This paper evaluates the design and optimization of an islanded hybrid microgrid system by assessing the optimal sizing of each component and the power, voltage and frequency profiles. The test case location is the Kangaroo Island, South Australia. The sizing of the Kangaroo Island hybrid microgrid system incorporating PV, wind, diesel generator, and battery storage have been optimized for four different power dispatch strategies: (i) load following, (ii) cycle charging, (iii) generator order and (iv) combined dispatch. The islanded microgrid has been optimized to minimize the CO2 emission, net present cost (NPC) and Levelized cost of energy (LCOE). All four dispatch strategies have been implemented in HOMER microgrid software platform, and subsequently the transient studies have been performed in MATLAB/Simulink platform. The results provide a guideline to estimate the generation-mix and required resources for optimal operation of an islanded microgrid with different dispatch scenarios.