0
Research Papers

Deterministic and Stochastic Approaches for Day-Ahead Solar Power Forecasting

[+] Author and Article Information
Marco Pierro

Institute for Renewable Energy,
EURAC Research,
Bolzano 39100, Italy;
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Rome 00133, Italy
e-mail: marco.pierro@gmail.com

Francesco Bucci

Department of Enterprise Engineering,
University of Rome Tor Vergata,
Rome 00133, Italy

Matteo De Felice

ENEA,
Casaccia R.C.,
Climate Impacts and Modelling Laboratory,
Rome 00123, Italy

Enrico Maggioni, Alessandro Perotto

IDEAM S.r.l.,
Cinisello Balsamo 20092, Italy

Francesco Spada

IDEAM S.r.l.,
Cinisello Balsamo 20092,Italy

David Moser

Institute for Renewable Energy,
EURAC Research,
Bolzano 39100, Italy

Cristina Cornaro

CHOSE,
Department of Enterprise Engineering,
University of Rome Tor Vergata,
Rome 00133, Italy

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received February 5, 2016; final manuscript received September 6, 2016; published online November 30, 2016. Assoc. Editor: Carlos F. M. Coimbra.

J. Sol. Energy Eng 139(2), 021010 (Nov 30, 2016) (12 pages) Paper No: SOL-16-1066; doi: 10.1115/1.4034823 History: Received February 05, 2016; Revised September 06, 2016

Photovoltaic (PV) power forecasting has the potential to mitigate some of effects of resource variability caused by high solar power penetration into the electricity grid. Two main methods are currently used for PV power generation forecast: (i) a deterministic approach that uses physics-based models requiring detailed PV plant information and (ii) a data-driven approach based on statistical or stochastic machine learning techniques needing historical power measurements. The main goal of this work is to analyze the accuracy of these different approaches. Deterministic and stochastic models for day-ahead PV generation forecast were developed, and a detailed error analysis was performed. Four years of site measurements were used to train and test the models. Numerical weather prediction (NWP) data generated by the weather research and forecasting (WRF) model were used as input. Additionally, a new parameter, the clear sky performance index, is defined. This index is equivalent to the clear sky index for PV power generation forecast, and it is here used in conjunction to the stochastic and persistence models. The stochastic model not only was able to correct NWP bias errors but it also provided a better irradiance transposition on the PV plane. The deterministic and stochastic models yield day-ahead forecast skills with respect to persistence of 35% and 39%, respectively.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

IEA, 2014, “ 2014 Snapshot of Global PV Markets,” IEA PVPS, International Energy Agency, Paris, Technical Report No. IEA PVPS T1-26:2015.
IEA, 2014, “ Technology Roadmap Solar Photovoltaic Energy: 2014 Edition,” IEA Renewable Energy Division, Paris.
Alet, P. J. , Baccaro, F. , De Felice, M. , Efthymiou, V. , Mayr, C. , Graditi, G. , Juel, M. , Moser, D. , Petitta, M. , Tselepis, S. , and Yang, G. , 2015, “ Photovoltaics Merging With the Active Integrated Grid: A White Paper of the European PV Technology Platform,” European PV Technology Platform, Brussels, Belgium.
Perez, R. , Lorenz, E. , Pelland, S. , Beauharnois, M. , Knowe, G. V. , Hemker, K. , Heinemann, D. , Remund, J. , Müller, S. C. , Traunmüller, W. , Steinmauer, G. , Pozo, D. , Ruiz-Arias, J. A. , Lara-Fanego, V. , Ramirez-Santigosa, L. , Gaston-Romero, M. , and Pomares, L. M. , 2013, “ Comparison of Numerical Weather Prediction Solar Irradiance Forecasts in the US, Canada and Europe,” Sol. Energy, 94, pp. 305–326. [CrossRef]
Perez, R. , Moore, K. , Wilcox, S. , Renné, D. , and Zelenka, A. , 2007, “ Forecasting Solar Radiation—Preliminary Evaluation of an Approach Based Upon the National Forecast Database,” Sol. Energy, 81(6), pp. 809–812. [CrossRef]
Lorenz, E. , Hurka, J. , Heinemann, D. , and Beyer, H. G. , 2009, “ Irradiance Forecasting for the Power Prediction of Grid-Connected Photovoltaic Systems,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 2(1), pp. 2–10. [CrossRef]
Pierro, M. , Bucci, F. , Cornaro, C. , Maggioni, E. , Perotto, A. , Pravettoni, M. , and Spada, F. , 2015, “ Model Output Statistics Cascade to Improve Day Ahead Solar Irradiance Forecast,” Sol. Energy, 117, pp. 99–113. [CrossRef]
Lorenz, E. , Hurka, J. , Karampela, G. , Heinemann, D. , Beyer, H. G. , and Schneider, M. , 2008, “ Qualified Forecast of Ensemble Power Production by Spatially Dispersed Grid-Connected PV Systems,” 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, Spain, Sept. 1–5, pp. 3285–3291.
Lorenz, E. , Scheidsteger, T. , Hurka, J. , Heinemann, D. , and Kurz, C. , 2010, “ Regional PV Power Prediction for Improved Grid Integration,” Prog. Photovoltaics: Res. Appl., 19(7), pp. 757–771. [CrossRef]
Pelland, S. , Galanis, G. , and Kallos, G. , 2011, “ Solar and Photovoltaic Forecasting Through Post-Processing of the Global Environmental Multiscale Numerical Weather Prediction Model,” Prog. Photovoltaics: Res. Appl., 21(3), pp. 284–296. [CrossRef]
Yona, A. , Senjyu, T. , Saber, A. Y. , Funabashi, T. , Sekine, H. , and Kim, C.-H. , 2008, “ Application of Neural Network to 24-Hour-Ahead Generating Power Forecasting for PV System,” IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, Institute of Electrical and Electronics Engineers (IEEE).
Chen, C. , Duan, S. , Cai, T. , and Liu, B. , 2011, “ Online 24-h Solar Power Forecasting Based on Weather Type Classification Using Artificial Neural Network,” Sol. Energy, 85(11), pp. 2856–2870. [CrossRef]
Tao, C. , Shanxu, D. , and Changsong, C. , 2010, “ Forecasting Power Output for Grid-Connected Photovoltaic Power System Without Using Solar Radiation Measurement,” 2nd International Symposium on Power Electronics for Distributed Generation Systems, Institute of Electrical and Electronics Engineers (IEEE), June 16–18, pp. 773–777.
Wang, S. , Zhang, N. , Zhao, Y. , and Zhan, J. , 2011, “ Photovoltaic System Power Forecasting Based on Combined Grey Model and BP Neural Network,” International Conference on Electrical and Control Engineering, Sept. 16–18, Institute of Electrical and Electronics Engineers (IEEE), pp. 4623–4626.
Mellit, A. , Pavan, A. M. , and Lughi, V. , 2014, “ Short-Term Forecasting of Power Production in a Large-Scale Photovoltaic Plant,” Sol. Energy, 105, pp. 401–413. [CrossRef]
Larson, D. P. , Nonnenmacher, L. , and Coimbra, C. F. M. , 2016, “ Day-Ahead Forecasting of Solar Power Output From Photovoltaic Plants in the American Southwest,” Renewable Energy, 91, pp. 11–20. [CrossRef]
Bacher, P. , Madsen, H. , and Nielsen, H. A. , 2009, “ Online Short-Term Solar Power Forecasting,” Sol. Energy, 83(10), pp. 1772–1783. [CrossRef]
Mellit, A. , and Pavan, A. M. , 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(5), pp. 807–821. [CrossRef]
Li, Y. , Su, Y. , and Shu, L. , 2014, “ An ARMAX Model for Forecasting the Power Output of a Grid Connected Photovoltaic System,” Renewable Energy, 66, pp. 78–89. [CrossRef]
Zamo, M. , Mestre, O. , Arbogast, P. , and Pannekoucke, O. , 2014, “ A Benchmark of Statistical Regression Methods for Short-Term Forecasting of Photovoltaic Electricity Production, Part I: Deterministic Forecast of Hourly Production,” Sol. Energy, 105, pp. 792–803. [CrossRef]
da Silva Fonseca, J. G., Jr. , Oozeki, T. , Ohtake, H. , Shimose, K.-i. , Takashima, T. , and Ogimoto, K. , 2014, “ Regional Forecasts and Smoothing Effect of Photovoltaic Power Generation in Japan: An Approach With Principal Component Analysis,” Renewable Energy, 68, pp. 403–413. [CrossRef]
da Silva Fonseca, J. G., Jr. , Oozeki, T. , Ohtake, H. , Takashima, T. , and Ogimoto, K. , 2015, “ Regional Forecasts of Photovoltaic Power Generation According to Different Data Availability Scenarios: A Study of Four Methods,” Prog. Photovoltaics: Res. Appl., 23(10), pp. 1203–1218. [CrossRef]
Zamo, M. , Mestre, O. , Arbogast, P. , and Pannekoucke, O. , 2014, “ A Benchmark of Statistical Regression Methods for Short-Term Forecasting of Photovoltaic Electricity Production, Part II: Probabilistic Forecast of Daily Production,” Sol. Energy, 105, pp. 804–816. [CrossRef]
Almeida, M. P. , Perpiñán, O. , and Narvarte, L. , 2015, “ PV Power Forecast Using a Nonparametric PV Model,” Sol. Energy, 115, pp. 354–368. [CrossRef]
Davò, F. , Alessandrini, S. S. , Sperati, S. , Monache, L. D. , Airoldi, D. , and Vespucci, M. T. , 2016, “ Post-Processing Techniques and Principal Component Analysis for Regional Wind Power and Solar Irradiance Forecasting,” Sol. Energy, 134, pp. 327–338. [CrossRef]
Sperati, S. , Alessandrini, S. , and Delle Monache, L. , 2016, “ An Application of the ECMWF Ensemble Prediction System for Short-Term Solar Power Forecasting,” Sol. Energy, 133, pp. 437–450. [CrossRef]
Paulescu, M. , Paulescu, E. , Gravila, P. , and Badescu, V. , 2012, Weather Modeling and Forecasting of PV Systems Operation, Springer Science+Business Media, Berlin.
Kleissl, J. , 2013, Solar Energy Forecasting and Resource Assessment, Academic Press, Cambridge, MA.
IEA, 2013, “ Photovoltaic and Solar Forecasting: State of the Art,” IEA PVPS, International Energy Agency, Paris, Technical Report No. IEA-PVPS T14-01: 2013.
Belluardo, G. , Ingenhoven, P. , Sparber, W. , Wagner, J. , Weihs, P. , and Moser, D. , 2015, “ Novel Method for the Improvement in the Evaluation of Outdoor Performance Loss Rate in Different PV Technologies and Comparison With Two Other Methods,” Sol. Energy, 117, pp. 139–152. [CrossRef]
Bertani, D. , Guastella, S. , Belluardo, G. , and Moser, D. , 2015, “ Long Term Measurement Accuracy Analysis of a Commercial Monitoring System for Photovoltaic Plants,” IEEE Workshop on Environmental, Energy and Structural Monitoring Systems (EESMS), July 9–10, pp. 84–89.
Skamarock, W. , Klemp, J. , Dudhia, J. , Gill, D. , Barker, D. , Duda, M. G. , Huang, X.-Y. , Wang, W. , and Powers, J. G. , 2008, “ A Description of the Advanced Research WRF Version 3,” NCAR, Boulder, CO, Technical Note NCAR/TN-4751STR.
Rogers, E. , Black, T. , Ferrier, B. , Lin, Y. , Parrish, D. , and DiMego, G. , 2001, “ Changes to the NCEP Meso Eta Analysis and Forecast System: Increase in Resolution, New Cloud Microphysics, Modified Precipitation Assimilation, Modified 3DVAR Analysis,” Office of Metrology, National Weather Service, Silver Spring, MD.
Paulson, C. A. , 1970, “ The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer,” J. Appl. Meteorol., 9(6), pp. 857–861. [CrossRef]
Tewari, M. , Chen, F. , Wang, W. , Dudhia, J. , LeMone, M. , Mitchell, K. , Ek, M. , Gayno, G. , Wegiel, J. , and Cuenca, R. , 2004, “ Implementation and Verification of the Unified NOAH Land Surface Model in the WRF Model,” 20th Conference on Weather Analysis and Forecasting/16th Conference on Numerical Weather Prediction, pp. 11–15.
Hong, S.-Y. , Noh, Y. , and Dudhia, J. , 2006, “ A New Vertical Diffusion Package With an Explicit Treatment of Entrainment Processes,” Mon. Weather Rev., 134(9), pp. 2318–2341. [CrossRef]
Kain, J. S. , 2004, “ The Kain–Fritsch Convective Parameterization: An Update,” J. Appl. Meteorol., 43(1), pp. 170–181. [CrossRef]
Beyer, H. G. , Polo Martinez, J. , Suri, M. , Torres, J. L. , Lorenz, E. , Müller, S. C. , Hoyer-Klick, C. , and Ineichen, P. , 2009, “ Report on Benchmarking of Radiation Products,” Management and Exploitation of Solar Resource Knowledge (MESOR), Sixth Framework Programme, Contract No. 038665.
Houghton, J. , 2002, The Physics of Atmospheres, Cambridge University Press, Cambridge, UK.
Liu, B. , and Jordan, R. , 1961, “ Daily Insolation on Surfaces Tilted Towards Equator,” ASHRAE J., 10, p. 5047843.
King, D. L. , Kratochvil, J. A. , and Boyson, W. E. , 2004, “ Photovoltaic Array Performance Model,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2004-3535.
Pierro, M. , Bucci, F. , and Cornaro, C. , 2014, “ Full Characterization of Photovoltaic Modules in Real Operating Conditions: Theoretical Model Measurement Method and Results,” Prog. Photovoltaics: Res. Appl., 23(4), pp. 443–461. [CrossRef]
Basheer, I. , and Hajmeer, M. , 2000, “ Artificial Neural Networks: Fundamentals, Computing, Design, and Application,” J. Microbiol. Methods, 43(1), pp. 3–31. [CrossRef] [PubMed]
Zhang, G. , Patuwo, B. E. , and Hu, M. Y. , 1998, “ Forecasting With Artificial Neural Networks: The State of the Art,” Int. J. Forecasting, 14(1), pp. 35–62. [CrossRef]
Mellit, A. , 2008, “ Artificial Intelligence Technique for Modelling and Forecasting of Solar Radiation Data: A Review,” Int. J. Artif. Intell. Soft Comput., 1(1), pp. 52–76. [CrossRef]
Cornaro, C. , Pierro, M. , and Bucci, F. , 2015, “ Master Optimization Process Based on Neural Networks Ensemble for 24-h Solar Irradiance Forecast,” Sol. Energy, 111, pp. 297–312. [CrossRef]
Marquez, R. , and Coimbra, C. F. , 2013, “ Proposed Metric for Evaluation of Solar Forecasting Models,” ASME J. Sol. Energy Eng., 135, p. 0110161.
Lorenz, E. , Remund, J. , Müller, S. C. , Traunmüller, W. , Steinmaurer, G. , Pozo, D. , Ruiz-Arias, J. A. , Fanego, V . L. , Ramirez, L. , Romeo, M. G. , and Kurz, C. , 2009, “ Benchmarking of Different Approaches to Forecast Solar Irradiance,” 24th European Photovoltaic Solar Energy Conference, Hamburg, Germany, Vol. 21, p. 25.
Klucher, T. M. , 1979, “ Evaluation of Models to Predict Insolation on Tilted Surfaces,” Sol. Energy, 23(2), pp. 111–114. [CrossRef]
Gueymard, C. A. , 2008, “ From Global Horizontal to Global Tilted Irradiance: How Accurate are Solar Energy Engineering Predictions in Practice?,” SOLAR 2008, San Diego, CA, American Solar Energy Society, pp. 1434–1456.
Pierro, M. , Bucci, F. , and Cornaro, C. , 2015, “ Impact of Light Soaking and Thermal Annealing on Amorphous Silicon Thin Film Performance,” Prog. Photovoltaics: Res. Appl., 23(11), pp. 1581–1596. [CrossRef]
Huang, Y. , Lu, J. , Liu, C. , Xu, X. , Wang, W. , and Zhou, X. , 2010, “ Comparative Study of Power Forecasting Methods for PV Stations,” International Conference on Power System Technology, Oct. 24–28, Institute of Electrical and Electronics Engineers (IEEE).
Lorenz, E. , 2015, “ PV Production Forecast of Balance Zones in Germany,” IEA PVPS and SHC Workshop at EUPVSEC 2013: Solar Resource and Forecast Data for High PV Penetration, EA PVPS Task 14 and SHC Task 46, Paris.
Gulin, M. , Vašak, M. , and Baotic, M. , 2013, “ Estimation of the Global Solar Irradiance on Tilted Surfaces,” 17th International Conference on Electrical Drives and Power Electronics (EDPE 2013), pp. 334–339.
Mlawer, E. J. , Taubman, S. J. , Brown, P. D. , Iacono, M. J. , and Clough, S. A. , 1997, “ Radiative Transfer for Inhomogeneous Atmospheres: RRTM, a Validated Correlated-k Model for the Longwave,” J. Geophys. Res.: Atmos., 102, pp. 16663–16682. [CrossRef]
Fu, Q. , and Liou, K. , 1992, “ On the Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Atmospheres,” J. Atmos. Sci., 49(22), pp. 2139–2156. [CrossRef]
Oreopoulos, L. , and Barker, H. W. , 1999, “ Accounting for Subgrid-Scale Cloud Variability in a Multi-Layer 1D Solar Radiative Transfer Algorithm,” Q. J. R. Meteorol. Soc., 125(553), pp. 301–330.
Grell, G. A. , Peckham, S. E. , Schmitz, R. , McKeen, S. A. , Frost, G. , Skamarock, W. C. , and Eder, B. , 2005, “ Fully Coupled ‘Online’ Chemistry Within the WRF Model,” Atmos. Environ., 39(37), pp. 6957–6975. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematics of the different approaches for day-ahead PV power forecast

Grahic Jump Location
Fig. 2

(a) Daily reference yield (Yr) and final yield (Yf) from Jan. 1, 2011 to Dec. 31, 2014 and (b) monthly average of daily power yield for all the considered years

Grahic Jump Location
Fig. 3

Daily trend of clear sky index (Kcs), performance ratio (PR), and clear sky performance index (PKcs) in a clear sky day and in an overcast day

Grahic Jump Location
Fig. 4

Inputs (X) and output (Y) of the RHNN model

Grahic Jump Location
Fig. 5

Minimum, maximum, and average values of RMSE obtained by different irradiance forecast approaches reported in Ref. [44] and the RMSE achieved by the MOSRH(WRF) solar irradiance prediction for Bolzano site versus the RMSE of the clear sky persistence model

Grahic Jump Location
Fig. 6

Liu–Jordan isotropic transposition errors in different typologies of days identified by the daily clear sky index

Grahic Jump Location
Fig. 7

Hourly trend of power and performance ratio, measured and estimated by the SAPM

Grahic Jump Location
Fig. 8

Accuracy comparison of PV power generation forecast (yearly trends)

Grahic Jump Location
Fig. 9

Accuracy comparison of PV power generation forecast

Grahic Jump Location
Fig. 10

Behavior of residuals of the deterministic and stochastic models: (1) power distribution of hourly errors, (2) bias errors versus rated power (Pm/Pn), and (3) Kolmogorov–Smirnov test

Grahic Jump Location
Fig. 11

(a) Error propagation in the deterministic model, in box (b) error propagation not considering the nominal power degradation of the PV modules

Grahic Jump Location
Fig. 12

(a) RMSE of the isotropic transposition model on actual GHI data (RMSEG0), RMSE of GHI and GPOAI prediction (RMSEG1 and RMSEG2), and the forecast error due to the transposition model (RMSEd = RMSEG2 − RMSEG1) ((b) and (c)) RMSE and MBE comparison of the deterministic and stochastic power forecast in different typologies of days (RMSEP0–MBEP0 of the model Pm(MOSRH) considering only the GHI forecast; RMSEP1–MBEP1 of the full deterministic model Pm(MOSRH + IM + SAPM), and RMSEP2–MBEP2 of the stochastic model Pm(RHNN))

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In