1

Implementation of Pitch Angle Controller For

Variable Speed Wind Turbine Gaurav Singh Bhandari1, Dr. M. Kowsalya1

1School of Electrical Engineering, VIT UNIVERSITY, Vellore, 632014, India

gauravusic09@gmail.com, mkowsalya@vit.ac.in

Abstract: In this paper, it is shown that how the variable speed wind turbine can be used to generate a fixed value of voltage at the output with the help of a PI controller and it is done by varying the pitch angle of the blades Pitch angle control is the most common means for adjusting the aerodynamic torque of the wind turbine when wind speed is above rated speed and various controlling variables may be chosen, such as wind speed, generator speed and generator power. As conventional pitch control usually use PI controller, the mathematical model of the system should be known well. The block diagram of the proposed speed control system which consists of speed controller and the turbine linearized model is simulated by Matlab-Simulink software package. the simulation results show that the controller accurately adjusts the blade pitch angle to set the wind turbine power output to its reference value so that it is possible to maximum power tracking using pitch angle controller below base wind speed and control rated power above base wind speed

Keywords: Pitch Control, Varible Speed Wind Turbine, Induction Generator,Power Smoothing,Maximum power

1 Introduction

Recent years, a fast growing in wind energy is experienced in worldwide, Renewable energy sources is widely used in industry for avoid pollution and economic purpose. Solar energy is used for power generation with solar rays, hydro energy is used for power generation using waters hydrostatic energy, wind energy is used for power generation using wind.

Mostly wind energy is used for power generation purpose in comparison with hydro and solar energy due to following reasons. Wind farm setup require small geographical area in comparison with hydro energy due to setup hydro power plant that effects in humans life, commercial user, residential area etc. wind energy can be obtained in day and night in comparison with solar energy because solar energy is obtained in only day if continuous rainy season occurs then solar energy is not possible for power generation purpose so power generation using wind energy is more comparison to solar energy.

In this paper wind energy is modeled for power generation and torque is generated using wind turbine is given to Induction Generator (IG) that dives generator and controller active and reactive power using pitch angle regulation so that it is possible to avoid losses, [1,2].

Pitch regulated variable-speed wind turbines have become the dominating type of yearly installed wind turbines. In low wind speed below rated value, the speed controller can continuously adjust the speed of the rotor to maintain the tip speed ratio constant at the level which gives the maximum power coefficient. Pitch angle regulation is required in conditions above the rated wind speed where the power output is kept constant [5, 6].

Variable speed operation yields 20 to 30 percent energy than the fixed speed operation, reduces power fluctuations and improves reactive power supply. Small changes in pitch angle can have a dramatic effect on wind turbine, then the pitch angle controller may play important role on power control and fatigue load minimizing [7,8]. The traditional pitch angle control strategy with gain scheduling is shown in Fig. 1. The error signal of the rated power and the generator power is sent to a PI regulator. The PI regulator produces the reference pitch angle ref. Due to the non-linear variation of the pitch angle versus wind speed for large wind speeds, where the sensitivity of aerodynamic torque to pitch angle is very small when the wind speed is close to the rated, a much larger regulator gain is required here than at higher wind speeds, where a small change in pitch can have a large effect on torque.

Main objectives of controller in wind turbine are to optimize energy conversion as well as reduction in dynamic load which is experiencing by mechanical components. Undeniably dynamic load strongly may change turbine life time and designing cost[9]. Subsequently adopting an appropriate controller with fast response can cause to avoid mechanical fatigue and increase wind turbine life time with lower cost materials in the design phase. Extraction of wind energy is depending on strong none linear characteristics with influence of several factors such as wind speed, load demand changing and metrological condition. Consequently availability of an autonomous control becomes vital.

In this paper, the optimal control will apply to the pitch angle regulation at high wind speed, where double objectives, one is the maximum power tracking from wind, another is minimum fatigue load for wind turbine, are put forward. The proposed controller uses value of active power generation or rotor speed by induction generator and wind speed from anemometer as two input signals simultaneously and continuously as well as pitch angle command as an output to set appropriate angle of servo motor which is connected to the each blade to set their position, this paper proposes wind speed and wind turbine model under steady and transient condition. Fig.1 defines

2

the pitch regulation system with corresponding fluctuation in wind speed.

Fig. 1 Traditional control strategy of pitch angle of wind turbine

2 Matlab/Simulink Based Modelling

Fig.2 presents the proposed simulation model which consists of following components.

(1): Wind speed model for generating wind speed that can be applied to the rotor.

(2): Wind Turbine model for converting kinetic energy contained in wind into mechanical power that is given to Induction Generator.

(3): Generator model converting mechanical power into electric power and determining rotor speed.

(4): Pitch angle controller for changing the blade pitch above Nominal wind speed preventing the rotor speed from becoming too high.

(5): Design of components is explained in [2, 3].

2.1 Wind Speed Model

Wind speed is a combination of four components, gust speed, ramp speed, base speed and noise speed. Design is proposed in [3].

WIND GUST RAMP BASE NOISEV = V + V + V V (1)

2.1.1 Gust Speed

Gust speed sudden change in wind speed .it is given as:

1

GUST COS 1G 1G G

1G G

0 t T

V V T < t < T + T

0 t > T + T

G

(2)

1GCOS G GMAXG TTV = 1- cos2 - 2 T T (3)

TG = Gust Period in sec, T1G = Gust starting time in sec, MAXG = Gust peak in m/sec, t = Time in sec.

Fig. 2 Components proposed of simulation model

2.1.2 Ramp Speed

Ramp speed is continuous varies with time. it is given as:

1R

RAMP RAMP 1R 2R

2R

0 t < T

V = V T < t < T

0 t > T

(4)

T1R = Ramp starting time(s), T2R = Max time(s).

2.1.3 Base Speed

Base speed is constant speed. It is given as:

BASE BV = K Where KB constant (5)

2.1.4 Noise Speed

Noise speed is continuous triangular wave or random variable with time, it is given as:

N

NOISE V i i ii = 1

V = 2 S cos t + (6)

Where i = (i 1/2) , i = a random variable on time interval o to 2

2N i

V i4

2 32 i

2K F S

F 1 +

(7)

Where: K N = Surface drag coefficient (0.004) F = Turbulence scale (2000), = Mean wind speed at reference height.

2.2 Wind Turbine Design

Shaft Design of Turbine is given as following equations:

Mechanical power extracted using wind turbine, it is given as:

3

m P WP = C , P (8)

Where Pm = Mechanical power developed.

PW = Kinetics Energy Contained in Wind

CP (, ) = Power Coefficient of turbine

3W WP = 0.5AV (9)

Where = Air Density

A = Turbine Swept Area (R2)

R = Radius of Turbine Blade

VW = Wind Speed

r Blade

W

R = V

(10)

Where = Tip Speed Ratio

r = Generator Speed

RBlade = Blade Radius

P - 2

C , 0.44 Sin - 0.00184 - 2 13- 0.3

- 0.0167 (11)

From Fig. 3 Represents power coefficient of variable speed wind turbine.

Fig. 3 CP (, ) Characteristics Curve

Cp (, ) represents the efficiency of wind turbine. Suppose CP = 0.48 it means that efficiency of wind turbine is 48% (48 percentage of total wind energy is extracted using wind turbine), shown from Fig. 3 represent changing the value of Power Coefficient (CP) with changing value of pitch angle(angle between plane of rotation and turbine blade), if pitch angle at minimum position (0 degree) at this condition Power Coefficient is at maximum value so it is possible to extracted more wind energy using wind turbine ,and if pitch angle is increasing from minimum position then less air contracts the surface of turbine blade so resultant value of power coefficient is decreasing(less wind energy is extracted using wind turbine),efficiency of wind turbine goes down .

2.3 Design of Induction Generator

Single fed induction generator is used for power generation purpose because it is very economical and low cost. The two common reference frames used in the analysis of machine are the stationary and synchronously rotating reference frames. Each has its own advantage for some purpose. In the stationary rotating reference, the dq variables of the machine are in the same frame as those normally used for the supply network. It is convenient choice of frame when supply network is large or complex design is proposed in [2, 3, 4].

The Relationship between abc and qd0 quantities of a reference frame rotating at an angular speed , as shown in Fig 4. The transformation equation from abc to this qd0 reference frame is given by:

q a

d qd0 b

0 c

f f

f T f

f f

(12)

Where the variable f can be phase voltage, current, or flux linkage of machine. From Fig.4 the transformation angle, (t), between the q-axis of reference frame rotating at a speed of and the a-axis of stationary stator winding may be expressed as:

t

0

t t dt + 0 elect. rad. (13)

Likewise, the rotor angle, r (t), between the axes of the stator and the rotor a-phase for a rotor winding with speed r (t) may be expressed as :

t

r r

0

t dt + 0 elect. rad. (14)

The angle, (0) and r (0), are the initial values of these angles at beginning of time t, the qd0 transformation matrix, [Tqd0 ()] is given as:

Fig. 4 Relationship between abc and qd0 Axis

4

qd0

2 2cos cos - cos +

3 3

2 2 2T sin sin - sin +

3 3 3

1 1 1

2 2 2

(15)

1

qd0

cos sin 1

2 2T cos - sin - 1

3 3

2 2cos + sin + 1

3 3

(16)

Stationary reference frame is used so speed of reference

frames () = 0 and = 0, Following steps is taken for designing of Induction Generator:

Step.1: Transformation of stator phase voltage to qd0

stationary voltage by = 0.

as bs cs2 1 1

v v - v - v 3 3 3

s

qs (17)

cs bs

0s as bs cs

1v v - v

3

1v = v + v + v

3

s

ds

(18)

Step.2: Transformation of rotor phase voltage to qd0

stationary voltage.

r s s

q qs r r

r s s

d ds r qs r

v v cos t + v sin t

v v cos t - v sin t

ds

(19)

Step.3: Transformation of flux linkage () and current of stator and rotor axis to qd0 axes.

ss s s s

bqs qs mq qsls

r v - dt

x

(20)

ss s s s

bds ds md dsls

r v - dt

x

(21)

b

0s 0s 0s s

ls

i = v - i r dt

x (22)

r rr r r s rbq q d mq q

b lr

r rr r r s rbd d q md d

b lr

r v - dt

x

r v - dt

x

(23)

b

0r 0r 0r r

lr

i = v - i r dt

x (24)

s s s sqs mqs s ds md

qs dsls ls

r s r sq mqr r d md

q dlr lr

- - i , i

x x

- - i , i

x x

(25)

WhereM m ls lr

1 1 1 1

x x x x (26)

s r s rqs qs s ds

M Mmq mdls lr ls lr

x + , x +

x x x x

d

(27)

Step.4: Electromagnetic torque (Tem) equation is expressed

as:

s s s sem ds qs qs dsb

3 PT = i - i . .

2 2 N m (28)

And Speed is given by:

rb

em mech damp

d

2H T + T - T in per unitdt

(29)

From equation (20, 21) represent transform stator flux

linkage to qd0 axis, equation (23) represent transform rotor

flux linkage to qd0 axis. Equation (22, 24) represents zero

sequence components in stator and rotor axis, equation (25)

represents transform stator and rotor current to qd0 axis,

equation (27) transform magnetic flux linkage to q and d axis.

2.4 Design of Pitch Angle Controller

The pitch angle control of the blade is used to limit the output power and to protect the turbines at higher value than the rated wind speed. The wind turbine generation systems usually run at a wind speed from 3.5 m/sec up to 25 m/sec and rated power is obtained at 12-16 [m/sec] wind speed [9].

There are two operating regions depending on wind speed. Below wind speed blade pitch angle is set to give maximum power. The shape of the curve in this region reflects the basic law of power production, in which power is proportional to cube of wind speed. The second region is operated when the wind is sufficiently high for the rated power. In this region blade pitch angle control regulates the output power to be rated power of generator as shown in Fig 8. Pitch angle of wind turbine blade is controlled in order to have the generator power limited to rated power.

The pitch angle is set to the minimum value when

mechanical power is less than rated power. if wind speed

increases at higher value than corresponding rated power,

pitch angle is increased to have power limited to rated power

as shown in Fig. 8. Step is followed for designing for pitch

angle controller as given in Fig. 5

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Fig. 5 Block Diagram of Pitch Angle Controller

From Fig. 5 represents Pitch angle controller, it consists of

speed and power controller, speed controller is controlling

wind variation and power controller is controlled generated

power.

3 Simulation Study

Simulation model is given in Fig. 6. It consists wind speed model, wind turbine model, Induction Generator model and designing of Pitch angle Controller.

Wind model for generating wind speed, Wind turbine for generating mechanical torque that drive Induction Generator, IG model for converting mechanical energy to electrical energy.

From Fig. 7 wind speed is combination of four

components base speed, ramp speed, gust speed, noise

speed), Noise speed is a continuous triangular wave, it

depends on spectral density coefficient SV (i), from here noise speed is designed using SV (i ) for (N = 1 to 50).

For i = 1, SV (1) = 0.000973. i = 2, SV (2) = 0.000156.

For i = 3, SV (3) = 0.0000665. i = 4, SV (4) = 0.0000380.

For i = 5, SV (5) = 0.0000249. i = 6, SV (6) = 0.0000178.

For i = 7, SV (7) = 0.0000135. i = 8, SV (8) = 0.0000106.

i = 9, SV (9) = 0.00000866. i = 10, SV (10) = 0.0000071.

i = 11, SV (11) = 0.00000609. i = 12, SV (12) = 0.00000523.

i = 13, SV (13) = 0.00000455. i = 14, SV (14) = 0.00000400.

i = 15, SV (15) = 0.00000355. i = 16, SV (16) = 0.00000318.

i = 17, SV (17) = 0.00000286. i = 18, SV (18) = 0.00000259.

i = 19, SV (19) = 0.00000236. i = 20, SV (20) = 0.00000217.

i = 21, SV (21) = 0.00000199. i = 22, SV (22) = 0.00000184.

i = 23, SV (23) = 0.00000170. i = 24, SV (24) = 0.00000159.

i = 25, SV (25) = 0.00000148. i = 26, SV (26) = 0.00000138.

i = 27, SV (27) = 0.00000130. i = 28, SV (28) = 0.00000122.

i = 29, SV (29) = 0.00000115. i = 30, SV (30) = 0.00000108.

i =31, SV (31) = 0.00000102. i = 32, SV (32) = 0.000000975.

i = 33, SV (33) = 0.00000092. i = 34, SV (34) = 0.00000088.

i = 35, SV (35) = 0.00000083. i = 36, SV (36) = 0.00000079.

i = 37, SV (37) = 0.00000076. i = 38, SV (38) = 0.00000072.

i = 39, SV (39) = 0.00000069. i = 40, SV (40) = 0.00000066.

i = 41, SV (41) = 0.00000064. i = 42, SV (42) = 0.00000061

i = 43, SV (43) = 0.00000059. i = 44, SV (44) = 0.00000056.

i = 45, SV (45) = 0.00000054. i = 46, SV (20) = 0.00000052.

i = 47, SV (47) = 0.00000050. i = 48, SV (48) = 0.00000049.

i = 49, SV (45) = 0.00000047. i = 50, SV (50) = 0.00000045.

Wind Turbine rating is 2MW.From fig.8 Wind speed is varying from 3.5m/sec (cut in speed) to 11.35 m/sec .This speed is below base speed (12.35m/sec).Using simulation tool control wind speed for capturing maximum power from wind turbine.

From Fig.9 Cp is 0.488 at = 11.75 it means efficiency of wind turbine is 48.8% (48.8 of wind energy is extracted from wind turbine) after increasing lambda () power goes down.

From Fig.10 950 KW Mechanical power is generated that is (48.8% of Wind turbine rating); Mechanical Torque is

below base torque.

From Fig.11 represent the three phase input voltage (220 V) is given to Induction Generator at 60 Hz. From design point of view convert 3- phase (abc) to 2- phase (dq0) using reference frame transformation theory and next transform dq generated voltage into three phase generated voltage.

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Fig. 6 VSWT implemented in MATLAB/SIMULINK

Fig. 7 Step Speed, Ramp speed, Gust Speed and Noise Speed (m/sec).

Fig. 8 Wind Speed (m/sec)

3.1 Performance Tests under Variable Speed Wind

Turbine

Table 1 CP (, ) Characteristics Curve

Tip speed () Cp(, ) for Pitch Angle ( = 0 Degree)

0.5 0.035

2.5 0.10

4.0 0.13

5.84 0.2413

6.96 0.3311

7.92 0.3925

8.6 0.4307

9.59 0.46

11.75 0.488 - CP-MAX

12.35 0.4855

13.56 0.4706

15.71 0.4211

17.61 0.2942

20 0.1011

21 -0.05

7

Fig. 9 Cp (, ) Curve

Fig. 11 Input Voltage (V), DQ axis Voltage (V), Output Voltage (V)

From Fig.12 represent three phase output current for load resistance (3) as we know that induction motor work as generator for negative slip. In negative slip Rotor speed lies above synchronous speed and electromagnetic torque should be negative .From Fig. 12 initially Tem is positive and r lies below base speed after that Tem is going negative and r is increasing above base speed.

Fig. 12 Output Current (Amp), Rotor Speed (pu), Electromagnetic Torque (Tem in pu).

3.2 Pitch Angle Controller

Fig. 13 Wind Speed lies below Rated speed

Fig. 14 Cp (, ) below base speed

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Fig. 15 Wind speed above base

Fig. 16 Cp (, ) above base speed

Pitch angle controller is used for controlling mechanical power, if wind speed lies below base speed at this condition pitch angle controller set pitch angle at minimum position (0 degree), it means that mechanical power is proportional to cube of wind speed so that maximum power can be tracked using wind turbine as shown in Fig. 14, if wind speed lies above base speed at this condition pitch angle controller varies pitch angle for controlling rated mechanical power as shown in Fig. 16. Simulation model of pitch angle controller as given in Fig. 6.

Fig. 17 represents power curve define characteristics of pitch angle controller, below base speed region is called power optimization it means pitch angle at minimum position (0 degree) for tracking maximum power using wind turbine, above base speed region is called power limitation it means pitch angle is varying for limiting mechanical power so that mechanical power lies at rated value.

Fig.17 Power Curve between mechanical power and wind speed

4 Conclusions

In this paper we are analyzing VSWT performance in MATLAB/SIMULINK. Models of the subsystems of which a variable speed wind turbine consists were developed and practical values for the various parameters were given. It was concluded that both theoretical considerations and experimental evidence justify the representation of the two most important variable-speed wind turbine concepts with the same model in power system dynamics simulations. The integration of the developed model into a power system dynamics simulation software package was discussed and simulation results that were obtained with the derived model were analyzed When the response of the model to a measured wind.

Appendix A Wind Turbine Parameters

Wind Turbine Parameters are shown in Table A1.

Table A1 Wind Turbine Parameters

Pm Mechanical power extracted from wind(W)

PW Kinetic energy contained in wind

Cp(,) Power coefficient of Turbine

Air density(kg/m3)=0.55kg/m3

A(R2) Turbine swept area(m2)

R Turbine Radius(m) = 36.5m

Tip speed ratio of the rotor blade tip speed to wind speed

Vw Wind Speed (m/sec)

Nominal Wind Speed=12.35 m/sec

r Generator Speed (rad/sec

Generator Base speed (2.018 rad/sec)

Rating of wind turbine

2 MW

Blade Pitch Angle = 0 degree

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Appendix B Induction Generator Parameters

Induction Generator Parameters are shown in Table B1

Table B1 Induction Generator Parameters

Stator Resistance (rs) 3.35

Stator Leakage and Rotor leakage inductance (Lls = Llr

,) 6.94mH

Magnetic Inductance (Lm) 163.73mH

Rotor Resistance (rr,) 1.99

Number of pole 4

Frequency 60HZ

Rotor Inertia (Jrotor) 0.1kg/m2

Inertia Constant (H) 5.04

Damping Constant (D) 0

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1 Introduction2 Matlab/Simulink Based Modelling