  As more distributed energy resources (DERs) are connected to the power grid,
it becomes increasingly important to ensure safe and effective coordination
between legacy voltage regulation devices and inverter-based DERs. In this
work, we show how a distribution circuit model, composed of two LTCs and two
inverter devices, can create voltage oscillations even with reasonable choices
of control parameters. By modeling the four-device circuit as a switched affine
hybrid system, we analyze the system's oscillatory behavior, both during normal
operation and after a cyber-physical attack. Through the analysis we determine
the specific region of the voltage state space where oscillations are possible
and derive conditions on the control parameters to guarantee against the
oscillations. Finally, we project the derived parameter conditions onto 2D
spaces, and describe the application of our problem formulation to grids with
many devices.

Systems and Control;Systems and Control