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encompasses the storage of preview measurements. If the gains associated with the preview
storage are partitioned from the gains applied to turbine measurements, then the former
are correctly viewed as disturbance feedforward control and this is how they are depicted in
Fig. 148. In the course of design, it is determined that the majority of benefit of preview is
obtained using 0.5 s (10 samples) worth of feed-forward compensation, but this can change
depending on the dynamics of the turbine involved.
The FAST simulation code marches the TurbSim wind distribution past the turbine at
the mean speed of 18 m/s. The pre-processing induces evolution corresponding to distances
iTs×18 where Ts is the sample period and i is the number of preview samples used. Where
the evolution distance is greater than 10Ts×18, the process is equivalent to taking preview
measurements further in front of the turbine, and then waiting the appropriate amount of
time before applying the preview gains to the measurements.
10.7.1 H2 Optimal Preview Control
In this section, we describe the design of the preview controller and then evaluate its performance
in the presence of emulated wind evolution. Linearmodels are obtained from the FAST
wind turbine modeling code (Jonkman and Buhl, 2005) developed at NREL. The model is
based on a 40 m diameter, three-bladed controls advanced-research turbine (CART3) located
at NREL’s National Wind Technology Center (NWTC). The nominal operating point for design
(and simulation) is a uniform wind of 18 m/s, a blade pitch of 12.7 ◦ , and a rotor speed
of 41.7 rpm.
As in Laks et al. (2011b), the FAST linearizations are used to obtain a discrete-time statespace
model representing the turbine dynamics Pt with a 20 Hz sample rate. For controller
design,the linearizedmodel includes a first-ordergeneratordegree of freedom (DOF), secondorder
dynamics for each blade’s out-of-plane blade flap compliance, and a second-order drivetrain
compliance. This model is then augmented with simple pitch actuator dynamics that
provide the pitch rates generated by individual pitch commands. During simulation, all DOFs
provided by FAST are used except for yaw and teeter (the freedom of the rotor to tilt).
In addition, integral control on generator speed error Ωg (= ΩRNgb where Ngb is the gearbox
ratio and ΩR is the rotor speed) and rejection of 1P variation in the bending moments are
obtained by augmenting the turbine model with additional dynamics Pa driven by measurements
of these signals. We configure the control system to use individual point measurements
of the longitudinal wind that the blades will encounter at 75% span after a fixed time delay
of i samples, where the point measurements rotate in unison with the blades. As discussed in
Laks et al. (2011b), this corresponds to using a blade-local model, that describes the effect
on the turbine of wind speed perturbations local to each blade.
Thestatefeedbackisdesignedbyformingthegeneralizedplant(theFASTlinearizationwith
preview storage and augmented dynamics) with weighting on outputs that include generator
speed perturbations and perturbations in out-of-plane blade bending moments. The statefeedback
gains [Kx Ka Kff] are optimized to minimize the H2 norm from the preview wind
measurement to weighted versions of flap and speed perturbations; this includes a penalty on
excessive pitch rates so that the associated linear quadratic regulator problem is well posed. It
is possible to compute the optimal state feedback independent of the amount of preview used
(Hazell, 2008). This involves using the stabilizing solution of a Riccati equation to compute
both the optimal state-feedback and feedforward gains. Details can be found in Laks et al.
(2013).
In formulating the H2 cost, emphasis is initially focused on the flap response to wind
perturbations. Then, the penalty on pitch effort is increased until the (linear) closed-loop
response to a step change in collective wind produces pitch rates on the order of 10 ◦ /s.
Generally, the H2 performance improves with the number of samples of preview, but remains
bounded below so that there is a diminishing return; this lower bound is essentially reached
with the use of about 4 samples of preview at 20 Hz. However, the goal is not the precise
value of the H2 norm, but the attenuation of perturbations in blade load due to perturbations
212 DTU Wind Energy-E-Report-0029(EN)