Study of long-term stability analysis of power systems with renewable energy: Theory, modeling and numerical methods

Due to the growing load demand and aging transmission networks, many power systems have been pushed ever closer to their stability limits. Furthermore, the increasing penetration of renewable energies and rapid development of the smart grids result in more stability concerns beyond the short-term time scale. All above factors highlight the significance to study the long-term stability analysis of power systems.;This dissertation contributes to the long-term stability analysis of traditional power systems as well as the power grids with wind power by providing nonlinear analysis, establishing theoretical foundations, developing computational tools and implementing new numerical methods.;The quasi steady-state (QSS) model was regarded as a competent model to provide accurate stability analysis with fast speed in long-term stability analysis. Our study, however, has shown that the QSS model may provide incorrect (over-optimistic) stability assessment. Hence, in this dissertation, limitations of the QSS model are comprehensively analyzed in a nonlinear system framework. A theoretical foundation for the QSS model is developed, which provides sufficient conditions under which the QSS model can provide accurate approximations for the long-term stability model in terms of trajectories and o-limit set. Furthermore, two hybrid QSS models are proposed from the physical and theoretical perspectives respectively, which are remedies to the QSS model. Each hybrid QSS model is provided with efficient numerical schemes for practical implementation, and the generic hybrid QSS model is also equipped with a theoretical basis to ensure consistently accurate approximations for the long-term stability model.;Apart from the model development in long-term stability analysis, this dissertation also provides some numerical development. A theory-based numerical method, pseudo transient-continuation method, is improved and applied in long-term stability research to expedite simulation speed in the long-term stability model and overcome numerical difficulties in the QSS model. The work provides an alternative numerical method to the conventional integration methods in time domain simulation with good efficiency and stability properties.;In addition, this dissertation involves long-term stability analysis of the power systems integrating wind power. A stochastic formulation of power system models incorporating wind power is presented based on stochastic differential equations, and a novel methodology to conduct stability analysis for these systems is developed with a theoretical foundation. The work may represent the first attempt to exploit the singular perturbation method for SDE in power system stability research.