Kohonen Maps Combined to Fuzzy C-means, a Two Level Clustering Approach. Application to Electricity Load Data

In a deregulated electricity market, load forecasting is nowadays of paramount importance to estimate next day load resulting in energy save and environment protection. Electricity demand is influenced (among other things) by the day of the week, the time of year and special periods and/or days such as religious and national events, all of which must be identified prior to modelling. This identification, known as day type identification, must be included in the design stages either by segmenting the data and modelling each day type separately or by including the day type as an input, which implies data classification and cluster creation. Data classification consists in regrouping objects of a similar data set into homogenous classes. Two main types of classifications exist: supervised and unsupervised classification. Supervised classification is based on a set of objects L of known classes, called training set, with the main goal being to identify candidate objects into their belonging classes. Where, unsupervised classification consists in partitioning a set of data D into sub-sets of similar attributes called classes or clusters (Halgamuge, 2005). Unsupervised classification is termed clustering, and will be so in the remaining of the chapter. For clustering means, conventional research usually employs multivariate analysis procedures. However, it was found that clustering the data directly, becomes computationally heavy using statistical method as the size of the data set increases (Jain & Dubes, 1988; Xu & Wunsch, 2005). Despite this fact, many linear approaches such as Principal Component Analysis (PCA) (Jolliffe, 2002) and K-means were and remain, extensively used for classification and clustering purposes. Nonlinear classification and clustering approaches stand as a strong alternative in order to treat the complexity and visualisation problems issued from large multidimensional data sets. In recent years, due to their high performance in engineering, Artificial Neural Networks (ANN), more specifically Self Organising Maps (SOM), and fuzzy logic are now being used as alternate statistical tools. Combining both paradigms in a two-level approach may be profitable to reduce significantly the computational cost as shown in (Khadir et. al., 2010) where SOM and K-means were combined for time series clustering.