fuzzy algorithm for supervisory control of self-excited...

JKAU: Eng. Sci., Vol 17 No. 2, pp: 19 - 40 (2006A.D. /1427 A.H.)

Fuzzy Algorithm for Supervisory Control of

Self-Excited Induction Generator

Hussein F. Soliman, A. A. Attia*, S. M. Mokhymar**,

and M. A. L. Badr ***

Currently Elect. &Computer Dept., Faculty of Eng., King Abdulaziz

Univ., Jeddah, Saudi Arabia, and *National Research Institute of

Astronomy and Geophysics & **Electricity & Energy Ministry New &

Renewable Energy Authority, Wind Management*** & Elect. Power

and Machine, Faculty of Engineering , Ain Shams Univ.

Cairo, Egypt

Abstract. This paper presents an application of Fuzzy Logic Controller

(FLC) to regulate the reactive-power of the Self Excited Induction

Generator (SEIG) driven by Wind Energy Conversion Schemes

(WECS). The proposed FLC is used to tune the integral gain (KI) of

Proportional plus Integral (PI) controller. Two types of controls, for the

generator and the wind turbine, using FLC algorithm have been

introduced in this paper. The reactive-power control is performed to

adapt the terminal voltage via self excitation. The active-power control

is conducted to adjust the stator frequency through tuning the pitch

angle of WECS blades. Both controllers utilize the Fuzzy technique to

enhance the overall dynamic performance. The simulation result depicts

a better dynamic response for the system under study during the starting

period, and load variation. The percentage overshoot, rising time and

oscillation are improved by the fuzzy controller compared to that with

PI controller type.

1. Introduction

Many publications in the field of SEIG have been introduced to

overcome different problems [e.g., enhancing the performance, loading,

interfacing with the grid…etc]. Reference [1]

discuses a method of

control of 3 phase induction generator using the indirect field orientation

control, while reference [2]

introduces a FLC controller for wind energy

utilization scheme. According to our survey there are no researches

concentrating on a wind energy scheme system for supplying an isolated

load. The primary advantages of SEIG are less maintenance cost, better

transient performance, no need for dc power supply for field excitation,

19

Hussein F. Soliman, et al.

20

brushless construction (squirrel-cage rotor), etc. In addition, the

induction generators have been widely employed to operate as wind-

turbine generators and small hydroelectric generators of isolated power

systems [3,4]

.

The connection of the induction generators to large power systems,

to inject electric power, can be performed when the rotor speed of the

induction generator is greater than the synchronous speed of the air-gap-

revolving field. In this paper the dynamic performance is studied for

SEIG driven by WECS to feed an isolated load. The d-q axes equivalent

circuit model based on different reference frames extracted from

fundamental machine theory can be employed to analyze machine

transient's response in dynamic performance [3,4]

. The reactive-power

controller, for SEIG, is conducted to adapt the terminal voltage, via a

semiconductor switching system. The semiconductor switch regulates

the duty cycle which adjusts the value of capacitor bank connected to the

SEIG [5, 6]

. Also, the SEIG is equipped with an active-power controller to

regulate the mechanical input power. In addition, the stator frequency is

regulated. This is achieved by adjusting the pitch angle of wind turbine.

In this paper the integral gain (Ki) of the PI controller is supervised

using the FLC to enhance the overall dynamics response. The simulation

results of the proposed technique are compared with the results obtained

for the PI with fixed and variable Ki.

2. The System Under Study

Figure 1 shows the block diagram for the study system, which

consists of SEIG driven by WECS connected to isolated load. Two

control loops for terminal voltage and pitch angle using FLC to tune Ki

of the PI controller are shown in the same figure. The mathematical

model of SEIG driven by WECS is simulated using MATLAB /

SIMULINK package to solve the differential mathematical equations.

Meanwhile, two controllers have been developed for the system under

study. The first one is the reactive-power controller to adjust the

terminal voltage at the rated value. This is done by varying the switching

capacitor bank, for changing the duty cycle, to adjust the self excitation.

The second controller is the active-power controller to regulate the input

power to the generator and thus maintain the stator frequency constant.

This is achieved by changing the value of the pitch angle for the blade of

the wind turbine. First, the system under study is tested when equipped

with PI controller for both active and reactive-power controllers at

Fuzzy Algorithm for Supervisory Control of …

21

different fixed values KI. Then the technique is developed to drive the PI

controller by a variable KI to enhance the dynamic performance of the

SEIG. The KI is then tuned by using two different algorithms.

The simulation is carried out when the PI controller is driven by

variable KI using a linear function, with limitors, between KI and voltage

error for reactive control. Also, the simulation is include variable KI

based on the mechanical power error for active power controller.

Meanwhile, the variable KI has lower and upper limits. Then, the

simulation is conducted when the PI controller is driven by a variable KI

through a FLC technique. The simulation results depict the variation of

the different variables of the system under study, such as terminal

voltage, load current, frequency, duty cycles of switching capacitor

bank, variable KI in reactive controller KIV and variable KI in active

controller KIF.

3. Mathematical Model of the SEIG Driven by WECS

3.1. Electrical Equation of the SEIG

The stator and rotor voltage equations, equation number (1) to (6)

in Appendix-A, using Krause transformation [3,4]

, based on stationary

SEIG

Load

Semi

conducto

r

switchin

g

V-

FLC

For

Reactive

Control

+ Ref. Pm

Fig. 1. System under study.

__

Bus-Bar

Z-1

Change

in eV

eV

+

VRef.

FLC

For

Active

Control Z-1

Change

in Pm-error

Pm-

Pitch control

WECS Input

Mech-Power

Duty

cycle


22

reference frame. More details of the voltage equations are described in

Ref. [7].

3.2. Mechanical Equations of the WECS

The mechanical equations relating the power coefficient of the

wind turbine, tip speed ratio ( µ ) and pitch angle ( β ) are given in Ref.

[7-9]. The analysis of an SEIG in this research is performed taking the

following assumptions into account [3]

:

• All parameters of the machine can be considered constant except Xm.

• Per-unit values of both stator and rotor leakage reactance are equal.

• Core loss in the excitation branch is neglected.

• Space and time harmonic effects are ignored.

3.3. Equivalent Circuit

The d and q axes equivalent-circuit models for the three-phase

symmetrical induction generator are based on the equations given in

Appendixes A and B. In addition, Appendixes C and D describe the

other mathematical equations for the system under study. The

equivalent-circuit parameters used in the simulation results refer to a 1.1

kW, 127/ 220 V (line voltage), 8.3/4.8 A (line current), 60 Hz, 2 poles,

wound-rotor induction machine [4]

. More details about the machine are

descried in Ref. [7,8].

3.4. Reactive Power Control and Switching Capacitor Bank Technique

3.4.1. Switching

The switching of capacitors has been discarded in the past because of

the practical difficulties involved [5,6]

, i.e., the occurrence of voltage and

current transients. It has been argued, and justly so, that current ‘spikes’

for example, would inevitably exceed the maximum current rating as

well as the (di/dt) value of a particular semiconductor switch. The only

way out of this dilemma would be to design the semiconductor switch to

withstand the transient value at the switching instant.

The equivalent circuit in Fig. 2 is added to explain this situation of

switching capacitor bank due to the duty cycle. The details of this circuit

is given in Ref. [6]. For the circuit of Fig. 2, the switches are operated in


23

anti-phase, i.e., the switching function fs2 which controls switch S2 is the

inverse function of fs1 which controls switch S1. In other words, switch

S2 is closed during the time when switch S1 is open and vice versa. This

mean that S1 and S2 of branch 1 and 2 are operated in such a manner that

one switch is closed while the other is open.

V C1 C2

S1 S2

L1

fs1

fs2

Fig. 2. Semi conductor switches (S1,S2) circuit for capacitor bank.

3.4.2. Reactive Power Control

As shown in Fig. 1, the input to the controllers is the voltage error

while the output of the controllers is used to execute the duty cycle (λ).

The value of calculated λ is used as an input to semiconductor switches

to change the value of the capacitor bank according to the need for the

effective value of the excitation. Accordingly, the terminal voltage is

controlled by adjusting the self-excitation through automatic switching

of the capacitor bank.

3.5. Active Power Control

Active power control is applied to the system under study by

adjusting the pitch angle of the wind turbine blades. This is used to

maintain the SEIG operating at a constant stator frequency and reject the

effect of the speed disturbance. The pitch angle is a function of the

power coefficient “Cp” of the wind turbine WECS. The value of Cp is

calculated using the pitch angle value according to equations mentioned

in Ref. [7-9]. Consequently, the best adjustment for the value of pitch

angel leads to improve the mechanical power regulation, which, in turn,

achieves a better adaptation for frequency of the overall system.

Accordingly, the active power control regulates the mechanical power of

the wind turbine.


24

4. Controllers

Two different types of controller strategies have been conducted.

First, the application of the conventional PI controller with fixed and

variable gains is carried out. Second, the application of FLC is used to

adjust the value of KI for both active and reactive controllers.

4.1. Conventional PI Controller

The simulation program is carried out for different values of KI

while the value of the proportional gain is kept constant as shown in Fig.

3. It is noticed from the simulation results that the value of percentage

overshoot (P.O.S), rising time and settling time change as KI is changed.

Then the technique of having variable KI depending on the voltage error,

for reactive power control, is introduced to obtain the advantage of high

and low value of the integral gain of voltage loop KIV.

4.2. PI-Controller with Variable Gain

A program is developed to compute the value of the variable integral

gain KIV using the following rule based:

if ( eV < eV min), KIV =KIV min;

elseif (eV > eV max ), KIV =KIV max;

else (eV min < eV < eV max),

M=(KIV max - KIV min) / (eV max - eV min); C=KIV min – M × eV min;

KIV =M × eV +C;

end

Where, eV = the voltage error, eV min= the minimum value of the voltage

error, eV max= the maximum value of the voltage error, KIV min is the

minimum value of KIV, KIV max is the maximum value of KIV, C is a

constant and M is the slop value. Figure 4 shows these rules based, to

calculate the KIV of the KIV against the terminal voltage error eV. The

value of the eV min and eV max is obtained by trial and error to give the best

dynamic performance.


25

0 5 1 0 1 50

5 0

1 0 0

1 5 0

2 0 0

2 2 0

2 5 0

3 0 0

T im e (s e c )

Term

inal V

oltage (

Volt)

T e r m i n a l v o l ta g e fo r P I w i th v a r i o u s i n te g r a l g a i n s l o a d e d ( 8 0 o h m , 0 .1 2 h & 4 0 o h m , 0 .1 2 h )

1 2 3 4

2 0 0

2 2 0

2 5 0

va r i a b le KIV

KIV m in

= 0 . 0 0 5 1

KIV m a x

= 0 . 0 0 7

KIV

= 0 . 0 0 6 5

Fig. 3. Dynamic response of the terminal voltage with different values of integral gain for

reactive controller.

Fig. 4. Variable integral gain for pI controller.

Also, the proportional gains (KPV and KPF) are kept constant for the

reactive and active controllers respectively. Various characteristics are

tested to study the effect of changing the value of (KIV) to update the

reactive control. The simulation results cover the starting period and the

period when the system is subjected to a sudden increase in the load, at

instant 8 sec. Figure 3 shows the simulation results for the variable KIV.

Figures 5&6 show the effect of variable reactive integral gain KIV and

active KIF controllers versus time respectively.

Upper

Limit

Lower

Li i

eVmin eVmax

KIV-

KIV -

Voltage error (eV)


26

0 5 1 0 1 55 .2

5 .2 5

5 .3

5 .3 5

5 .4

5 .4 5

5 .5x 1 0

-3

T im e (s e c )

Inte

gra

l g

ain

fo

r re

active

co

ntr

ole

Va r ia b le In te g ra l g a in fo r P I tu n in g w i th F L C lo a d e d (8 0 o h m , 0 .1 2 h & 4 0 o h m , 0 .1 2 h )

1 2 3

5 .2 5

5 .3

5 .3 5

5 .4

5 .4 5

x 1 0-3

Fig. 5. Variable integral gain in PI-reactive controller with FLC.

0 5 1 0 1 5

4 . 5

4 . 6

4 . 7

4 . 8

4 . 9

5x 1 0

- 6

T i m e ( s e c )

Inte

gra

l g

ain

fo

r a

ctive

co

ntr

ole

V a r i a b l e I n t e g r a l g a i n f o r P I t u n i n g w i t h F L C l o a d e d ( 8 0 o h m , 0 . 1 2 h & 4 0 o h m , 0 . 1 2 h )

1 2 3 4 5

4 . 7

4 . 8

4 . 9

x 1 0- 6

Fig. 6. Variable integral gain in PI-active controller with FLC.

5. A Fuzzy Logic Controller (FLC)

To design the fuzzy logic controller “FLC”, the control engineer

must gather information on how the artificial decision maker should act

in the closed-loop system, and this would be done from the knowledge

base [10]

. Fuzzy system is constructed from input fuzzy sets, fuzzy rules

and output fuzzy sets, based on the prior knowledge base of the system.

Figure 7 shows the basic construction of the FLC. There are rules to

govern and execute the relations between inputs and outputs for the

system. Every input and output parameter has a membership function


27

which could be introduced between the limits of these parameters

through a universe of discourse. The better adaptation of fuzzy set

parameters the better tuning of the fuzzy output is conducted. The

proposed FLC is used to compute and adapt the variable integral gain KI

of PI controller.

defuzzifierRulesFuzzifier

Knowledge baseExpert Look up-table

SEIG / WECS

input

num

eric

al v

aria

ble

s

fuzzy values fuzzy values

outp

utnum

erical variables

Fig. 7. The three stages of fuzzy logic controller .

5.1. Global Input and Output Variables

For reactive control the fuzzy input vector consists of two

variable; first the terminal voltage deviation eV and second is the change

of the terminal voltage deviation ∆eV . Five linguistic variables are used

for each of the input variables as shown in Fig. 8(a & b) respectively.

While, the output variable fuzzy set is shown in Fig. 8(c & d) shows the

fuzzy surface. Also, for active control the fuzzy input vector consists of

two variable; first the mechanical power deviation eF and second is the

change of the mechanical power deviation ∆eF . Five linguistic variables

are used for each of the input variables as shown in Fig. 9 (a) and Fig. 9

(b) respectively. While, the output variable fuzzy set is shown in Fig. 9

(c) and Fig. 9 (d) shows the fuzzy surface. In Fig. (8 & 9) a linguistic

variables has been used, for input variables, P for Positive, N for

Negative , AV for Average, B for Big and S for Small. For example PB

is Positive Big and NS is Negative Small ….etc. After constructing the

fuzzy sets for input and output variables it is required to develop the set

of rules, so-called Look-up Table, which define the relation between the

input variables, eV, eF, ∆eV and ∆eF and the output variable of the fuzzy


28

logic controller. The output from fuzzy controller is the integral gain

value of KI used in the PI controller. The look-up Table is given in Table 1.

Table 1. Look up table.

Voltage Deviation Change (∆eV)

PB PS AV NS NB

Voltage Deviation

(eV)

AV NS NB NB NB NB

PS AV NS NB NB NS

PB PS AV NS NB AV

PB PB PS AV NS PS

PB PB PB PS AV PB

- 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 5 0 1 0 0 1 5 0 2 0 0

0

0 . 2

0 . 4

0 . 6

0 . 8

1

eV

me

mb

ers

hip

de

gre

e

N B N S A V P S P B

Fig. 8 (a). Membership function of voltage error.

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0

0

0 .2

0 .4

0 .6

0 .8

1

d e lt a eV

me

mb

ers

hip

de

gre

e

N B N S A V P S P B

Fig. 8 (b). Membership function of change in voltage error.


29

5 5 . 1 5 . 2 5 . 3 5 . 4 5 . 5

x 1 0- 3

0

0 . 2

0 . 4

0 . 6

0 . 8

1

KIV

me

mb

ers

hip

de

gre

e

N B N S A V P S P B

Fig. 8 (c). Membership function of variable KIV.

- 2 0 0

- 1 0 0

0

1 0 0

2 0 0

- 2 0

- 1 0

0

1 0

2 0

5 .1

5 .2

5 .3

5 .4

x 1 0- 3

eV

d e lta eV

KIV

Fig. 8 (d) . Fuzzy surface.

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

eF

me

mb

ers

hip

de

gre

e

NB NS AV PS PB

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

delta eF

me

mb

ers

hip

de

gre

e

NB NS AV PS PB

Fig. 9 (a). Membership function of mech. Fig. 9 (b). Membership function of

change power error. on mech. power error.


30

4 4 . 1 4 . 2 4 . 3 4 . 4 4 . 5 4 . 6 4 . 7 4 . 8 4 . 9 5

x 1 0- 6

0

0 . 2

0 . 4

0 . 6

0 . 8

1

KIF

me

mb

ers

hip

de

gre

e

N B N S A V P S P B

Fig. 9 (c). Membership function of variable KIF.

- 1

- 0 . 5

0

0 . 5

1

- 0 . 1

- 0 . 0 5

0

0 . 0 5

0 . 1

4 . 2

4 . 4

4 . 6

4 . 8

x 1 0- 6

eF

d e l t a eF

KIF

Fig. 9 (d). Fuzzy surface.

5.2. The Defuzzification Method

The Minimum of Maximum method has been used to find the

output fuzzy rules representing a polyhedron map as shown in Fig. 10.

First, the minimum membership grade, which is calculated from the

min. value for the intersection of the two input variables ( x1 and x2) with

the related Fuzzy set in that rule. This min. membership grade is

calculated to rescale the output rule, then the maximum is taken, as

shown in Fig. 10. Finally, the centroid or center of area has been used to

compute the fuzzy output, which represents defuzzification stage, as

follows:

∫∫

=

dyy

dyyy

K I )(

)(

µ

µ


31

More details about the variable of the above equation are given in Ref. [10].

Rule1: if Verror (X1) is NS and Change in Verror (X2) is AV then output (integral gain (Y)) is NSRule2: if Verror (X1) is AV and Change in Verror (X2) is PS then output (integral gain (Y)) is PS

X1 X2 Y

X1

X2

Y

µ-NS (X1) µ-AV (X2) µ-NS (Y)

µ-AV(X1) µ-PS (Y)µ-PS (X2)

min

min

µ- (Y)

Y

Fig. 10. Schematic diagram of the defuzzification method using the center of area.

6. Simulation Results

6.1. Dynamic Performance due to Suddenly Load Variation

The FLC utilizes the terminal voltage error (eV) and its rate of

change (∆eV) as an input variables, to represent the reactive power

control. The output of FLC is used to tune up the KI of PI controller.

Also, another FLC is used to regulate the mechanical power via the

blade angle adaptation of the wind turbine. Figs. (8.a,b,c and d) depict

the fuzzy sets of eV, ∆eV , KIV and fuzzy surface, respectively. The

terminal voltage error (eV) varies between (-220 and 220) and its change

(∆eV) varies between (- 22 and 22), and the output of the FLC is the KIV

which changes between (5e-003 and 5.5e-003). Table 1 shows the

lookup table of fuzzy set rules for reactive control. The same technique

is applied for active power controller where the two inputs for FLC are

the mechanical power error (eF ) which varies between (-1 and 1) and its

change (∆eF)varies between (-0.1 and 0.1). The output of the FLC is the

KIF which changes between (4e-006 and 5e-006). The output of the PI-

FLC in the active controller adapts the pitch angel value to enhance the

stator frequency. Figure 9 (a,b, c & d) shows the fuzzy sets of eF, ∆eF,

the related output fuzzy set and fuzzy surface, respectively.

Based on the mathematical model of the system under study,

equipped with two controllers (PI & FLC) for terminal voltage and blade


32

angle, the simulation is carried out using the MATLAB- Simulink

Package. Running for PI controller with various integral gain finding a

relation between the voltage or frequency error and the value of this

gains. Figures 11-13 show the simulation results for the terminal voltage

for different loads, at time = 8 sec the system is subjected to sudden

change in load. But Fig. 14 shows the stator frequency. The system is

equipped with conventional controller having fixed and variable integral

gain and FLC algorithm. The proposed FLC is used to adapt the KI to

give a better dynamic performance for the overall system, as shown in

Fig. 11-13, regarding P.O.S and settling time compared with fixed PI

and PI with variable KI for different loads.

Also, Fig. 15 & 16 depict the simulation results for the load current

and controller’s duty cycle. The same conclusion is achieved as

explained for Fig. 11.

6.2. Dynamic Performance due to Suddenly Wind Speed Variation

Another simulation result is conducted when the overall system is

subjected to a sudden disturbance in the wind speed from 7 m/s to 15

m/s. in Fig. 17 & 18 show the simulation results of the wind speed

variation and the stator frequency respectively. The simulation given in

Fig. 18 shows the ability of the proposed controller to overcome the

speed variation for variable and fixed integral gain.

0 5 1 0 1 50

0 .5

1

1 .5

2

2 .5

3

3 .5

4

T im e ( s e c )

Lo

ad

Cu

rre

nt

(Am

p)

L o a d C u r r e n t fo r P I tu n i n g w i th a n d w i th o u t F L C l o a d e d ( 8 0 o h m , 0 .1 2 h & 4 0 o h m , 0 .1 2 h )

v a r ia b le KIV

w ith s lo p

KIV m a x

= 0 .0 0 7

KIV m in

= 0 .0 0 5 1

va r i a b l e KI V

w i th F L C

Fig. 11. Dynamic response of load current for PI with and without FLC.


33

0 5 1 0 1 50

5 0

1 0 0

1 5 0

2 0 0

2 2 0

2 5 0

3 0 0

T ime (se c)

Te

rmin

al V

olta

ge

(V

olt)

Te rm in a l vo lta g e fo r P I tu n in g w ith a n d w ith o u t FL C lo a d e d (8 0 o h m , 0 .1 2 h & 4 0 o h m , 0 .1 2 h )

KIV max

=0 .0 0 7

KIV min

=0 .0 0 5 1

KIV

va r ia b le with s lo p

KIV

va r ia b le with F L C

Fig. 11. Dynamic response of terminal voltage for PI with and without FLC.


Sudden application

for Load



34

0 5 1 0 1 50

1 0

2 0

3 0

4 0

5 0

6 0

7 0

T i m e ( s e c )

Sta

tor

Fre

qu

en

cy (

Hz)

S t a t o r F r e q u e n c y f o r P I t u n i n g w i t h a n d w i t h o u t F L C l o a d e d ( 8 0 o h m , 0 . 1 2 h & 4 0 o h m , 0 . 1 2 h )

KIV m a x

= 0 . 0 0 7

KIV m in

= 0 . 0 0 5 1 v a r i a b l e K

IV w i t h s l o p

v a r i a b l e KI V

w i t h F L C

Fig. 14. Dynamic response of stator frequency for PI with and without FLC.

Fig. 15. Dynamic response of load current for PI with and without FLC.

0 5 1 0 1 50 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

T im e ( s e c )

Du

ty C

ycle

D u ty C y c l e fo r P I t u n i n g w i th a n d w i th o u t F L C l o a d e d ( 8 0 o h m , 0 .1 2 h & 4 0 o h m , 0 .1 2 h )

v a r i a b l e KI V

w i th F L C

v a r ia b le KIV

w i t h s lo p

KIV m a x

= 0 . 0 0 7

KIV m in

= 0 . 0 0 5 1

Fig. 16. Dynamic response of duty cycle for PI with and without FLC.

0 5 10 150

0.5

1

1.5

2

2.5

3

3.5

4

Time(sec)

Load C

urr

ent (A

mp)

Load Current for PI tuning with and without FLC loaded (80 ohm, 0.12 h & 40 ohm, 0.12 h)

variable KIV

with slop

KIV ma x

=0.007

KIV min

=0.0051

variable KIV

with FLC


35

0 2 4 6 8 1 0 1 2 1 4 1 6 1 80

2

4

6

8

1 0

1 2

1 4

1 6

T im e ( s e c )

Va

iab

le W

ind

Sp

ee

d m

/s

V a r i a b l e W i n d S p e e d fo r S E IG D r i v e n b y W E C l o a d e d ( 8 0 o h m , 0 . 1 2 h ) & C o n t r o l l e d b y P I - F L C

1 2 1 4 1 6

1 5 . 1

1 5 . 2

1 5 . 3

1 5 . 4

1 5 . 5

2 4 6 8

7 . 1 5

7 . 2

7 . 2 5

7 . 3

Fig. 17. Sudden variation for the wind speed versus time .

0 2 4 6 8 1 0 1 2 1 4 1 6 1 80

1 0

2 0

3 0

4 0

5 0

6 0

7 0

T im e ( s e c )

Sta

tor

fre

qu

ency (

Hz)

S t a t o r f r e q . o f S E IG lo a d e d ( 8 0 o h m , 0 . 1 2 h ) & c o n t d . b y P I- F L C

v a ia b le KIV

w it h F L C

KIV m i n

= 0 . 0 0 5 3

KIV m a x

= 0 . 0 0 7

1 0 1 0 . 5 1 1

4 5

5 0

5 5

6 0

6 5

2 3 4

5 8

6 0

6 2

6 4

6 6

6 8

Fig. 18. Stator frequency according to the wind speed variation

for SEIG controlled by FLC & PI.

7. Conclusion

This paper presents an application of FLC to self excited induction

generator driven by wind energy. The proposed FLC is applied to active

and reactive power controls of the system under study to enhance its

dynamic performance. The FLC is used to regulate the duty cycle of the

switched capacitor bank to adjust the terminal voltage of the induction

generator. Another FLC is applied to regulate the blade angle of the

wind energy turbine to control the stator frequency of the overall system.

The simulation results show an enhancement of the dynamic

performance of the overall system using the FLC controller compared

with variable PI type. Another simulation is conducted to study the

dynamic performance to this system with a suddenly disturbance for the


36

wind speed variation. Where, a comparison is conducted for the stator

frequency in the dynamic performance with variable and fixed KI.

References

[1] El_Sousy, F., Orabi, M. and Godah, H. “Indirect field orientation control of self-excited

induction generator for wind energy conversion system” ICIT, December (2004).

[2] Mashaly, A.M. S., Mansour, M. and Abd-Satar, A.A., “ A fuzzy logic controller for wind

energy utilization scheme”, Proceedings of the 3rd IEEE Conference of Control Application,

Glasgow, Scotland, UK, August 24-26 (1994).

[3] Li, Wang, and Jian-Yi-SU, “Dynamic Performance of An Isolated Self Excited Induction

Generator Under Various Loading Conditions”, IEEE Transactions on Energy Conversion, 15

(1) March: 93-100 (1999).

[4] Li, Wang and Lee, Ching- Huei, “Long- Shunt and Short- Shunt Connections on Dynamic

Performance of a SEIG Feeding an Induction Motor Load”, IEEE Transactions on Energy

Conversion, 14 (1): 1-7 (2000).

[5] Atallah, A. M. and Ahmed, A.,"Terminal Voltage Control of Slef Excited Induction

Generators" Sixth Middle-East Power Systems Conference (MEPCON'98), Mansoura,

Egypt, Dec. 15-17, pp: 110-118 (1998).

[6] Marduchus, C., “Switched Capacitor Circuits for reactive power generation “ , Ph.D. Thesis,

Brunuel University (1983).

[7] Hussein, F. S., Attia, A., Sabry, M., Badr M. M..A.L. and Ahmed, .A. E.M.S., « Dynamic

Performance Enhancement of Self Excited Induction Generator Driven By Wind Energy

Using ANN Controllers ”، Sci. Bull. Fac. Eng. Ain Shams Univ., ISSN 1110-1385, Part II,

39(2) June 30: 631 -651 (2004).

[8] Sabry, M.M., « Enhancement of The Performance of Wind Driven Induction Generators

Using Artificial Intelligence Control”, Ph.D. Thesis, Fac. Eng. Ain Shams Univ., March.

10, (2005).

[9] Abdin, E. S. and Xu, Wilson, “Control Design and Dynamic Performance Analysis of a Wind

Turbine- Induction Generator Unit”, IEEE Transaction on Energy Conversion, 15 (1) March:

91-96 (2000).

[10] Passino, K.M. and Yurkovich, S., " Fuzzy Control ", Library of Congress Cataloging-in-

Publication Data. Includes bibliographical references and index. ISBN 0-201-18074-X.

Addison Wesley Longman, Inc. (1998).


37

Appendix (A)

SEIG differential equations at no load:

vds “Stator Voltage 's (volt) Differential Equation at Direct Axis”

( )( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+−+−−

−=

b

dspiqsiqrxmiqsXls

bidssds

ω

ϕ

ω

ω..

Rv

Where: ids is the stator current (amp) at direct axis, iqs is the stator current at quadrant

axis and iqr : is the rotor current at quadrant axis.

Xl is the leakage reactance, s and r denoted for stator and rotor respectively. ωb is

the speed base. p is the differentiation parameter = d/dt.

(A-1)

vqs “Stator Voltage 's Differential Equation at Quadrate Axis”

( )( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

−−

b

qs

dsdrmdslsb

qsqs piixiXis ω

ϕ

ω

ω..

Rv

Where: idr : is the rotor current (amp) at direct axis.

(A-2)

vdr “Rotor Voltage 's Differential Equation at Direct Axis”

( )( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛+−+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−=

b

dr

qsqrmqrlrb

r

drrdr piixiXiω

ϕ

ω

ωω..

Rv

Where: iqs : is the stator current at quadrant axis.

(A-3)

vqr “Rotor Voltage 's Differential Equation at Quadrate Axis”

( )( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛+−+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −+=

b

qr

dsdrmdrlrb

r

qrrqr piixiXiω

ϕ

ω

ωω..

Rv

(A-4)

( )dsqssqsb

qs

iRdt

dϕ

ϕ

ω −+= .v.

Where: ω b is the base speed.

(A-5)

( )qsdssdsb

ds

iRdt

dϕ

ϕ

ω −+= .v.

(A-6)

Appendix (B)

Magnetizing reactance & load case differential equations:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛= RLci l

Lds

lds

ds

dsdtdt

did.. v

v (B-1)

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= RLci l

Lqs

lqs

qs

qsdt

di

dt

dV.... v

(B-2)

( ) ( )( ) 5.022

iiiii dsdrqsqrm−+−=

(B-3)

( ) ( )[ ]iiT dsqsqsdse.. ϕϕ −=

(B-4)


38

[ ] 864.00.0.................................105.77 <≤= ix mm

at (B-5)

( ) ( ) 051.1864.0..................35.2340.2 <≤+= iix mmm

at (B-6)

( ) ( ) 476.1051.1..................22.1227.4 <≤+= iix mmm

at (B-7)

( ) ( ) 717.1476.1..................3.9202.3 <≤+= iix mmm

at (B-8)

( ) ( ) iix mmm

at ≤+= 717.1..................3.6179.8 (B-9)

Appendix (C)

Excitation equations Differential equations:

( )vv ****cqscdcd

Cpci ω−=

Where: ω s is the synchronous speed (rad/sec) & i cd: is the capacitor current in

direct axis and i cq: is the capacitor current in quadrant axis & C: is the value of the

capacitor bank.

(C-1)

⎟⎠⎞⎜

⎝⎛ += vv ****

cdscqcq cpci ω

(C-2)

( )ii Ldsds

ds

dt

dC −=⎟

⎠

⎞⎜⎝

⎛ v*

Where: ILds is the load current in direct axis and ILqs: is the load current in quadrant

axis & RL: is the load resistance (ohm) & LL: is the load inductance (Henry).

(C-3)

( )ii Lqsqs

qs

dt

dC −=⎟⎟

⎠

⎞⎜⎜⎝

⎛ v

*

(C-4)

( ) ( )iRpiL LdsLdsLdsL−= v*

(C-5)

( ) ⎟⎠⎞

⎜⎝⎛=

− iRpiL LqsLqsLqsL v*

(C-6)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛−−=⎟

⎠

⎞⎜⎝

⎛RLi L

Lds

Ldsds

ds

dtdt

dVC

diV **

(C-7)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛RLi L

Lqs

Lqsqs

qs

dtdt

dVC

di

V **

(C-8)

( ) ( )( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−=

22

max

1 λσλ

cceff

where Ceff : is the effective capacitor bank value

(micro-farad), Cmax: is the maximum capacitor value & Cmin: is the minimum

capacitor value & σ = (C max / C min) & λ: is the duty cycle value .

(C-9)


39

Appendix (D)

Mechanical Differential equations

( )( )ωω

ω

.2 . BTTH remb

r

dt

d−−=

where: ω r is the rotor speed (rad/sec).

(D-1)

⎟⎠⎞⎜

⎝⎛⎟

⎠

⎞⎜⎝

⎛= VDCP

3

w

2

pm8

1πρ

(D-2)

ωm = (2 πn) / 60 (D-3)

( )ω mmm PT = (D-4)

( )( )

( ) ⎥⎦

⎤⎢⎣

⎡−−⎟⎟

⎠

⎞⎜⎜⎝

⎛

−

−⎟⎠⎞⎜

⎝⎛ −= βµ

β

µπβ 300184.0

*3.015

3.0167.044.0 SinC p

(D-5)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

60V

nD

Ww

mV

R πωµ

(D-6)

( )ωωω

raem

br.

H2dt

d

BTT −−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

Where: ω m: is the mechanical speed (rad/sec)& P m: is the mechanical power (KW)

& Tm : is the mechanical torque (nm) & n : is the rotor revolution per minute (rpm)

& C p : is the power coefficient of the wind turbine & β : is the blade pitch angle

(degree) & µ: is the tip speed ratio & V w : is the wind speed (m/s) & R: is the of the

rotor radius (m) of the wind turbine & D: is the of the rotor Diameter (m) of the

wind turbine & Ba: is the friction factor & T e: is the electrical torque (nm)& π =

3.14 & ρ = Air density (kg/m3).

(D-7)


40

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