This paper presents an optimization framework for minimizing both operational and emission-related costs in power grids through demand response (DR) actions, such as load shifting. The proposed approach accounts for the network and location-specific aspects of load, addressing the inherent complexity of bilinear terms in the optimization problem. By applying McCormick relaxation to approximate bilinear interactions between demand shifts and emission factors, we transform the problem into a solvable convex form. A two-step approach is further employed to refine emission values, ensuring accurate emission calculations and optimal demand response strategies. This work contributes to the integration of DR in decarbonized grids, providing a framework for reducing the environmental impact of electricity consumption while maintaining grid stability.
