Abstract：The growing integration of renewable energy sources has spurred widespread adoption of grid-connected inverters. However, the dynamic interaction between these inverters and weak grids introduces new stability challenges. The symmetrical phase-locked loop（SPLL）incorporates an additional d-axis control loop, achieving a symmetrical control structure that effectively eliminates the frequency coupling inherent in the traditional synchronous reference frame phase-locked loop（SRF-PLL). Although the symmetrical structure of the SPLL provides significant benefits, its impact on the stability of three-phase grid-connected systems under weak-grid conditions remains to be explored. The complex vector impedance model is commonly employed to evaluate the effect of the SPLL structure on the stability of grid-connected systems. However, this modelling method obscures the internal dq-axis dynamic coupling within the SPLL. In particular, the effect of the additional d-axis control remains unclear. Therefore, a new modeling method and analytical framework are required to elucidate the causes of instability and develop corresponding stabilization strategies. To begin with, the closed-loop coupling relationship among the “SPLL-current loop-grid impedance-PCC voltage-SPLL” is investigated. From the perspective of SPLL dynamics, the SPLL-based system can be equivalently represented by a dq-axis-coupled double-complex torque model. This model reveals that the d-axis control of the SPLL introduces a critical closed-loop dynamic coupling path of “q-axis→d-axi→q-axis”. Compared with the complex torque model, the additional damping introduced by this path is identified as the key factor driving the differing impacts of the two PLLs on grid-connected system stability under weak grid conditions. Furthermore, from a quantitative perspective, the damping of the dominant oscillation mode in the SPLL-based system is decomposed into two components: the inherent damping of an SRF-PLL-based system and the additional damping introduced by the dq-axis control coupling. Under weak-grid conditions, this additional damping component introduces negative damping, and its magnitude increases with rising grid impedance. Therefore, this negative damping constitutes the root cause of oscillatory instability in the SPLL-based system. This paper proposes an improved current-loop control strategy with a symmetrical structure to enhance system stability. In this strategy, the phase perturbation from the SPLL is utilized as a feedforward input for a dedicated compensation controller, which injects corrective terms into both the d-axis and q-axis current loops. These terms are designed to cancel the component of output current disturbance that is directly induced by the SPLL phase perturbation, thereby weakening the critical “PLL-current loop” coupling path. Consequently, the negative damping component introduced by the dq-axis coupling in the equivalent complex torque is significantly attenuated. Furthermore, by appropriately tuning the compensation controller parameters, the improved grid-connected system exhibits enhanced robustness against grid impedance variations while maintaining excellent dynamic and transient performance. Finally, a hardware-in-the-loop experimental platform is constructed based on RT-Lab. The experimental results demonstrate that the proposed improved current-loop control strategy ensures system stability under weak-grid conditions by effectively suppressing oscillations. Meanwhile, in dynamic scenarios involving sudden grid voltage sags and grid frequency fluctuations, the system with the proposed control strategy maintains excellent robustness and dynamic performance, confirming its effectiveness across different operating conditions.
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2026, Vol. 41 
