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The main contribution of this paper is the development of
A wind energy conversion system is a mechanical electronic hydraulic integrated system which consists of rotor, drive train, gear box, generator and other mechanical equipment. WECS driven by stochastic wind power signal indicate nonlinear switching system properties. Control systems play a vital role in satisfying harvested power and load alleviation objectives in wind turbines. The performance of the designed controller can be easily interrupted by possible faults and failures in different parts of the system. Therefore, designing a faulttolerant controller is very beneficial in wind turbine operations.
So far, the design of faulttolerant control for wind turbine systems is still lacking in studies. In [
The above mentioned methods are all restricted to the nonlinear characteristics of wind turbines. In order to overcome the nonlinear characteristics of wind turbines,
Piecewise linear systems provide a powerful tool of analysis and design for nonlinear control systems. The piecewise linear system framework can be used to analyze smooth nonlinear systems with arbitrary accuracy. Many other classes of nonlinear systems can also be approximated by piecewise linear systems [
A number of results have been obtained in controller design of such piecewise continuous time linear systems during the last few years [
The structure of a WECS is described as
The equation of wind
The available power in the wind
From the available power in the wind, the power captured by the rotor
The tipspeed ratio
The drive train model includes a lowspeed shaft, a highspeed shaft, a gear box and flexible device. The drive train dynamics function is given:
The pitch system can be modeled by a secondorder transfer function [
The generator and converter dynamics can be modeled by a firstorder transfer function:
The realtime power is described by:
Then, the dynamics of the WECS can be obtained by combining
The basic control strategy is described as
If
For wind speed under
During the partial load region, the generator control is the only active control and aims at maximizing the energy captured from the wind and/or at limiting the rotational speed at rated. This is possible by continuously accelerating or decelerating the generator speed in such a way that the optimum tip speed ratio is tracked.
During the full load region, the control objective is to keep the realtime power
When the wind speed is close to
In this paper, we use Maximum Power Point Tracking (MPPT) algorithm to obtain the optimal generator speed
In summary, WECS is mainly based on four regions for modeling and control. According to the different wind speeds, models and control strategies need to switch. This section introduces the basic principles of PWA, and then gives the idea of WECS modeling.
A linear stochastic discretetime PWA system is defined by the statespace equation:
Furthermore, if cells
The linearized drive train dynamics function is described as follows:
Then a linearized overall state space model describing the dynamics of the WECS can be given:
Although wind can provide the energy that drives the wind turbine, due to its intermittent nature, it also acts as a disturbance. Hence, the effective wind (
Combining with
Choose 3 working points for the parameters of WECS described as
In this section, we consider both actuator and sensor faults. Let
where
The PWA model of the system with the loss of gain
Consider the PWA actuator faults system
The
Clearly, it is possible to apply the control approach proposed in [
In this way, the controller can also consider the displacement term
By applying the control law
From the above, we can have the following main results:
Consider system
Furthermore, if the following matrix inequalities:
By recalling that
Since
Moreover, if
Obviously, if condition
This implies that system
Now we focus on the possibility of finding a statefeedback control law of the type
For PWA system
If there exist matrices
Using Schur's lemma, then
Now, let
Let:
Since
For PWA system
If there exist matrices
Similar to the proof of Theorem 1,
Now, let
According to the modeling method described in part 3, we can obtain the following PWA model of WECS:
If 0 <
If 8 <
If 12 <
According to Theorem 1 and Theorem 2, we can successfully obtain the piecewise linear state feedback matrixes
The normal WECS:
In these three cases, feedback gains
The generator speed and generator power responses are shown in
However, comparing with
From the discussion in Section 3, it is shown that the stochastic PWA model offers an ideal framework for capturing the stochastic property of wind speed and the nonlinear dynamics of WECS. The pictures that emerge from the proposed method and simulation results in Sections 3 and 4, suggest that the presented
This work was simultaneously supported by the National Natural Science Foundation of China under Grant No. 61304049, No.61174116, and the Beijing Natural Science Foundation Program 4132021.
The authors declare no conflict of interest.
The structure of WECS.
The control strategy for wind turbine.
The tendency of the
Wind speed
Actuators fault of WECS without fault tolerant control: (
Sensors fault of WECS without fault tolerant control: (
Model parameters.
90,000  kg · m^{2}  225  kW  
10  kg · m^{2}  4.29  rad/s  
8 × 10^{6}  Nm/rad  105.534  rad/s  
8 × 10^{4}  kg · m^{2}/(rad · s)  3.5  rad/s  
24.6    86.1  rad/s  

14.5  m  0  deg  
0.15  s  25  deg  
0.1  s   
10  deg/s 
Parameters of linearized model in different working points.
 

0.409  0.50  1.90  0.3125  2.92  0.9375  
0.479  0.53  2.31  0.33  3.65  2.3  
0.833  0.53  2.50  0.625  5  5 
The faults considered.
actuator  gain Factor  
sensor  gain Factor 