Impedance model analysis and measurement for power system stability

Abstract

Electric power systems are transforming from synchronous machine (SG) dominated systems to composite grids in which inverter-based resources (IBRs) coexist with SGs. The lack of standardisation of IBRs leads vendors to treat their control algorithms as commercial secrets and they are willing to disclose only black-box models that give input-output relationships but no internal details. An impedance model spectrum is commonly put forward as a black-box model useful for stability analysis. Several types of impedance models have been proposed to represent the dynamic characteristics of a complete power networks. A study is undertaken to compare two types of networked impedance models: those based on direct nodal or loop analysis and those based on a whole-system formulation. The underlying relationship between eigenvalues of the impedance matrix and the oscillatory modes of the network for both model types have been unclear but are resolved here and the relative merits of the models are established. Through examining eigenvalue sensitivity, a proposal is made for an impedance participation factor that can identify root-causes of low damping. It is proved that the impedance participation factor is related to the classic state-space participation via a chain-rule relationship. Based on the chain-rule, a grey-box approach is developed as a generic method for root-cause tracing in impedance models. It has three degrees of transparency according to the available information and they are aggregated participation, damping contribution, and key parameters. The grey-box approach can indicate appropriate re-tuning of parameters that would shift the oscillatory mode in a desired direction in complex plain so as to stabilise the system. The theoretical contributions are verified through three different scales of case study: a simple three-node passive circuit, a modified IEEE 14-bus system and a modified NETS-NYPS 68-bus system. A significant advantage of using an impedance model is that the model can, in principle, be measured online with injection of a small-signal perturbation. However, a vital issue of concern is error caused by noise in the measured signals since this will determine the magnitude of injected perturbation required and the practicality of arranging that. To address this issue, a noise analysis process for impedance measurement is proposed in this thesis, from which guidance on selecting an appropriate injection magnitude can be provided. To verify the proposed analysis process, a power-hardware-in-the-loop system is built where a high-bandwidth power amplifier (OP1400 series) is used to inject the perturbation. The theoretical developments and noise analysis presented in this thesis combine to offer stability analysis and root-cause tracing of the type normally found only in white box state-space models but here are available in models built from equipment manufacturers' black-box models or from measurement-based models.