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The ongoing developments in the area of Smart Grids drastically have changed the objectives of the electricity power industry towards extensive monitoring, management and conservation of energy in the competitive power market and independent regulatory environment. In order to achieve a reliable, autonomous and intelligent Power Consumption Control System, that enables households to monitor, manage and conserve energy, we have integrated ICT as an enabling technology to gain energy savings and to reduce the energy bill of the households. The challenge of our research was to enable an efficient control of several home appliances plugged-in to multi-socket extension connected to a single power socket sensor. In this process, we had several problems to deal with, but the most important and challenging task was to identify exactly which of the appliances plugged-in to multi-socket extension was actually running. Therefore, the scope of this paper focuses on developing an algorithm for data clustering based on the box-dimension as a correlation measure between the monitored values from the power socket sensor data. The prediction analysis confirmed the operating states from our test bed and therefore met the evaluation criteria for our algorithm. As a result, the recognition of the operating states of the appliances provides an opportunity for their successful control, simultaneously increasing the energy efficiency.