Recent trend of research is oriented in different methods of emulating the inertia to increase the sustainability of the system. In the case of dynamic performance of power systems especially in frequency control of interconnected system, there are concerns considering the matter of virtual inertia. This paper proposes a new approach on modeling and analyzing the dynamic performance of the system with derivative based virtual inertia capability. As an important part of this paper the dynamic effects of PLL estimations on system performance are discussed and analyzed. The effects of PLL are considered by introducing a second-order function. Simulations performed by Matlab software demonstrate the effectiveness of virtual inertia on the system performance.