As the variety of loads in microgrids continues to grow rapidly, the drawbacks of using conventional voltage and current double closed-loop PI control are becoming increasingly intolerable. These disadvantages include poor static tracking of the output and the need for complicated tuning of optimal PI control parameters. Model predictive control (MPC) is widely studied in recent years and gradually applied to the inverter as a modern control strategy. Currently, the research on MPC mainly focuses on reducing the computational burden of algorithms and improving computing skills. In this paper, the control theory of continuous-control-set model predictive control (CCS-MPC), optimal switching vector model predictive control (OSV-MPC), quasi-sliding mode model predictive control (QS-MPC) and optimal switching sequence model predictive control (OSS-MPC) are elaborated. Also, the disadvantages of adopting conventional voltage and current double closed-loop PI control on microgrids are clarified. Moreover, aiming at evaluating the influence of connecting and/or removing the common loads, such as electric vehicles to the microgrid on the output performance of microgrids in practical engineering applications, single three-phase voltage source inverter with LC filter system with two-phase pure resistance load, three-phase diode rectifier bridge nonlinear load, constant power load and constant current source load applying four different MPC methods, are simulated. The simulation results show that under different types of load, system with nonlinear load applying OSV-MPC method has the biggest value of total harmonic distortion (THD) of the output voltage and the biggest steady state root mean square (RMS) tracking error of the output voltage, which are 1.33% and 2.1 V, respectively. The performances of the output voltage of the system adopting MPC are generally improved compared to the system using conventional voltage and current double close-loop PI control. Regarding the output voltage performance of a system under load step change, a system using the OSS-MPC method with a nonlinear load exhibits the smallest overshoot of the output voltage and the smallest root mean square value of the tracking error (RMSE) between the output voltage and the reference value within 20ms after the load step change. Specifically, the overshoot and RMSE are 2.804 V and 0.810 V, respectively. The simulation results provide valuable guidance for selecting the appropriate model predictive control strategy for microgrid integrating complex loads, such as electric vehicles in practical applications.