Defining the Grid Strength Measure through the Existence of Quasi-equilibrium Points

The large-scale integration of renewable generation and widespread application of high-voltage direct current (HVDC) transmission lead to a continuous increase in the penetration of power electronic devices. To quantify the grids' ability to integrate power electronic devices, different types of grid strength measures, e.g., short circuit ratio (SCR), have been developed and used in system planning. However, a rigorous definition of grid strength measure with a solid mathematical foundation is still lacking, especially considering the complex dynamical interactions among power electronic devices. To fill this gap, we develop a grid strength measure for power electronics penetrated power systems (PEPPS) and establish its theory foundation via the existence of quasi-equilibrium points. Specifically, we begin by defining a grid characteristic function based on the current balance form of the quasi-steady state model of the PEPPS, which fully captures the dynamic interactions between the grid-connected devices and the infeed device under consideration. After that, based on the Brouwer fixed point theorem, a sufficient condition is established through the grid characteristic function to guarantee the existence of a quasi-equilibrium point. The proposed grid strength and critical grid strength measures are thus defined based on the sufficient condition, which respectively quantify the voltage support capability and stability margins of PEPPS. Finally, simulation results show that the quasi-equilibrium points indeed exist when the critical grid strength requirement is satisfied, which verifies the correctness of the equilibrium point existence condition and the validity of the proposed grid strength measures.