Date of Award

Summer 2016

Degree Type


Degree Name

Master of Science (MS)


Electrical Engineering

Committee Chair

Dan Trudnowski

First Advisor

Matt Donnelly

Second Advisor

Curtis Link


Long transmission lines create opportunities for synchronous generators to oscillate or swing against one another at frequencies known as inter-area modes that are well observed. Some modes become less damped during times of heavy loading on the power system. Due to these modes, transmission systems are generally constrained by dynamic limits. Approaches to improve system damping are being researched. One method being evaluated is modulating power flows on the Pacific Direct Current Intertie (PDCI). A derivative feedback control system using phasor measurement unit (PMU) data has been shown in simulation to improve system damping. However, any feedback control scheme utilized on the power grid must do no harm. So, it is critical to monitor the power system in real-time for any potential instability that may be exacerbated by the controller. Two such supervisory elements are discussed here.

First, detection of out-of-control-band oscillations is critical. Using an RMS energy filter is a simple and powerful approach. For a defined frequency band, an RMS energy filter estimates the total RMS energy of a signal. This approach has been implemented in the operation control center at the Bonneville Power Administration, and has been implemented in a real-time damping control supervisory system. This thesis describes RMS energy filter design requirements, approaches, and alternatives. Simulation examples demonstrate the performance.

Second, the phase and gain margin are of particular concern to any feedback controller. By employing a probing signal of known frequencies injected into the system, the response can be evaluated via spectral analysis methods to estimate the open-loop transfer function at those frequencies. The estimates can be compared to experimentally attained norms to determine stability margins. This paper analyzes two of the methods, their ability to calculate spectral estimates, and the optimal approach for attaining an estimate quickly. Simulation examples demonstrate the performance.