On the determination of coherent solar microclimates for utility planning and operations

Abstract This work presents a cluster analysis for the determination of coherent zones of Global Horizontal Irradiance (GHI) for a utility scale territory in California, which is serviced by San Diego Gas & Electric. Knowledge of these coherent zones, or clusters, would allow utilities and power plants to realize cost savings through regional planning and operation activities such as the mitigation of solar power variability through the intelligent placement of solar farms and the optimal placement of radiometric stations. In order to determine such clusters, two years of gridded satellite data were used to describe the evolution of GHI over a portion of Southern California. Step changes of the average daily clear-sky index at each location are used to characterize the fluctuation of GHI. The k-means clustering algorithm is applied in conjunction with a stable initialization method to diminish its dependency to random initial conditions. Two validity indices are then used to define the quality of the cluster partitions as well as the appropriate number of clusters. The clustering algorithm determined an optimal number of 14 coherent spatial clusters of similar GHI variability as the most appropriate segmentation of the service territory map. In addition, 14 cluster centers are selected whose radiometric observations may serve as a proxy for the rest of the cluster. A correlation analysis, within and between the proposed clusters, based both on single-point ground-based and satellite-derived measurements evaluates positively the coherence of the conducted clustering. This method could easily be applied to any other utility scale region and is not dependent on GHI data which shows promise for the application of such clustering methods to load data and/or other renewable resources such as wind.

[1]  Robert Tibshirani,et al.  Estimating the number of clusters in a data set via the gap statistic , 2000 .

[2]  J. Kleissl,et al.  Validation of the NSRDB–SUNY global horizontal irradiance in California , 2010 .

[3]  T. Caliński,et al.  A dendrite method for cluster analysis , 1974 .

[4]  Chris H. Q. Ding,et al.  K-means clustering via principal component analysis , 2004, ICML.

[5]  Gianluca Bontempi,et al.  New Routes from Minimal Approximation Error to Principal Components , 2008, Neural Processing Letters.

[6]  Carlos A. Berenstein,et al.  Implementation and Application of Principal Component Analysis on Functional Neuroimaging Data , 2001 .

[7]  Hui Xiong,et al.  Understanding of Internal Clustering Validation Measures , 2010, 2010 IEEE International Conference on Data Mining.

[8]  L. Wald,et al.  Worldwide Linke turbidity information , 2003 .

[9]  Patricio A. Vela,et al.  A Comparative Study of Efficient Initialization Methods for the K-Means Clustering Algorithm , 2012, Expert Syst. Appl..

[10]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[11]  Clifford F. Mass,et al.  Origin of the Catalina Eddy , 1989 .

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

[13]  Philip Chan,et al.  Determining the number of clusters/segments in hierarchical clustering/segmentation algorithms , 2004, 16th IEEE International Conference on Tools with Artificial Intelligence.

[14]  Carlos F.M. Coimbra,et al.  Hybrid solar forecasting method uses satellite imaging and ground telemetry as inputs to ANNs , 2013 .

[15]  Philip Chan,et al.  Learning States and Rules for Detecting Anomalies in Time Series , 2005, Applied Intelligence.

[16]  J. Kleissl,et al.  Intra-hour forecasting with a total sky imager at the UC San Diego solar energy testbed , 2011 .

[17]  Pasi Fränti,et al.  Knee Point Detection on Bayesian Information Criterion , 2008, 2008 20th IEEE International Conference on Tools with Artificial Intelligence.

[18]  Olatz Arbelaitz,et al.  An extensive comparative study of cluster validity indices , 2013, Pattern Recognit..

[19]  I. Noy-Meir,et al.  Data Transformations in Ecological Ordination: I. Some Advantages of Non-Centering , 1973 .

[20]  Baowen Xu,et al.  Stable initialization scheme for K-means clustering , 2009, Wuhan University Journal of Natural Sciences.

[21]  André Hardy,et al.  An examination of procedures for determining the number of clusters in a data set , 1994 .

[22]  George D. Rodriguez,et al.  A utility perspective of the role of energy storage in the smart grid , 2010, IEEE PES General Meeting.

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

[24]  Philip S. Yu,et al.  Top 10 algorithms in data mining , 2007, Knowledge and Information Systems.

[25]  P. Ineichen Comparison of eight clear sky broadband models against 16 independent data banks , 2006 .

[26]  P. Rousseeuw Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[27]  Luís Miguel Nunes,et al.  Optimizing the location of weather monitoring stations using estimation uncertainty , 2012 .

[28]  G. W. Milligan,et al.  An examination of procedures for determining the number of clusters in a data set , 1985 .

[29]  Lucien Wald,et al.  Solar radiation climate in Africa , 2004 .

[30]  C. Coimbra,et al.  Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database , 2011 .

[31]  Sergios Theodoridis,et al.  Pattern Recognition, Fourth Edition , 2008 .

[32]  P. Ineichen,et al.  A new airmass independent formulation for the Linke turbidity coefficient , 2002 .

[33]  I. Jolliffe Principal Component Analysis , 2002 .

[34]  Clifford W. Hansen,et al.  Global horizontal irradiance clear sky models : implementation and analysis. , 2012 .

[35]  Ersan Kabalci Development of a feasibility prediction tool for solar power plant installation analyses , 2011 .

[36]  Godfrey Boyle,et al.  Renewable Electricity and the Grid : The Challenge of Variability , 2007 .

[37]  P. Ineichen,et al.  A new operational model for satellite-derived irradiances: description and validation , 2002 .

[38]  Andreas Kazantzidis,et al.  Determination of measuring sites for solar irradiance, based on cluster analysis of satellite-derived cloud estimations , 2013 .

[39]  Andrew McCallum,et al.  Dynamic conditional random fields: factorized probabilistic models for labeling and segmenting sequence data , 2004, J. Mach. Learn. Res..

[40]  W. T. Williams,et al.  Data Transformations in Ecological Ordination: II. On the Meaning of Data Standardization , 1975 .

[41]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[42]  I. Jolliffe,et al.  ON RELATIONSHIPS BETWEEN UNCENTRED AND COLUMN-CENTRED PRINCIPAL COMPONENT ANALYSIS , 2009 .

[43]  A. Schmalwieser,et al.  A monitoring network for erythemally-effective solar ultraviolet radiation in Austria: determination of the measuring sites and visualisation of the spatial distribution , 2001 .

[44]  Alexandros G. Charalambides,et al.  Enhanced values of global irradiance due to the presence of clouds in Eastern Mediterranean , 2014 .

[45]  Kamaruzzaman Sopian,et al.  Issues concerning atmospheric turbidity indices , 2012 .

[46]  C. Gueymard,et al.  Assessment of spatial and temporal variability in the US solar resource from radiometric measurements and predictions from models using ground-based or satellite data , 2011 .

[47]  Anil K. Jain Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[48]  Geothermal Energy Western Wind and Solar Integration Study , 2010 .

[49]  Russell S. Vose,et al.  A Method to Determine Station Density Requirements for Climate Observing Networks , 2004 .

[50]  David Eidelberg,et al.  Scaled subprofile modeling of resting state imaging data in Parkinson's disease: Methodological issues , 2011, NeuroImage.