Reduction of overall system inertia in response to increasing penetration level of Micro-Grids (MGs) makes frequency control more challenging. In this paper, a new analytical approach to mathematically investigate the impact of Micro-Grids penetration level on power system frequency stability is proposed. The method interprets the frequency dynamic behavior of the penetrated system based on the conventional system in terms of minimum instantaneous frequency, steady state deviation and a 15-second rolling window. Then, new indices are proposed to determine the maximum allowable MGs penetration level. These indices are derived by adapting the developed analytical approach to the required standards regarding the aforementioned criteria. Each index determines an upper bound on reduction of system inertia, which, in turn specifies the associated maximum penetration level. The maximum value of the inertia constant related to the developed indices (whichever is the larger) determines the system maximum allowable penetration level. The effectiveness of the proposed analytical approach and indices is demonstrated on a 16-machine 68-bus system and the IEEE 50-machine systems. Simulation results for large-scale power systems with high stiffness reveal that based on the operating condition, one of the minimum instantaneous frequency or 15-second rolling window impose an upper bound on penetration level.
