Voltage security region of a three-phase unbalanced distribution power system with dynamics

Distributed energy resources (DER) and control assets on the grid provide mechanisms to ensure voltage support and power quality, and can be used as a means to maintain voltages close to nominal values. In this work, we study the security region of a system in the presence of devices with. We focus our efforts on the dynamics of devices that apply discrete changes, such as voltage regulators or capacitor banks, and DERs that change the power injections with Volt/Var/Watt functionality. The slow dynamics of these devices, coupled through the power flow equations, are modeled as a switching dynamical system where the switching condition depends on the operating point of the system. We identify the feasible set of DER power injections that prevent the switching of devices and oscillations in the voltage profile, and formulate an optimization problem that finds a robust operating point for voltage control. This operating point is the center of the largest Euclidean ball inscribed in the security region, and the radius of the ball is the security margin of the system. We showcase our models using the IEEE test cases. Our work has applications in voltage control and distribution planning