This paper addresses the problem of overloading in power distribution networks, which stems from the transmission systems being incapable of delivering power from source to consumers during peak hours. This causes frequent power-outages (or blackouts), requiring the consumers to rely on alternative energy sources, e.g., Uninterrupted Power Supply (UPS) systems with batteries to meet their essential needs. This paper proposes a demand response (DR) framework to eliminate the problem of network overloading. The flexibility in the consumption of batteries and air conditioners (ACs) is exploited in the proposed framework. The operation of ACs is manipulated while maintaining occupant comfort, and the power flow from mains and batteries is scheduled based on an ensemble of demand forecast avoiding network overloading and consequent power-outages. The problem is modeled in an optimal control setting and solved using a stochastic model predictive control strategy, and a computationally effective method is also proposed to efficiently solve the underlying optimization problems. Towards the end, simulation results show the efficacy of the proposed framework to avoid overloading.