This paper proposes a more realistic model for automatic generation control (AGC) design in an interconnected power system by considering the generation rate constraint (GRC), dead band, and time delays. These physical constraints imposed to power system by governor turbine, filters, thermodynamic process, and communication channels. The simplicity of structure and acceptable response Of the well-known integral controller make it attractive for Power system AGC issue. In this paper, a genetic algorithm (GA) approach is employed to calculate the controller parameters to achieve an optimal performance. Importance of considering the physical constraints is demonstrated by examination of the closed loop performance in a 3-control area power system. It is shown that neglecting above physical constraints, simultaneously or in part, leads to impractical and invalid results. Taking to account the advantages of the GA besides considering a more complete dynamic model provides a flexible and more realistic AGC system in comparison of existing conventional schemes.