In conventional generation systems, the possibility of system restoration and reducing power swings among different generation units is high, as an adequate reserve can be supplied from neighboring generation units to restore the operation. In contrast, the situation is different in the case of isolated microgrids, as the system reserve and capabilities of the whole system to recover from disturbances are limited, especially when the microgrid is supplied by intermittent sources as wind energy. This paper presents the state space modelling of isolated microgrids supplied by different energy sources, and thereafter, the eigenvalue sensitivity analyses are conducted. The main contribution of this paper is that a detailed model of an isolated microgrid supplied by different energy sources, particularly battery units and doubly-fed induction generators is presented. Moreover, in contrast to the most recent papers, which have discussed the state space modelling of several energy sources and have not studied the effect of load dynamics on the stability of power systems, this paper includes the dynamics of two of the most common loads, heating and induction machines. Their effects on the stability of the microgrid are discussed in detail.