In this study a logarithmic modeling for Direct Load Control programs (DLC) as incentive-based Demand Response Programs (DRPs) is presented. The proposed model considers nonlinear behavioral characteristic of elastic loads which causes to more realistic modeling of demand response to DLC rates. To demonstrate the validity of the proposed technique, a real world power system is considered as test system. Where, Iranian power system is investigated. Simulation results emphasis on the effectiveness impact of running DLC programs using proposed logarithmic model on load profile of the peak day of the proposed power system.