UBC Theses and Dissertations
Shifted frequency analysis for EMTP simulation of power system dynamics Zhang, Peng
Electromagnetic Transients Program (EMTP) simulators are being widely used in power system dynamics studies. However, their capability in real time simulation of power systems is compromised due to the small time step required resulting in slow simulation speeds. This thesis proposes a Shifted Frequency Analysis (SFA) theory to accelerate EMTP solutions for simulation of power system operational dynamics. A main advantage of the SFA is that it allows the use of large time steps in the EMTP solution environment to accurately simulate dynamic frequencies within a band centered around the fundamental frequency. The thesis presents a new synchronous machine model based on the SFA theory, which uses dynamic phasor variables rather than instantaneous time domain variables. Apart from using complex numbers, discrete-time SFA synchronous machine models have the same form as the standard EMTP models. Dynamic phasors provide envelopes of the time domain waveforms and can be accurately transformed back to instantaneous time values. When the frequency spectra of the signals are close to the fundamental power frequency, the SFA model allows the use of large time steps without sacrificing accuracy. Speedups of more than fifty times over the traditional EMTP synchronous machine model were obtained for a case of mechanical torque step changes. This thesis also extends the SFA method to model induction machines in the EMTP. By analyzing the relationship between rotor and stator physical variables, a phase-coordinate model with lower number of equations is first derived. Based on this, a SFA model is proposed as a general purpose model capable of simulating both fast transients and slow dynamics in induction machines. Case study results show that the SFA model is in excess of seventy times faster than the phase-coordinate EMTP model when simulating the slow dynamics. In order to realize the advantage of SFA models in the context of the simulation of the complete electrical network, a dynamic-phasor-based EMTP simulation tool has been developed.
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