UJIAN
AKHIR SEMESTER
1. Gambar di bawah memperlihatkan
diagram segaris dari system tenaga 5-bus. Data saluran transmisi diperlihatkan pada Tabel.
Semua data adalah dalam pu pada dasar 100 MVA.
Gambar Sistem Tenaga 5 Bus
Tabel Data
Saluran
|
Bus-Ke-Bus p – q |
Impedansi Seri zpq |
|
1 –
2 |
0,02
+ j0,ab |
|
1 –
3 |
0,08
+ j0,24 |
|
2 –
3 |
0,06
+ j0,18 |
|
2 –
4 |
0,ab
+ j0,18 |
|
2 –
5 |
0,04
+ j0,12 |
|
3 –
4 |
0,01
+ j0,03 |
|
4 –
5 |
0,08
+ j0,24 |
Table data bus :
|
Bus code |
Assumade bus voltage |
Generation |
Load |
||
|
MW |
MVAR |
|
|
||
|
1 |
1.06 + j0.0 |
0 |
0 |
0 |
0 |
|
2 |
1.00 + j0.0 |
40 |
30 |
20 |
10 |
|
3 |
1.00 + j0.0 |
0 |
0 |
45 |
15 |
|
4 |
1.00 + j0.0 |
0 |
0 |
40 |
5 |
|
5 |
1.00 + j0.0 |
0 |
0 |
60 |
10 |
Berdasarkan data tersebut, tentukan:
a. Admitansi-admitansi diri, Y11, Y22,
Y33, Y44, Y55.
b. Admitansi-admitansi bersama antar bus
c.
Matriks admitansi bus Ybus.
d. Vektor dari sudut/besar tegangan bus dan
selisih daya (power mismatch).
e. Tuliskan rumus untuk elemen-elemen dari
vektor selisih daya.
f. Tuliskan rumus untuk matriks Jacobian.
g. Tuliskan persamaan iteratif Newton-Raphson
untuk solusi aliran daya.
h. Lakukan perhitungan iterasi Newton Raphson
sebanyak 5 iterasi (boleh
menggunakan Matlab atau Exel).
i.Tunjukkan hasil perhitungan aliran daya
yang saudara dapatkan dari 5 iterasi tersebut.
Catatan :
·
Untuk Impedansi 1 – 2 nilai imajinernya dengan huruf ab merupakan dua angka terakhir NIM
masing-masing
·
Untuk Impedansi 2 – 4 nilai realnya dengan huruf ab merupakan dua angka terakhir NIM
masing-masing
Jawab :
Admintansi Seri :
|
p-q |
|
|
1-2 |
15,38-j23,07 |
|
1-3 |
1,25 – j3,75 |
|
2-3 |
1,66 – j4,99 |
|
0,90-J5,40 |
|
|
2-5 |
2,50 – j7,50 |
|
3-4 |
9,99 – j29,99 |
|
4-5 |
1,25-j3,73 |
a.)
Admitansi Diri Y11,Y22,Y33,Y44,Y55
Y11 = Y12+Y13
= (15,38-j23,07) + (1,25 - 3,75 j)
= 16,63 – j6,82j
Y22 = Y12
+ Y23 + Y24 + Y25
= ( 15,38-j23,07) + (1,66 – 4,99 j) + ( 1,18-j5,29)+(2,50 –
7,50j)
= 20,72 – j40,85
Y33 = Y13+
Y23+ Y34
= (1,25 – 3,75 j) + (1,66
– 4,99 j) + (9,99 – 29,99 j)
=12,9 – 38,73 j
Y44 = Y24+
Y34+ Y45
= (0,90 – J5,40) + (9,99 – 29,99 j) +
(1,25-3,73 j)
= 12,14– j 39,12
Y55 = Y25 +
Y45
= ( 2,50 – 7,50 j) + (
1,25-3,73 j )
= 3,75 – 11,25 j
b) Admitansi – admitansi bersama antar bus
Y12 = Y21 = - Y12 = -15,38 + j23,07
Y13 = Y31 = - Y13 = -1,25 + 3,75 j
Y14 = Y41 = 0
Y15 = Y51 = 0
Y23 = Y32 = - Y23 = -1,66 + 4,99 j
Y24 = Y42 = - Y24 = -0,90 + J5,40
Y25 = Y52 = -Y25 = -2,50 + 7,50 j
Y34 = Y43 = - Y34 = -9,99 + 29,99 j
Y35 = Y53 = 0
Y45 = Y54 + -Y45 = -1,25 + 3,75 j
c) Matriks admitansi bus Ybus.
Y = 
d)
Vektor dari
sudut/besar tegangan bus dan selisih daya (power mismatch).
Jawab:
oleh karena bus 1 dengan tegangan 1.06 maka disebut bus slack dan bus 3 adalah
bus PV , maka vector dari sudut/besar tegangann bus dan vector dari selisih
daya adalah :
e) Tuliskan
rumus untuk elemen-elemen dari vektor selisih daya.
Jawab :
f) Tuliskan rumus untuk matriks Jacobian.
Jawab :
g)
Tuliskan persamaan iteratif Newton-Raphson
untuk solusi aliran daya
Jawab :
h) Lakukan perhitungan iterasi Newton Raphson sebanyak 5
iterasi (boleh menggunakan Matlab
atau Exel).
Ø Jawab
: program menggunakan matlab
clear
clc
format short
% Diketahui nilai Impedansi
z = [0.02+j*0.03;0.08 +
j*0.24;0.06 + j*0.18;]
%Data Bus
V1=1.06
delta1=0.00
PL1=0.00
QL1=0.00
V2=1.00
PG2=40
PL2=30
QL2=20
PG3=0.00
QG3=45
PL3=60
QL3=15.38
%Mencari admitansi saluran
y = 1./z
%Menyocokkan urutan admitansi
saluran
y12=y(1,1)
y13=y(2,1)
y23=y(3,1)
%Membuat matrik admitansi bus
Ybus = [y12+y13 -y12 -y13;...
-y12 y12+y23 -y23;...
-y13 -y23 y13 + y23]
Y = abs(Ybus)
Teta = angle(Ybus);
% Iterasi ke-0
delta2=0.00
delta3=0.00
V3=1.00
Vektor_Tegangan_Awal =
[delta2;delta3;V3]
%Perhitungan Power Mismatch
dengan estimasi awal
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+
(V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+ (V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+
(V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+ (V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
%Sehingga Matrik Jakobian
Menjadi :
Jakobi_11 =
V1*V2*Y(2,1)*sin(Teta(2,1) + delta1 - delta2) + V2*V3*Y(2,3)*sin(Teta(2,3) -
delta2 + delta3)
Jakobi_12 =
-V2*V3*Y(2,3)*sin(Teta(2,3) - delta2 + delta3)
Jakobi_13 =
V2*Y(2,3)*cos(Teta(2,3) - delta2 + delta3)
Jakobi_21 =
-V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_22 = V1*V3*Y(3,1)*sin(Teta(3,1)
+ delta1 - delta3) + V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_23 =
V1*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*Y(3,2)*cos(Teta(3,2) + delta2 -
delta3) + 2*V3*Y(3,3)*cos(Teta(3,3))
Jakobi_31 =
-V2*V3*Y(3,2)*cos(Teta(3,2) + delta2 - delta3)
Jakobi_32 =
V1*V3*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*cos(Teta(3,2) +
delta2 - delta3)
Jakobi_33 = -
V1*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) - V2*Y(3,2)*sin(Teta(3,2) + delta2 -
delta3) - 2*V3*Y(3,3)*sin(Teta(3,3))
Jakobian = [Jakobi_11 Jakobi_12
Jakobi_13;Jakobi_21 Jakobi_22 Jakobi_23;Jakobi_31 Jakobi_32 Jakobi_33]
% Nilai-nilai koreksi untuk
estimasi solusi:
Inverse_Jakobian =
inv(Jakobian)
Nilai_Koreksi_Vektor_Tegangan =
Inverse_Jakobian*Vektor_Power_Mismatch
% Nilai estimasi Iterasi ke-1
disp ('Iterasi 1')
Vektor_Tegangan_Baru =
Vektor_Tegangan_Awal + Nilai_Koreksi_Vektor_Tegangan
delta2 =
Vektor_Tegangan_Baru(1,1)
delta3 =
Vektor_Tegangan_Baru(2,1)
V3 = Vektor_Tegangan_Baru(3,1)
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+
(V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+
(V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+
(V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+
(V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
%Sehingga Matrik Jakobian
Menjadi :
Jakobi_11 =
V1*V2*Y(2,1)*sin(Teta(2,1) + delta1 - delta2) + V2*V3*Y(2,3)*sin(Teta(2,3) -
delta2 + delta3)
Jakobi_12 =
-V2*V3*Y(2,3)*sin(Teta(2,3) - delta2 + delta3)
Jakobi_13 =
V2*Y(2,3)*cos(Teta(2,3) - delta2 + delta3)
Jakobi_21 =
-V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_22 =
V1*V3*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*sin(Teta(3,2) +
delta2 - delta3)
Jakobi_23 =
V1*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*Y(3,2)*cos(Teta(3,2) + delta2 -
delta3) + 2*V3*Y(3,3)*cos(Teta(3,3))
Jakobi_31 =
-V2*V3*Y(3,2)*cos(Teta(3,2) + delta2 - delta3)
Jakobi_32 =
V1*V3*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*cos(Teta(3,2) +
delta2 - delta3)
Jakobi_33 = -
V1*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) - V2*Y(3,2)*sin(Teta(3,2) + delta2 -
delta3) - 2*V3*Y(3,3)*sin(Teta(3,3))
Jakobian = [Jakobi_11 Jakobi_12
Jakobi_13;Jakobi_21 Jakobi_22 Jakobi_23;Jakobi_31 Jakobi_32 Jakobi_33]
% Nilai-nilai koreksi untuk
estimasi solusi:
Inverse_Jakobian =
inv(Jakobian)
Nilai_Koreksi_Vektor_Tegangan =
Inverse_Jakobian*Vektor_Power_Mismatch
% Nilai estimasi Iterasi ke-2
disp ('Iterasi 2');
Vektor_Tegangan_Baru =
Vektor_Tegangan_Awal + Nilai_Koreksi_Vektor_Tegangan
delta2 =
Vektor_Tegangan_Baru(1,1)
delta3 =
Vektor_Tegangan_Baru(2,1)
V3 = Vektor_Tegangan_Baru(3,1)
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+ (V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+
(V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+
(V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+
(V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
%Sehingga Matrik Jakobian
Menjadi :
Jakobi_11 =
V1*V2*Y(2,1)*sin(Teta(2,1) + delta1 - delta2) + V2*V3*Y(2,3)*sin(Teta(2,3) -
delta2 + delta3)
Jakobi_12 =
-V2*V3*Y(2,3)*sin(Teta(2,3) - delta2 + delta3)
Jakobi_13 =
V2*Y(2,3)*cos(Teta(2,3) - delta2 + delta3)
Jakobi_21 =
-V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_22 =
V1*V3*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*sin(Teta(3,2) +
delta2 - delta3)
Jakobi_23 =
V1*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*Y(3,2)*cos(Teta(3,2) + delta2 -
delta3) + 2*V3*Y(3,3)*cos(Teta(3,3))
Jakobi_31 =
-V2*V3*Y(3,2)*cos(Teta(3,2) + delta2 - delta3)
Jakobi_32 =
V1*V3*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*cos(Teta(3,2) +
delta2 - delta3)
Jakobi_33 = -
V1*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) - V2*Y(3,2)*sin(Teta(3,2) + delta2 -
delta3) - 2*V3*Y(3,3)*sin(Teta(3,3))
Jakobian = [Jakobi_11 Jakobi_12
Jakobi_13;Jakobi_21 Jakobi_22 Jakobi_23;Jakobi_31 Jakobi_32 Jakobi_33]
% Nilai-nilai koreksi untuk
estimasi solusi:
Inverse_Jakobian =
inv(Jakobian)
Nilai_Koreksi_Vektor_Tegangan =
Inverse_Jakobian*Vektor_Power_Mismatch
% Nilai estimasi Iterasi ke-3
disp ('Iterasi 3');
Vektor_Tegangan_Baru =
Vektor_Tegangan_Awal + Nilai_Koreksi_Vektor_Tegangan
delta2 = Vektor_Tegangan_Baru(1,1)
delta3 =
Vektor_Tegangan_Baru(2,1)
V3 = Vektor_Tegangan_Baru(3,1)
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+
(V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+
(V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+
(V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+
(V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+ (V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
%Sehingga Matrik Jakobian
Menjadi :
Jakobi_11 =
V1*V2*Y(2,1)*sin(Teta(2,1) + delta1 - delta2) + V2*V3*Y(2,3)*sin(Teta(2,3) -
delta2 + delta3)
Jakobi_12 =
-V2*V3*Y(2,3)*sin(Teta(2,3) - delta2 + delta3)
Jakobi_13 =
V2*Y(2,3)*cos(Teta(2,3) - delta2 + delta3)
Jakobi_21 =
-V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_22 =
V1*V3*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*sin(Teta(3,2) +
delta2 - delta3)
Jakobi_23 =
V1*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*Y(3,2)*cos(Teta(3,2) + delta2 -
delta3) + 2*V3*Y(3,3)*cos(Teta(3,3))
Jakobi_31 = -V2*V3*Y(3,2)*cos(Teta(3,2)
+ delta2 - delta3)
Jakobi_32 =
V1*V3*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*cos(Teta(3,2) +
delta2 - delta3)
Jakobi_33 = -
V1*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) - V2*Y(3,2)*sin(Teta(3,2) + delta2 -
delta3) - 2*V3*Y(3,3)*sin(Teta(3,3))
Jakobian = [Jakobi_11 Jakobi_12
Jakobi_13;Jakobi_21 Jakobi_22 Jakobi_23;Jakobi_31 Jakobi_32 Jakobi_33]
% Nilai-nilai koreksi untuk
estimasi solusi:
Inverse_Jakobian =
inv(Jakobian)
Nilai_Koreksi_Vektor_Tegangan =
Inverse_Jakobian*Vektor_Power_Mismatch
% Nilai estimasi Iterasi ke-4
disp ('Iterasi 4');
Vektor_Tegangan_Baru =
Vektor_Tegangan_Awal + Nilai_Koreksi_Vektor_Tegangan
delta2 =
Vektor_Tegangan_Baru(1,1)
delta3 =
Vektor_Tegangan_Baru(2,1)
V3 = Vektor_Tegangan_Baru(3,1)
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+
(V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+
(V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+ (V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+
(V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
%Sehingga Matrik Jakobian
Menjadi :
Jakobi_11 =
V1*V2*Y(2,1)*sin(Teta(2,1) + delta1 - delta2) + V2*V3*Y(2,3)*sin(Teta(2,3) -
delta2 + delta3)
Jakobi_12 = -V2*V3*Y(2,3)*sin(Teta(2,3)
- delta2 + delta3)
Jakobi_13 =
V2*Y(2,3)*cos(Teta(2,3) - delta2 + delta3)
Jakobi_21 =
-V2*V3*Y(3,2)*sin(Teta(3,2) + delta2 - delta3)
Jakobi_22 =
V1*V3*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) + V2*V3*Y(3,2)*sin(Teta(3,2) +
delta2 - delta3)
Jakobi_23 =
V1*Y(3,1)*cos(Teta(3,1) + delta1 - delta3) + V2*Y(3,2)*cos(Teta(3,2) + delta2 -
delta3) + 2*V3*Y(3,3)*cos(Teta(3,3))
Jakobi_31 =
-V2*V3*Y(3,2)*cos(Teta(3,2) + delta2 - delta3)
Jakobi_32 = V1*V3*Y(3,1)*cos(Teta(3,1)
+ delta1 - delta3) + V2*V3*Y(3,2)*cos(Teta(3,2) + delta2 - delta3)
Jakobi_33 = -
V1*Y(3,1)*sin(Teta(3,1) + delta1 - delta3) - V2*Y(3,2)*sin(Teta(3,2) + delta2 -
delta3) - 2*V3*Y(3,3)*sin(Teta(3,3))
Jakobian = [Jakobi_11 Jakobi_12
Jakobi_13;Jakobi_21 Jakobi_22 Jakobi_23;Jakobi_31 Jakobi_32 Jakobi_33]
% Nilai-nilai koreksi untuk
estimasi solusi:
Inverse_Jakobian =
inv(Jakobian)
Nilai_Koreksi_Vektor_Tegangan =
Inverse_Jakobian*Vektor_Power_Mismatch
% Nilai estimasi Iterasi ke-5
disp ('Iterasi 5');
Vektor_Tegangan_Baru =
Vektor_Tegangan_Awal + Nilai_Koreksi_Vektor_Tegangan
delta2 =
Vektor_Tegangan_Baru(1,1)
delta3 =
Vektor_Tegangan_Baru(2,1)
V3 = Vektor_Tegangan_Baru(3,1)
P2 = -PG2 + PL2...
+
(V2*Y(2,1)*(V1)*cos(delta2-delta1-Teta(2,1)))...
+
(V2*Y(2,2)*(V2)*cos(delta2-delta2-Teta(2,2)))...
+
(V2*Y(2,3)*(V3)*cos(delta2-delta3-Teta(2,3)));
P3 = -PG3 + PL3...
+
(V3*Y(3,1)*V1*cos(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*cos(delta3-delta2-Teta(3,2)))...
+ (V3*Y(3,3)*V3*cos(delta3-delta3-Teta(3,3)));
Q3 = PG3 + PL3...
+
(V3*Y(3,1)*V1*sin(delta3-delta1-Teta(3,1)))...
+
(V3*Y(3,2)*V2*sin(delta3-delta2-Teta(3,2)))...
+
(V3*Y(3,3)*V3*sin(delta3-delta3-Teta(3,3)));
Vektor_Power_Mismatch =
[P2;P3;Q3]
i) Tunjukkan
hasil perhitungan aliran daya yang saudara dapatkan dari 5 iterasi tersebut.
Jawab :
z =
0.0200 + 0.0300i
0.0800 + 0.2400i
0.0600 + 0.1800i
V1 =
1.0600
delta1 =
0
PL1 =
0
QL1 =
0
V2 =
1
PG2 =
40
PL2 =
30
QL2 =
20
PG3 =
0
QG3 =
45
PL3 =
60
QL3 =
15.3800
y =
15.3846 -23.0769i
1.2500 - 3.7500i
1.6667 - 5.0000i
y12 =
15.3846 -23.0769i
y13 =
1.2500 - 3.7500i
y23 =
1.6667
- 5.0000i
Ybus =
16.6346 -26.8269i -15.3846 +23.0769i
-1.2500 + 3.7500i
-15.3846 +23.0769i 17.0513 -28.0769i -1.6667 + 5.0000i
-1.2500 + 3.7500i -1.6667 +
5.0000i 2.9167 - 8.7500i
Y =
31.5657 27.7350 3.9528
27.7350 32.8490 5.2705
3.9528 5.2705 9.2233
delta2 =
0
delta3 =
0
V3 =
1
Vektor_Tegangan_Awal =
0
0
1
Vektor_Power_Mismatch =
-10.9231
59.9250
59.775
Jakobi_11 =
29.4615
Jakobi_12 =
-5
Jakobi_13 =
-1.6667
Jakobi_21
-5
Jakobi_22 =
8.9750
Jakobi_23 =
2.8417
Jakobi_31 =
1.6667
Jakobi_32 =
-2.9917
Jakobi_33 =
8.5250
Jakobian =
29.4615
-5.0000 -1.6667
-5.0000 8.9750 2.8417
1.6667 -2.9917 8.5250
Inverse_Jakobian =
0.0375 0.0210 0.0003
0.0209 0.1120 -0.0332
0.0000 0.0352 0.1056
Nilai_Koreksi_Vektor_Tegangan =
0.8684
4.4949
8.4194
Iterasi 1
Vektor_Tegangan_Baru =
0.8684
4.4949
9.4194
delta2 =
0.8684
delta3 =
4.4949
V3 =
9.4194
Vektor_Power_Mismatch =
51.0301
276.8460
905.5870
Jakobi_11
-6.0971
Jakobi_12 =
34.3483
Jakobi_13 =
3.8053
Jakobi_21 =
48.9847
Jakobi_22 =
-69.2499
Jakobi_23 =
50.4944
Jakobi_31 =
8.0659
Jakobi_32 =
-41.9331
Jakobi_33 =
172.1906
Jakobian =
-6.0971 34.3483 3.8053
48.9847 -69.2499 50.4944
8.0659 -41.9331 172.1906
Inverse_Jakobian =
0.0442 0.0274 -0.0090
0.0362 0.0049 -0.0022
0.0067 -0.0001 0.0057
Nilai_Koreksi_Vektor_Tegangan =
1.6818
1.1785
5.4674
Iterasi 2
Vektor_Tegangan_Baru =
1.6818
1.1785
6.4674
delta2 =
1.6818
delta3 =
1.1785
V3 =
6.4674
Vektor_Power_Mismatch =
39.3224
177.4369
385.1159
Jakobi_11 =
47.0246
Jakobi_12 =
-33.5262
Jakobi_13 =
0.9515
Jakobi_21 =
-23.1285
Jakobi_22 =
40.8757
Jakobi_23 =
37.0215
Jakobi_31 =
25.0389
Jakobi_32 =
-4.5603
Jakobi_33 =
106.8597
Jakobian =
47.0246 -33.5262 0.9515
-23.1285 40.8757 37.0215
25.0389 -4.5603 106.8597
Inverse_Jakobian =
0.0460 0.0363 -0.0130
0.0345 0.0508 -0.0179
-0.0093 -0.0063 0.0116
Nilai_Koreksi_Vektor_Tegangan =
3.2511
3.4721
2.9903
Iterasi 3
Vektor_Tegangan_Baru =
3.2511
3.4721
3.9903
delta2 =
3.2511
delta3 =
3.4721
V3 =
3.9903
Vektor_Power_Mismatch =
9.7252
104.1785
195.1179
Jakobi_11 =
-8.0889
Jakobi_12 =
-18.0089
Jakobi_13 =
-2.7220
Jakobi_21 =
-20.9241
Jakobi_22 =
4.2052
Jakobi_23 =
22.7099
Jakobi_31 =
2.1161
Jakobi_32 =
-2.2625
Jakobi_33 =
68.7767
Jakobian =
-8.0889 -18.0089 -2.7220
-20.9241 4.2052 22.7099
2.1161 -2.2625 68.7767
Inverse_Jakobian =
-0.0115 -0.0420 0.0134
-0.0502 0.0186 -0.0081
-0.0013 0.0019 0.0139
Nilai_Koreksi_Vektor_Tegangan =
-1.8698
-0.1370
2.8900
Iterasi 4
Vektor_Tegangan_Baru =
-1.8698
-0.1370
3.8900
delta2 =
-1.8698
delta3 =
-0.1370
V3 =
3.8900
Vektor_Power_Mismatch =
-29.6718
117.1583
174.5297
Jakobi_11 =
-32.3241
Jakobi_12 =
9.5349
Jakobi_13 =
-4.6658
Jakobi_21 =
-3.2620
Jakobi_22 =
17.8759
Jakobi_23 =
26.0395
Jakobi_31 =
-20.2409
Jakobi_32 =
13.0231
Jakobi_33 =
63.4796
Jakobian =
-32.3241 9.5349 -4.6658
-3.2620 17.8759 26.0395
-20.2409 13.0231 63.4796
Inverse_Jakobian =
-0.0263 0.0220 -0.0110
0.0106 0.0709 -0.0283
-0.0106 -0.0075 0.0181
Nilai_Koreksi_Vektor_Tegangan =
1.4458
3.0539
2.5839
Iterasi 5
Vektor_Tegangan_Baru =
1.4458
3.0539
3.5839
delta2 =
1.4458
delta3 =
3.053
V3 =
3.5839
Vektor_Power_Mismatch =
11.6055
121.5691
180.8612
>>
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