Environmental Engineering Reference
In-Depth Information
philosophy, there can be so much aerodynamic damping and cross-modal damping that only
a rigorous aeroelastic analysis of the complete system can be meaningful. This must
include a full accounting for the action of the control system.
The accuracy with which a subsystem model need be constructed will depend on the
degree to which the subsystem modes persist as significant components of the system modes
or act as an influence upon dynamic stability. Often this will be best understood only after
a preliminary version of the complete simulation is running and subjected to study. There
are, however, some results of dynamic modeling experience that can be cited here.
Rotor Models
Whether a HAWT rotor is hinged or hingeless, a blade simulation model should be
adequate if it consists of a beam analysis that is divided into 10 to 15 spanwise segments
for both aerodynamic and inertial loads. There should be little need for finer segmentation,
because a blade designed for fatigue life under cyclic gravity loading (at a frequency of 1
P
)
will have a beam structure that is stiff in-plane, strongest at the hub, and essentially a
continuous structure from blade-to-blade through the hub. Design for adequate fatigue life
under gravity loading will also result in a high torsional stiffness of the blade and of the
pitch control elements in series with the blade. Thus, a 10-segment model will be more
than adequate for simulating the torsional deflections of the blade and the resulting changes
in blade angle.
Because VAWT blades are not subjected to cyclic gravity loading and tend to have
stiffness discontinuities at their attachment fittings, a VAWT blade model requires much
greater detail and many more segments than a HAWT blade model. Further complicating
the blade responses are the constant cycling of air loadings and the difficulty in supplying
damping from the non-rotating part of the VAWT structure. Rotor hub modeling is first
a matter of correctly modeling the inter-blade structure and the impedance with which the
hub is restrained. Then, to enable correct aeroelastic results, the influence upon blade angle
of attack of hub motions and blade-to-hub motions must be accounted for. This means that
modeling of the rotor as an isolated subsystem will usually not provide a realistic simula-
tion. This is discussed in detail in the next chapter.
Power Train Models
Constant-Speed Generators
If the rotor is stiffly coupled to a synchronous generator, the resonant modal
frequencies will not be importantly affected by the generator model. Moreover, the coupled
rotor/power train vibration modes will be poorly damped, making frequency placements
relatively critical. If, however, the drive system is made torsionally soft, the lower rotor
modal frequencies will be essentially uncoupled and unaffected by drive system modeling
details. In such a system, elements that provide damping should be included in the model,
since the analyst will want to explore cases in which beneficial damping will reach the
lower-frequency rotor modes.
Attempts to provide attenuation of power train rotor loads by varying
excitation control
on a synchronous generator have often been made but have failed. Because the speed of
the synchronous generator is very stiffly locked to an electrical grid frequency (60 Hz in
the U.S. and 50 Hz in Europe), it acts as a clamped end for the rotor/power train torsional
modes, with no significant response to excitation forces. Therefore, there is no useful
purpose in including the detailed dynamic features of a synchronous generator in the power-
train model for an on-line analysis.
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