to be carefully filtered to have a beneficial effect. Furthermore, a simulation study using the simultaneously measured turbine and lidar data confirms that a filter fitted to the correlation yields the best results and that loads can be further reduced by relaxing the feedback controller independent from the filter design.
The collective pitch feedforward controller will on the one hand benefit from further improve-ment in the field of lidar data processing as discussed in Sections 4.4 and 5.7. On the other hand, there are several possibilities for future research regarding the pure control part:
• The benefit gained in rotor speed variation can be transformed in further load reduction by relaxing the feedback controller gains as for example stated in [89] and [21]. Further investigations are necessary to quantify this effect and to provide a method to tune the controller based on the quality of the lidar measurements. The approach presented in [9] which calculates the standard deviation of turbine states based on the measurement coherence might be very useful.
• The collective pitch controller aims to directly reduce the rotor speed variation and only indirectly addresses the turbine loads. More advanced Multiple-Input Multiple-Output (MIMO) controllers such as NMPC provide the possibility to penalize tower movements and thus reduces tower bending loads directly. However, these controllers replace existing feedback controllers, rely on estimated turbine states, and are computational more com-plex. Therefore, these concepts might not be robust enough for real applications. Thus, further investigations are necessary to design nonlinear, robust, and simple feedforward controllers, which reduce the structural loads similar to these advanced controllers with-out their drawbacks. A first attempt is made by the flatness-based approach presented in Chapter 8.
• For the collective pitch feedforward controller, the control problem is solved independently of the measurement problem. This is done by first designing the controller under the assumption of perfect knowledge of the rotor effective wind speed and then the adaptive filter is responsible to fit the lidar estimate to a signal that is representative of the real signal. Approaches addressing both problems together like the one presented by [18] in combination with nonlinear methods might provide a more consistent solution.
• In this work, feedforward and feedback is strictly separated based on the “two-degree-of-freedom” idea and since it also facilitated the field testing. However, further research is necessary to investigate the benefit of the approaches which calculate the collective pitch feedforward-update based on measured turbine data such as the current pitch angle, as presented in [21] and [22].
7
Direct Speed Control
The main purpose of variable speed control for wind turbines below rated wind speed is to maximize the electrical power extraction [41]. Therefore, the turbine has to operate with the rotor blades held at the optimal angle of attack. Maximum power extraction is achieved by adjusting the generator torque MG and thereby tracking the optimal tip speed ratioλopt. This chapter explains how tracking λopt can be improved by using the knowledge of the incoming wind and it is an extension to [38, 77].
Unfortunately, the findings in this chapter show that while the tracking of the optimal tip speed ratio is possible, it is not reasonable due to increased loads for marginal benefit. These findings coincide with the results in [21]. However, other work in this field, for example [33, 34, 35]
claim significant improvements.
This chapter is organized as follows: In Section 7.1 the lidar-assisted torque controller is derived and its potential is theoretically estimated in Section 7.2. Simulations using perfect wind preview, simulated lidar measurements, and real turbine and lidar data in Sections 7.3 to 7.5 show that tracking the optimal tip speed ratio can be significantly improved. However, the energy yield is only marginal and additional shaft loads cannot be avoided. This effect is consistent with the theoretical potential. A summary of the chapter and a proposal for extensions are given in Section 7.6.
WT v0
ISC DSC
ΩG
MG,ISC
∆MG,FF
MG
Figure 7.1: Torque control loop for below rated operation and additional feedforward update assum-ing perfect wind measurement.
7.1 Direct Speed Controller Design
The main control goal of the baseline torque controller as described in Section 3.4.1 is to maintain constant power in above rated wind conditions and to maximize the energy yield in below rated wind conditions. This is done by operating with the rotor blades held at the optimal angle of attack and consequently with the optimal power coefficient. The power coefficient for the 5 MW reference wind turbine is displayed in Figure 3.12 and in below rated wind speed depends only on λ, since the pitch angle is set to 0 deg. The optimal tip speed ratioλopt can be found at the peakcP,max. Thus, the aerodynamic optimum can be achieved by tracking λopt by adjusting the generator torqueMG as shown in Figure 7.1. Nonlinear state feedback controllers are commonly used in wind energy to control λ indirectly, measuring the generator speed ΩG. Therefore, the baseline torque controller is also known as the Indirect Speed Controller (ISC).
If the rotor effective wind speedv0is known, the tip speed ratioλcan be controlled directly, and therefore the proposed controller is considered as the Direct Speed Controller (DSC). Similar to Section 6.1, the controller design is split into two subsections. In a first step, the controller is design assuming perfect knowledge of the incoming wind speed and in the second step, realistic wind preview is considered.
7.1.1 Direct Speed Controller for Perfect Wind Preview
For the design of the direct speed controller, perfect knowledge of the rotor effective wind speed v0is assumed in a first step. The basic idea of the proposed DSC is to keep the ISC feedback law (3.39) and to find a feedforward update as illustrated in Figure 7.1 to compensate for changes in the wind speed similar to the one used for collective pitch control in Chapter 6.
The advantages of this structure are:
• The baseline controller can be kept. This is important especially for industrial application.
7.1 Direct Speed Controller Design 139
• The stability behavior of the speed control loop is not modified.
• If no wind preview is available, the feedforward part can be simply set to zero and the feedback can continue to operate without further adjustments.
• The feedforward update can be multiplied with a gain to smoothly enable the lidar-assisted control during testing or in the transition to region 2.
For the design of the feedforward controller the rotor speed error ε is introduced
ε= Ω−Ωopt, (7.1)
where the optimal rotor speed Ωopt is defined as Ωopt = λoptv0
R . (7.2)
Using the drive train dynamics (3.3a) from the reduced model and (7.2), the dynamics of the error ε can be described by:
˙
ε= ˙Ω− ˙Ωopt = 1 J
Ma− MG
iGB
−λopt
R v˙0. (7.3)
With the proposed DSC
MG=MG,ISC−iGBJλopt
R v˙0
| {z }
∆MG,FF
(7.4)
the error dynamics become
˙ ε= 1
J
Ma− MG,ISC
iGB
= 1 2ρπR5
cP
λ3 −cP,max
λ3opt
Ω2. (7.5)
Similar to [73], it can be shown that ˙ε < 0 if ε > 0 and ˙ε > 0 if ε < 0 as long as the tip speed ratio resides above a calculable lower limit. In the nominal case, changes in the wind will be perfectly compensated by the feedforward part ∆MG,FF. For the non-nominal case, caused by inaccurate measurements or model uncertainties, the feedback part MG,ISC compensates deviations from optimal operation.
WT EVO
V
ISC AF
DSC
L
ΩG MG,ISC
∆MG,FF MG
v0 v0L
v0L,f
v0L,f [m/s]
gFF[-]
7 8 9 10 11
0 0.2 0.4 0.6 0.8 1
Figure 7.2: Left: Torque control loop for below rated operation and additional feedforward update assuming realistic wind preview. Right: gain to enable the feedforward update only in region 2 and
to have a smooth transition.
7.1.2 Direct Speed Controller for Realistic Wind Preview
In the previous subsection, perfect knowledge of the rotor effective wind speedv0 is required for the DSC. However, the lidar technology is only able to provide an estimate v0L as pointed out in Chapter 4. The lidar measures in front of the wind turbine within the wind field V which will evolve on its way towards the rotor as illustrated in Figure 7.2 (left).
Similar to the adjustment of the collective pitch feedforward controller in Section 6.1, the adaptive filter proposed in Section 5.5 is used to fit the lidar estimatev0L to the rotor effective wind speed v0.
Additionally, the DSC is enabled with a gain function gFF depending on the estimated and filter wind speed v0L,f:
∆MG,FF =−gFF(v0L,f)iGBJλopt
R v˙0. (7.6)
The function is depicted in Figure 7.2 (right) and is set to 1 in region 2 (from 7.9 to 10.2 m/s) and 0 outside region 2 with linear ramps in between the sections starting at 7.7 m/s and ending at 10.4 m/s, for a smooth transition.
Higher-order error dynamics can be chosen and extended DSCs can be found as proposed in [77] and [98]. However, this entails additional feedback of the generator speed and is not further considered in this work.