Euler's Formula-Based Stability Analysis for Wideband Harmonic Resonances

Abstract

During propagation along medium- or high-voltage feeders, the currents generated by distributed generation power plants (DGPP) can exhibit harmonic tendencies to deteriorate over wide frequency ranges. These phenomena are construed as wideband harmonic resonances. Although the shapes of these harmonic resonances can be delineated by using the Π-type feeder model with hyperbolic functions, the involved sinh or cosh terms can hinder researchers from obtaining the relative stability of the systems by applying classic stability criteria. To this end, we proposed transforming the hyperbolic functions via Euler's formula for complex numbers. These transformations enable us to evaluate the relative stability of the system in terms of poles and zeros in the complex plane. We find that: first, the underlying causes of the wideband harmonic resonances correlate with the motion patterns of the eigenvalues on the complex plane; second, a recommended coordinated damper restricts the motion ranges of the eigenvalues as the system frequency varies, and this restriction guarantees the invariability of the time-domain performance of the systems. Simulation, experimental results, and a case study verify the applicability of the proposed stability-analysis method.