Publishers version - DTU Orbit

ΣMA
ū
ΣAF
ΣFF
ΣISC
Mg,ISC
ˆk
G0
˙v0Lf
Mg,FF
v0L
ΣSA
ΣO
v0R
Mg
ΣL
θ
V
ΣE
Σ
v0
Ω
v0[m/s]
Mg [kNm]
λ[-]
10
9
8
60
40
20
0
8
7.5
7
50 55 time [s] 60 65
Figure 122: (left) Direct Speed Controller with adaptive filter. (right) Reaction to a gust in
case of perfect measurement using the 5 MW NREL turbine in FAST (Jonkman et al., 2009):
Baseline controller only (black) and with additional feedforward (grey).
9.6 Lidar Assisted Speed Control
The main purpose of variable speed control for wind turbines below rated wind speed is to
maximize the electrical power extraction (Burton et al., 2001). Therefore, the turbine has to
operate with the rotor blades held at the optimal angle of attack. This blade inflow angle is
represented by λ (197c). The optimal tip speed ratio λopt can be found at the peak ĉP of the
power coefficient. The aerodynamic optimum can be achieved by tracking λopt via adjusting
the generator torque Mg. This section depicts how tracking λopt can be done dynamically by
using the knowledge of the incoming wind, more details see Schlipf et al. (2011, 2013b).
9.6.1 Controller Design
The baseline speed control (Burton et al., 2001) to maintain in steady state the maximum
power coefficient ĉP can be determined with the reduced nonlinear model (197) by:
Mg,ISC = 1 ĉP
ρπR5
2 λ3 i
opt
3
Ω
2 g. (208)
Equation (208) with constant kISC is known as the indirect speed control (ISC). Using the
lidar technology, v0 and thus λ become measurable, and therefore, the proposed controller is
considered as direct speed control (DSC). The basic idea of the proposed DSC is to keep the
ISC feedback law (208) and to find a feedforward update Mg,FF to compensate changes in
the wind speed similar to the one used for collective pitch control, see Figure 120. With the
derivative of the rotor effective wind speed ˙v0 the DSC is:
kISC
Mg,DSC = Mg,ISC−iJ λopt
R ˙v0 . (209)
Mg,FF
Higher order DSCs can be found (Schlipf et al., 2013b). Similar to the collective pitch feedforward
controller, this controller in the nominal case perfectly maintains λ at its optimal
value. This still holds, using a full aero-elastic model, assuming perfect measurement of v0.
But Figure 122 shows, that Mg has to be negative already with a small gust with 1 m/s
amplitude due to the high inertia J, introducing high loads on the shaft.
180 DTU Wind Energy-E-Report-0029(EN)