Spatiotemporal interpolation and forecast of irradiance data using Kriging

Abstract Solar power variability is a concern to grid operators as unanticipated changes in PV plant power output can strain the electric grid. The main cause of solar variability is clouds passing over PV modules. However, geographic diversity across a region leads to a reduction in the cloud-induced variability. In this paper, spatiotemporal correlations of irradiance data are analyzed and spatial and spatiotemporal ordinary Kriging methods are applied to model irradiation at an arbitrary point based on the given time series of irradiation at some observed locations. The correlations among the irradiances at observed locations are modeled by general parametric covariance functions. Besides the isotropic covariance function (which is independent of direction), a new non-separable anisotropic parametric covariance function is proposed to model the transient clouds. Also, a new approach is proposed to estimate the spatial and temporal decorrelation distances analytically using the applied parametric covariance functions, which reduce the size of the computations without loss in accuracy (parameter shrinkage). The analysis has been performed and the Kriging method is first validated by using two spatially and temporally resolved artificial irradiance datasets generated from Large Eddy Simulation. Then, the spatiotemporal Kriging method is applied on real irradiance and output power data in California (Sacramento and San Diego areas) where the cloud motion had to be estimated during the process using cross-correlation method (CCM). Results confirm that the anisotropic model is most accurate with an average normalized root mean squared error (nRMSE) of 7.92% representing a 66% relative improvement over the persistence model.

[1]  A. Cronin,et al.  Intra-hour forecasts of solar power production using measurements from a network of irradiance sensors , 2013 .

[2]  W. V. van Sark,et al.  Power Output Variability in randomly spaced dutch urban rooftop solar photovoltaic systems , 2013, 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC).

[3]  Modeling the Semivariogram: New Approach, Methods Comparison and Case Study , 2004 .

[4]  J. Kleissl,et al.  Embedded nowcasting method using cloud speed persistence for a photovoltaic power plant , 2015 .

[5]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[6]  D. Heinemann,et al.  Local short-term variability in solar irradiance , 2016 .

[7]  Vasilis Fthenakis,et al.  On the spatial decorrelation of stochastic solar resource variability at long timescales , 2015 .

[8]  J. Kleissl,et al.  Factors Controlling Stratocumulus Cloud Lifetime over Coastal Land , 2016 .

[9]  P. Guttorp,et al.  Nonparametric Estimation of Nonstationary Spatial Covariance Structure , 1992 .

[10]  Laura M. Hinkelman,et al.  Differences between along-wind and cross-wind solar irradiance variability on small spatial scales , 2013 .

[11]  Dazhi Yang,et al.  Very short-term irradiance forecasting at unobserved locations using spatio-temporal kriging , 2015 .

[12]  T. Hoff,et al.  Short-term irradiance variability: Preliminary estimation of station pair correlation as a function of distance , 2012 .

[13]  Thomas Reindl,et al.  Solar irradiance forecasting using spatio-temporal empirical kriging and vector autoregressive models with parameter shrinkage , 2014 .

[14]  Wilfried van Sark,et al.  Spatial power fluctuation correlations in urban rooftop photovoltaic systems , 2015 .

[15]  Frank Vignola,et al.  Chapter 5 – Bankable Solar-Radiation Datasets , 2013 .

[16]  Dale L. Zimmerman,et al.  Computationally efficient restricted maximum likelihood estimation of generalized covariance functions , 1989 .

[17]  Marc G. Genton,et al.  Highly Robust Variogram Estimation , 1998 .

[18]  Nan Chen,et al.  Solar irradiance forecasting using spatial-temporal covariance structures and time-forward kriging , 2013 .

[19]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[20]  Martin Schlather,et al.  Some covariance models based on normal scale mixtures , 2011 .

[21]  E. Arias-Castro,et al.  A Poisson model for anisotropic solar ramp rate correlations , 2014 .

[22]  Miguel-Ángel Manso-Callejo,et al.  Spatial Estimation of Sub-Hour Global Horizontal Irradiance Based on Official Observations and Remote Sensors , 2014, Sensors.

[23]  Jan Kleissl,et al.  Research on impacts of distributed versus centralized solar resource on distribution network using power system simulation and solar now-casting with sky imager , 2015, 2015 IEEE 42nd Photovoltaic Specialist Conference (PVSC).

[24]  J. Kleissl,et al.  Aggregate Ramp Rates of Distributed Photovoltaic Systems in San Diego County , 2013, IEEE Transactions on Sustainable Energy.

[25]  R. Inman,et al.  Solar forecasting methods for renewable energy integration , 2013 .

[26]  Dale L. Zimmerman,et al.  Classical Geostatistical Methods , 2010 .

[27]  J. Kleissl,et al.  Performance analysis of power output of photovoltaic systems in San Diego County , 2012, 2012 IEEE Power and Energy Society General Meeting.

[28]  Jan Kleissl,et al.  Cloud speed impact on solar variability scaling – Application to the wavelet variability model , 2013 .

[29]  Joakim Widén,et al.  A model of spatially integrated solar irradiance variability based on logarithmic station-pair correlations , 2015 .

[30]  Mathieu David,et al.  Spatial and Temporal Variability of Solar Energy , 2016 .

[31]  Tetsuo Sasaki,et al.  Areal Solar Irradiance Estimated by Sparsely Distributed Observations of Solar Radiation , 2016, IEEE Transactions on Power Systems.

[32]  Nicholas A. Engerer,et al.  QCPV: A quality control algorithm for distributed photovoltaic array power output , 2017 .

[33]  P. Burrough,et al.  Principles of geographical information systems , 1998 .

[34]  P. Guttorp,et al.  Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry , 2007 .

[35]  Takashi Washio,et al.  Spatio-temporal Kriging of solar radiation incorporating direction and speed of cloud movement (人工知能学会全国大会(第26回)文化,科学技術と未来) -- (International Organized Session「Application Oriented Principles of Machine Learning and Data Mining」) , 2012 .