Linear Optimization of Demand Response with Endogenous Estimation of Marginal Price

Traditionally, modeling and optimizing DR has faced challenges such as uncertainty in consumer response and the complexity of coordinating a large number of participants. Many optimization approaches treat energy prices as exogenous parameters, which simplifies the problem but may not fully capture the dynamic interaction between demand and market prices, especially when the magnitude of DR is significant.

The proposed approach focuses on a linear optimization model for managing Demand

Response. The main innovation of this approach lies in the endogenous estimation of the marginal price of the power system within the optimization problem itself. This means that the marginal price is not considered a fixed input, but a variable determined as part of the optimal solution. Models that incorporate demand sensitivity to prices and their impact on marginal prices have been explored in the literature, highlighting the importance of this interrelation. The linear model aims to minimize the total costs of operating the power system, considering that the activation of DR must meet a relationship with the marginal cost ensuring the maximization of social welfare (SWM). Initially, this problem had to be solved iteratively, making the decision difficult if the number of DR offers was very long.