In conventional power system operation, droop control methods are used to facilitate load sharing among different generation sources. This method compensates for both active and reactive power imbalances by adjusting the output voltage magnitude and frequency of the generating unit. Both P-ω and Q-V droops have been used in synchronous machines for decades. Similar droop controllers were used in this study to develop a control algorithm for a three-phase isolated (islanded) inverter. Controllers modeled in a synchronous dq reference frame were simulated in PLECS and validated with the hardware setup. A small-signal model based on an averaged model of the inverter was developed to study the system's dynamics. The accuracy of this mathematical model was then verified using the data obtained from the experimental and simulation results. This validated model is a useful tool for the further dynamic analysis of a microgrid.