 6.**Exemplary results of a clear-sky day (

**a**) and an overcast day (

**b**) of 2017 digital twin PV power simulation trained with the 30 days before. Deviations between simulated PV power and measured PV power of a clear-sky day and an overcast day are shown in subfigures (

**c**,

**d**), respectively.

**Figure 7.**Parametrization results of the GA optimization. Left hand side subfigures (

**a**,

**c**,

**e**,

**g**,

**i**,

**k**) show the parametrization results considering all-sky conditions as training data and right hand side subfigures (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**) show the parametrization results considering only clear-sky conditions as training data.

**Figure 8.**Digital twin now-casting results based on GA optimization. 52 chosen days of year 2017. Six different training data sets for each day were considered: all-sky and clear-sky conditions with 30, 60, and 90 days of training data sets. The lines represent the mean value and the shadows show a confidence interval of 95%, only daytime values are considered.

Parameter | Value |
---|---|

Tilt angle (°) | 20 |

Azimuth angle (°) | 181 |

Albedo | 0.2 |

Temperature coefficient (%/°C) | −0.43 |

Heydenreich a | 0.001084 |

Heydenreich b | −7.247061 |

Heydenreich c | −156.5457 |

DC to AC ratio | 1.04 |

Nominal power (kW_{p}) | 553 |

**Table 2.**Parametrization results of the genetic algorithm (GA) optimization including all-sky and clear-sky conditions.

Training Data Set Length | |||||||
---|---|---|---|---|---|---|---|

Parameter | Error Metric | All-Sky Conditions | Clear-Sky Conditions | ||||

30 Days | 60 Days | 90 Days | 30 Days | 60 Days | 90 Days | ||

Nominal Power | Reported (kW_{p}) | 553 | 553 | ||||

Mean (kW_{p}) | 468.76 | 890.13 | 954.05 | 509.19 | 517.5 | 503.17 | |

MBD (kW_{p}) | −84.24 | 337.13 | 401.05 | −43.81 | −35.5 | −49.83 | |

MAPD (%) | 16.94 | 88.14 | 90.73 | 9.92 | 9.95 | 10.69 | |

RMSD (kW_{p}) | 125.46 | 2073.5 | 1995.17 | 64.33 | 66.2 | 65.31 | |

Azimuth | Reported (°) | 181 | 181 | ||||

Mean (°) | 185.79 | 183.09 | 204.09 | 187.37 | 185.06 | 183.47 | |

MBD (°) | 4.79 | 2.09 | 23.09 | 6.37 | 4.06 | 2.47 | |

MAPD (%) | 6.63 | 8.55 | 13.51 | 4.58 | 4.24 | 2.53 | |

RMSD (°) | 22.18 | 33.43 | 50.81 | 13.91 | 15.79 | 9.3 | |

Tilt | Reported (°) | 20 | 20 | ||||

Mean (°) | 29.06 | 29.95 | 22.65 | 17.71 | 17.13 | 17.71 | |

MBD (°) | 9.06 | 9.95 | 2.65 | −2.29 | −2.87 | −2.29 | |

MAPD (%) | 66.16 | 77.56 | 52.12 | 28.23 | 25.83 | 17.71 | |

RMSD (°) | 25.72 | 38.88 | 26.02 | 7.29 | 6.72 | 5.1 | |

Albedo | Reported | 0.2 | 0.2 | ||||

Mean | 1.46 | 0.26 | 1.43 | 0.19 | 0.18 | 0.18 | |

MBD | 1.26 | 0.06 | 1.23 | −0.01 | −0.02 | −0.02 | |

MAPD (%) | 659.04 | 59.42 | 633.46 | 30.58 | 36.15 | 31.15 | |

RMSD | 8.02 | 0.34 | 6.85 | 0.08 | 0.09 | 0.07 | |

Temperature coefficient | Reported (%/°C) | −0.43 | −0.43 | ||||

Mean (%/°C) | −1.87 | −97.69 | −0.28 | −0.42 | −0.41 | −0.34 | |

MBD (%/°C) | −1.44 | −97.26 | 0.15 | 0.01 | 0.02 | 0.09 | |

MAPD (%) | 428.71 | 22702.5 | 46.15 | 39.04 | 35.87 | 28.89 | |

RMSD (%/°C) | 11.52 | 496.7 | 0.25 | 0.28 | 0.23 | 0.18 | |

DC to AC | Reported | 1.04 | 1.04 | ||||

Mean | 0.74 | 0.73 | 0.9 | 0.67 | 0.73 | 0.68 | |

MBD | −0.3 | −0.31 | −0.14 | −0.37 | −0.31 | −0.35 | |

MAPD (%) | 38.05 | 37.94 | 69.62 | 47.12 | 44.84 | 44.01 | |

RMSD | 0.5 | 0.53 | 1.72 | 0.57 | 0.58 | 0.57 |

**Table 3.**Optimized parameters for Heydenreich et al. model considering all-sky and clear-sky conditions.

Parameter | All-sky | Clear-Sky |
---|---|---|

Heydenreich a | 0.011515 | 0.003708 |

Heydenreich b | −11.160905 | −14.834605 |

Heydenreich c | −173.888934 | −208.739158 |

**Table 4.**Basic parameters reported from the PV plant located in south-west Germany and mean bias deviation (MBD) of 10 days optimized with a training data set comprised of clear-sky moments from 90 days before.

Parameter | Reported Value | Optimized Value (MBD) |
---|---|---|

Tilt angle (°) | 20 | 19.6 |

Azimuth angle (°) | 181 | 180.24 |

Albedo factor | 0.2 | 0.13 |

Temperature coefficient (%/°C) | −0.43 | −0.41 |

Heydenreich a | 0.001084 | 0.003708 |

Heydenreich b | −7.247061 | −14.834605 |

Heydenreich c | −156.5457 | −208.739158 |

DC to AC ratio | 1.04 | 0.87 |

Nominal power (kW_{p}) | 553 | 482.9 |

**Table 5.**Accuracy results of the digital twins created for 52 randomly chosen days in the year 2017. Six different training data sets including all-sky and clear sky-conditions with lengths of 30, 60, and 90 days.

Error Metric | Training Data Set Length | ||
---|---|---|---|

30 Days | 60 Days | 90 Days | |

All-sky conditions | |||

MBD (W/kW_{p}) | −9.01 | 28.12 | −7.79 |

MAPD (%) | 6.18 | 10.59 | 5.74 |

RMSD (W/kW_{p}) | 44.04 | 45.92 | 48.67 |

Clear-sky conditions | |||

MBD (W/kW_{p}) | 1.53 | −1.3 | −0.39 |

MAPD (%) | 5.2 | 5.3 | 5.4 |

RMSD (W/kW_{p}) | 41.32 | 41.96 | 41.95 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guzman Razo, D.E.; Müller, B.; Madsen, H.; Wittwer, C. A Genetic Algorithm Approach as a Self-Learning and Optimization Tool for PV Power Simulation and Digital Twinning. *Energies* **2020**, *13*, 6712.
https://doi.org/10.3390/en13246712

**AMA Style**

Guzman Razo DE, Müller B, Madsen H, Wittwer C. A Genetic Algorithm Approach as a Self-Learning and Optimization Tool for PV Power Simulation and Digital Twinning. *Energies*. 2020; 13(24):6712.
https://doi.org/10.3390/en13246712

**Chicago/Turabian Style**

Guzman Razo, Dorian Esteban, Björn Müller, Henrik Madsen, and Christof Wittwer. 2020. "A Genetic Algorithm Approach as a Self-Learning and Optimization Tool for PV Power Simulation and Digital Twinning" *Energies* 13, no. 24: 6712.
https://doi.org/10.3390/en13246712