hello
I’m Alireza Jam
I wrote this code in gams but it can’t solve it and don’t converge!!!
this formulation is for stochastic optimal power flow
could anyone help me
thanks
A.J
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$Ontext
This model has been coded April to … 2012 by A.J
$Offtext
sets
i “number of 1st point buses” / 1 * 41 /
g “state number” / 1 * 120 /
ls “load’s stats” / 1 * 10 /
ws “wind’s states” / 1 * 12 /
pl “load_percentage & probability” / peak_load , probability_load /
w “wind_power & probability” / rated_power , probability_wind /
pq “load_data(P&Q)” / P_kw , Q_kvar /
M “loads” / M1 * M26 /
l “lines” / L1 * L20 , L22 * L23 , L24+L26 , L27 * L28 , L29+L30 , L31 * L40 /
lid “lines data” / from , to , L , R , X , Y , Teta_deg , Teta_rad /
c “matrix_c_columns” / wind_power_state , load_state /
pc “P(c)” / P_c /
n “kind of turbines” / 1 /
Pr “rated power of each kind of turbines” / P_r /;
alias(i,j);
sets Candidate(i) Candidate buses for DG placement /19,23,24,26,28,32,33,35,37,38,39,40/;
parameters
Sbase base power 10000 KVA /10000/
Ibase base current 300 A /300/
Vbase base voltage 33.33 KV /33.33/
Zbase base ampedance 111.1 ohm /111.1/
CF Capacity Factor of kind n DG /0.2209/;
integer variables
N_DG(i,n) “number of DG kind of n at bus i” ;
variables
P_loss(g) “total power loss during state g”
P_DG(i,n) “power of DG with kind of n in bus i”
V(g,i) “voltage of bus i in state g”
Delta(g,i) “pgase of bus i in state g”
Z “the objective function value”
Igij(g,i,j) “branch current from i to j”;
V.lo(g,i)=0.95;
V.up(g,i)=1.05;
*V.l(g,i)=1.03;
*power of wind turbines is p.u. based on 16180 kw
table Wind_Turbine(n,Pr) “one dg for this time (MW)”
P_r
1 1.1
table Load_State(ls,pl) “table 2”
peak_load probability_load
1 100 0.01
2 85.3 0.056
3 77.4 0.1057
4 71.3 0.1654
5 65 0.1654
6 58.5 0.163
7 51 0.163
8 45.1 0.0912
9 40.6 0.0473
10 35.1 0.033 ;
table Wind_Power_Probability(ws,w) “Table 4”
rated_power probability_wind
1 100 0.078425
2 94.9696 0.025
3 84.9728 0.032648
4 74.976 0.045091
5 64.9792 0.050114
6 54.9824 0.077283
7 44.9856 0.09121
8 34.9888 0.112215
9 19.9936 0.103653
10 14.9952 0.112329
11 4.9984 0.066096
12 0 0.205936 ;
table Load_Data(M,pq) “Table 6”
P_kw Q_kvar
M1 6251.96 2054.92
M2 152 49.96
M3 9.5 3.12
M4 187.92 106.5
M5 715.14 405.29
M6 3187.25 1047.60
M7 576.00 507.98
M8 19.00 0.00
M9 19.00 6.24
M10 142.50 46.84
M11 161.50 53.08
M12 23.75 7.81
M13 47.50 15.61
M14 289.75 95.236219
M15 152 49.959984
M16 194.75 64.011229
M17 142.5 46.837485
M18 123.5 40.592487
M19 104.5 34.347489
M20 147.25 48.398734
M21 204.25 67.133728
M22 47.5 15.612495
M23 57 18.734994
M24 2166 711.92977
M25 80.75 26.541241
M26 9.5 3.122499 ;
table Load(i,pq) “loads based on buses!!”
P_kw Q_kvar
1 0 0
2 0 0
3 0 0
4 6413.46 2108
5 0 0
6 903.06 511.79
7 0 0
8 3187.25 1047.6
9 0 0
10 576 507.98
11 0 0
12 0 0
13 19 0
14 346.75 113.97
15 0 0
16 0 0
17 0 0
18 0 0
19 0 0
20 0 0
21 0 0
22 47.5 15.61
23 9.5 3.122499
24 0 0
25 289.75 95.236219
26 0 0
27 152 49.959984
28 0 0
29 0 0
30 194.75 64.011229
31 517.75 170.176195
32 0 0
33 0 0
34 204.25 67.133728
35 0 0
36 80.75 26.541241
37 104.5 34.347489
38 0 0
39 0 0
40 0 0
41 2166 711.92977 ;
table Line_Data(l,lid) “Table 7”
from to L R X Y Teta_deg Teta_rad
L1 1 2 5.7 0.169111 0.418206 0.388909452 -67.98294683 -1.186526257
L2 2 3 1.01 0.169111 0.418206 2.194835521 -67.98294683 -1.186526257
L3 2 4 0.4 0.169111 0.418206 5.541959691 -67.98294683 -1.186526257
L4 4 5 0.38 0.169111 0.418206 5.83364178 -67.98294683 -1.186526257
L5 5 6 0.13 0.169111 0.418206 17.05218367 -67.98294683 -1.186526257
L6 5 7 0.17 0.169111 0.418206 13.03990516 -67.98294683 -1.186526257
L7 7 9 0.26 0.169111 0.418206 8.526091833 -67.98294683 -1.186526257
L8 9 10 0.14 0.169111 0.418206 15.83417055 -67.98294683 -1.186526257
L9 9 11 0.38 0.169111 0.418206 5.83364178 -67.98294683 -1.186526257
L10 11 12 0.56 0.169111 0.418206 3.958542637 -67.98294683 -1.186526257
L11 12 13 0.3 0.169111 0.418206 7.389279589 -67.98294683 -1.186526257
L12 12 14 3.33 0.169111 0.418206 0.665700864 -67.98294683 -1.186526257
L13 14 15 1.03 0.169111 0.418206 2.152217356 -67.98294683 -1.186526257
L14 16 17 1.08 0.169111 0.418206 2.052577663 -67.98294683 -1.186526257
L15 17 18 1.64 0.169111 0.418206 1.351697486 -67.98294683 -1.186526257
L16 18 19 0.47 0.169111 0.418206 4.71656144 -67.98294683 -1.186526257
L17 19 20 0.47 0.348124 0.468482 3.645339112 -53.38435157 -0.931732704
L18 21 22 0.96 1.391924 0.478811 0.707665679 -18.98281748 -0.331312666
L19 19 23 0.19 0.348124 0.468482 9.017417804 -53.38435157 -0.931732704
L20 23 24 1.94 0.348124 0.468482 0.883149166 -53.38435157 -0.931732704
L22 24 25 2.45 0.348124 0.468482 0.699309952 -53.38435157 -0.931732704
L23 24 26 1.63 0.348124 0.468482 1.051110051 -53.38435157 -0.931732704
L24+L26 26 27 1.2 0.552276 0.485241 1.133532349 -41.30320147 -0.720876857
L27 26 28 2.12 0.348124 0.468482 0.808164803 -53.38435157 -0.931732704
L28 28 29 0.73 0.552276 0.485241 1.863340848 -41.30320147 -0.720876857
L29+L30 29 30 0.75 0.552276 0.485241 1.813651759 -41.30320147 -0.720876857
L31 28 31 2.54 0.348124 0.468482 0.674531253 -53.38435157 -0.931732704
L32 23 32 0.36 0.276519 0.45858 5.187277059 -58.91045729 -1.028181444
L33 32 33 0.26 0.276519 0.45858 7.18238362 -58.91045729 -1.028181444
L34 33 34 3.58 0.552276 0.485241 0.379954977 -41.30320147 -0.720876857
L35 33 35 0.77 0.276519 0.45858 2.425220443 -58.91045729 -1.028181444
L36 35 36 2.08 0.348124 0.468482 0.823706434 -53.38435157 -0.931732704
L37 35 37 4.51 0.276519 0.45858 0.414062027 -58.91045729 -1.028181444
L38 37 38 3.24 0.169111 0.418206 0.684192554 -67.98294683 -1.186526257
L39 38 39 0.3 0.169111 0.418206 7.389279589 -67.98294683 -1.186526257
L40 39 40 0.5 0.169111 0.418206 4.433567753 -67.98294683 -1.186526257 ;
*T1 has 0.01i p.u. equivalent ampedance!!!
*T3 has 0.01i p.u. equivalent ampedance!!!
*T4 has 0.01i p.u. equivalent ampedance!!!
*Line 15-16 is the same as 16-17
table Ybus_abs(i,j) “Ybus abs value”
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
1 0.38890944 0.388909452 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0.388909452 8.125704988 2.194835521 5.541959691 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 2.194835521 2.194835521 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 5.541959691 0 11.37560147 5.83364178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 5.83364178 35.92508326 17.05218367 13.03990516 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 17.05218367 17.05218367 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 13.03990516 0 120.26529 100 8.526091833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 100 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 8.526091833 0 30.19390416 15.83417055 5.83364178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 15.83417055 15.83417055 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 5.83364178 0 9.792184417 3.958542637 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 3.958542637 12.0136142 7.389279589 0.665700864 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 7.389279589 7.389279589 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0.665700864 0 2.817944759 2.152217356 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 2.152217356 4.204795019 2.052577663 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.052577663 4.105155327 2.052577663 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.052577663 3.404275149 1.351697486 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.351697486 6.068258925 4.71656144 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.71656144 17.26794956 3.645339112 0 0 9.017417804 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.645339112 102.9489103 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 100.2324265 0.707665679 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.707665679 0.707665679 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9.017417804 0 0 0 13.86623489 0.883149166 0 0 0 0 0 0 0 5.187277059 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.883149166 2.63356917 0.699309952 1.051110051 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.699309952 0.699309952 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.051110051 0 2.977169733 1.133532349 0.808164803 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.133532349 1.217457549 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.808164803 0 3.343746272 1.863340848 0 0.674531253 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.863340848 3.676992606 1.813651759 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.813651759 1.813651758 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.674531253 0 0 0.674531253 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.187277059 0 0 0 0 0 0 0 0 12.36966068 7.18238362 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7.18238362 9.970421509 0.379954977 2.425220443 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.379954977 0.379954977 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.425220443 0 3.417572921 0.823706434 0.414062027 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.823706434 0.823706434 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.414062027 0 1.095022738 0.684192554 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.684192554 8.073472143 7.389279589 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7.389279589 11.82284734 4.433567753 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.433567753 104.1235041 100
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 100 ;
*T1 has 0.01i p.u. equivalent ampedance!!!
*T3 has 0.01i p.u. equivalent ampedance!!!
*T4 has 0.01i p.u. equivalent ampedance!!!
*Line 15-16 is the same as 16-17
table Ybus_angle(i,j) “Ybus angle value in radians”
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
1 -1.18652641 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1.955066396 -1.18652635 1.955066396 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1.955066396 -1.18652625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 1.955066396 0 -1.18652625 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 1.955066396 -1.16853354 1.955066396 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 1.955066396 -1.18652625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 1.955066396 0 -1.50352158 1.570796327 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 1.570796327 -1.57079633 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 1.955066396 0 -1.18652626 1.955066396 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 1.955066396 0 -1.18652626 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652319 1.955066396 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 1.955066396 0 -1.18652245 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.00062619 2.209859949 0 0 2.209859949 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 -1.54967514 1.570796327 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.570796327 -1.56411999 2.810279987 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.810279987 -0.33131267 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 0 0 0 -0.88955796 2.209859949 0 0 0 0 0 0 0 2.113411210 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 -0.9317327 2.209859949 2.209859949 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 -0.9317327 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 0 -0.8519601 2.420715796 2.209859949 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.420715796 -0.63200085 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 0 -0.81878728 2.420715796 0 2.209859949 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.420715796 -0.72087686 2.420715796 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.420715796 -0.72087686 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 0 0 -0.9317327 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.113411210 0 0 0 0 0 0 0 0 -1.02818144 2.11341121 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.11341121 -1.01665381 2.420715796 2.113411210 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.420715796 -0.72087686 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.113411210 0 -0.92922816 2.209859949 2.113411210 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.209859949 -0.9317327 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.113411210 0 -1.12686569 1.955066396 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.18652626 1.955066396 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.955066396 -1.55483319 1.570796327
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.570796327 -1.57079633 ;
*T1 has 0.01i p.u. equivalent ampedance!!!
*T3 has 0.01i p.u. equivalent ampedance!!!
*T4 has 0.01i p.u. equivalent ampedance!!!
*Line 15-16 is the same as 16-17
table G_matrix(i,j) “G value”
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
1 0.145795303 0.145795362 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0.145795362 3.046184213 0.82280551 2.077583915 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0.82280551 0.822805526 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2.077583915 0 4.264514431 2.186930437 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 2.186930437 14.06472428 6.392565893 4.888432742 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 6.392565893 6.392566013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 4.888432742 0 8.084715287 0.0 3.196282946 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0.0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 3.196282946 0 11.31916736 5.935954044 2.186930437 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 5.935954044 5.935954008 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 2.186930437 0 3.670918925 1.483988511 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 1.483988511 4.503728348 2.770111887 0.249559629 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 2.770111887 2.77011187 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0.249559629 0 1.05640823 0.806828704 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0.806828704 1.576304219 0.769475523 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.769475523 1.538951039 0.769475523 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.769475523 1.2762033 0.506727784 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.506727784 2.274884294 1.768156523 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.768156523 9.320812296 2.174241061 0 0 5.378385782 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.174241061 2.1742415 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.669180466 0.669180107 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.669180107 0.669180107 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.378385782 0 0 0 8.732337157 0.526749122 0 0 0 0 0 0 0 2.67859077 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.526749122 1.570776843 0.417099305 0.626928404 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.417099305 0.417099308 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.626928404 0 1.96049394 0.851540393 0.48202514 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.851540393 0.982302095 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.48202514 0 2.284137757 1.399769891 0 0.402320196 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.399769891 2.762257052 1.36246463 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.36246463 1.362464627 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.402320196 0 0 0.402320199 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.67859077 0 0 0 0 0 0 0 0 6.387408798 3.708817989 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.708817989 5.246578686 0.285432533 1.252328152 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.285432533 0.285432533 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.252328152 0 2.045255149 0.491294855 0.213812123 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.491294855 0.491294858 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.213812123 0 0.470303961 0.256491841 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.256491841 3.02660371 2.770111887 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.770111887 4.432178991 1.662067132 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.662067132 1.662067149 0.0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.0 ;
table matrix_C(g,c) “Table 8”
wind_power_state load_state
1 1 1
2 1 0.853
3 1 0.774
4 1 0.713
5 1 0.65
6 1 0.585
7 1 0.51
8 1 0.451
9 1 0.406
10 1 0.351
11 0.949696 1
12 0.949696 0.853
13 0.949696 0.774
14 0.949696 0.713
15 0.949696 0.65
16 0.949696 0.585
17 0.949696 0.51
18 0.949696 0.451
19 0.949696 0.406
20 0.949696 0.351
21 0.849728 1
22 0.849728 0.853
23 0.849728 0.774
24 0.849728 0.713
25 0.849728 0.65
26 0.849728 0.585
27 0.849728 0.51
28 0.849728 0.451
29 0.849728 0.406
30 0.849728 0.351
31 0.74976 1
32 0.74976 0.853
33 0.74976 0.774
34 0.74976 0.713
35 0.74976 0.65
36 0.74976 0.585
37 0.74976 0.51
38 0.74976 0.451
39 0.74976 0.406
40 0.74976 0.351
41 0.649792 1
42 0.649792 0.853
43 0.649792 0.774
44 0.649792 0.713
45 0.649792 0.65
46 0.649792 0.585
47 0.649792 0.51
48 0.649792 0.451
49 0.649792 0.406
50 0.649792 0.351
51 0.549824 1
52 0.549824 0.853
53 0.549824 0.774
54 0.549824 0.713
55 0.549824 0.65
56 0.549824 0.585
57 0.549824 0.51
58 0.549824 0.451
59 0.549824 0.406
60 0.549824 0.351
61 0.449856 1
62 0.449856 0.853
63 0.449856 0.774
64 0.449856 0.713
65 0.449856 0.65
66 0.449856 0.585
67 0.449856 0.51
68 0.449856 0.451
69 0.449856 0.406
70 0.449856 0.351
71 0.349888 1
72 0.349888 0.853
73 0.349888 0.774
74 0.349888 0.713
75 0.349888 0.65
76 0.349888 0.585
77 0.349888 0.51
78 0.349888 0.451
79 0.349888 0.406
80 0.349888 0.351
81 0.199936 1
82 0.199936 0.853
83 0.199936 0.774
84 0.199936 0.713
85 0.199936 0.65
86 0.199936 0.585
87 0.199936 0.51
88 0.199936 0.451
89 0.199936 0.406
90 0.199936 0.351
91 0.149952 1
92 0.149952 0.853
93 0.149952 0.774
94 0.149952 0.713
95 0.149952 0.65
96 0.149952 0.585
97 0.149952 0.51
98 0.149952 0.451
99 0.149952 0.406
100 0.149952 0.351
101 0.049984 1
102 0.049984 0.853
103 0.049984 0.774
104 0.049984 0.713
105 0.049984 0.65
106 0.049984 0.585
107 0.049984 0.51
108 0.049984 0.451
109 0.049984 0.406
110 0.049984 0.351
111 0 1
112 0 0.853
113 0 0.774
114 0 0.713
115 0 0.65
116 0 0.585
117 0 0.51
118 0 0.451
119 0 0.406
120 0 0.351 ;
table P_C(g,pc) “Table 9”
P_c
1 0.000761
2 0.004338
3 0.008348
4 0.012587
5 0.012587
6 0.012405
7 0.012595
8 0.00694
9 0.0036
10 0.002694
11 0.000252
12 0.001439
13 0.00277
14 0.004176
15 0.004176
16 0.004115
17 0.004179
18 0.002303
19 0.001194
20 0.000894
21 0.000331
22 0.001885
23 0.003627
24 0.005468
25 0.005468
26 0.005389
27 0.005472
28 0.003015
29 0.001564
30 0.00117
31 0.000457
32 0.002604
33 0.005012
34 0.007556
35 0.007556
36 0.007446
37 0.007561
38 0.004166
39 0.002161
40 0.001617
41 0.000483
42 0.002756
43 0.005304
44 0.007997
45 0.007997
46 0.007881
47 0.008002
48 0.004409
49 0.002287
50 0.001712
51 0.000783
52 0.004462
53 0.008587
54 0.012947
55 0.012947
56 0.012759
57 0.012954
58 0.007139
59 0.003702
60 0.002771
61 0.000923
62 0.005263
63 0.01013
64 0.015273
65 0.015273
66 0.015051
67 0.015282
68 0.008421
69 0.004368
70 0.003269
71 0.001136
72 0.006474
73 0.01246
74 0.018787
75 0.018787
76 0.018514
77 0.018798
78 0.010359
79 0.005372
80 0.004021
81 0.00105
82 0.005984
83 0.011516
84 0.017364
85 0.017364
86 0.017112
87 0.017374
88 0.009574
89 0.004966
90 0.003716
91 0.001137
92 0.006478
93 0.012468
94 0.018799
95 0.018799
96 0.018526
97 0.01881
98 0.010365
99 0.005376
100 0.004023
101 0.000648
102 0.003694
103 0.007109
104 0.010718
105 0.010718
106 0.010562
107 0.010724
108 0.00591
109 0.003065
110 0.002294
111 0.002039
112 0.011621
113 0.022365
114 0.033721
115 0.033721
116 0.033232
117 0.033741
118 0.018593
119 0.009643
120 0.007217 ;
*Parameter value setting
\
- Constraints Declaration
equations
Obj “objective function definition”
PowerFlow_P(i,g) “active power flow equation for bus i in state g”
PowerFlow_Q(i,g) “reactive power flow equation for bus i in state g”
PowerLoss(g) “power loss equation”
BranchCurrent(g,i,j) “branch current equation”
BranchCurrentLimit(g,i,j)
Bus_Penetration(i) “Sum of Power of DG in bus i”
Sys_Penetration “Penetration of DG in system”
Discret_DG_Power(i,n)“Discret power for each kind of DG”;
\ - Constraints Definition
*Objective Function ok
Obj… Z =e= sum((g),P_loss(g)*P_C(g,‘P_c’))*8760;
*Cons 1-1 P_Gg1 Rmoved !!! and don’t use power flow eq. for bus 1 ok
PowerFlow_P(i,g)$(ord(i)1)… matrix_C(g,‘wind_power_state’)sum((n),P_DG(i,n)) - matrix_C(g,‘load_state’)(Load(i,‘P_kw’)/Sbase) =e=
sum((j),V(g,i)V(g,j)(Ybus_abs(i,j)Zbase) cos(Ybus_angle(i,j)+Delta(g,j)-Delta(g,i))) ;
Cons 1-2 Q_Gg1 Rmoved !!! and don’t use power flow eq. for bus 1 ok
PowerFlow_Q(i,g)$(ord(i)1)… - matrix_C(g,‘load_state’)(Load(i,‘Q_kvar’)/Sbase) =e=
- sum((j),V(g,i)V(g,j)(Ybus_abs(i,j)Zbase) sin(Ybus_angle(i,j)+Delta(g,j)-Delta(g,i))) ;
Cons 2 not ok G converted to Y !!!
PowerLoss(g)… P_loss(g) =e= 0.5sum((i,j),(G_matrix(i,j)Zbase)(power(V(g,i),2) + power(V(g,j),2)
- 2*V(g,i)V(g,j) cos(Delta(g,j)-Delta(g,i)))) ;
*Cons 3 ok
BranchCurrent(g,i,j)… Igij(g,i,j) =e= (Ybus_abs(i,j)*Zbase)*sqrt(abs(power(V(g,i),2) + power(V(g,j),2)
- 2*V(g,i)V(g,j) cos(Delta(g,j)-Delta(g,i)))) ;
*Cons 4-1 ok
V.fx(g,‘1’)=1.025;
*Cons 4-2 ok
Delta.fx(g,‘1’)=0;
*Cons 5 ok
*Cons 6 ok
BranchCurrentLimit(g,i,j)… abs(Igij(g,i,j))=l=1;
*Cons 7 ok
Discret_DG_Power(i,n)$(Candidate(i))… P_DG(i,n) =e= N_DG(i,n)*Wind_Turbine(n,‘P_r’)/Sbase;
Cons 8 0.2 assumed as max peneteration in each bus !!!
Bus_Penetration(i)$(Candidate(i))… sum((n),P_DG(i,n)) =l= Load(i,‘P_kw’)/Sbase;
CONS 9
Sys_Penetration… sum((i,n),CFP_DG(i,n))=l=0.3sum((i),(Load(i,‘P_kw’)/Sbase));
model AJ / all /;
AJ.reslim = 12000000;
AJ.iterlim = 10000000;
*AJ.optfile = 1 ;
*option minlp = sbb ;
*minlp=lindoglobal
Solve AJ using rminlp Minimizing Z ;
\
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