5. Simulation results of the designed robust controller

The considered wind model in this paper is as follows.

Figure 11 depicts the speed of the wind in the third operating area that is a value between 15 and 25 m/s. In this study, the model of the wind has randomly varies from 15 to 24 m/s In our research, the speed of the wind is considered be highly changeable during the times [8, 9]. As in early times the speed of wind turbine is growing, then its parameter is constant in time and its value fell in the end of the period of the time. The reason for selecting this kind of plant of the random wind is, presentation the robust controller has a good performance in various

Figure 11. Wind model in different speeds.

speeds. This express that a sudden variation in the wind speed, the robust controller attempts to control the pitch angle for setting the electrical power at it's at most efficiency in the third performance area.

Due to the linear dependency among the speed of the rotor and the speed of generator over the gear ratio, the results of applying the control scheme which seeks to maintain the electrical power fixed and regulate speed of the generator- can be examined after modeling of speed of the wind turbine and modeling the robust μ controller.

Considering Figure 12(a), the deflection of output about the nominal value which is changed by noise and disturbance in wind is not high that is acceptable. Maximum variation around the reference value is 2.1% and it is equal to 0.027 kW that expresses nice disturbance cancelation in areas in the matching scheme. In Figure 12(b), at most variations around nominal values are equivalent to 3.068 rad/s and it is equal to 9.2%. It is sates a disturbance cancelation and nice following of generator reference parameter in the existence of disturbance with wind speed in the good way and with the least variations.

than 1 in any frequency. Also, the gamma parameter denotes the value that the function

Iteration number γ value achieved Maximum μ value Controller order

 1201.403 11.648 5 5.35 3.837 11 1.763 0.748 16 0.734 0.733 17 0.732 0.730 17

Figure 11 depicts the speed of the wind in the third operating area that is a value between 15 and 25 m/s. In this study, the model of the wind has randomly varies from 15 to 24 m/s In our research, the speed of the wind is considered be highly changeable during the times [8, 9]. As in early times the speed of wind turbine is growing, then its parameter is constant in time and its value fell in the end of the period of the time. The reason for selecting this kind of plant of the random wind is, presentation the robust controller has a good performance in various

Flð Þ P;K infinity norm is fewer than that value.

Figure 11. Wind model in different speeds.

Table 2. Obtained results of the robust controller (μ).

74 Stability Control and Reliable Performance of Wind Turbines

The considered wind model in this paper is as follows.

5. Simulation results of the designed robust controller

In Figure 13, it can be found that the control effort or the adjustment of pitch angle is between of 14 and 22.5. Due to changed areas of wind turbine efficiency, aim in this work is, regulating the power and speed of the generator at the nominal parameter in the third performance part. So, in this scenario by growing the value of wind to cut-out, the pitch angle has been improved, and this scenario leads to the decrease of power coefficient and the power is at its nominal value [4]. Furthermore, by reducing the speed of the wind, the blade pitch angle is decreased and at this step, to regulate the power and generator speed at nominal value, robust controller is designed. This controller attempts to control the pitch angle for accessing the high electric power and adjust the speed of generator about its nominal value. So, by applying this kind of controller, the control effort remains fewer than 25, that is the utmost pitch angle of the wind turbine, stays bounded in the third area.

Figure 12. (a) The response of electric power produced by wind turbines to track input reference electrical power using μ controller. (b) The response of speed of the wind turbine generator to track input reference speed of generator using μ controller.

Vestas V29 wind turbine characteristic Value Electrical power of generator 225 KW Rotor diameter 29 m Rotor RPM 41/30.8 RPM Angular speed of rotor 4.29 rad/s Angular speed of generator 105.6 rad/s Frequency 50–60 Hz

1 Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran

[1] Hau E. Wind Turbines: Fundamental, Technologies, Application, Economics Handbook.

[2] Blaabjerg F, Ma Ke. Future on power electronics for wind turbine systems. IEEE Journal of

[3] Kaldellis J, Zafirakis D. The wind energy revolution: A short review of a long history.

[4] Bazilevs Y, Korobenko A, Deng X, Yan J. Novel structural modeling and mesh moving techniques for advanced fluid–structure interaction simulation of wind turbines. Interna-

[5] Evangelista C, Valenciaga F, Puleston P. Active and reactive power control for wind turbine based on a MIMI 2-sliding mode algorithm with variable gains. IEEE Transactions

[6] Mirzaei M, Henrik H, Niemannand Kjolstad N. A μ ıt-synthesis approach to robust control of a wind turbine. In: Proceedings of 50th IEEE Conference on Decision and

2 Department of Electrical Engineering, Tehran University, Tehran, Iran

Emerging and Selected Topics in Power Electronics. 2013;1:139-152

tional Journal of Numerical Methods in Engineering. 2015;102:766-783

Control and European Control Conference, Orlando; 2011. pp. 645-650

, Hamed Pourgharibshahi<sup>3</sup>

Designing Mu Robust Controller in Wind Turbine in Cold Weather Conditions

, Hassan Zeynali<sup>1</sup> and

http://dx.doi.org/10.5772/intechopen.74626

77

Author details

Tahere Pourseif<sup>1</sup>

Arash Shams<sup>1</sup>

References

3rd ed; 2013

\*, Majid Taheri Andani<sup>2</sup>

\*Address all correspondence to: t.pourseif@gmail.com

3 Advanced Technology University, Kerman, Iran

Renewable Energy. 2011;36:1887-1901

on Energy Conversion. 2013;28:682-689

Figure 13. Pitch angle adjustment using the μ controller.

### 5. Conclusion

This work wanted to control the pitch angle of the wind turbine to regulate the speed of the wind turbine generator in the third area of procedure. In the third area, the generator speed, and electrical power are fix in their nominal parameter, and do constant. The existence of noise and disturbance in the model of wind are the main reason for high error rate in the generation of electrical power and generators' speed. Therefore, this paper suggested that the generation of electrical power and adjustment of the generator speed are practical if robust controller is employed and current errors (uncertainties) in the wind turbine system are taken into account. In most previous works have done, spring constant, damping coefficient and insignificant deviations of the linearization process are listed as uncertainties. These uncertainties are deemed to be true in appropriate weather conditions. Although, cold climate leads the turbine blades to freeze that is followed by mass growth. This mass development results in the decrease of electrical power generation, incorrect model operation and wrong data sending. So, new uncertainties were employed to the system in order to work out the mentioned challenges. After employing these uncertainties, μ controller is presented. Minimal variation about the reference parameter and fewer control action for variation the blades' angle (to obtain optimal power and adjust the speed of the generator) needs the use of μ controller. To be more accurate, the μ controller is more justifiable system in terms of disturbance cancelation.

## A. Appendix

The wind turbine that is considered in this paper has the following specifications:

Characteristic of Vestas V29 Wind turbine

