9645767 Verghese Dynamic studies in power systems have long exploited analytic simplifications gained by approximating all voltages and currents in the network as sinusoids of "slowly varying" magnitude and phase. With this assumption, network behavior in dynamic analyses is characterized by power flow equations that represent time-domain bus voltages via complex phasors. This is typically referred to as the "sinusoidal quasi-steady-state" approximation (abbreviated here by the acronym "SQSS"), and is widely utilized in modern computer packages used to study electromechanical behavior and control system dynamics. For faster time-scale phenomena, the most widely used techniques are time-domain simulations in which all relevant network voltages and currents are represented as three-phase, time-domain signals, without any requirement of nearly sinusoidal behavior. This latter approach involves tremendous computational burden and analytic complexity, because one uses instantaneous quantities rather than phasor, and dynamic circuit models rather than algebraic impedance relations. The goal of the research outlined in this proposal is to provide a middle ground between the approximations inherent in an impedance-based SQSS representation, and the analytic complexity and computational burden associated with representing network voltages and currents as time-domain quantities in a three-phase circuit. In particular, this work will adopt a viewpoint on phasors that is closer to time/frequency representations utilized in signal processing, but extending these representations to a dynamic formulation. The result will be termed "Phasor Dynamics" (PD) models, and will involve a carefully constructed hybrid of the impedance and circuit representations. This approach will allow an important extension that is not possible in standard phasor representations: a dynamic analysis that includes higher order harmonics. The work proposed will treat these cases by re presenting relevant states as weighted sums of narrow-band signals, each located about a harmonic center frequency of interest. The time evolution of the weights are governed by dynamic equations derived directly from the original instantaneous model. ***
