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

Harry Ramenah; Philippe Casin; Moustapha Ba; Michel Benne; Camel Tanougast; Harry Ramenah; Philippe Casin; Moustapha Ba; Michel Benne; Camel Tanougast

doi:10.3934/energy.2018.1.19

AIMS Energy

2018, Volume 6, Issue 1: 19-48. doi: 10.3934/energy.2018.1.19

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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

Received: 27 October 2017 Accepted: 19 December 2017 Published: 02 January 2018

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.
- 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[J]. AIMS Energy, 2018, 6(1): 19-48. doi: 10.3934/energy.2018.1.19

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Abstract

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.

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