Control design

The economic cost of electricity generated by wind turbines can be reduced by decreasing the construction cost, while increasing the life-time and efficiency of the energy conversion. The question is to what extent a (feedback) control system can contribute to this reduction of cost.

In general, the purpose of using feedback is to combat uncertainty [169]. After all, if there were no disturbances, or in other words if there were no uncertainty about the behavior of the plant, then open-loop series compensation would suffice. Of course, such an ideal situation never occurs, and is very rarely even approached. It will be shown below that using feedback it is also possible to alter the following linear system properties: stability, disturbance rejection, and robustness.

Consider thereto the "classical" feedback system in Fig. 2.7. In this feedback system the reference signals r, filtered by F, are compared with the measured output y which is corrupted by a disturbance v. Based on this difference, the controller C produces an input u to the plant (i.e. wind turbine) P. The output y as function of r and v is given by:

with L = PC the loop gain, S = (I + L)-1 the sensitivity function and T = (I + L)-1 (L) the complementary sensitivity function of the closed-loop system.

Figure 2.7: Classical feedback system.

From Eq. (2.1) follows that stability of the feedback system is related to stability of (I + L)-1(L) and consequently can be altered by a controller C. Disturbances can be attenuated by reducing S in some sense. It should be added that the "disturbance" v can represent various sources of uncertainty in the plant (including model uncertainty) and hence by attenuating disturbances the robustness of the closed-loop system is improved. A detailed analysis can be found in [21, 169].

It can be concluded that a feedback controller interacts with the dynamics of the wind turbine and has implications for, among others, the energy production and fatigue life. Ideally, use of a controller should imply an optimal energy production and increased fatigue life.

Nowadays, industrial standard PID-type (proportional-integral-derivative) controllers are normally used for wind turbine control [24, 30, 115, 283]. These are model-free, single-input-single-output (SISO), and hence single-objective approaches for which no controller synthesis algorithm is available. This implies that the controller parameters are to be determined by using rules of thumb. For a comprehensive survey of tuning methods of PID controllers, the reader is referred to Astrom and Hagglund [5]. More advanced tuning methods use optimization theory to determine the PID controller parameters. The SISO controller structure, however, is not capable of simultaneously satisfying the more or less conflicting control objectives [186]. The conflicting nature of these objectives is caused by substantial interaction between the inputs (wind, pitch angle, and electromechanical torque) and outputs (electrical power and dynamic loads) of the wind turbine.

Recent advances in power electronics applied to wind turbines have drawn the attention to turbines which possess the ability to continuously adapt the rotational speed to the actual felt wind velocity. Such variable rotational speed wind turbines are multi-input-multi-output (MIMO) systems and this opens the possibility to exploit the interactions between the inputs and outputs in the system to reduce dynamic loads as well as maintaining a desired amount of energy production.

The key issue in model based control design is the use of accurate mathematical models of the system to be controlled. In general, the following holds true: "The more accurate the model describes reality, the higher the achievable performance will be". The majority of the state-of-the-art design codes has been developed for dealing with wind turbine design calculations and time-domain simulations, and consequently do not include the linearization step to obtain linear model descriptions of the complete wind turbine required for control design. Only ADAMS/WT, DUWECS, and GAROS provide a facility for linearizing the non-linear wind turbine model around an operating point. The linearization module of ADAMS/WT (i.e. ADAMS/WT/linear), however, neglects rotating frame effects due to the fact that the wind turbine modes can be extracted only in parked position. The result being that the significant gyroscopic coupling effects of a rotating wind turbine are neglected [171, 283]. This limitation excludes the design of controllers that exploit the dependency on both azimuth (i.e. rotor position) and rotational speed.

Generally it can be said that consciousness is raising that the control design should be integral part of the design of the complete system, since the dynamics of a controller interact with the rest of the dynamics of the wind turbine and so have implications for the behavior and performance of the complete system, including energy production and fatigue life.

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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