Elsevier

Renewable Energy

Volume 44, August 2012, Pages 63-71
Renewable Energy

A robust LMI-based pitch controller for large wind turbines

https://doi.org/10.1016/j.renene.2011.12.016Get rights and content

Abstract

This paper utilizes the linear matrix inequalities’ techniques (LMI) for designing a robust collective pitch controller (CPC) for large wind turbines. CPC operates during up rated wind speeds to regulate the generator speed in order to harvest the rated electrical power. The proposed design takes into account model uncertainties by designing a controller based on a polytopic model. The LMI-based approach allows additional constraints to be included in the design (e.g. H problem, H2 problem, H/H2 trade-off criteria, and pole clustering). These constraints are exploited to include requirements for perfect regulation, efficient disturbance rejection, and permissible actuator usage. The proposed controller is combined with individual pitch controller (IPC) that reduces the periodic blade’s load by alleviating once per revolution (1P) frequency fatigue loads. FAST (Fatigue, Aero-dynamics, Structures, and Turbulence) software code developed at the US National Renewable Energy Laboratory (NREL) is used to verify the results.

Highlights

► The paper investigates designing robust pitch controller For 5 MW wind turbine. ► The wind turbine model characteristics are first presented. ► An LMI robust controller is designed based on single model, then polytopic model. ► Individual pitch controller is designed to mitigate mechanical fatigue loads. ► Finally, simulation compares between the proposed controller and a PI controller.

Introduction

The use of wind power is increasing rapidly. At the same time the need for better cost effectiveness of wind power plants has stimulated growth in wind turbines’ size and power. In above-rated wind conditions, the goals for turbine operation change from control of generator torque for maximum power tracking to those of regulating power at rated levels with mitigating fatigue loading on the turbine structure. An ordinary PI pitch controller regulates the generator speed without taking into consideration the unstructured dynamics of the blades, the drivetrain nor the tower. The nonlinear variation of rotor torque with wind speed and the pitch angle are typically not considered in design. Further, the pitch actuator also has restricted limits on pitch angle and pitch rate [1]. Other challenging problems are the presence of nonlinearities in the system dynamics, and the continuous change of the operating points during operation. All previous reasons motivate the need for robust pitch controller that provides an accepted performance, and disturbance rejection at different operating points within the allowed actuator constrains. In this paper, a multi-objective collective pitch controller will be designed using LMI techniques for generator speed regulation.

Another objective is to reduce the structural mechanical loads by using IPC. This should be fulfilled within the permissible range and rate of the pitch angle of the actuator. The importance of load reduction becomes vital as turbines become larger and more flexible. When the turbine blade sweeps, it experiences changes in wind speed due to wind shear, tower shadow, yaw misalignment and turbulence. These variations lead to (1P) large component in the blade loads, it’s essential to design (IPC) to cancel this component [2].

Pitch controller is designed using H technique in [3], [4]. In these papers, the controller main objective is to regulate the speed by improving disturbance rejection. The required control effort isn’t considered in the design. In [5], it is proposed to design gain scheduled feedback/feed forward CPC for speed regulation combined with IPC for load reduction. Also in [6], optimal LQG feedback/feed forward CPC is proposed for speed regulation combined with IPC for load reduction. Combined CPC with IPC is proposed in [7] both as PI controllers. In [5], [6], [7], all the proposed controllers is based on a single linearized model, which only reflects one single operating point. A multi-objective (H2/H) pitch controller is proposed in [8], but it doesn’t provide (H2/H) trade-off criteria. It also doesn’t consider improving the transient response at different operating points. In our proposed work in this paper, an LMI-based CPC is considered. The controller design constraints include H problem for better speed regulation, and H2 problem for optimizing control action with performance. The design also addresses H/H2 trade-off criteria for the optimization of the two previous problems. Pole clustering for improving transient response is also considered. The controller is based on a polytopic model to overcome model uncertainty at different operating points. CPC is combined with IPC to mitigate mechanical fatigue loads.

In Section 2, the turbine model specifications plus the turbine linearized models are discussed. In Section 3, the proposed CPC design, and the controller objectives are shown. The design considers two cases; single operating point-based model, and a polytopic-based model. In Section 4, IPC design is discussed. The simulation results showing a comparison between the proposed controller and a conventional PI controller are shown in Section 5. Finally the conclusions are stated in Section 6.

Section snippets

Model description

Simulations are performed on a full nonlinear turbine model provided by the FAST (Fatigue, Aero-dynamics, Structures, and Turbulence) software code developed at the US National Renewable Energy Laboratory (NREL) [9]. The model used is a 3-bladed, variable-speed 5 MW wind turbine model with the specifications given in Table 1.

More specifications could be found in [10, pp. 26]. The pitch actuator, represented as a second order model, has a pitch angle range from 0 to 90° with maximum rate of 8°/s.

Designing an LMI-based collective pitch controller

The proposed technique is to design state feedback, LMI-based collective pitch controller (CPC) to regulate the generator speed in region 3. This controller is combined with IPC that mitigates the flapwise moment by canceling (1P) frequency. The proposed control strategy is shown in Fig. 3.

M1,2,3 are the blade tip flapwise moments of each blade. ωgen is the generator speed. The total control action (β) is calculated as follows:β=βipc+βcpc+β¯where (β¯) is the pitch angle operating point. It is

Individual pitch controller design

To reduce the periodic blade flapwise moment, periodic individual pitching technique of the rotor blades are proposed (see e.g. [2], [16]). In this approach, each of the blades needs to be pitched according to the intermittent loads that it experiences. The spectrum of the blade root bending moment caused by wind shear has a dominant component at frequency (1p) while higher harmonics could be damped [17]. However, there are some methods for reduction of higher load harmonics (called higher

Simulation results

The proposed controller is tested using FAST nonlinear model. Two uncertainties will be tested. The first is a stochastic wind model profile applied to the turbine. This wind profile covers all operating points. It represents a perfect disturbance to test the controller performance under severe conditions. The turbine model will be tested against stochastic full field wind profile developed by the NREL TurbSim wind simulator [19]. The second is an unstructured model uncertainty represented by

Conclusion

This paper has addressed the problem of designing an LMI-based robust CPC for large variable-speed variable-pitch wind turbines. The CPC is integrated with IPC to reduce the mechanical loads. CPC has been first designed based on single operating point-based model, but the desired constraints were not met at all operating points. A polytopic model-based approach has been considered to overcome this issue. The design constraints have included H problem, H2 problem, H/H2 trade-off criteria, plus

References (19)

  • Jonkman JM. Dynamics modeling and loads analysis of an offshore floating wind turbine. Technical report,...
  • E.A. Bossanyi

    Individual blade pitch control for load reduction

    Wind Energy

    (2003)
  • Geyler M, Caselitz P. Individual blade pitch control design for load reduction on large wind turbines. Proceedings of...
  • Laks JH, Pao LY, Wright A. Combined feed forward/feedback control of wind turbines to reduce blade flap bending...
  • Fiona Dunney, Lucy Y. Paoz, Alan D. Wrightx, Bonnie Jonkman, Neil Kelle. Combining standard feedback controllers with...
  • K. Selvam et al.

    Feedback feed forward individual pitch control for wind turbine load reduction

    Int J Robust Nonlinear Control

    (2008)
  • Wilson DG, Berg DE, Resor BR, Barone MF, Berg JC. Combined individual pitch control and active aerodynamic load...
  • Lescher F, Zhao JY, Martinez A. Multi objective H∞/H2 control of a pitch regulated wind turbine for mechanical load...
  • J.M. Jonkman et al.

    FAST users guide

    (August 2005)
There are more references available in the full text version of this article.

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    Thus, pitch control technology is indispensable to restrain wind power fluctuations, ensuring steady operation of wind turbines. Although PI [2], linear quadratic Gaussian (LQG) [3], model predictive control (MPC) [4], and robust control [5] have been proposed for pitch control, some challenges still exist. For example, partial mathematical model and uncertainty dynamics are essential for designing a robust controller [6]; LQG and PI rely on the model linearized at a specific working point [7].

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