The dynamic pricing environment offers flexibility to the consumers to reschedule their switching appliances. Though the dynamic pricing environment results in several benefits to the utilities and consumers, it also poses some challenges. The crowding among residential customers is one of such challenges. The scheduling of loads at low-cost intervals causes crowding among residential customers, which leads to a fall in voltage of the distribution system below its prescribed limits. In order to prevent crowding phenomena, this paper proposes a priority-based demand response program for local energy communities. In the program, past contributions made by residential houses and demand are considered as essential parameters while calculating the priority factor. The non-linear programming (NLP) model proposed in this study seeks to reschedule loads at low-cost intervals to alleviate crowding phenomena. Since the NLP model does not guarantee global optima due to its non-convex nature, a second-order cone programming model is proposed, which captures power flow characteristics and guarantees global optimum. The proposed formulation is solved using General Algebraic Modeling System (GAMS) software and is tested on a 12.66 kV IEEE 33-bus distribution system, which demonstrates its applicability and efficacy.