Phasor Domain Modeling of Type-III Wind Turbines

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This dissertation research focuses on developing an accurate steady-state phasor model for Doubly Fed Induction Generator (DFIG)-based wind turbines (Type-III WTs). Unlike the classical synchronous or asynchronous generators, Type-III WTs are electronically coupled to the power grid. The steady-state and dynamic responses of the DFIG-based WTs depend on the behavior of the converters controllers. Accurate modeling requires reproducing the behavior of the power electronics and the control system for various operating scenarios. The analysis of this research area is carried out in two stages or tasks. The first task focuses on the balanced stator voltage situation, while the unbalanced stator voltage is considered in the second task. In the first task, two methods to compute steady-state operating conditions of Type-III WTs considering the control limits are proposed. The proposed methods are applicable for ideal operating conditions and undervoltage scenarios. In the first method, an optimization problem is first formulated to identify the voltage thresholds at which the behavior of the control system changes due to the current limits. Using the identified limits, an efficient algorithm for steady-state calculations is designed. The problem is formulated as equality and inequality constraints and solved using a non-linear programming solver. In the second method, a one-step algorithm is developed. An efficient algorithm using Mixed Integer Non-Linear Programming (MINLP) is developed to compute the steady-state operating point of Type-III WTs. For a given stator voltage and wind speed, the electrical and mechanical variables of the system can be computed. A full-order model of DFIG-based WT is considered. Some overly simplifying assumptions that are commonly adopted in the literate are avoided. Losses in the back-to-back converters, and nonzero reactive power support through the grid-side converter (GSC) are considered. Compared to state-of-the-art, the proposed methods are much more accurate computation models for DFIGs. The proposed methods are validated with electromagnetic transient (EMT) simulations. In the second task, an adequate model of Type-III WTs under grid unbalance is proposed. The proposed model takes into consideration not only positive-, negative-sequence circuits but also the 3rd harmonic circuit. In addition to modeling, we design an efficient algorithm for steady-state analysis. To this end, harmonic circuit analysis of the induction machine, the rotor-side converter (RSC), the dc-link, and the GSC ac side is first carried out. Furthermore, relationships between dc side variables and ac side variables of the two dc/ac converters are investigated. The steady-state analysis problem is formulated as a set of algebraic equality constraints. This formulation is defined in YALMIP, a MATLAB interface for optimization problems. The optimization problem is solved by a non-linear optimization solver. The results of the steady-state analysis are phasors of harmonic components at steady-state. They are compared with and validated by the phasors obtained from Fourier transforms of electromagnetic transient (EMT) simulation results.