Evaluation of the performance of clustering algorithms for a high voltage industrial consumer
Introduction
Electricity consumer classification is a prominent scheme in the deregulated markets, since it can serve as the basis for designing suitable tariffs that directly reflect the generation costs. The consumers of the same class present similar daily demand patterns and different pricing policies can be applied, leading to increased profitability of retailers (Mahmoudi-Kohan et al., 2010). Load profiling is a tool that provides the required information about the demand behavior among various kinds of consumers, so that the aforementioned actions can be effectively implemented.
Given a set of metered load data, the task of grouping them in a sophisticated manner is a subject of many requirements (Panapakidis et al., 2013). First of all, a representative sample of load curves must be obtained when dealing with the load profiling of either an individual consumer or a group of consumers. After gathering the metered data, we need to specify the load condition. This refers to the periodic attributes of the demand. For example, the load profiling may consider only working days excluding holidays and weekends. In our work, we formulated nine yearly daily load data sets. Next, a suitable preprocessing of the data is necessary. The data are normalized in the appropriate range, since in the clustering operation we are concerned mainly with the load curve shape similarities. The load profiling process involves the proper selection of one or more clustering algorithms. Each algorithm has unique characteristics, such as input parameter requirements, speed and computational complexity. The purpose of the clustering procedure is the search of structures within a data sample. The formation of groups takes place, where the population within the same group shows more similar characteristics compared with the members of the other groups. The clustering procedure is data driven. In the majority of the applications there is no a priori knowledge about the relations between the data, their geometry or special attributes.
Section snippets
Literature survey and contributions
In most cases, the appropriate number of daily load curve clusters is unknown. Therefore a load profiling problem is formulated as an unsupervised learning task (Panapakidis et al., 2013). Clustering based load profiling is a two-stage process. In the first stage, each consumer is studied separately. His daily load curves are clustered and certain classes are formed. Each class is represented by the average daily load curve, which is actually the normalized load profile. In the second stage, a
Data collection
The data set used in this work is composed by nine subsets, corresponding to different years, between 2003 and 2011. To provide a general overview of the yearly demand, Table 1 registers the minimum, maximum and average load and daily consumed energy per year, together with the annual variation from the base year of 2003. The null values of Table 1 refer to temporary terminations of the industrial activity. It can be noticed that the maximum load continually increases until 2007. Then for the
Sensitivity analysis for the calibration of the algorithms parameters
The operation of almost all the algorithms depends strongly on the initialization conditions. The random choice of the centroids is the main drawback for achieving a fast convergence and a global minimum of the corresponding objective function. The first step in current analysis is the investigation of the sensitivity of the algorithms for varying performance parameters. For this analysis the selected data set includes only 365 daily load curves for one year, namely year 2011 throughout this
Discussion and summary
The main contributions of the paper can be summarized in the following:
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The studies in the literature present comparisons among several algorithms only in terms of minimizing the clustering error. In this study, five additional conditions are introduced in order to provide a more in depth comparative analysis of the performance of the algorithms.
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The most commonly used algorithms of the literature are considered. It is shown that to optimize their performance, a parameter calibration prior to
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