Method of Modeling the Swing Equation Using Time Synchronized Measurements

Abstract

In three phase, high-voltage transmission systems, synchronous generators accelerate or decelerate to adapt to changing power transfer requirements that occur during system disturbances. In network electrical power systems, frequency changes constantly based on system dynamics. Modeling network dynamics from oscillations and transients using time-synchronized measurements can provide real-time information, including angular displacements, voltage and current phasors, frequency changes, and rate of signal system decay from positive-sequence components. Power system voltage and current waveforms are not steady-state sinusoids, especially during system disturbances. These waveforms contain sustained harmonic and non-harmonic components. Additionally, because of faults and other switching electromagnetic transients, there may be step changes in the magnitude and phase angles of these waveforms. Resonances in the power network create additional frequencies. Other disturbances may exhibit relatively slow changes in phase angles and magnitudes due to oscillations of machine rotors during electromechanical disturbances. Power System stability is that property of a system that enables the synchronous machines of the system to respond to a disturbance and return to normal operating conditions. To determine the system characteristics, analysis of system stability can be performed by transient, dynamic, and steady-state stability studies. Power systems are heavily inter-connected with many hundreds of machines that interact dynamically through the medium of their high voltage networks. Transient stability studies are performed to study the power system electromechanical dynamic behavior and are aimed to determine if the system will remain in synchronism following major disturbances. The measurement equipment and computer modeling required, both in time and cost, can be extensive. The equation governing the motion of the rotor of a synchronous machine is based on an elementary principle of dynamics, where accelerating torque is the product of the moment of inertia of the rotor times its angular acceleration. During a disturbance, how the rotor will accelerate or decelerate is described in relative motion by the swing equation. This research uses archived Phasor Measurement Unit (PMU) data obtained from the Bonneville Power Administration (BPA) to demonstrate a feasible technique for transient stability system analysis. This work demonstrates a practical method of using Rate of Change of Frequency (ROCOF) from PMU data with an analysis fit filter program to determine the system coefficients used to calculate the damping coefficient D, and inertia constant H, which are necessary to create a practical swing equation. Because PMU data have become an important component in wide-area measurements used in many power systems, PMU