With the increase of the renewable energy generator capacity, the requirements of the power system for grid-connected converters are evolve, which leads to diverse control schemes and increased complexity of systematic stability analysis. Although various frequency-domain models are developed to identify oscillation causes, the discrepancies between them are rarely studied. This study aims to clarify these discrepancies and provide circuit insights for stability analysis by using different frequency-domain models. This study emphasizes the limitations of assuming that the transfer function of the self-stable converter does not have right half-plane (RHP) poles. To ensure that the self-stable converters are represented by a frequency-domain model without RHP poles, the applicability of this model of grid-following (GFL) and grid-forming (GFM) converters is discussed. This study recommends that the GFM converters with ideal sources should be represented in parallel with the $P/Q-\theta/V$ admittance model rather than the V-I impedance model. Two cases are conducted to illustrate the rationality of the $P/Q-\theta/V$ admittance model. Additionally, a hybrid frequency-domain modeling framework and stability criteria are proposed for the power system with several GFL and GFM converters. The stability criteria eliminates the need to check the RHP pole numbers in the non-passive subsystem when applying the Nyquist stability criterion, thereby reducing the complexity of stability analysis. Simulations are carried out to validate the correctness of the frequency-domain model and the stability criteria.

The diode-rectifier unit (DRU)-based high-voltage direct current (HVDC) transmission system offers an economical solution for offshore wind power transmission. However, this approach requires offshore wind farms to establish a strong grid voltage. To meet this requirement while fulfilling the dynamic characteristics of the DRU, this paper proposes an advanced grid-forming (GFM) control strategy for offshore wind turbines connected to DRU-HVDC. The strategy incorporates a P-U controller and a Q-$\omega$ controller based on reactive power synchronization. Furthermore, a novel virtual power-based pre-synchronization method and an adaptive virtual impedance technique are integrated into the proposed GFM control to improve system performance during wind turbine (WT) integration and low-voltage ride-through (LVRT) scenarios. The virtual power-based pre-synchronization method reduces voltage spikes during the integration of new wind turbines, while the adaptive virtual impedance technique effectively suppresses fault currents during low-voltage faults, enabling faster recovery. Simulation results validate the effectiveness of the proposed GFM control strategy, demonstrating improved start-up and LVRT performance through the pre-synchronization and adaptive virtual impedance methods.