Power Regulation and Pitch Control of Wind Turbines using Actuator Fault Tolerant Adaptive Control

Power Regulation and Pitch Control of Wind Turbines using Actuator Fault Tolerant Adaptive Control

Meenu P.V.

Electrical and Electronics Engineering Lourdes Matha College of Science and Technology

Thiruvananthapuram, India

Cibumol B. Babu

Electrical and Electronics Engineering Lourdes Matha College of Science and Technology

Thiruvananthapuram, India

AbstractHigh performance, reliability and power maximization are required for the wind turbines to compensate unbalanced loads caused by the unpredictable wind speed and turbulences. This paper studies the control methodology for optimal power capture in a variable speed variable pitch wind turbine. The pitch actuator faults can affect the pitching performance with slow dynamics and results in generator power instability. The dynamic change in the pitch actuator, effectiveness loss and bias are considered as uncertainties and augmented into the pitch dynamic model. The nonlinear model of the wind turbine is presented and a model based non-linear controller is designed considering the effects of non-linear system dynamics, actuator fault uncertainties and unknown external disturbances. The adaptive controller is designed to be robust against unexpected actuator faults, model uncertainties, unknown control direction and disturbances including wind speed and model noises. The simulations are performed to confirm the effectiveness of the proposed control strategy and the simulation results shows that the performance of the adaptive controller to be superior to that of a conventional controller.

KeywordsWind Energy Conversion System; Adaptive PID controller; fault-tolerant; pitch control;self-tuning gains; unknown control direction; wind turbine power regulation

1. INTRODUCTION

   Wind Power generation has widely grown during the recent years and nowadays is one of the promising type of renewable energy capable of supplying worlds power demand. However, fluctuations in the output power caused by the uncontrollable and stochastic wind severely affects the stabilities of the grid. In this paper, a pitch angle controller is designed so as to produce rated power via blade pitch angle control to avoid probable catastrophic operation.

   As analyzed from [1], the control of pitch angle is not easy because the system behaviour is highly nonlinear. Many studies have been reported about the wind turbine pitch control.

   the linearized wind turbine model may not render the expected performance on the non linear model [4].

   The main objective of this paper is to design a suitable pitch controller robust against wind speed variation. Moreover, the controller should be robust to pitch actuator faults and model uncertainties. The proposed adaptive controller ensures auto tuning of the gains, functions satisfactorily and provides acceptable performance for industrial applications.

2. SYSTEM MODELLING

In this section, the mathematical modelling of the Variable Speed Wind Turbine (VSWT) is described. A variable speed wind turbine consists of following components i.e. aerodynamics which converts kinetic energy into mechanical energy, a drive train, which allows increasing the speed and decreasing the torque, a tower model, a pitch system, a converter and a generator, which transfers mechanical energy into electrical energy.

Fig. 1. Combined schematic model of wind turbine.

A. Wind Turbine Modelling

The aerodynamic power captured by the turbine blades is given by the following nonlinear equation.

Advanced fault detection, accommodation schemes are necessary for reliable operation of wind power system. A passive and active fault tolerant scheme is proposed in [2].

Pa 1 aR

2

2CP (, )Vr3

(1)

However, detection of sensor faults are not considered. In [3], proposed fuzzy controller shows better robustness feature than the conventional controller but actuator fault detection and diagnosis schemes are not considered in this paper. Moreover,

where a and R are the air density and blade length respectively. Cp, the power coefficient depends on the blade pitch angle and tip speed ratio, which is stated as in (2).

reducing mechanical stress of the actuator is important for

CP (, ) B1 B2 B3 B4 .expB5 B6

(2)

efficient operation. The controller which has been designed for

i

i

where;

1 1

0.035

(3)

where xt is the nacelle displacement, measured from its equilibrium point, Mt is the nacelle mass, Bt is the damping

i

i

0.08 2 1

where the parameters Bi are known constants without units. The rotor speed, r is defined as;

ratio and Kt is the elasticity coefficient of the tower.

1. Drive Train Model

   Fig.3 shows the two mass model of the wind turbine.

   Rr

   vr

   (4)

   Fig. 3. Two mass model of wind turbine.

   The dynamics of the rotor is modeled by the following differential equation.

   Jr r

   Ta

   • Kdt

     . (Br

     • Bdt

       )r

     • Bdt

     g

     g

     Ng

     (10)

     dt

     dt .Bdt

     dt Bdt

     (11)

     N

     N

     Jg g

     g

     Kdt

     N

     N

     g

     r Bg

     Ng 2

     g Tg

     Fig. 2. Wind turbine Power Coefficient Curve.

     The aerodynamic torque is expressed as;

     where Jr and Jg are inertia of the rotor and generator shaft respectively, which are rotating at speeds r and g respectively. Ng is the drive train ratio, Kdt is the torsion stiffness and Bdt is the torsion damping. Br and Bg are viscous frictions of rotor and generator respectively. is the drive train torsional angle which is defined as;

     Ta 1 Cq (, )R3V 2

     2

     (5)

     r

   • g

   N g

   (12)

   The aerodynamic thrust is stated as;

   Ft 1 R2CT (, )V 3

   2

   (6)

   where r and g are rotation angles of rotor and generator respectively. dt is the drive train efficiency.

2. Converter Model

A converter is located in between the generator and the grid

where the torque coefficient, Cq and thrust coefficient, CT is given by the following equations.

to adjust the generated power frequency. The converter is modeled as a first order system with a time delay as;

C (, ) Cp (, )

q

(7)

Tg agTg agTg,ref

(13)

~ ~ E. Generator Model

CT 0.5CT 1 sign(CT )

The power, P

produced in the generator is given by;

~

A A

A

.exp A

g

Pg ggTg

(14)

CT 1 2 3 4

A52.exp A6 A73.exp A8

(8)

where Tg is the generator shaft torque and g is the generator efficiency.

where the parameters Ai are known constants without units.

B. Tower Model

This nacelle motion is modeled as the following equation.

F. Pitch Actuator Model

The considered wind turbine has a hydraulic pitch system to rotate the blades and adjust the pitch angle to reference pitch angle, which is commanded by the pitch controller. It is

Mt xt Ft Bt xt Kt xt

(9)

modeled as second order dynamic system.

n2

2nd n

2ref

(15)

Assumption 2: It can be stated that -L Ta / -U < 0, where 0 < U lt; L, which implies that with increasing pitch

The three major pitch actuator dynamic changes are pump wear, high air content in the oil and hydraulic leakage. These leads to slower response speeds and consequently, poor power

angle, the aerodynamic torque will decrease.

Considering Assumption 1,

a

a

T

regulation.

The dynamic changes can be considered as an uncertainty and augmented into the dynamic model, and the rewritten pitch actuator model is stated as the given equation.

Ta Vw ,r ,

Considering (18), (19) and (20),

a T )

(20)

~ r F (x, t) G(x, t)p(t)ref

(t) D(x, t) (21)

n, N 2 2n, NN n, N 2ref fPAD

(16)

~ 2

~ ~ 2

where,

fPAD f 1(n ) 2 f 2(n ) f 1(n )ref

2

(n ) n,HL2 n, N 2

F (x, t) c1r c2g c3Ta c4Tg

n, N a3Ta ) a3Ta )

~ ~ 2 N

2n, N N

(n ) n,HACHAC n, N N

(17)

G(x, t)

n, N a3Ta ) 2 N

~

D(x, t) a3Ta ) f PAD

2n, N N

(22)

Assumption 3: There is an unknown non negative constant, af and non negative function f such that

F (x, t) (t)G(x, t) D(x, a f f (x)

(23)

Fig. 4. Dynamic Change Effects on Pitch Actuator

1. FAULT TOLERANT ADAPTIVE CONTROLLER The proposed fault tolerant controller is designed to

   regulate the pitch angle in the presence of wind speed variation, model uncertainty and unexpected actuator faults. It is aimed to provide automatic adaptive gain tuning without trial and error processes. The tracking error and its derivative is defined as,

   N, HAC, PW, HL represent normal, high air content, pump

   w

   er (t) r (t) r,rated

   (24)

   ear and hydraulic leakage respectively. The effectiveness loss and bias can be modeled as,

   e t) t)

   r ( r (

   r,rated

   n, N

   2 2n, N N

   Second time derivative of error considering dynamic model,

   n, N

   2 p(t)

   ref

   (t) (t) f ~

   PAD

   PAD

   (18)

   F (x,t) G(x, t)p(t)

   (t) D(x,t)

   e

   e

   r

   where (t) is the unknown pitch actuator bias that causes

   ref

   (25)

   unbalanced rotor rotation and p(t) represents the unknown pitch actuator effectiveness.

   The tracking error filter is defined as,

   t

   2

   (26)

   1. WIND TURBINE DYNAMICS

      It is desirable to keep the drive train torsion angle variation

      Z (t) 2er (t)

      er ( )d er (t)

      0

      as small as possible, which, consequently leads to reduction in the drive train stress. The desirable operational dynamic equation of the wind turbine with reduced drive train stress can be stated as,

      The filtered error, Z(t) is formed by combination of proportional, integral and derivative terms of the tracking error, er(t). Combining (18) and (26),

      Z H (x, t) B(x, t)ref

      (27)

      r c1r c2g c3Ta c4Tg a3 Ta

      (19)

      where,

      Assumption 1: Ta (Vr, r, *) and * for any given pair (Vr,r) are constant through time.

      B(x, t) p(t)G(x, t)

      H (x, t) 2 (t) 2e (t) F (x, t) (t)G(x, t) D(x,t)

      er r

      (28)

      The adaptive controller is defined as,

      ref

      (DO D )N ( )Z (t)

      (29)

      The controller gain is obtained via the following adaptive gains.,

      Fig. 6. Generated Power using Adaptive and PID controller

      D a 2

      (DO D )Z 2

      2 2

      where,

      a 0 a 1

      NgTg,max

      Z

      n, N a3U

      f c1r c2g c3

      dt

      c4Tg

      2 N

      (31)

      ~ ~ 2

      a3U n, N a3U a3U(n ) a3U(n )(max min )

      Fig. 7. Drive train torsion angle variation using Adaptive and PID controller

      2n, N N

      2 N

      n, N N

      2n, N N

      B. Faulty Actuation Mode

      Case1: Pitch Actuator Bias, (t) = 15

      (x) f (x) er

      er 1

      (32)

      The Nussbaum – type function is defined as,

      N ( ) 2Cos( )

      1. SIMULATION RESULTS

         A. Normal Actuation Mode

         (33)

         The performance of the wind turbine in normal actuation mode using the proposed controller and a conventional PID controller, under the wind profile shown in Fig.5 are demonstrated and compared in Fig.6 and Fig.7.

         Fig. 5. Wind Speed Profile

         Fig. 8. Generated Power using Adaptive and PID controller during pitch actuator bias

         Case2: Effectiveness loss, p(t) = 0.4

         Fig. 9. Generated Power using Adaptive and PID controller during effectiveness loss

         Case3:Dynamic Change Effect; High Air Content

         Fig. 10. Generated Power using Adaptive and PID controller during high air content in the oil

         Case4: Pitch Actuator Bias = 10, Pump Wear

         Fig. 11. Generated Power using Adaptive and PID controller during pitch actuator bias and pump wear

      2. CONCLUSION

In this paper, an adaptive fault tolerant controller with adaptive gain adjustment for non linear wind turbines is designed and simulated. The simulation results shows that the adaptive controller shows better robustness than a conventional PID controller, with less overshoot and shorter settling time, during both faulty and fault free cases. The proposed controller is robust against model uncertainties, unpredictable wind speed variations, unknown control direction and unexpected pitch actuator faults. Future studies may include the integration of controller for both operational regions considering the generator faults.

REFERENCES

[1]. H.Geng, G.Yang ,Output power control for variable speed variable pitch wind generation system, IEEE Transactions on energy conversions, vol.25, no.2, pp. 495-503, 2010.

[2]. Hamed Badihi, Youmin Zang and Henry Hong, Wind turbine fault diagnosis and fault tolerant torque load control against actuator faults, IEEE Transactions on control system technology, vol.10, no 3, pp. 390- 405, 2014.

[3]. Jianxing Liu, Yabin Gau and Sijia Geng Non linear control of variable speed turbines via fuzzy techniques, IEEE Transactions on energy conversions, vol.25, no.2, pp. 495-503, 2017.

[4]. P. F. Odgaard and J. Stoustrup, A benchmark evaluation of fault tolerant wind turbine control concepts, IEEE Trans. Control Syst. Technol., vol. 23, no. 3, pp. 12211228, May 2015.