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In this paper, thorough analysis is carried out on a microgrid system with a constant power load. Constant power loads make the system to be unstable due to their negative impedance characteristics and this is proved for the microgrid system by deriving the small signal state space model for the system and then observing the location of the system poles. Subsequently, a sensitivity analysis is carried out to check whether it is possible to eliminate the instability of the system by tuning the voltage and current controller gain values of the microgrid inverter system. Also by transforming small signal state space model to Laplace domain, stability conditions are derived for the microgrid with a constant power load connected parallel with other loads. From these conditions, the loading limit of the constant power load for making the system stable is obtained. These theoretical loading limits obtained are proven using a model of microgrid simulated in Matlab/Simulink platform.