Non-Intrusive Load Monitoring (NILM) plays an important role in energy management and energy reduction in buildings and homes. An NILM system does not need a large amount of deployed power meters to monitor the power usage of home devices. Instead, only one meter on the main power line is necessary to detect and identify the operating devices. There are many approaches to solve the problem of device determination in NILM. The features applied in low-frequency based approach essentially include the step-change (or edge) and the steady state. This paper introduces three algorithms to solve the l1-norm minimization problem in NILM and results on power measurements obtained from a real appliance deployment. With a small number of devices, the obtained precision varies from 75% to 99%, depending on the tolerance criterion to determine the steady state of a given device.