Analysis of Interval Type-2 Fuzzy PI Controller For Load Frequency Control on Multi Area Power System Using Genetic Algorithm

Analysis of Interval Type-2 Fuzzy PI Controller For Load Frequency Control on Multi Area Power System Using Genetic Algorithm

MUH BUDI R WIDODO

2206100121

Introduction

Beban Pembangkit

Bus i Bus j

Gambar 1, Single Line Sistem Tenaga Listrik

1. Plant yang digunakan STL 2 Area

2. Beban statis 3. Kontroler yang

digunakan I, PI, IT2FPI, IT2FPI

1. MEMBUAT PENGENDALI

FREKUENSI (KONTROLER) : IT2FPI-GA

TUJUAN

FREQUENCY

BATAS MASALAH

Telaah Pustaka

1. Pengendalian LFC menggunakan IT2FPI controller [4]

2. Pengendalian LFC menggunakan Artificial Immune System Via Clonal Selection.[5]

3. Pengendalian LFC menggunakan Genetic Algorithm based PI Controller [6]

4. Pengendalian LFC menggunakan Hybride evolutionary

fuzzy PI Controller [21]

METODOLOGI

START

Studi Literatur

Simulasi dan Analisis menggunakan MATLAB

Pengumpulan data dan referency tentang LFC,

PI controler, dan GA

Performance

optimal ? STOP

Tidak ya

MENURUT HUKUM NEWTON

Sedangkan,

1.

Ditinjau dari Beban

(T _G -T _B )=H.dω/dt

f= ω/ 2.π

Frequency Regulation

T

_G

- T

_B

=ΔT<0, maka dω/dt<0 , frekuensi turun

T

_G

- T

_B

=ΔT>0, maka dω/dt>0 , frekuensi naik

Skema Load Frequency Control (LFC)1

Turbine Steam

Governor

(LFC) Load Frequency

Control Frequency

sensor Pv

Pc

Ptie

PG

Voltage sensor

QG

AVR Excitation

system

Gen field.

G

Block Lengkap Pengaturan Frekuensi Pada Pembangkit

sT

G

1 1 R 1

CH

1 1 sT

( )

1 2Hs D

Governor Turbin Inersia rotor dan

beban

pu ^r

P

m ₊

-

P

L

P

v

+ -

P

reff

Respon Frekuensi terhadap Perubahan beban

fo f’

f’’

Kerja governor mulai terasa

Sebelum ada penambahan beban

TG-TB>0, f akan terus naik

t0 t1 t2 t3 t4 t5

t(waktu) Frekuensi (f) dan KopenT)

Garis frekuensi

Sistem Listrik Dua Area

Area 1 Area 2

P

12

X

tie

1. Dihubungakan oleh X

_tie

, 2. Tahanan stator diabaikan 3. Beban statis

4. Kondisi sistem seimbang

SPESIFIKASI

Sistem Tenaga Listrik 2 Area

2 2

1 D

1 sM

1

1 D

sM T/s

1 1

1

sTCH 1 2

1 sTCH

1 1

1

sTg 1 ₂

1 sTg

2

1 RG 1

1 RG

+

+

+ +

+ +

- -

- -

-

-

Pc1 Pc₂

Y1 Y₂

Pm2

Pm1 1

PL P_L2

Ptie

1 2

f1 f₂

Fuzzy PI Controller Digital

Bi

1/T Kontrol Area (i)

+ ACE

+/-

Ki1

f

tie i

P _, Pdi

KPi

+ +

fuzzy

1/z

KuPi

+ 1/z

-

+ +

Interval type-2 fuzzy PI Controller

STL 2 Area dengan Controller

cH1i

1 1 T s

1i

1

1 Tg s _{1i 1i}

1 sM D

1i

1 R B1i

2i

1 1 Tg s

2i

1 R

B2i

T s

ACE1

ACE2 +

+ -

- -

+ - -

-

- +

PD1i

PD 2i 2

PV P_m2

1

PV

1

Pm f_1i

f2i

Ptie

Governor 1 Turbin 1 Load 1

Governor 1 Turbin 2 Load 2

Bias

Speed Drop

Bias Speed Drop

U1 Kontroller

Kontroller

U2

+ +

cH 2i

1 1 T s

2i 2i

1

sM D

Interval Type-2 Fuzzy PI coantroller

+

Cara Kerja Fuzzy Type-2

fuzzifier

Rules

inference

Output processing Fuzzy Logic system

Crips output (type-0) Type-reducerd

Set(type-1) Crips input

Fuzzy output set (type-2)

Fuzzy Output sets (Type-2)

defuzzifier

Type-reducer Output of inference engine

Type-2

Type reducer Set (type-1)

Crips output Type-0

y f x( ) Y

Output processing

Algortima untuk Defuzzyfikasi

Inisialisasi өi A i i A

i μ x μ x

2 θ 1

Hitung c’

N

1 i

i N

1 i

i i N

1

θ θ x ,... θ

θ c c'

Cari nilai K 1 k

k c' x

x

C” =C’ C” =C’

Centroid = ( Cl + Cr ) /2

STOP START

Y T

Y T

C’=Cr”

N

1 k i

i A k

1 i

i A

N

1 k i

A i i k

1 i

i A i

r

μ x μ x

μ x x μ x

x

"

c

Hitung c” untuk Cr

Hitung c” untuk Cl

N

1 k i

i A k

1 i

A i N

1 k i

i A i k

1 i

i A i l

μ x μ x

μ x x μ x

x

"

c

C’=Cl”

Membership function

Evn(delta error positif)

0 L

-L

1

Upper _MF Lower

_MF

Epn (error negatif) Epp (error positif)

Evp(delta error positif)

x1 x2 x3 x4

opp opn

0 L

-L

1

Upper _MF

Lower _MF zo

x5 x6 x9 x10 x7 x8

Ouput

error

Delta error

Rule out

Error dan Delta Error

Rule Based

Delta error (ev)

Error (ep)

Rule

evn evp

epn on zo

epp zo op

Input

Ouput

Aplikasi GA pada Interval type-2 Fuzzy PI Controller

0 1 0 0 1 1 1 0 1 0

g1 g2 g2 g3 g4 g5 g6 g7 g8 g9

0

g10

x1 x2 x3 x4 x5 x6 x7 x8 x9 x10

Diagram Alir GA

Nvar=10 JumGen=Nvar

UkPop=50 Psilang=0.8

Pmut=0.1 MaxG=50

Inisialisasi Populasi, N kromosom

Start

Dikodekan kromosom [x1,x2….x10]

Xn=1 x jumGen

Evaluasi Individu

ITAE=abs(frek_1^2+frek_2^2+P_tie^2) *(t)

N kromosom

1 2

tidak

ya

Pilih salah satu kromosom

LFC

Elitisme

Pilih Kromosom

Linear Fitness rangking

Roulette wheel

Pindah silang

Mutasi

N-kromosom baru

Generation Replecement [x1,x2,..x10]

Karnik Mandel Algortihm (IT2FPI) Frek_1 Frek_2 Ptie_3

Plant ACE sudah nol??

tidak

STOP 2

1

ya

tidak

ya

Performasi Frekuensi Tanpa Kontroler

0 5 10 15 20 25 30 35 40 45 50

-0.015 -0.01 -0.005 0

X: 37.51 Y: -0.01184 respon frekuensi area 1(pu)

Waktu (detik)

amplitude (pu)

Tanpa KOntroller

0 5 10 15 20 25 30 35 40 45 50

-0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0

X: 44.83 Y: -0.01183 respon frekuensi area 2(pu)

Waktu (detik)

amplitude (pu)

Tanpa KOntroller

0 5 10 15 20 25 30 35 40 45 50

-0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

X: 42.56 Y: -0.02736 respon P-tie area 1(pu)

Waktu (detik)

Tanpa KOntroller

Respon frekuensi area 1 dengan perubahan beban 0.05 p.u

0 5 10 15 20 25 30 35 40 45 50

-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015

respon frekuensi area 1(pu)

Waktu (detik)

amplitude (pu)

kontrol integral kontrol PI IT1FPIC IT2FPIC

Kontroler Overshoot Time settling Y (p.u) X (detik) Integral -0.01239 153.2

PI -0.008938 41.5

IT1FPI -0.004662 19.06 IT2FPI -0.003622 14.27

Respon frekuensi area 2 dengan perubahan beban 0.05 p.u

0 5 10 15 20 25 30 35 40 45 50

-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015

respon frekuensi area 2(pu)

Waktu (detik)

amplitude (pu)

kontrol integral kontrol PI IT1FPIC IT2FPIC

Kontroler

Overshoot (p.u)

Time settling

(detik)

y x

Integral -0.01028 154.7

PI -0.006401 34.64

IT1FPI -0.002335 24.19

IT2FPI -0.001535 21.11

Respon P-tie antar Area dengan Perubahan Beban 0.05 p.u

0 5 10 15 20 25 30 35 40 45 50

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03

respon P-tie area 1(pu)

Waktu (detik)

kontrol integral kontrol PI IT1FPIC IT2FPIC

Kontroler Overshot Time Settling Y(p.u) X (detik) Integral -0.02353 153.

PI -0.01455 37.25

IT2FPI -0.00469 17.12

IT2FPI -0.002794 15.69

Respon Frekuensi dan Ptie dengan IT2FPI-GA

0 5 10 15 20 25 30 35 40 45 50

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5x 10^-3

X: 11.76 Y: 1.685e-005

respon frekuensi area 1(pu)

Waktu (detik)

amplitude (pu)

IT2FPI-GA

0 5 10 15 20 25 30 35 40 45 50

-16 -14 -12 -10 -8 -6 -4 -2 0 2x 10^-4

X: 3.277 Y: -0.001529

respon frekuensi area 2(pu)

Waktu (detik)

amplitude (pu)

IT2FPI-GA

0 5 10 15 20 25 30 35 40 45 50

-2.5 -2 -1.5 -1 -0.5 0

x 10^-3

X: 22.53 Y: -1.838e-005 respon P-tie area 1(pu)

Waktu (detik)

IT2FPI-GA

Respon Area 1 Area 2 P-tie Overshot -0.003613 -0.001529 -0.002774

Settling Time 11.76 21 22.53

Daya Mekanik Sistem

0 5 10 15 20 25 30 35 40 45 50

0 0.01 0.02 0.03 0.04 0.05 0.06

respon daya mekanik area 1(pu)

Waktu (detik)

amplitude (pu)

4 3 1 2

1. IT2FPI Controller 2. IT1FPI Controller 3. PI Controller 4. Integral Controller

0 5 10 15 20 25 30 35 40 45 50

-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

respon daya mekanik area 2(pu)

Waktu (detik)

amplitude (pu) ¹

2 3

4

1. IT2FPI Controller 2. IT1FPI Controller 3. PI Controller 4. Integral Controller

0 5 10 15 20 25 30 35 40 45 50

0 0.01 0.02 0.03 0.04 0.05 0.06

X: 1.417 Y: 0.05918

respon daya mekanik area 1(pu)

Waktu (detik)

amplitude (pu)

0 5 10 15 20 25 30 35 40 45 50

-6 -4 -2 0 2 4 6x 10^-3

X: 15.58 Y: 0.0001261

respon daya mekanik area 2(pu)

Waktu (detik)

amplitude (pu)

ITFPI-GA ITFPI-GA

-0.1 -0.05 0 0.05 0.1 -0.1

-0.05 0 0.05

0.1 -20 dB

Nyquist Diagram

Real Axis

Imaginary Axis

Nyquist Plot

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

Nyquist Diagram

Real Axis

Imaginary Axis

-3 -2 -1 0 1 2 3 4

x 10^-3 -4

-3 -2 -1 0 1 2 3

x 10^-3 Nyquist Diagram

Real Axis

Imaginary Axis

1 2

3

1. I Controller 2. PI Controller

3. IT1FPI Controller

Nyquist Plot(2)

-1.5 -1 -0.5 0 0.5 1 1.5

x 10^-3 -1.5

-1 -0.5 0 0.5 1 1.5

x 10^-3 Nyquist Diagram

Real Axis

Imaginary Axis

-1.5 -1 -0.5 0 0.5 1 1.5

x 10^-3 -1.5

-1 -0.5 0 0.5 1 1.5

x 10^-3

System: sys Real: -0.000107 Imag: 0.000799

Frequency (rad/sec): -0.804 Nyquist Diagram

Real Axis

Imaginary Axis

4 5

4. IT2FPI Controller

4. ITFPI-GA

-500 -400 -300 -200 -100 0

Magnitude (dB)

10^-2 10^-1 10⁰ 10¹ 10² 10³

-720 -540 -360 -180 0

Phase (deg)

Bode Diagram

Frequency (rad/sec)

Bode Plot

-500 -400 -300 -200 -100 0

Magnitude (dB)

10^-2 10^-1 10⁰ 10¹ 10² 10³

-720 -540 -360 -180 0

Phase (deg)

Bode Diagram

Frequency (rad/sec)

-500 -400 -300 -200 -100 0

Magnitude (dB)

10^-1 10⁰ 10¹ 10² 10³

-720 -540 -360 -180 0

Phase (deg)

Bode Diagram

Frequency (rad/sec)

1 2

3

1. I Controller 2. PI Controller

3. IT1FPI Controller

Bode Plot(2)

-500 -400 -300 -200 -100 0

Magnitude (dB)

10^-2 10^-1 10⁰ 10¹ 10² 10³

-720 -540 -360 -180 0

Phase (deg)

Bode Diagram

Frequency (rad/sec)

-500 -400 -300 -200 -100 0

Magnitude (dB)

10^-2 10^-1 10⁰ 10¹ 10² 10³

-720 -540 -360 -180 0

Phase (deg)

Bode Diagram

Frequency (rad/sec)

4 5

4. IT2FPI Controller

5. IT2FPI-GA

Kesimpulan

1. Penggunaan Interval Type-2 fuzzy PI controller yang dioptimasi dengan Genetic Algorithm (GA) pada sistem tenga listrik dua area sangat efektif, dan performansi sistem mampu ditingkatkan

2. Respon frekuensi sistem yang menggunakan IT2FPI-GA memiliki overshot dan settling time yang paling kecil yaitu -0.003572 p.u dan 11.76 detik untuk area 1, -0.001532 p.u dan 21 detik di area 2

3. Respon transfer daya antar area sistem yang menggunakan IT2FPI- GA juga memiliki overshot dan setling time yang paling kecil yaitu -0.00277 p.u dan 22.53 detik

4. Rerspon daya mekanik sistem juga memperlihatkan yang sama, sistem yang dikontrol dengan IT2FPI-GA memiliki overshot dan setling time yang paling kecil yaitu 0.5918 p.u dan 14.15 detik untuk area 1, -0.00586 p.u dan 15.58 detik di area 2

5. Dari anlasis Bode Plot dan Nyquist plot memperlihatkan bahwa

sistem stabil

Saran

• Untuk penelitian selanjutnya dapat digunakan

metode lain misal, PSO, AIS, Bee Colony maupun

Ant Colony sebagai pembanding

Reference (1)

1. Imam Robandi,” Desain Sistem Tenaga Modern, Penerbit ANDI, Yogyakarta, 2006.

2. Hadi Saadat, Power System Analysis 2nd Edition, McGrowHill. 2004 3. Djiteng Marsudi,” Operasi sistem tenaga listrik”.2006. Graha ilmu,

Yogyakarta. ISBN 978-756

4. Muh Budi R Widodo, Muhammad abidillah, Imam Robandi,” optimal design load frequency Control on multi area power system using interval type-2 Fuzzy PI Controller. APTECS-2009. Paper number: 034.

5. Muhammad Abdillah, “Desain Optimal Fuzzy Logic Load Frequency Control pada Sistem Tenaga Listrik Menggunakan Artificial Immune System Via Clonal Selection. Tugas Akhir, Jurusan Teknik Elektro ITS, 2009.

6. Ceyhun YILDIZ, A. Serdar YILMAZ, Mahmet BAYRAK, “Genetic Algorithm based PI Controller for Load Frequency Control in Power system”. Proceding of 5^th International symposium on Intelegent Manufacturing System, may 29-31,2006:1202-1210

Reference (2)

7. Jawad Talaq and Fadel Al-basri, Adapteve gain sceduling for load frequency control, IEEE Transc. on Power Systems, Vol 14. No 1, February, pp. 145-150, 1999.

8. Charles E. Fosha, Jr., and Olle I.Elgerd, The Megawatt-Frequency Control Problem: New approach via Optimal Control Theory, IEEE Trans. Vol. PAS. No.4, April 1970, pp.563-577.

9. Anderson P.M, Fouad A.A, Power Control and Stability, The lowa State University, Press.1982.

10. Kundur,.P, Power System Stability and Control, McGraw-Hill,Inc.,1994.

11. Imam Robandi, and Bedy kharisma,” Design of Interval type-2 Fuzzy Logic Based Power system stabilizer. PWASET VOLUME 31 July 2008 ISSN 1307-6884.

12. WU, DONGRUI, ”Design and Analysis of Type-2 Fuzzy Logic System”. Thesis submitted for the degree of master engineering

departement of electrical and computer engineering national university of singapore.

Reference (3)

13. Muh Budi R Widodo, muhammad abdillah, imam robandi aplikasi Fuzzy PIPD pada Singel Machine Infinite Bus (SMIB), Seminar on intelegnet technology and it’s Aplication (SITIA). 2009. Pp-090

14. Xinyu Du and Hao Ying, “Deriving Analitical stucture of Type-2 Fuzzy PD/PI Controller”. IEEE-2008.978-1-4244-2352

15. G .Chen, “Qilian Liangand, Jerry M. Mandel, ”Interval Type-2 Fuzzy Logic System Theory and Design”,IEEE, 2000.

16. Juan R.Castro, Oscar Castillo, “Interval Type-2 Fuzzy Logic for Intelligent Control Aplication”, IEEE, 2007.

17. Jerry M.Mandel, Robert I. Bob John,” Type-2 Fuzzy Sets Made Simple”, IEEE, April, 2002.

18. Muh Budi R Widodo, Imam Robandi, “Optimization of Fuzzy PIPD Controller for Excitation System Stability Analysis on Single Machine Infinite Bus (SMIB) using Genetic Algorithm (GA)” ICAST. 2009.

Reference(4)

19. B.Venkata Prasant, Dr. S. V. Jayaram Kumar,” Load Frequency Control for a Two Area Interconnected Power System Using Robust Genetic Algorithm Controller, Jatit 2005-2008.

20. D.E Goldberg, Genetic Algorithm (GA) in Serch, Optima-tion and Mechine Learning, Addition-wesley Publishing Compani,In.,1989.

21. C,-F.Juang and C,-F.Lu, “Load Frequency Control By hybrid

Evolutionary Fuzzy PI Controller”. IEE Proceeding online nmo.2005176 22. Suyanto,” Algoritma Genetika dalam MATLAB”. 2005. ANDI

yogyakarta