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

A conflict has been existing between the phenomenon descriptions and the stability assessments for the wideband harmonic resonances in distributed generation power plants. That is, the complex hyperbolic functions, which characterize feeders' model, are the prerequisite to describing these phenomena; however, these functions make classic stability analysis methods fail to be utilized. To this end, we proposed to transform these functions equivalently by using Euler's formula; this transformation enables us to establish the correlation between the time-domain eigenvalue and the system frequency. And then, stability assessments can be conducted in terms of the motion patterns of the eigenvalue in the complex plane as the frequency varies. The assessments indicated that (i) with the frequency increasing, once the dominate pole traverses the negative real axis from top to bottom in the left-half complex plane, the non-dominant pole fails to cancel the zero exactly, which would enlarge the residue at the non-dominant pole, resulting in insufficient stabilities; (ii) the proper value for the control coefficient of the coordinated damper could restrict the motion range of the eigenvalue with the frequency varying, ensuring the invariability of time-domain performances over a wide frequency range. Lastly, the validity of the chosen value for the control coefficient was verified by building an experimental platform to simulate the distributed generation power plant. © 2020 Chin. Soc. for Elec. Eng.