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 Bus i
Pembangkit
Bus j
Beban
Gambar 1, Single Line Sistem Tenaga Listrik
BATAS MASALAH 1. Plant yang digunakan STL 2 Area 2. Beban statis 3. Kontroler yang digunakan I, PI, IT2FPI, IT2FPI
TUJUAN 1. MEMBUAT PENGENDALI FREKUENSI (KONTROLER) : IT2FPI-GA FREQUENCY
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
Pengumpulan data dan referency tentang LFC, PI controler, dan GA
Simulasi dan Analisis menggunakan MATLAB
Tidak
Performance optimal ?
ya
STOP
Frequency Regulation MENURUT HUKUM NEWTON
(TG-TB)=H.dω/dt Sedangkan,
1.
f= ω/ 2.π Ditinjau dari Beban TG - TB =ΔT<0, maka dω/dt<0 , frekuensi turun TG - TB =ΔT>0, maka dω/dt>0 , frekuensi naik
Skema Load Frequency Control (LFC)1 Excitation system
AVR
Gen .field
Voltage sensor
Turbine
Steam G Pv
PG
Ptie
Governor
Pc
Load Frequency Control (LFC)
Frequency sensor
QG
Block Lengkap Pengaturan Frekuensi Pada Pembangkit 1 R
Preff
+
-
1 1 sTG Governor
Pv
1 ( 1 sTCH )
1 2Hs D
Pm + -
Turbin
PL
Inersia rotor dan beban
r
pu
Respon Frekuensi terhadap Perubahan beban Frekuensi (f) dan KopenT)
f’’ Kerja governor mulai terasa
fo
Garis frekuensi
f’ Sebelum ada penambahan beban TG-TB>0, f akan terus naik
t0
t1
t2
t3
t4
t5 t(waktu)
Sistem Listrik Dua Area P12
Area 1
X tie SPESIFIKASI
1. 2. 3. 4.
Dihubungakan oleh Xtie, Tahanan stator diabaikan Beban statis Kondisi sistem seimbang
Area 2
Sistem Tenaga Listrik 2 Area f1
f2
-
+ 1
2
1
1 sM 1 D1
T/s
sM 2 D2 Ptie
PL1
-
+
Pm1
1 1 sTCH 1 1 RG1
Y1
1 1 sTg1
-
+
PL 2
Pm2
+
1 1 sTCH 2 1 RG 2
Y2
1 1 sTg 2
-
+
+
Pc1
Pc2
Fuzzy PI Controller Digital
Pdi
Bi
+
ACE
1/T
K i1 +
fuzzy
KuPi
+
+/-
+
Kontrol Area (i)
+
f 1/z
+ Interval type-2 fuzzy PI Controller
1/z
-
K Pi
Ptie ,i
STL 2 Area dengan Controller B1i Bias
1 R 1i PD1i
Speed Drop
U1
+ +
ACE1
-
Kontroller
+ Interval Type-2 Fuzzy PI coantroller
1 1 Tg1i s
PV 1
Governor 1
1 1 TcH1i s
Pm1
-
f1i
1
-
sM1i D1i Load 1
Turbin 1
Ptie
T s
+
-
U2 Kontroller
+
+
ACE2
-
1 1 Tg 2i s Governor 1
Bias
B2i
PV 2
1 1 TcH 2i s
Pm 2
+
1 sM 2i D 2i
-
Turbin 2
1 R 2i Speed Drop
Load 2
PD 2i
f 2i
Cara Kerja Fuzzy Type-2 Fuzzy Logic system Rules Crips input Output processing
fuzzifier
inference Fuzzy output set (type-2)
Type-reducerd Set(type-1)
Fuzzy Output sets (Type-2)
Output processing defuzzifier Output of inference engine Type-2
Crips output (type-0)
Crips output Type-0 y
Type-reducer Type reducer Set (type-1)
f( x ) Y
Algortima untuk Defuzzyfikasi START Inisialisasi өi 1 μ xi 2 A
θi
μA xi
Hitung c’
N
x iθ i i 1 N
c θ 1 ,... θ N
c'
θi i 1
Cari nilai K
xk
c'
xk
1
C’=Cl”
C’=Cr” Hitung c” untuk Cl k
xi μA xi cl "
Hitung c” untuk Cr k
N
i 1
xi μ
k
μA xi
μ
cr "
i k 1 N
k
μ i 1
xi μA xi
xi A
i 1
xi
i k 1 A
i 1
T
A
i k 1 N
N
xi μ
xi
μ
xi A
i k 1 A
C” =C’
C” =C’ Y
Y Centroid = ( Cl + Cr ) /2
STOP
T
xi
Membership function Error dan Delta Error Epn (error negatif) Evn(delta error positif)
Epp (error positif) Evp(delta error positif)
1
error Upper _MF
Rule
out
Lower _MF
x1
-L
0
x2
Delta error
x3
L
x4
Ouput opn
zo
opp
1
Upper _MF
Lower _MF
x5
-L
x6
x9
0
x10
x7
L
x8
Rule Based Input Delta error (ev) Error (ep)
Rule epn epp
evn on zo
evp zo op
Ouput
Aplikasi GA pada Interval type-2 Fuzzy PI Controller
x1
x2
x3
x4
x5
x6
x7
x8
x10
x9
0
1
0
0
1
1
g1
g2
g2
g3
g4
g5
1
0
1
0
0
g6
g7
g8
g9
g10
Diagram Alir GA Start 2
Nvar=10 JumGen=Nvar UkPop=50 Psilang=0.8 Pmut=0.1 MaxG=50
Elitisme
Pilih Kromosom
Inisialisasi Populasi, N kromosom
1 Linear Fitness rangking
Dikodekan kromosom [x1,x2….x10] Xn=1 x jumGen
tidak
ya
Roulette wheel
Pilih salah satu kromosom
ACE sudah nol??
Pindah silang STOP Mutasi
LFC
Frek_1 Frek_2 Ptie_3 tidak
Evaluasi Individu ITAE=abs(frek_1^2+frek_2^2+P_tie^2) *(t)
N-kromosom baru
ya
tidak N kromosom
ya
2
Plant
Generation Replecement [x1,x2,..x10]
1
Karnik Mandel Algortihm (IT2FPI)
Performasi Frekuensi Tanpa Kontroler respon frekuensi area 1(pu)
respon frekuensi area 2(pu)
0
0 Tanpa KOntroller
Tanpa KOntroller -0.002
-0.004
amplitude (pu)
amplitude (pu)
-0.005
-0.01
X: 37.51 Y: -0.01184
-0.006
-0.008
-0.01 X: 44.83 Y: -0.01183
-0.012
-0.015
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
respon P-tie area 1(pu) 0 Tanpa KOntroller -0.005 -0.01 -0.015 -0.02 X: 42.56 Y: -0.02736
-0.025 -0.03 -0.035 -0.04
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
-0.014
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Respon frekuensi area 1 dengan perubahan beban 0.05 p.u respon frekuensi area 1(pu) 0.015 kontrol integral kontrol PI IT1FPIC IT2FPIC
0.01
amplitude (pu)
0.005 0
Overshoot
Time settling
Integral
Y (p.u) -0.01239
X (detik) 153.2
PI
-0.008938
41.5
IT1FPI
-0.004662
19.06
IT2FPI
-0.003622
14.27
Kontroler -0.005 -0.01 -0.015 -0.02 -0.025
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Respon frekuensi area 2 dengan perubahan beban 0.05 p.u respon frekuensi area 2(pu) 0.015 kontrol integral kontrol PI IT1FPIC IT2FPIC
0.01
amplitude (pu)
0.005 0 -0.005
Kontroler -0.01
Integral PI IT1FPI IT2FPI
-0.015 -0.02 -0.025
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Overshoot (p.u) y -0.01028 -0.006401 -0.002335 -0.001535
Time settling (detik) x 154.7 34.64 24.19 21.11
Respon P-tie antar Area dengan Perubahan Beban 0.05 p.u respon P-tie area 1(pu) 0.03 kontrol integral kontrol PI IT1FPIC IT2FPIC
0.02 0.01 0 -0.01 -0.02
Kontroler
Overshot
Time Settling
Y(p.u)
X (detik)
-0.03
Integral
-0.02353
153.
-0.04
PI
-0.01455
37.25
-0.05
IT2FPI IT2FPI
-0.00469 -0.002794
17.12 15.69
0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Respon Frekuensi dan Ptie dengan IT2FPI-GA -3
0.5
-4
respon frekuensi area 1(pu)
x 10
2
0
0 X: 11.76 Y: 1.685e-005
-0.5
-2 -4
amplitude (pu)
amplitude (pu)
-1 -1.5 -2
-6 -8
-2.5
-10
-3
-12
-3.5 -4
respon frekuensi area 2(pu)
x 10
IT2FPI-GA
0
5
10
-3
15
x 10
20
25 30 Waktu (detik)
respon P-tie area 1(pu)
35
40
45
X: 3.277 Y: -0.001529
-14
50
-16
0
5
10
IT2FPI-GA
15
20
25 30 Waktu (detik)
35
40
45
0 X: 22.53 Y: -1.838e-005
-0.5
Respon
Overshot
-1
Settling Time
-1.5
-2
-2.5
IT2FPI-GA 0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Area 1
Area 2
P-tie
-0.003613 -0.001529 -0.002774 11.76
21
22.53
50
Daya Mekanik Sistem respon daya mekanik area 2(pu)
respon daya mekanik area 1(pu)
0.02
0.06 1
2
0.015 0.05
0.01
amplitude (pu)
3 0.03
4
0.02
0
2
1
3
IT2FPI Controller IT1FPI Controller PI Controller Integral Controller
0.005
0
-0.005 1. 2. 3. 4.
0.01
IT2FPI Controller IT1FPI Controller PI Controller Integral Controller
-0.01
-0.015 0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
0
5
10
-3
respon daya mekanik area 1(pu) 0.06
6
15
20
25 30 Waktu (detik)
35
40
45
50
respon daya mekanik area 2(pu)
x 10
X: 1.417 Y: 0.05918
0.05
4
0.04
2
amplitude (pu)
amplitude (pu)
amplitude (pu)
0.04
1. 2. 3. 4.
4
0.03
0.02
0
-2
0.01
0
X: 15.58 Y: 0.0001261
-4
ITFPI-GA 0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
-6
ITFPI-GA 0
5
10
15
20
25 30 Waktu (detik)
35
40
45
50
Nyquist Plot Nyquist Diagram
Nyquist Diagram
0.015
-20 dB
0.1
0.01
0.05
Imaginary Axis
Imaginary Axis
0.005
0
0
-0.005
-0.05
-0.01
1
-0.1
2
-0.015 -0.1
-0.05
0
0.05
0.1
-0.015
Real Axis -3
-0.01
-0.005
0
0.005
0.01
Real Axis
Nyquist Diagram
x 10
3
2
1. 2. 3.
Imaginary Axis
1
0
-1
-2
3
-3
-4 -3
-2
-1
0 Real Axis
1
2
3
4 -3
x 10
I Controller PI Controller IT1FPI Controller
0.015
Nyquist Plot(2) -3
Nyquist Diagram
x 10
1.5
1.5
1
1
0.5
0.5 Imaginary Axis
Imaginary Axis
-3
Nyquist Diagram
x 10
0
-0.5
-1
System: sys Real: -0.000107 Imag: 0.000799 Frequency (rad/sec): -0.804
0
-0.5
-1
4
-1.5
-1.5
-1
-0.5
0 Real Axis
0.5
1
5
-1.5
1.5 -3
-1.5
-1
-0.5
x 10
0 Real Axis
4. 4.
0.5
1
1.5 -3
x 10
IT2FPI Controller ITFPI-GA
Bode Plot Bode Diagram
-100
-100
Magnitude (dB)
0
-200 -300
-200 -300
-400
-400
-500 0
-500 0
-180
-180
Phase (deg)
Phase (deg)
Magnitude (dB)
Bode Diagram 0
1
-360 -540
2
-360 -540
-720
-720 -2
10
-1
0
10
1
10
2
10
3
10
10
-2
10
-1
10
Frequency (rad/sec)
0
10
1
10
2
10
Frequency (rad/sec)
Bode Diagram 0
Magnitude (dB)
-100
1. 2. 3.
-200 -300 -400 -500 0
Phase (deg)
-180
3
-360 -540 -720 -1
10
0
10
1
10
Frequency (rad/sec)
2
10
3
10
I Controller PI Controller IT1FPI Controller
3
10
Bode Plot(2) Bode Diagram
-100
-100
Magnitude (dB)
0
-200 -300
-200 -300
-400
-400
-500 0
-500 0
-180
-180
Phase (deg)
Phase (deg)
Magnitude (dB)
Bode Diagram 0
4
-360 -540
5
-360 -540
-720 -2
10
-1
10
0
10
1
10
2
10
3
10
-720 -2
10
-1
10
Frequency (rad/sec)
0
10
1
10
2
10
Frequency (rad/sec)
4. 5.
IT2FPI Controller IT2FPI-GA
3
10
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 IT2FPIGA 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 5th International symposium on Intelegent Manufacturing System, may 29-31,2006:1202-1210
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