# Evaluation and Comparison of Spatial Clustering for Solar Irradiance Time Series
## 1 Introduction  
Renewable energy is commonly referred to as clean energy, as it comes from natural processes or sources that are constantly being renewed. However, it is recognized that the knowledge of the \"availability\" and \"variability\" of these renewable sources [1] is an important task and a great challenge, considering that the development of solar energy over the world is increasing and will continue to increase in the future [2, 3, 4]. The main problem of this energy source, which could inhibit or reduce its development, is its intermittence and randomness, which make its management difficult for an energy system operator [5]. Thus, to reduce and even to delete, at least partially, this inconvenience, three research axes must be developed in parallel:  
* The development of energy storages: They will allow us to store the energy in excess and to restore it when the load requires it [6];* The development of smart concepts of electrical grid: The produced and consumed energy and power must be managed efficiently with smart algorithms, using information and communication technologies [7];
* The forecasting of the intermittent renewable energy production: Solar- or wind-prediction tools must be integrated into energy and power management systems to anticipate the future actions [8]. The benefit of solar radiation prediction is effectively proven [9]. There are a large number of publications in the literature that address the problem of solar-irradiance prediction. The techniques applied to prediction depend on the time horizon of the prediction and the time step of the solar irradiation [10]. Between these methods, time-series-based methods are based on statistical models applied to ground data measured in the past and at the instant of the prediction, using regression techniques [11], artificial intelligence methods [12], or statistical approaches [13]. They are used to forecast solar data from some minutes to about a 6 h horizon. They often have the disadvantage of being efficient only for the site on which the model has been trained and to be not generalizable elsewhere. It should be interesting to verify if a model developed on a given site must be applied to other ones with \"similar\" characteristics not only from the received-solar-energy point of view but also from the point of view of the dynamic behavior of the solar irradiation one. With this final objective, the purpose of this study was to group the meteorological stations by \"solar radiation affinities\". Clustering is a technique used in data mining to identify clusters of elements according to a measure of similarity between them. In addition, clustering to minimize the dimensionality of the data while handling a large number of variables is used [14]. On the other hand, the clustering of geographically spaced data has been addressed in the literature. Still, this one seeks to cluster similar or geographically proximate data in geographic-information-system (GIS) information layers [15]. The study of the behavior of times series applied to a large territory by using statistic and artificial intelligence (AI) methods, grouping in \"clusters\" time series with the same behavior (i.e., with the same variability), was realized particularly in two papers written by [PERSON] [16] and [PERSON] et al. [17]. The first one [16] summarized previous works on clustering time-series data into various application domains and discussed criteria for evaluating the performance of clustering results and measures for determining the similarity/dissimilarity between two time series. The second one [17] realized a high-dimensional time-series clustering work, using algorithms based on distance metrics that generally fail because they cannot handle missing data. Instead, time series are clustered based on global features extracted from each series and can be fed into clustering algorithms. In these works, statistical operations describe the time series: trend, seasonality, periodicity, serial correlation, kurtosis, chaos, nonlinearity, and self-similarity.