This paper presents a design-oriented modeling approach to analyze the Q-V control loop of grid-forming distributed generators (DGs). Unlike previous modeling methods, the proposed approach covers all typical operation modes of grid-forming DGs. No matter which type of inner control scheme is applied, once its state-space model in grid-connected mode is established, the models in islanded single-DG mode and islanded multi-DG mode can be obtained through the proposed formulas. With this novel framework, we analyze and compare two major Q-V control schemes of grid-forming DGs, i.e. the voltage/current double loop-based control, and the reactive power loop-based control, through respective reduced-order models. Closed-loop pole analyses of both control schemes in all three operation modes are investigated to highlight the different features between control schemes and operation modes. These analyses are verified by step-response analyses, which well match corresponding experimental results. The findings of this paper help us to better understand the Q-V control loop of grid-forming DGs, e.g., the different features and relations in each operation mode, the pros/cons of the two major control schemes, and the design concerns of inner-loop parameters considering all operation modes.
