Frequency-Adaptive Network Modeling for Integrative Simulation of Natural and Envelope Waveforms in Power Systems and Circuits

Algorithms for the simulation of transients in power electric systems and circuits can be classified into two major categories. For the simulation of diverse transients in ac and dc networks, the algorithms process instantaneous signals in the time domain to track natural waveforms as observed in reality. For the simulation of lower frequency transients that modulate ac carriers in ac networks, algorithms that process phasor signals to track envelope waveforms are popular. The methodology proposed in this paper uses analytic signals to bridge the merits of instantaneous and phasor signals and enable the efficient simulation of both natural and envelope waveforms as well as the smooth transition between both. The key enabling method referred to as frequency-adaptive simulation of transients (FAST) is distinguished by the introduction of the shift frequency as a simulation parameter in addition to the time-step size. This distinguishes the methodology from the known methods of power system and circuit simulation, which only use the setting of the time-step size to adapt the simulation process. By setting the shift frequency to a nonzero value, the Fourier spectra of the analytic signals are shifted and adapted according to the waveform type of interest. This adds value because different types of transients with and without an ac carrier can be simulated efficiently and accurately within one and the same simulation run. To provide compatibility with existing tools, the numerical integration is formulated to model the network branches such that nodal analysis can readily be used to construct the overall network model. Calculations of the accuracy as well as test studies that cover network energization and deenergization, angle modulation, and amplitude modulation substantiate the claims made and demonstrate the application of the methodology