PV systems are typically equipped with reactive power compensation devices when connected to the grid, and static synchronous compensator (STATCOM) devices are widely employed due to their flexible control capabilities. The increasing utilization of power electronic devices in the power grid has resulted in a shift from physical synchronization to control synchronization as the dominant mode of system operation. Analyzing static synchronization stability problem is more challenging for these systems compared to conventional power systems, as converter output characteristics are influenced by control strategies. Therefore, it is imperative to urgently address the problem of static synchronization stabilization under control strategy dominance.

First, this paper establishes the static synchronous stability analysis model of the grid-connected converter based on the control loop and circuit structure of each converter in a parallel system under the respective dq reference frame. The dq reference frame of the converter is determined by the phase information provided by the control loop in a multiple converter parallel system, thus enabling a unified coordinate system for static synchronization stability analysis. Subsequently, an equivalent small signal model is developed for analyzing multiple grid-connected converters. In comparison with existing coordinate conversion methods, Kirchhoff's current law is incorporated to enhance accuracy and reduce errors.

Then, the stability criterion for impedance analysis is enhance, and the static grid-synchronization performance indices are created. The small perturbation oscillation characteristics are measured using overshooting and regulation time, while the participation factor is employed to analyze the impact of each pole of the system. Finally, the attenuation coefficient is utilized to assess static synchronization stability performance.

The model is developed in Matlab/Simulink for simulation verification. Subsequently, an analysis is conducted on the impact of parameters such as the control loop parameters and STATCOM capacity on static synchronization stability. The main conclusions are summarized as follows:

(1) Optimizing the reactive power output of the grid-connected converter based on known control parameters can significantly enhance static synchronization stability performance, with the dominant influence of small perturbations after oscillation mode being attributed to poles generated by phase-locked loop control.

(2) The attenuation coefficient of the system exhibits a rapid increase in proximity to the critical stability region. Hence, it is imperative for the system to possess a certain margin of attenuation coefficient during operation. Based on the simulation analysis results presented in this study, static synchronous instability phenomena occur when the attenuation coefficient of the PV system exceeds 300. Conversely, when the attenuation coefficient falls below 250, the system remains in a state of static synchronous stability. These findings establish a criterion for analyzing and assessing static synchronization stability within such systems.

(3) The addition of STATCOM to the PV system primarily impacts the conductance matrix transfer function of the q-coupled channel. The phase-locked-loop coupling oscillations between the grid-connected converters do not affect the dd channel. Within the stable operating region, an increase in bandwidth for the DC voltage control loop, active current control loop, and reactive current control loop results in an amplification of both attenuation coefficient and system oscillation amplitude.

(4) When the phase-locked loop parameters of the STATCOM are the same as the PV system, the stability performance of the system is mainly affected by the grid impedance and the equivalent conductance transfer function of each grid-connected converter. And each grid-connected converter can independently connect to the grid and achieve stable operation to ensure that the system achieves static synchronous stability in this case.

(5) In cases where the active output of the PV system is low, STATCOM typically adjusts its capacitive or inductive reactive power provision to improve static synchronization stability performance. Conversely, when compensating for capacitive reactive power, utilizing STATCOM may yield superior results compared to using the PV grid-connected converter alone. Hence, allocating an optimal capacity for STATCOM can significantly enhance static synchronization stability performance.