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The rapid growth of smart grid systems demands efficient management of smart grid services. Smart grids are expected to enable the delivery and management of electricity in a more reliable, efficient, economical, and secured manner. Thus, the development of effective power management solutions for smart grids to meet these challenges is an important area of research in recent times. In this article, we propose using learning automata (LA), a computational learning utility, for efficient power management in smart grids (LAPM). The proposed system, LAPM, helps in identifying the electricity required for various distribution substations and controls the usage of power by various devices (i.e., preventing unauthorized use of power). The use of LA enables performing a dynamic analysis of power usage and providing decision making for its effective usage. The system is evaluated on a real-life-resembling environment, with respect to parameters such as power utilization and customer satisfaction.