The worldwide demand for more diverse and greener energy supply has had a significantudimpact on the development of wind energy in the last decades. From 2 GW in 1990,udthe global installed capacity has now reached about 100 GW and is estimated to grow toud1000 GW by 2025. As wind power penetration increases, it is important to investigate itsudeffect on the power system. Among the various technologies available for wind energyudconversion, the doubly-fed induction generator (DFIG) is one of the preferred solutionsudbecause it offers the advantages of reduced mechanical stress and optimised power captureudthanks to variable speed operation. This work presents the small-signal modelling andudanalysis of the DFIG for power system stability studies.udThis thesis starts by reviewing the mathematical models of wind turbines with DFIGudconvenient for power system studies. Different approaches proposed in the literature forudthe modelling of the turbine, drive-train, generator, rotor converter and external powerudsystem are discussed. It is shown that the flexibility of the drive train should be representedudby a two-mass model in the presence of a gearbox.udIn the analysis part, the steady-state behaviour of the DFIG is examined. Comparisonudis made with the conventional synchronous generators (SG) and squirrel-cage inductionudgenerators to highlight the differences between the machines. The initialisation of theudDFIG dynamic variables and other operating quantities is then discussed. Various methodsudare briefly reviewed and a step-by-step procedure is suggested to avoid the iterativeudcomputations in initial condition mentioned in the literature.udThe dynamical behaviour of the DFIG is studied with eigenvalue analysis. Modaludanalysis is performed for both open-loop and closed-loop situations. The effect of parametersudand operating point variations on small signal stability is observed. For theudopen-loop DFIG, conditions on machine parameters are obtained to ensure stability ofudthe system. For the closed-loop DFIG, it is shown that the generator electrical transientsudmay be neglected once the converter controls are properly tuned. A tuning procedure isudproposed and conditions on proportional gains are obtained for stable electrical dynamics. Finally, small-signal analysis of a multi-machine system with both SG and DFIG isudperformed. It is shown that there is no common mode to the two types of generators.udThe result confirms that the DFIG does not introduce negative damping to the system,udhowever it is also shown that the overall effect of the DFIG on the power system stabilityuddepends on several structural factors and a general statement as to whether it improves oruddetriorates the oscillatory stability of a system can not be made.
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