Evaluation of nonlinear models for time-based rates demand response programs

Demand Response (DR) programs have been implemented in many competitive electricity markets to prevent price spikes and power systems unreliability. Mathematical modeling of these programs helps regulators to evaluate the impact of price responsive loads on market conditions. In this paper, several nonlinear economic models of price responsive loads are derived based on price elasticity of demand and customer benefit function. The main objectives of the paper include extracting different mathematical models for Time of Use (TOU) programs, and comparing these models to find out which model shows more conservative and which one shows non-conservative results compared with the initial load curve. This could be used by ISOs or DR programs developers as a guideline to use conservative models to have lower error in load profile characteristics estimation, such as variation in peak load or amount of energy consumptions. In order to evaluate the performance of the proposed nonlinear DR models, numerical studies are conducted on the load curve of different markets. Results obtained by using different models are presented and compared considering different scenarios for price, elasticity and potentiality of DR programs implementation. Characteristics of both linear and nonlinear economic models of price responsive loads have been evaluated.