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The phase-locked loop (PLL)-based grid-following inverters have been widely used as the interface between renewable energy resources (e.g., wind and solar power) and the utility grid. In addition to the basic PLL and inner current control loop that are responsible for tracking the phase angle of the point of common coupling (PCC) voltage and regulating the current injection according to the estimated phase angle, respectively, these grid-following inverters are commonly also equipped with outer power and voltage control loops. Some examples are outer active power/dc-link voltage control loops and outer reactive power/PCC voltage control loops, which provide the <inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>-axis current references for the inner current control loop. However, the existing literature generally focuses on specific outer control modes within a specific small-signal modeling framework, e.g., state-space or admittance modeling framework. In addition, different research groups usually repeatedly derive these small-signal models without a systematic modeling and analysis procedure. Furthermore, the systematic and comprehensive comparative modal and admittance analysis of these outer control modes is still missing in the literature. To avoid reinventing the wheel, provide the small-signal stability analysis community with handy both state-space and admittance models, and investigate the effects of various outer control loops on the small-signal models, this article presents a comprehensive and systematic small-signal modeling, analysis, and comparison framework of the PLL-based grid-following inverters, where the state-space and <inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>-domain admittance models of eleven control modes are derived step by step in a completely followable style. All of these derived small-signal models are verified by the time-domain step responses and frequency-domain <inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>-domain admittance measurement. The insights into the effects of these outer control modes on the poles and residues of the <inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>-domain admittance model are also explored, which help to understand how these outer control modes contribute to the <inline-formula> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula>-domain admittance shaping.

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Comprehensive Modeling, Analysis, and Comparison of State-Space and Admittance Models of PLL-Based Grid-Following Inverters Considering Different Outer Control Modes