Estimation of solar radiation using a combination of Hidden Markov Model and generalized Fuzzy model

Abstract

Estimation of solar radiation is of considerable importance because of the increasing requirement for the design, optimization and performance evaluation of the solar energy systems. This paper presents the development of pattern similarity based clustering algorithm and its application in solar radiation estimation. In the present work continuous density, Hidden Markov Model (HMM) with Pearson R model is utilized for the extraction of shape based clusters from the input meteorological parameters and it is then processed by the Generalized Fuzzy Model (GFM) to accurately estimate the solar radiation. Instead of using distance function as an index of similarity here shape/patterns of the data vectors are used as the similarity index for clustering, which overcomes few of the shortcomings associated with distance based clustering approaches. The estimation method used here exploits the pattern identification prowess of the HMM for cluster selection and generalization and nonlinear modeling capabilities of GFM to predict the solar radiation. The data of solar radiation and various meteorological parameters (sun shine hour, ambient temperature, relative humidity, wind speed and atmospheric pressure) to carry out the present work is taken from the comprehensive weather monitoring station made at Solar Energy Centre, Gurgaon, India. To consider the effect of each meteorological parameter on the estimation of solar radiation the proposed model is applied on 15 different sets comprising of various combinations of input meteorological parameters. The meteorological data of three years from 2009 to 2011 (915days) is used to estimate the solar radiation. Out of these 915days data, the first 750days data is used for the training of the proposed paradigm and rest 165days data is used for validating the model. The results of estimation using all the sets of various combination of meteorological parameter are analyzed and it is found that the sunshine duration is the prime parameter for the estimation of solar radiation. The next important parameter, which influences the estimation of solar radiation, is temperature followed by relative humidity, atmospheric pressure and wind speed. It is interesting to note that worse results are obtained for the sets which are not using sunshine duration as an input. The best performance is achieved by the set which uses all the parameters except the wind speed. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and correlation co-efficient (R-value) of the proposed paradigm for the best performing combination of meteorological parameter are 7.9124, 3.0083 and 0.9921 respectively which shows that the proposed model results are in good agreement with the actual measured solar radiation.