With the increasing need for economic operation of the power grid, the system is being operated closer to their limits and there is a need to address the increasing risk of voltage instability in the power grid. In this thesis, methods that can monitor and mitigate the both short-term and long-term voltage instability by utilizing Phasor Measurement Units (PMUs), controllable loads and distributed energy resources are proposed.

In the first part of the thesis, the fault induced delayed voltage recovery (FIDVR) phenomenon is studied. The FIDVR phenomenon is monitored by the load admittance at the substation PMU. The admittance provides the PMU at the substation with an estimate of the stalled motors and can be used to estimate the time to recovery and determine control actions for voltage recovery within a set amount of time. To test the real-time nature of the method, the FIDVR phenomenon is simulated in a real-time test-bed and is shown to be able to determine the control amount in an online manner. This methodology is extended to analyze FIDVR in distribution networks and to estimate the trajectory sensitivities in an online manner which are used in a linear formulation to result in a voltage recovery that prevent DER disconnection. Finally, In order to handle the dynamics of non-linear 3-ϕ motors, a data-driven surrogate linear dynamical model is estimated from data which is used to monitor both 1-ϕ and 3- ϕ motors for short term voltage instability.

In the second part of the thesis, the long term voltage stability phenomenon is studied. A Sensitivity based Thevenin Index (STI) which uses PMU data and (linear) state estimator data is proposed to monitor long term voltage stability. This sensitivity base index can be modified to account for various what-if scenarios (reactive limit reached, line outage, etc.) in a computationally efficient manner. Finally, A 3ϕ long-term voltage stability indicator (VSI) using the idea of a 3ϕ Thevenin equivalent that can identify critical loads in an unbalanced multi-phase system is proposed to account for the impact of distribution networks to long term voltage instability. The estimation of the 3ϕ Thevenin equivalent is formulated as a convex optimization using PMU & μPMU measurements, making it possible to calculate VSI in a model-free online manner.