This paper proposes the two nonlinear controllers for variable speed wind turbine (VSWT) operating at below rated wind speed. The objective of the controller is to maximize the energy capture from the wind with reduced oscillation on the drive train. The conventional controllers such as aerodynamic torque feedforward (ATF) and indirect speed control (ISC) are adapted initially, which introduce more power loss, and the dynamic aspects of WT are not considered. In order to overcome the above drawbacks, modified nonlinear static state with feedback estimator (MNSSFE) and terminal sliding mode controller (TSMC) based on Modified Newton Raphson (MNR) wind speed estimator are proposed. The proposed controllers are simulated with nonlinear FAST (fatigue, aerodynamics, structures, and turbulence) WT dynamic simulation for different mean wind speeds at below rated wind speed. The frequency analysis of the drive train torque is done by taking the power spectral density (PSD) of low speed shaft torque. From the result, it is found that a tradeoff is to be maintained between the transient load on the drive train and maximum power capture.
In recent years, wind energy is one of the major renewable energy sources because of environmental, social, and economic benefits. The major classifications of wind turbines (WT) are fixed speed wind turbine (FSWT) and VSWT. Compared with FSWT, VSWT has many advantages such as improved energy capture, reduction in transient load, and better power conditioning [
The objective of this paper is to prove the efficacy of nonlinear controllers which considers the dynamic aspect of the wind and aero turbine, without the wind speed measurement. Finally, the objective is to track the reference rotor speed asymptotically. This paper is organized as follows. The objective of the work is discussed in Section
Generally, WT is classified into two types, that is, fixed and variable speed WT. Variable speed WT has more advanced and flexible operation than fixed speed WT. Operating regions in variable speed WT are divided into three types. Figure
Power operating region of wind turbines.
Region 1 represents the wind speed below the cutin wind speed. Region 2 represents the wind speed between cutin and cutout. In this region, the main objective is to maximize the energy capture from the wind with reduced oscillation on the drive train. Region 3 describes the wind speed above the cutout speed. In this region, pitch controller is used to maintain the WT at its rated power.
Figure
WT control scheme.
A WT is a device which converts the kinetic energy of the wind into electric energy. Simulation complexity of the WT purely depends on the type of control objectives. In case of WT modelling complex simulators are required to verify the dynamic response of multiple components and aerodynamic loading. Generally, dynamic loads and interaction of large components are verified by the aeroelastic simulator. For designing a WT controller, instead of going with complex simulator, the design objective can be achieved by using simplified mathematical model. In this work, WT model is described by the set of nonlinear ordinary differential equations with limited degree of freedom. In this paper, the control law is designed based on simplified mathematical model with the objective of optimal power capture at below rated wind speed and reduced oscillation of the drive train. The proposed controllers are tested with different wind profiles. Finally, the controllers are validated for FAST WT model. The parameters of the twomass model are given in [
Schematic of WT.
Equation (
The values of approximated coefficients are given in Table
Coefficients’ values.






Figure
Twomass model of the aero turbine.
In order to compare the results of proposed and existing conventional controllers, a brief description of the wellknown control techniques, that is, ISC and ATF, is discussed in this section. In ISC, it is assumed that the WT is stable around its optimal aerodynamic efficiency curve. The twomass model control signal is given in the following:
In ATF, proportional control law is used to control the WT. The rotor speed and the aerodynamic torque (
The above existing control techniques have three major drawbacks, that is, the ATF control having more steady state error, so an accurate value of
The estimation of effective wind speed is related to aerodynamic torque and rotor speed provided the pitch angle is at optimal value:
Let us consider the linear sliding surface:
The Lyapunov candidate function is chosen as
In [
CARTs (Control Advanced Research Turbines) are located in the center of the national wind NREL (National Renewable Energy Laboratory), near Golden, Colorado. The CART3 is a threebladed variable speed and variable pitch wind turbine and has a rating of 600 kW. It mainly consists of three parts, namely, the rotor, the tower, and the nacelle. The generator is connected to the grid through power electronics that can directly control generator torque [
FAST was developed by the NREL; it is used for WT aeroelastic simulator. The modelling of two and threeblade horizontal axis wind turbines (HAWT) is obtained by FAST. This FAST code can be able to predict extreme and fatigue loads. Tower and flexible blade server are modelled by “assumed mode method.” WT loads are calculated by using BEM (Blade Element Momentum) and multiple component of wind speed profile [
Figure
Test wind speed profile.
The proposed and conventional controllers are implemented using FAST interface with MATLAB Simulink. The main objectives of the controllers are to maximize the energy capture with reduced stress on the drive train. The efficiency of the controllers is compared by using the following terms, that is, aerodynamic
Maximization of the power capture is evaluated by the aerodynamic and electrical efficiency which is defined in (
The reduced oscillation on the drive train and control torque smoothness are measured by the STD (standard deviation) and maximum value.
Comparison of different control strategies based on twomass model using FAST simulator.
Control strategy  ISC  ATF  MNSSFE  TSMC 

STD ( 
9.629  23.03  23.13  16.00 
Max ( 
45.62  130.8  136.7  107.81 
STD ( 
0.142  0.369  0.280  0.246 
Max ( 
1.010  2.500  1.807  1.835 

69.73  72.87  76.23  74.81 

85.59  85.06  94.67  94.36 
Rotor speed comparison for ATF and ISC for FAST simulator.
Rotor speed comparison for TSMC and MNSSFE for FAST simulator.
Table
To analyze the controller performances in a more detailed fashion, Figures
Box plot for low speed shaft torque using FAST simulator.
Box plot for generator torque using FAST simulator.
Figure
Box plot for rotor speed using FAST simulator.
The frequency analysis is carried out by using the PSD on the low speed shaft torque which is shown in Figure
PSD for low speed shaft torque using FAST simulator.
As shown in Figure
Comparison for baseline control with other controllers for generated average power.
In order to avoid the torsional resonance mode by choosing the proper tracking dynamics, a tradeoff is made between power capture optimization and reduced transient load on low speed shaft torque. A good dynamic tracking, that is, similar to WT fast dynamics, gives better power capture but it requires more turbulence in control torque. Conversely slow tracking gives smooth control action with less power capture. Therefore, a compromise should be made between the power capture and transient load reduction. The better optimal speed tracking leads to better power capture for TSMC controller. The simulations are performed with different wind speed profiles with the mean wind speed at below rated wind speed. The results are given in Tables
TSMC performance for different wind speed profiles.
Mean wind speed (m/sec)  Electrical efficiency (%) 

Max ( 

7 (m/sec)  74.81  16.00  1.835 
8 (m/sec)  73.51  16.83  1.683 
8.5 (m/sec)  73.33  13.34  1.955 
MNSSFE performance for different wind speed profiles.
Mean wind speed (m/sec)  Electrical efficiency (%) 

Max ( 

7 (m/sec)  76.23  23.13  1.807 
8 (m/sec)  74.85  23.35  1.995 
8.5 (m/sec)  74.52  23.58  2.076 
Figure
Performance comparison for MNSSFE and TSMC with industrial baseline controller.
Baseline  MNSSFE  TSMC  

STD ( 
565.00  529.96  502.89 

73.72  77.82  75.73 
Comparison for baseline control with other controllers for electrical power.
Figure
Additive disturbance performance comparison for MNSSFE and TSMC.
MNSSFE  TSMC  

STD ( 
0.279  0.253 
STD ( 
23.06  17.97 

75.68  75.72 
Rotor speed comparison for MNSSFE and TSMC with constant additive disturbance of 1 kNm/
This paper deals with the problem of controlling the maximum power generation at below rated wind speed of VSWT. The objective is to design a robust controller that maximizes the energy extraction from the wind while reducing the transient loads. For the above purpose, two nonlinear controllers, that is, TSMC and MNSSFE, which have the ability to reject disturbance and accommodate parameter uncertainty, are proposed in this study. Finally, it is concluded that a tradeoff is to be maintained between the efficiency and mechanical stress on the drive train. The performances of these controllers are compared with the conventional ATF and ISC using FAST aeroelastic simulator. The proposed controllers are found to produce satisfactory results in achieving the control objectives.
Low speed shaft stiffness (N
Power coefficient
Torque coefficient
Generator inertia (kg·m^{2})
Rotor inertia (kg·m^{2})
Generator external damping (N·m·rad^{−1}·s^{−1})
Low speed shaft damping (N·m·rad^{−1}·s^{−1})
Rotor external damping (N·m·rad^{−1}·s^{−1})
Gearbox ratio
Aerodynamic power (W)
Electrical power (W)
Rotor radius (m)
Aerodynamic torque (N·m)
Generator (electromagnetic) torque (N·m)
High speed shaft torque (N·m)
Low speed shaft torque (N·m).
The authors declare that there is no conflict of interests regarding the publication of this paper.