Analysis of voltage-power security and stability boundaries for virtual synchronous control based on a transient energy function

To address the difficulty in accurately characterizing the stable operating boundary of a voltage-type virtual synchronous generator (VSG) connected to a bulk AC grid, where voltage dynamics and power dynamics are strongly coupled, this paper proposes a transient-energy-function-based method for analyzing voltage–power security and stability boundaries. First, the bulk AC grid at the point of interconnection is represented by a Thévenin equivalent voltage source in series with an equivalent impedance, and a third-order nonlinear dynamic model of the VSG is established with the power angle, frequency deviation, and internal voltage magnitude as state variables. Second, based on the active power–frequency control and reactive power–voltage control mechanisms of the VSG, the coupling relationships among the internal voltage magnitude, power angle, active power, and reactive power are derived, and a transient energy function incorporating the internal voltage magnitude E is constructed. Furthermore, the transient stability region in the state space is defined using the critical energy, and a composite voltage–power security and stability region is established by incorporating both internal voltage constraints and point of common coupling voltage constraints. Finally, the state-space stability region is mapped onto the P-Q plane through the power mapping relationship, thereby obtaining the voltage–power security and stability boundary of the VSG. The proposed method characterizes voltage–power coupling from an energy perspective and provides a theoretical basis for secure operating-region assessment of VSGs connected to bulk AC grids.