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Consumers increasingly want to make informed and proactive decisions based on an understanding of their energy consumption. However, current energy monitoring solutions are either too limited in the information they provide or are too intrusive. We consider a solution for disaggregating the electrical power consumption of individual appliances connected in a residential electricity network, with a single point of measurement. We pose the power disaggregation problem in the framework of multi-user detection. Two linear detection algorithms are then provided to determine which appliances are active in the network and in turn to determine their individual power consumptions. An experimental setup is described that was used to evaluate the performance of the algorithms along with simulation results.