An important feature of renewable power systems is their high penetration of power electronic devices. The large-scale integration of power electronic devices is profoundly reshaping power system dynamics and giving rise to new stability problems. The difficulty in analyzing these problems lies in that massive numbers of power electronic devices

once interconnected through the power grid

form high-dimensional multi-input multi-output (MIMO) systems. For such systems

conventional eigenvalue analysis in the state space or generalized Nyquist criteria in the frequency domain can hardly provide an intuitive description of the dynamic interactions between devices and the grid

and cannot explain how these interactions determine closed-loop stability. They also offer limited guidance on how to reasonably regulate device behavior to ensure stability. This paper characterizes the “source-grid” dynamic interactions from geometric perspectives

using the Davis-Wielandt (DW) shell of complex matrices

as well as their numerical ranges

gain

and phase. Decentralized small-signal stability conditions and a modular analysis method based on the “geometric separation” principle are proposed. Our approach provides an intuitive visualization of the geometric features of various devices and the grid in terms of dynamic behavior

and reveals how their geometric interactions determine the system stability. It thus offers a geometric viewpoint for understanding stability characteristics

instability mechanisms

and identifying critical devices that undermine system stability. Building on this framework

the paper further discusses how to ensure closed-loop stability of large-scale heterogeneous multi-device systems via appropriate regulation of their geometric external characteristics

and how to construct the system in a modular fashion.