This paper presents a comparative study on the implementation of incentive-based demand response programs in power grid management, comparing the results obtained from linear and nonlinear models. The challenges faced by power grids in balancing supply and demand and managing price spikes during peak periods are addressed, and demand response programs are proposed as an effective strategy. The focus is on implementing incentive-based programs where load serving entities determine the optimal incentive price and demand reduction. A novel approach is presented for simulating consumer behavior based on the price elasticity of demand and consumers’ utility function, incorporating both linear and nonlinear economic models. The calculation of demand reduction aims to maximize consumers’ welfare, while the determination of the optimal incentive price maximizes the profit of the load serving entities. Real data are utilized, and the proposed models are implemented using the mixed-integer nonlinear programming (MINLP) method. The results demonstrate the effectiveness of providing incentives to consumers during peak hours compared to other approaches, with a comparison between the linear and nonlinear models.

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