The worldwide demand for more diverse and greener energy supply has had a significant
impact on the development of wind energy in the last decades. From 2 GW in 1990,
the global installed capacity has now reached about 100 GW and is estimated to grow to
1000 GW by 2025. As wind power penetration increases, it is important to investigate its
effect on the power system. Among the various technologies available for wind energy
conversion, the doubly-fed induction generator (DFIG) is one of the preferred solutions
because it offers the advantages of reduced mechanical stress and optimised power capture
thanks to variable speed operation. This work presents the small-signal modelling and
analysis of the DFIG for power system stability studies.
This thesis starts by reviewing the mathematical models of wind turbines with DFIG
convenient for power system studies. Different approaches proposed in the literature for
the modelling of the turbine, drive-train, generator, rotor converter and external power
system are discussed. It is shown that the flexibility of the drive train should be represented
by a two-mass model in the presence of a gearbox.
In the analysis part, the steady-state behaviour of the DFIG is examined. Comparison
is made with the conventional synchronous generators (SG) and squirrel-cage induction
generators to highlight the differences between the machines. The initialisation of the
DFIG dynamic variables and other operating quantities is then discussed. Various methods
are briefly reviewed and a step-by-step procedure is suggested to avoid the iterative
computations in initial condition mentioned in the literature.
The dynamical behaviour of the DFIG is studied with eigenvalue analysis. Modal
analysis is performed for both open-loop and closed-loop situations. The effect of parameters
and operating point variations on small signal stability is observed. For the
open-loop DFIG, conditions on machine parameters are obtained to ensure stability of
the system. For the closed-loop DFIG, it is shown that the generator electrical transients
may be neglected once the converter controls are properly tuned. A tuning procedure is
proposed 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 is
performed. It is shown that there is no common mode to the two types of generators.
The result confirms that the DFIG does not introduce negative damping to the system,
however it is also shown that the overall effect of the DFIG on the power system stability
depends on several structural factors and a general statement as to whether it improves or
detriorates the oscillatory stability of a system can not be made.