This paper aims to demonstrate the effect of re-heat and non-reheat turbines and some important physical constraints such as generation rate constraint (GRC), time delay and speed governor dead band on the dynamic behaviour of automatic generation control (AGC) in an interconnected power system. The mentioned constraints imposed to power system by governor-turbine, thermodynamic process, and communication channels. Simple structure beside acceptable response of the conventional integral controller makes it attractive for power system AGC issue. Optimum integral gains are computed by genetic algorithm (GA) technique for an interconnected three control areas with non-reheat/reheat generating units to achieve an optimal performance. Simulations results reveal that the scope of optimum solutions was limited by considering physical constraints in addition to the increasing of settling time and over/under-shoots.