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This study investigates modelling of doubly-fed induction generator (DFIG)-based wind turbines for low-frequency oscillation analysis of power systems with high penetration of distributed energy. A reduced order model of wind turbine with DFIG is proposed for small signal stability analysis in electromechanical time scale for low-frequency oscillation analysis. Furthermore, a Thévenin equivalent model of DFIG with internal voltage is also presented. Base on the derived model, the effect of phase-locked loop is emphasised, and explained by using the internal voltage derived. The model proposed is well verified by modal analysis and time-domain simulations. [ABSTRACT FROM AUTHOR]

In this paper, we explore the structure theory of L(ℝ, μ) under the hypothesis L(ℝ, μ) ⊧ “AD + μ is a normal fine measure on ” and give some applications. First we show that “ ZFC + there exist ω2 Woodin cardinals”1 has the same consistency strength as “ AD + ω1 is ℝ-supercompact”. During this process we show that if L(ℝ, μ) ⊧ AD then in fact L(ℝ, μ) ⊧ AD+. Next we prove important properties of L(ℝ, μ) including Σ1 -reflection and the uniqueness of μ in L(ℝ, μ). Then we give the computation of full HOD in L(ℝ, μ). Finally, we use Σ1 -reflection and ℙmax forcing to construct a certain ideal on (or equivalently on in this situation) that has the same consistency strength as “ZFC+ there exist ω2 Woodin cardinals.” [ABSTRACT FROM PUBLISHER]

Grey resource efficacy model is effective for describing the developing stage (rapid varying phase) of resource efficacy S curve. In order to further complement the model system, this paper deduces five derived models based on the original resource efficacy model proposed by Professor Deng. The properties of these derived models are then studied respectively. The results show that different models have different structures, contents, solutions and properties, implying the principal of non-uniqueness in grey system theory. [ABSTRACT FROM AUTHOR]