Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Accurate determination of parameters relationship for photovoltaic power output by augmented dickey fuller test and engle granger method

1 LCOMS Laboratory, University of Lorraine, 7 Rue Marconi, 57070 Metz, France
2 LE2P Laboratory, University of Reunion, 40 Avenue René Cassin, 97400 Saint-Denis, France

Topical Section: Solar Energy

Power output from photovoltaic (PV) systems in outdoor conditions is substantially influenced by climatic parameters such as solar irradiance and temperature. PV manufacturers always provide technical specifications in laboratory conditions but reliable relationship for the power output must be determined for accurate prediction under real operating conditions. For the present study, solar irradiance G, temperature T and electrical power output P data under real conditions are methodically and regularly inscribed in dataloggers. Hence, in this paper, we investigate rigorous and robust statistical methods for small sample such as Augmented Dickey-Fuller and Engle Granger for stationary series to determine the estimate regression between variables P, G & T. A first regression of power output P time series variable on solar irradiance G time series has shown spurious results and thus spurious regression. The first differences of such time series are stationary and a regression is proposed whereas temperature variable is identified as not significant and where autocorrelation of residuals is suspected. Finally, the novelty of this paper is the Engle & Granger method that is used to provide a relationship between variables P and G in a difference level. A final relationship without suspicious heteroscedasticity has been determined. Our model is formulated on the basis of PV real conditions statistical approach and is more realistic than steady approach models.
  Article Metrics

Keywords photovoltaic; unit root; Augmented Dickey Fuller; correlograms; Engle Granger test; difference series; spurious regression; heteroscedasticity

Citation: Harry Ramenah, Philippe Casin, Moustapha Ba, Michel Benne, Camel Tanougast. Accurate determination of parameters relationship for photovoltaic power output by augmented dickey fuller test and engle granger method. AIMS Energy, 2018, 6(1): 19-48. doi: 10.3934/energy.2018.1.19


  • 1. Agrawal S, Solanki SC, Tiwari GN (2011) Design, fabrication and testing of micro-channel solar cell therrmal (MCSCT) tiles in door condition. World Renewable Energy Congress-Sweden, 2916–2923.
  • 2. Singh GK, Agrawal S, Tiwari A (2012) Analysis of different types of hybrid phtovoltaic thermal air collectors: A comparative study. J Fund Renew Energ Appl 2: 1–4.
  • 3. Rajoria CS, Agrawal S, Dash AK, et al. (2015) A newer approach on cash flow diagram to investigate the effect of energy payback time and earned carbon credits on life cycle cost of different photovoltaic thermal array systems. Sol Energy 124: 254–267.
  • 4. Ross RGJ (1976) Interface design considerations for terrestrial solar cell modules. Proceedings of the 12th IEEE Photovoltaic Specialists Conference, Baton Rouge LA, USA, 15–18: 801–806.
  • 5. Skoplaki E, Palyvos JA (2009) Operating temperature of photovoltaic modules: A survey of pertinent correlations. Renew Energ 34: 23–29.    
  • 6. Skoplaki E, Palyvos JA (2009) On the temperature dependence of photovoltaic module electrical performance: A review of efficiency/power correlations. Sol Energy 83: 614–624.    
  • 7. Peled A, Appelbaum J (2017) Enhancing the power output of PV modules by considering the view factor to sky effect and rearranging the interconnections of solar cells. Prog Photovolt Res Appl 25: 810–818.    
  • 8. Ramenah H, Tanougast C, Cicero L (2014) Toward a prediction of the photovoltaic based power production from Experimental Thermal modeling. Transportation Electrification Asia-Pacific. IEEE, 1–4.
  • 9. Skoplaki E, Boudouvis AG, Palyvos JA (2008) A simple correlation for the operating temperature of photovoltaic modules of arbitrary mounting. Sol Energ Mat Sol C 92: 139–1402.
  • 10. Jakhrani AQ, Othman AK, Rigitand ARH, et al. (2011) Comparison of solar photovoltaic module temperature models. World Appl Sci J 14: 1–8.
  • 11. Radziemska E (2003) The effect of temperature on the power drop in crystalline silicon solar cells. Renew Energ 28: 1–12.    
  • 12. Singh P, Ravindra NM (2012) Temperature dependence of solar cell performance-an analysis. Sol Energ Mat Sol C 101: 36–45.    
  • 13. Krauter S, Araújo RG, Schroer S, et al. (1999) Combined photovoltaic and solar thermal systems for facade integration and building insulation. Sol Energy 67: 239–248.    
  • 14. García MCA, Balenzategui JL (2004) Estimation of photovoltaic module yearly temperature and performance based on nominal operation cell temperatures calculations. Renew Energ 29: 1997–2010.    
  • 15. Trinuruk P, Sorapipatana C, Chenvidhya D (2009) Estimating operating cell temperature of BIPV modules in Thailand. Renew Energ 34: 2515–2523.    
  • 16. Savvakis N, Tsoutsos T (2015) Performance assessment of a thin film photovoltaic system under actual Mediterranean climate conditions in the island of Crete. Energy 90: 1435–1455.    
  • 17. Rosell JI, Ibáñez M (2006) Modelling power output in photovoltaic modules for outdoor operating conditions. Energ Convers Manage 47: 2424–2430.    
  • 18. Pashiardis S, Kalogirou SA, Pelengaris A (2017) Statistical analysis for the characterization of solar energy utilization and inter-comparison of solar radiation at two sites in Cyprus. Appl Energ 190: 1138–1158.    
  • 19. Raza MQ, Nadarajah M, Ekanayake C (2016) On recent advances in PV output power forecast. Sol Energy 136: 125–144.    
  • 20. De Giorgi MG, Congedo PM, Malvoni M (2014) Photovoltaic power forecasting using statistical methods: impact of weather data. Iet Sci Meas Technol 8: 90–97.
  • 21. Boland J (2008) Time series modeling of solar radiation. Modeling Solar Radiation at the Earth's Surface. Springer Berlin Heidelberg, 283–312.
  • 22. Steland A (2017) Fusing photovoltaic data for improved confidence intervals. AIMS Energy 5: 125–148.    
  • 23. Kemmoku Y, Orita S, Nakagawa S, et al. (1999) Daily insolation forecasting using multi-stage neural network. Sol Energy 66: 193–199.    
  • 24. Mellit A, Menghanem M, Bendekhis M (2005) Artificial neural network model for prediction solar irradiance data: application for sizing stand-alone photovoltaic power system. Power Engineering Society General Meeting. IEEE 1: 40–44.
  • 25. Sfetsos A, Coonick AH (2000) Univariate and Multivariate forecasting of hourly solar irradiance with artificial intelligence techniques. Sol Energy 68: 169–178.    
  • 26. Adel Mellit, Alessandro MP (2010) A 24-h forecast of solar irradiance using artificial neural network: Application for performance prediction of a grid-connected PV plant at Trieste Italy. Sol Energy 84: 807–821.    
  • 27. Mahmoud D, Violeta H (2016) Fault detection algorithm for grid connected photovoltaic plants. Sol Energy 137: 236–245.    
  • 28. Ba M, Ramenah H, Tanougast C (2017) Forseeing energy photovoltaic output determination by a statistical model using real module temperature in the north east of France. Renew Energ, in press.
  • 29. Huld T, Amillo AMG (2015) Estimating PV module performance over large geographical regions: The role of irradiance, air temperature, wind speed and solar spectrum. Energies 8: 5159–5181.    
  • 30. Dickey D, Fuller W (1979) Distribution of the estimates for the autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431.
  • 31. Gujarati DN (2004) Basic of Econometric, Fourth Edition. The McGraw-Hill Econometrics, Fourth Companies.
  • 32. Engle RF, Granger CWJ (1987) Co-integration and error correction: representation, estimation, and testing. Essays in econometrics. Harvard University Press, 251–276.
  • 33. Casin P (2009) Econométrie méthodes et applications avec Eviews: Editeur Technip. Available from: https://www.eyrolles.com/Entreprise/Livre/econometrie-9782710809272.
  • 34. Ramenah H, Tanougast C, Kalogirou SA, et al. (2016) Reliably model of microwind power energy output under real conditions in France suburban area. Renew Energ 91: 1–10.
  • 35. Applied Economic Time Series (1995) Wiley Series in Probability and Statistics: 420.
  • 36. Hamilton JD (1994) Time Series Analysis. Princeton University Press, 767–768.


Reader Comments

your name: *   your email: *  

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved