Nonlinear Modeling of the Demand Response Programs in the Power Systems, Considering Indefinite Consumer Participation

The challenge of excessive energy consumption, related environmental issues, and optimal utilization of restructured power systems require proper management on the demand side. In this context, demand response programs, try to encourage, persuade, or force consumers to adjust their consumption patterns within that established by the system operator. In this article, to improve accuracy, nonlinear models for demand response programs (power, exponential, and logarithmic models) for incentive-based and time-based programs, have been developed based on price elasticity and customer profit function. Then, the behavior of the proposed models against changes in elasticity, encouragement/penalty rate, and the effect of consumer participation have been investigated in several scenarios. Since consumer participation in these programs depends on various economic, cultural, and social factors, it cannot be accurately predicted. In addition, consumer participation has a significant effect on the program results. So, the consumer participation percentage has been considered an uncertain parameter based on a normal probability distribution function. The results show that the non-linear models are more accurate and more conservative than the linear model. Moreover, considering consumer participation as an uncertain normal parameter results in more reliable responses with more peak reduction and a greater reduction in total energy consumption.