Highlights What are the main findings? Proposed a comprehensive modeling layout for the optimal management of power and heat in the distribution system, taking into account load emergencies such as overload and load shedding. Incorporated different energy sources, such as renewables, batteries, power to hydrogen, CHP sources, and heat storage tanks, as well as demand response programs for both electrical and thermal loads. What is the implication of the main finding? The proposed approach aims to effectively balance the energy supply and demand in the network, especially during emergency situations, to certify the system's reliability and stability. Provided a cost-effective and environmentally friendly solution for managing the distribution network, while also improving its resilience and reducing the risk of energy supply disruptions.Highlights What are the main findings? Proposed a comprehensive modeling layout for the optimal management of power and heat in the distribution system, taking into account load emergencies such as overload and load shedding. Incorporated different energy sources, such as renewables, batteries, power to hydrogen, CHP sources, and heat storage tanks, as well as demand response programs for both electrical and thermal loads. What is the implication of the main finding? The proposed approach aims to effectively balance the energy supply and demand in the network, especially during emergency situations, to certify the system's reliability and stability. Provided a cost-effective and environmentally friendly solution for managing the distribution network, while also improving its resilience and reducing the risk of energy supply disruptions.Highlights What are the main findings? Proposed a comprehensive modeling layout for the optimal management of power and heat in the distribution system, taking into account load emergencies such as overload and load shedding. Incorporated different energy sources, such as renewables, batteries, power to hydrogen, CHP sources, and heat storage tanks, as well as demand response programs for both electrical and thermal loads. What is the implication of the main finding? The proposed approach aims to effectively balance the energy supply and demand in the network, especially during emergency situations, to certify the system's reliability and stability. Provided a cost-effective and environmentally friendly solution for managing the distribution network, while also improving its resilience and reducing the risk of energy supply disruptions.Abstract This study introduces an advanced Mixed-Integer Linear Programming model tailored for comprehensive electrical and thermal energy management in small-scale smart grids, addressing emergency load shedding and overload situations. The model integrates combined heat and power sources, capable of simultaneous electricity and heat generation, alongside a mobile photovoltaic battery storage system, a wind resource, a thermal storage tank, and demand response programs (DRPs) for both electrical and thermal demands. Power-to-hydrogen systems are also incorporated to efficiently convert electrical energy into heat, enhancing network synergies. Utilizing the robust Gurobi solver, the model aims to minimize operating, fuel, and maintenance costs while mitigating environmental impact. Simulation results under various scenarios demonstrate the model's superior performance.