29-06-2013, 03:43 PM
Damping of Torsional Vibrations in a Variable-Speed Wind Turbine
Damping of Torsional.pdf (Size: 1.7 MB / Downloads: 60)
Abstract
Torsional dampers are employed in wind turbines
to damp vibrations in the drive-train. The conventional design is
based on band-pass filters (BPF); however, its effectiveness can be
compromised due to parametric uncertainty. To restore the performance
of the damper, it is a common practice to re-tune it during
the commissioning of wind turbines. To overcome this shortcoming,
a model-based torsional damper was designed and its performance
compared to the conventional approach when subjected to
model uncertainty. A stability analysis was conducted and simulations
were performed in Simulink. A real-time hardware-in-theloop
experiment was carried out, with experimental and simulation
results showing good agreement. The proposed model-based torsional
vibration damper showed a superior performance over the
conventional BPF-based approach. Results also showed that the
model-based damper can eliminate the need for retuning procedures
associated with BPF-based designs.
INTRODUCTION
AS the size of wind turbines increases, manufacturers face
more challenges including achieving better cost effectiveness.
This is currently being addressed through reduction of
component masses leading to turbines becoming less tolerant of
fatigue loads [1].
This study is concerned with themitigation of fatigue loads in
the drive-train of variable-speed wind turbines. Turbulent winds
and gusts can excite modes that can lead to torsional vibrations
in the drive-train, which in turn produce large stresses on
components. Ultimately, this may reduce the lifetime of components,
such as the gearbox [2], [3]. Moreover, when torsional
vibrations are present in the drive-train, they will be converted
to electrical power oscillations. This is highly undesirable for
the operation of the power system because such oscillations
can interact with the power system modes and resonance may
result [4], [5].
WIND TURBINE MODEL
A generic 2 MW variable-speed wind turbine based on a
permanent-magnet synchronous generator (PMSG) with a threestage
gearbox and an FRC was implemented in Simulink. The
block diagram of the system is shown in Fig. 1. All parameters
of the wind turbine model are given in Appendix A.
Mechanical Model
Torsional vibrations can be initiated directly by exciting the
drive-train natural frequency mode or indirectly by exciting the
blade in-plane symmetrical mode [12], [13]. Hence, a threemass
model which considers both modes has been employed
[18]. To simplify the rotor dynamics, the in-plane dynamics of
the blades were represented as a torsional system [19], [20]. The
three masses correspond to the inertia of the effective flexible
part of the blades J1 , the inertia representing the hub and the
rigid part of the blades J2 , and the inertia of the generator J3 .
The three inertias are separated by the effective blades stiffness
K1 and the resultant stiffness of the low and high-speed shafts
K2 , respectively [18].
Control System
The basic control objectives are to optimize the power production
for below-rated wind speed and to limit the aerodynamic
power for above-rated wind speed.
For below-rated wind speed, the generator speed was varied
by controlling the generator torque to follow an optimal torque
versus speed curve derived from a generic 2 MW wind turbine
model in Bladed. A vector control scheme was used to control
the generator torque.
BPF-Based Torsional Vibration Damper
The structure of the damper used here consists of a notch
filter cascaded with two BPFs and is shown in Fig. 3.
A suitably tuned 2nd-order BPF was employed to extract the
vibration frequency from the generator speed [12]–[14]. This
information was used to add a small ripple at the vibration
frequencies to the generator torque demand in order to damp
torsional vibrations. The nominal mechanical frequencies associated
with (2)–(4) are relatively far apart (2.54 and 3.7 Hz);
hence, two BPFs tuned at these frequencies were used [18].
CONCLUSION
A performance comparison of two torsional vibration damper
design approaches has been conducted through simulations
and a real-time experiment. The results obtained are in good
agreement.
The stability analysis of the system with the two different
dampers was assessed in the frequency domain. In the case of
the BPF-based torsional damper, the analysis showed significant
deterioration in both phase and gain margins when model
uncertainty was included. The stability margins of the system
with the model-based damper were marginally affected.
Simulation and experimental results showed that the performance
of the model-based torsional damper was not affected in
the presence of uncertainty whereas the BPF-based damper performance
was compromised. Correspondingly, the BPF-based
torsional damper had to be retuned to recover the intended
performance.