Capacity challenges are becoming more frequent phenomena in residential distribution networks with new forms of loads, distributed renewable energy resources (RES) and price-responsive applications. Different types of demand response programs have been introduced to tackle these challenges through iterative changes in price and/or contractual participations based on incentives. In this research, a dynamic network tariff-based demand response program is proposed to address congestion problems in low-voltage (LV) networks. The formulation takes advantage of the scalable architecture of the agent-based systems that allows local decision making with limited communication. Energy consumption schedules are developed on a day-ahead basis depending on the expected cost of overloading for a number of probable scenarios. The performance of the proposed approach has been tested through simulations in the unbalanced IEEE European LV test feeder. Simulation results reveal up to 82% reduction in congestion on a monthly basis, while maintaining the quality of supply in the network.