This paper investigates the synchronization stability of one multiple virtual synchronous generators (VSGs) embedded power system with the current saturation and limits of frequency. The dynamic model of the multiple VSGs integrated system with controller limits is built. Accordingly, the transient energy function (TEF) for the autonomous system without touching controller limits is established, and the stability region is determined via the method of the closet unstable equilibrium point (UEP). Further, it is found that the system leaves away from the bounds of frequency at several leaving bound points . Among these, there exists two special ones with the minimal transient energy, and they are fixed irrespective of the switching times. Finally, one stabilizing condition is proposed that only if the energy of two special leaving bound points is less than the system critical energy, the global stability is ensured. The system critical energy is determined by the minimum of two values, namely, the method by closet UEP, and the maximum potential energy to ensure the system does not enter the mode of current limiting control (CLC). The numerical simulations of 9-buses and 39-buses power systems have verified the correctness of the proposed analysis.

This paper proposes a general power flow modeling method for power systems with control mode switching. Due to the diverse control strategies of power electronic device, a single converter-interfaced generator (CIG) may operate under multiple modes. Traditional Newton-based solvers typically rely on hard switching logic, which can lead to oscillations and non-convergence. To address this, This paper first reviews and analyzes two mainstream Newton-based iteration frameworks and reveal the mechanisms behind their convergence failures. Then a unified multi-mode modeling approach is presented. A set of binary variables are used to represent multiply mode. Based on the voltage and reactive power limits, the constraints are reformulated as a set of linear constraints exactly. Building on this, second-order cone (SOC) relaxation is applied to recast the power flow problem as a convex optimization model. This optimization-based framework not only facilitates computation but also allows tuning the objective function to reflect different operational preferences. An adaptive tightening strategy are developed to ensure the relaxed solutions can be recovered to physically feasible power flow solutions. Case studies on 33-bus and 118-bus systems demonstrate that the proposed method matches the Newton method when the latter converges, and still obtains feasible solutions when traditional algorithms oscillate, highlighting its robustness and applicability.

This paper investigates the transient stability of Grid-Forming (GFM) Permanent Magnet Synchronous Generator (PMSG) systems during grid faults. An analysis demonstrates how a fixed saturated current angle can trap the system in undesirable operating points, while reactive power coupling can degrade performance. Both factors pose a risk of turbine overspeed and instability. To overcome these vulnerabilities, a dual-mechanism control strategy is proposed, featuring an adaptive saturated current angle control that, unlike conventional fixed-angle methods, which risk creating Current Limiting Control (CLC) equilibrium points, dynamically aligns the current vector with the grid voltage to guarantee a stable post-fault trajectory. The effectiveness of the proposed strategy is validated through time-domain simulations in MATLAB/Simulink. The results show that the proposed control not only prevents overspeed trip failures seen in conventional methods but also reduces post-fault recovery time by over 60% and significantly improves system damping, ensuring robust fault ride-through and enhancing overall system stability.