Stiff Vs. Hinge Tower

In this second comparison the control action is the same while the model used is different. On one case there is the WT0 with stiff tower while on the other case there is inverted pendulum turbine model with its hinge tower.

In figure 4.25 the stochastic wind introduced to make the comparison in region IV is shown. In figures 4.30 to 4.31 the results are shown.

From figure 4.30 it can be seen that with the hinge tower the variation on the electrical power and of the rotational speed is much bigger. The standard deviation in the electrical power for the inverted pendulum turbine is 24 times bigger than for the WT0 while for the rotational speed the standard deviation of the inverted pendulum turbine is 32 times bigger than for the WT0. From figure 4.31 one can see that with the hinge tower is much difficult to follow

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Figure 4.30: Electrical power and rotational speed comparison between stiff and hinge tower in region IV.

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Figure 4.31: Pitch angle and generator torque comparison between stiff and hinge tower in region IV.

4.4 Comparison 87

the pitch reference due to the fact that the controller in the inverted pendulum turbine has also the objective of keeping the tower in a certain inclination while in the WT0 model not.

In the inverted pendulum turbine the inclination of the tower needs to be kept in a certain angle. In the full load region, region IV, the pitch angle is trying to maximize the produced electrical power while keeping the tower in the appro-priate inclination. This two objectives are difficult to achieve at the same time and as a result the produced electrical power has bigger variation.

Using as an input the stochastic wind defined in figure 4.20 one can obtain figures 4.32 and 4.33. With the data from 4.32 the electricity produced in 450 seconds for the inverted pendulum turbine is 372 kWh while for the WT0 is 384 kWh. In figure 4.33 it can be seen the pitch do not follow the reference in region II because the pitch actuator is busy keeping the tower in the appropriate inclination.

Figure 4.32: Electrical power and rotational speed comparison between stiff and hinge tower in all regions.

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−5 0 5 10 15

β[deg]

Reference Stiff Hinge

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0 1 2 3 4 5x 10⁴

Tg[Nm]

Time [s] —Ts= 0.05s

Figure 4.33: Pitch angle and generator torque comparison between stiff and hinge tower in all regions.

From this comparison one can conclude that trying to control the inverted pen-dulum turbine with the same control variables than a stiff tower turbine is difficult. As it was expected the electrical power produced with the inverted pendulum turbine is less than with a wind turbine with a stiff tower.

Chapter 5

Conclusions and Perspectives

In this chapter the conclusions of this project and the future perspectives of the inverted pendulum turbine are shown.

5.1 Conclusions

The main objective of this thesis is to study the feasibility of the inverted pen-dulum turbine. To reach this goal many sub-objectives have been achieved.

A model of the inverted pendulum turbine has been developed. The model considered is composed by a 2-order system of the hinge tower and a 1-order system of the rotor. The steady operation points for the inverted pendulum turbine have been obtained with the objective of maximizing the produced elec-trical power and keeping the hinge tower still. It has been shown that the steady state points of a stiff tower wind turbine and of a hinge tower wind turbine are the same but adding to the hinge tower the proper inclination angle. The non-linear model of the inverted pendulum turbine has been non-linearized at the steady operating points. The linear model obtained has been successfully compared with the non-linear one.

The model of the inverted pendulum turbine has been proved to be an unstable system, as it was expected. Using the same control inputs as current wind turbines, pitch angle β and generator torque T_g, it has been proved that the system is controllable. Having the measurements of the electrical power, the rotational speed and the angle of inclination is enough to be able to estimation of the states. All this measurements can easily be obtained with a proper sensor.

Once the model of the inverted pendulum turbine has been obtained and it has been proved that it can be controlled and observed the next step is designing the controller. It has been decided to use an optimal controller like the Linear Quadratic Regulator, which ensure a good performance, combined with an op-timal estimator based on a Kalman filter. This technique is known as Linear Quadratic Gaussian Controland it has been introduced and used in this project.

In order to get offset free control some methods likeDisturbance Modellingand Integral Action have been studied.

The steady operation points of the inverted pendulum turbine define four dif-ferent regions in the wind speed range, each one with difdif-ferent properties. In each region the controller designed has been tuned differently according to the control objective of the region. The region switching criteria used is based on the estimated wind. To get the wind estimation the inverted pendulum turbine model has been extended and aKalman filterhas been used. The final controller used in this project is a gain schedulingLQG controller based on the estimated wind.

Form the simulations it has been shown that the method used to estimate the wind is reliable. It has also been shown that the offset-free methods implemented do not provide such a good performance as it was expected. This could be explained for the undesirable effect of adding integrators to an unstable system.

The controller implemented has been proved to have good performance in all the operation regions. It also has been shown that in the transition between regions III and IV there is an issue on keeping the pitch actuator constrains while trying to keep the tower in a proper inclination, this would need to be investigated.

The controller of the inverted pendulum turbine has been implemented on a stiff tower wind turbine and it has been compared with the baseline controller designed by theNREL. It has been shown that the regulator designed in this thesis is able to produce more electrical power than the designed by theNREL.

The performance of the inverted pendulum turbine has been compared with a stiff tower wind turbine regulated by the controller design in this thesis. It has been shown that the variation of the electrical power for the hinge turbine is higher than for the stiff tower turbine. This variation could be damped by the

5.1 Conclusions 91

wind park and at the point of connection with the grid the oscillations would be much lower. As it was expected the produced electrical power for the inverted pendulum turbine is lower than for the stiff tower wind turbine.

With all the things mentioned above now one can discuss the feasibility of the inverted pendulum turbine. It has been shown that the inverted pendulum turbine can be controlled with the pitch and the generator torque with the issue already mention in the transition III to IV which should be investigated. It has also been shown that from a control point of view the mass of the tower could be reduced having as a result a lighter and cheaper structure. From (Fingersh et al., 2006) the relation between the mass of the tower and its price is linear.

Then from a control point of view the price of the tower could be reduced in a 20% having almost the same control problem, almost the same angle of inclination (4% bigger), while the produced electrical power would be slightly lower, according to figure 4.32 about 0.5% less. Then, from a control point of view and with deeper research on the issues mentioned, the inverted pendulum turbine is feasible. It is clear that the inverted pendulum turbine have new challenging problem to overcome, but the arising challenges from this design could be compensated by the benefit harvested.