Shifted Frequency Analysis (SFA) concepts for EMTP modelling and simulation of Power System Dynamics

This paper presents fundamental concepts associated with the method of Shifted Frequency Analysis (SFA) for modelling electric circuit transients at frequencies close to the fundamental rated power frequency (50Hz or 60Hz). In a Smart Grids scenario, where the inertia of the generating sources is much less than at the transmission system level, electric transients simulation tools like the Electromagnetic Transients Program — EMTP become particularly important to assess the impact of distributed generation and voltage and frequency dynamics. With SFA implemented in the EMTP, very accurate results can be achieved with relatively large time steps that can trace the envelopes of transient voltages and currents around the fundamental frequency. If required, instantaneous values can be obtained directly from the "dynamic phasor solution" obtained with SFA. This paper presents a rigorous mathematical derivation of SFA based on the Hilbert transform. Error analysis is performed in terms of the integration time step size and the width of the frequency band around the fundamental frequency. A test case illustrates the main modelling concepts.