## 1 Introduction  
With the widespread application of renewable energies such as photovoltaic and wind in power systems, the power electronic characteristics of these systems are becoming increasingly evident. As the key equipment for new energy integration, inverters have garnered considerable attention [1; 2]. However, there is a risk of oscillation in the interaction between the GCI and the power grid. Particularly when connected to a weak grid, this situation increases the likelihood of inducing broadband oscillations, which pose a serious threat to the stable operation of the power system [3; 4; 5]. Therefore, an in-depth analysis of the stability of GCIs holds important practical significance.  
Recently, the impedance analysis method has garnered significant attention in the study of inverter grid-connected stability due to its clear physical principles, straightforward measurability, and verifiability [6; 7; 8]. Currently, many studies have established impedance models of GCI that consider the current loop, PLL (phase-locked loop), and delay [9; 10]. However, the literature [11] points out that ignoring the frequency coupling characteristics can make the established impedance model inaccurate, which may lead to errors in stability analysis. In view of this, reference [12] has established a sequence impedance model considering the frequency coupling effect and has analyzed the mechanism of this effect. In references [13; 14], a frequency coupling admittance model of an L-type GCI considering various factors such as PLL, voltage outer loop, and current inner loop is established, and the GNC (generalized Nyquist criterion) is utilized to assess the stability of the system. Therefore, the use of impedance analysis for stability analysis has been widely studied.  
Based on the control domain differences, control methods can be categorized into PR control in the time domain and PI control in the \(dq\) (direct-quadrature) domain. It hasbeen established that, in terms of steady-state performance, time-domain PR control and \(dq\)-domain PI control are equivalent [15]. However, under conditions of a weak power grid, the stability of the two current-controlled GCI systems may differ [16]. Currently, the stability analysis of GCI systems controlled by PI in the \(dq\) domain using impedance analysis has been extensively studied [17; 18; 19; 20]. However, research on the stability analysis of GCI systems based on time-domain PR control using impedance analysis is limited. Moreover, the impact of voltage feedforward control on stability has not been considered in the aforementioned literature.  
Voltage feedforward control is commonly used to enhance the dynamic performance of GCI systems, suppress background harmonics, and alleviate imbalances caused by grid voltage fluctuations [21; 22; 23; 24]. However, in practical applications, it has been observed that voltage feedforward control significantly impacts the impedance characteristics and stability of the GCI system [25]. Therefore, it is crucial to analyze the impedance characteristics and stability of the GCI system with voltage feedforward control implemented.  
To address the stability analysis of the GCI system with different domain controls and considering voltage feedforward, a frequency coupling admittance model under time-domain PR control and \(dq\)-domain PI control is established using the multi-harmonic linearization method. The stability of these controls is then compared. This analysis elucidates the significance of different domain controls and voltage feedforward control in enhancing the stability of the GCI system.