Llanos Mora-López

Multiplicative ARMA models to generate hourly series of global irradiation

A methodology to generate hourly series of global irradiation is proposed. The only input parameter which is required is the monthly mean value of daily global irradiation, which is available for most locations. The procedure to obtain new series is based on the use of a multiplicative autoregressive moving-average statistical model for time series with regular and seasonal components. The multiplicative nature of this models enables us to capture the two types of relationships observed in recorded hourly series of global irradiation: on the one hand, the relationship between the value at one hour and the value at the previous hour; and on the other hand, the relationship between the value at one hour in one day and the value at the same hour in the previous day. In this paper the main drawback which arises when using these models to generate new series is solved: namely, the need for available recorded series in order to obtain the three parameters contained in the statistical ARMA model which is proposed (autoregressive coefficient, moving-average coefficient and variance of the error term). Specifically, expressions which enable estimatation of these parameters using only monthly mean values of daily global irradiation are proposed in this paper.

Characterization and simulation of hourly exposure series of global radiation

A statistical model which captures the main features of hourly exposure series of global radiation is proposed. This model is used to obtain a procedure to generate radiation series without imposing, a priori, any restriction on the form of the probability distribution function of the series. The statistical model was taken from the stationary stochastic processes theory. Data were obtained from ten different Spanish locations. As monthly hourly exposure series of global radiation are not stationary, they are modified in order to remove the observed trends. A multiplicative autoregressive moving average model with regular and seasonal components was used. It is statistically accepted that this is the true model which generates most of the analyzed sequences. However, the underlying parameters of the model vary from one location to another and from one month to another. Therefore, it is necessary to examine further the relationship between the parameters of the model and the available data from most locations.

Data mining and statistical techniques for characterizing the performance of thin-film photovoltaic modules

A method for characterizing the performance ratio of thin-film photovoltaic modules based on the use of data mining and statistical techniques is developed. In general, this parameter changes when modules are working in outdoor conditions depending on irradiance, temperature, air mass and solar spectral irradiance distribution. The problem is that it is usually difficult to know how to include solar spectral irradiance information when estimating the performance of photovoltaic modules. We propose five different solar spectral irradiance distributions that summarize all the different distributions observed in Malaga. Using the probability distribution functions of these curves and a statistical test, we first checked when two spectral distributions measured can be considered to have the same contribution of energy per wavelength. Hence, using this test and the k-means data mining technique, all the measured spectra, more than two hundred and fifty thousand, are clustered in only five different groups. All the spectra in each cluster can be considered as equal and the k-means technique estimates one centroid for each cluster that corresponds to the cumulative probability distribution function that is the most similar to the rest of the samples in the cluster. The results obtained proves that 99.98% of the functions can be considered equal to the centroid of its cluster. With these five types of functions, we have explained the changes in the performance ratio measured for thin-film photovoltaic modules of different technologies.

Modelling the distribution of solar spectral irradiance using data mining techniques

A procedure for modelling the distribution of solar spectral irradiance is proposed. It uses both statistical and data mining techniques. As a result, it is possible to simulate solar spectral irradiance distribution using some astronomical parameters and the meteorological parameters solar irradiance, temperature and humidity. With these parameters, the average photon energy and the normalization factor, which characterise the solar spectra, are estimated. First, the KolmogoroveSmirnov two-sample test is used to analyse and compare all measured spectra. The k-means data mining technique is subsequently used to cluster all measurements. We found that three clusters are enough to characterise all observed spectra. Finally, an artificial neural network and a multivariate linear regression are estimated to simulate the solar spectral distribution matching certain meteorological parameters. The results obtained show that over 99.98% of cumulative probability distribution functions of measured spectra are the same as simulated ones. 2013 Elsevier Ltd. All rights reserved.

Using probabilistic finite automata to simulate hourly series of global radiation

Abstract A model to generate synthetic series of hourly exposure of global radiation is proposed. This model has been constructed using a machine learning approach. It is based on the use of a subclass of probabilistic finite automata which can be used for variable-order Markov processes. This model allows us to represent the different relationships and the representative information observed in the hourly series of global radiation; the variable-order Markov process can be used as a natural way to represent different types of days, and to take into account the “variable memory” of cloudiness. A method to generate new series of hourly global radiation, which incorporates the randomness observed in recorded series, is also proposed. As input data this method only uses the mean monthly value of the daily solar global radiation. We examine if the recorded and simulated series are similar. It can be concluded that both series have the same statistical properties.

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov-Smirnov two-sample test

An adaptive clustering algorithm has been proposed.The measure distance proposed is Kolmogorov-Smirnov statistics.A practical application of the algorithm proves its power.The proposed algorithm allows better clustering solar spectra data than classical k-means. This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.s. The distance function for clustering c.p.d.f.s that is proposed is based on the Kolmogorov-Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov-Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.s in only 6 different clusters that correspond to 6 different c.p.d.f.s.

Modeling time series of climatic parameters with probabilistic finite automata

A model to characterize and predict continuous time series from machine-learning techniques is proposed. This model includes the following three steps: dynamic discretization of continuous values, construction of probabilistic finite automata and prediction of new series with randomness. The first problem in most models from machine learning is that they are developed for discrete values; however, most phenomena in nature are continuous. To convert these continuous values into discrete values a dynamic discretization method has been used. With the obtained discrete series, we have built probabilistic finite automata which include all the representative information which the series contain. The learning algorithm to build these automata is polynomial in the sample size. An algorithm to predict new series has been proposed. This algorithm incorporates the randomness in nature. After finishing the three steps of the model, the similarity between the predicted series and the real ones has been checked. For this, a new adaptable test based on the classical KolmogoroveSmirnov two-sample test has been done. The cumulative distribution function of observed and generated series has been compared using the concept of indistinguishable values. Finally, the proposed model has been applied in several practical cases of time series of climatic parameters. � 2004 Elsevier Ltd. All rights reserved.

Original article: Comparing distributions with bootstrap techniques: An application to global solar radiation

Abstract: A statistic to test whether the distributions of two observable variables are similar is proposed, where two distributions are defined as similar if they are the same except for a change in location and/or scale. The test statistic for similarity that is proposed extends the Kolmogorov-Smirnov statistic that is used to test for homogeneity of two samples, but it requires the use of a smooth bootstrap procedure to compute critical values. The application of the similarity test to the analysis of global solar radiation data from various Spanish regions reveals that the vast majority of distributions that can be compared are not homogeneous, but in many case there is no evidence to reject that they are similar. In practice, this implies that the use of prediction and simulation models that depend on global solar radiation data can be generalized to a wide variety of regions with almost no cost.

Modeling Daily Profiles of Solar Global Radiation Using Statistical and Data Mining Techniques

Solar radiation forecasting is important for multiple fields, including solar energy power plants connected to grid. To address the need for solar radiation hourly forecasts this paper proposes the use of statistical and data mining techniques that allow different solar radiation hourly profiles for different days to be found and established. A new method is proposed for forecasting solar radiation hourly profiles using daily clearness index. The proposed method was checked using data recorded in Malaga. The obtained results show that it is possible to forecast hourly solar global radiation for a day with an energy error around 10% which means a significant improvement on previously reported errors.

Framework for Monitoring and Assessing Small and Medium Solar Energy Plants

The monitoring and assessment of small and medium solar energy plants were ruled out as the existing programs for these tasks are expensive and they are designed to run directly on the installation site, making it necessary to have both a monitoring system, such as data logger, and specialized staff capable of analyzing the monitoring data. To address these problems, this paper presents a framework that allows the development of programs for remote monitoring and automatic evaluation of solar energy plants without using any additional hardware. Software architecture based on separating the software functionalities into several layers and on using a hierarchical model of the plant elements is proposed. This framework allows the integration of different technologies and communication protocols of devices used in solar energy plants. A monitoring and assessing program for several dispersed solar energy installations has been developed as practical example.