Control Systems Lab Project

(WIND TURBINE CONTROL)

Section:

G (H)

Project Team:

KHURUM HASHMI……………………………L2F08BSEE0660

NAJAM UD DIN…………………….…………L2F08BSEE0688

Session 2008-2012

FACULTY OF ENGINEERING UNIVERSITY OF CENTRAL PUNJAB LAHORE,

PAKISTAN

WIND TURBINE CONTROL ABSTRACT

The following system describes a wind turbine running an induction generator through a gear

train with the transformation ratio N. The following calculations are made in order to Control the

Closed Loop output bringing it to Near idea. The intrinsic constraints involved with varying the

parameters such as increased overshoot for quicker rise time have been dealt with accordiongly.

MAIN TRANSFER FUNCTION

Where N is the Gear Train Ratio

Substituting typical numerical values in above equation yields result

Putting N=1; we have

Gdt(s)=

1.023*1016

*s

------------------------------------------------------------------------------------------------

1.864*1011

*s5 + 9.32*10

12 *s

4 + 1.611*10

16 *s

3 + 7.211*10

17 *s

2 + 2.609*10

15 *s

Simplifying

Gdt(s)=

10228490495999998*s

--------------------------------------------------------------------------------------------------------------------

7840*s*(23776543*s4+1188827150*s

3+2054688049000*s

2+1972388250000*s+332820000000)

STATE SPACE

A=

B=

C= D= [0]

Time Response

The system attains its peak value in a very large time Span. Even though system is stable Peak

amplitude appears only at the termination of the response time

So Rise time, Peak time, Settling time all parameters are crowded at the end of the response

Rise Time 123 seconds

Settling time 220 seconds

%age Overshoot 0

Peak time > 1*10^3 seconds

Peak mag (closed loop) 0.796

Steady State error 21 %

Stability Stable

ROOT LOCUS

System Has two poles on real

axis and two on the imaginary

axis

One zero at origin

Intuitively from the position of

the poles the system appears to

be marginally stable

Effect of Varying N positively increasing

Figure shows Step

response for

Transfer functions

with Values of N

from1 to 10

The greater the

value of N. Closer

the response to

Ideal and System

Attains stability

much Quicker

We choose N at 10

substituting N=10

Gdt(s)=

1.023*1018

*s

-----------------------------------------------------------------------------------------------

6.17*1011

*s5 + 3.085*10

13 *s

4 + 2.004*10

16 *s

3 + 7.225*10

17* s

2 + 2.609*10

17* s

Simplified

Gdt(s)=

10228490495999998*N2*s

--------------------------------------------------------------------------------------------------------------------

2395512000000*s2*(688*s+(

*(

)+301000*N

2*(190120*s

2+12600000)*(688*s+(1

9*s2*(

))

STATE SPACE

A=

B=

C= D= [0]

TIME RESPONSE

System response has modified to

be nearer to the ideal. Still, Peak

amplitude occurs at the very End

and so with the rest of the

parameters

Rise Time 1.17 seconds

Settling time 2.12 seconds

%age Overshoot 0

Peak time >14 seconds

Peak mag

(closed loop)

0.796

Steady State

error

21 %

Stability Stable

ROOT LOCUS

As in case of N=1

System Has two poles on real axis and

two on the imaginary axis

One zero at origin

Intuitively from the position of the poles

the system appears to be marginally

stable

Frequency Response

For N=1

Showing Frequency Response and Phase angle

For varying

values of N from

1 to 10

With increase in

N

Corner frequency

occurs further on

at greater

frequencies

SIMULINK

Gear Ratio N=1 Original system

Controlling through PID chosen system of Gear Ratio N=10

State Space model

PID Controller GUI

Auto Tuning GUI

CONTROLLING OUTPUT

We have worked with the system with Gearing Ratio (N) =10 so less tuning has to be effected to

bring the system nearer to the ideal response

Original transfer function with N=10

Gdt(s)=

1.023*1018

*s

-----------------------------------------------------------------------------------------------

6.171*1011

s5 + 3.085*10

13 s

4 + 2.004*10

16*s

3 + 7.225*10

17*s

2 + 2.609*10

17*s

The Proportional Integral Derivative (P I D) method is used

Controller(s) =

1

Kp + Ki * --- + Kd *s

s

Auto tuning followed by limited trial and error leads to the following

Kp = 3.39008930751897

Ki = 1.4346893216856

Kd = -0.47

Multiplying this with the given transfer function yields

Gdt(s)=

-4.807*1017

*s3 + 3.468*10

18* s

2 + 1.467*10

18*s

---------------------------------------------------------------------------------------------------

6.17*1011

* s6 + 3.085*10

13*s

5 + 2.004*10

16*s

4 + 7.225*10

17*s

3 + 2.609*10

17*s

2

Solving in Feedback

Tf(s)=

-4.807*1017

*s3 + 3.468*10

18*s

2 + 1.467*10

18*s

------------------------------------------------------------------------------

6.17*1011

*s6 + 3.085*10

13*s

5 + 2.004*10

16*s

4 + 2.418*10

17*s

3 + 3.728*10

18*s

2+ 1.467*10

18*s

Which is the required transfer function

STATE SPACE

A=

B=

C= D= [0]

TIME RESPONSE

Seen in LTI view. Peak response occurs at17.7 seconds. Steady state error is zero the overshoot

is so ignorable that does not appear here and system is very close to ideal

Rise Time 0.379 seconds

Settling time 0.649 seconds

%age Overshoot 0.757

Peak time 1.34 seconds

Peak mag (closed loop) 1.01

Steady state error 1%

Stability Stable

ROOT LOCUS

Zoomed in

BODE PLOT

COMPARING PARAMETERS:

N=1 N=10 Tuned Output

Rise Time 123 seconds 1.17 seconds 0.379 seconds

Settling time 220 seconds 2.12 seconds 0.649 seconds

%age Overshoot 0 0 0.757

Peak time > 1*10^3

seconds

>14 seconds 1.34 seconds

Peak mag (closed

loop)

0.796 0.796 1.01

Steady State

error

21 % 21 % 1%

Stability Stable Stable Stable

Increasing the gear ratio Response nears ideal. In addition Propotional Derivative Integrator

Controller is used to control peak time and bring it nearer to the beginning of the response

References: Control Systems Engineering by Norman.S.Nise 6

th edition

www. Mathworks.com