Inverters are important devices in AC microgrids

and their control strategies are key issues on the safety

reliability

effectiveness

and economical operation of microgrids. From the viewpoint of frequency domain

a comprehensive survey and comparison is achieved on the fundamental and harmonic power control. In view of the fundamental power control of an inverter in the microgrid

Vf control and droop control are explained in detail for the islanded inverter

while the direct power control

direct voltage control

direct current control

and direct impedance control are fully summed up for the grid-connected inverter. With respect to the harmonic power control of an inverter in the microgrid

switching ripples suppressing

harmonic resonance damping

and compensating of low-order harmonic load current are discussed in depth. To integrate the multiple inverters in a microgrid

the coordination strategies by using centralized hierarchical control and decentralized multi-agent-based control are fully discussed and compared. Finally

the trends and future frameworks to control inverters in AC microgrids are also presented. This work is jointly supported by National Natural Science Foundation of China (No. 51377184)

Fundamental Research Funds for the Central Universities (No. 106112015CDJXY150005

No. CDJZR12150074)

and State Grid Corporation of China (No. SGHADK00PJJS1500060).