I'm trying to model the IEEE 6-bus system to minimize the cost, the code is working well but I have a problem in modeling start-up cost equation which can be found in equation number 12 and 13 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1664974
the problem in this line const5(gen,t).. suc(Gen,t)=e= GD (Gen , 'Scost')*(sum(t,u(Gen,t)));
* 6 bus system with 24 hours demand
set bus number of buses /1*6/
Gen number of generators /g1*g3/
t number of hours /t1*t24/
k /1*100/
nl number of segment /1*3/
slack(bus) / 1 /
j start up cost intervals /j1*j8/
n /1*24/;
alias(t,tt);
Scalar
Sbase / 100 /
VOLL / 10000 /
VOLW / 50 /;
Alias (bus,node);
Table GD(Gen,*) 'generating units characteristics'
Pmax Pmin a b c Scost Dcost fuelc MU MD RU RD
g1 220 100 0.05 10 100 100 10 1 4 4 55 55
g2 100 10 0.001 40.66 162 200 20 1 2 3 50 50
g3 20 10 0.006 22.06 171 0 0 1 20 20 ;
Set GB(bus,Gen) 'connectivity index of each generating unit to each bus'
/
1.g1
2.g2
6.g3/;
Table branch(bus,node,*) line information
x limit
1.2 0.170 200
1.4 0.258 100
2.3 0.037 100
2.4 0.197 100
3.6 0.018 100
4.5 0.037 100
5.6 0.140 100;
Table WD(t,*) hourly load demand
d
t1 175
t2 165
t3 158
t4 154
t5 155
t6 160
t7 168
t8 177
t9 186
t10 206
t11 228
t12 236
t13 242
t14 243
t15 248
t16 255
t17 256
t18 246
t19 245
t20 237
t21 236
t22 232
t23 208
t24 195;
Table BusData(bus,*) percent of hourly load of each bus
pd
3 0.20
4 0.40
5 0.40 ;
branch(bus,node,'x')$(branch(bus,node,'x')=0) = branch(node,bus,'x');
branch(bus,node,'Limit')$(branch(bus,node,'Limit')=0) = branch(node,bus,'Limit');
branch(bus,node,'bij')$branch(bus,node,'Limit') = 1/branch(bus,node,'x');
branch(bus,node,'z')$branch(bus,node,'Limit') = branch(bus,node,'x');
branch(node,bus,'z') = branch(bus,node,'z');
binary variable u(Gen,t) status of unit i in period t;
Variable OF, Pg(Gen,t),pk(Gen,t,k);
positive variable suc(Gen,t);
Parameter conex(bus,node);
conex(bus,node)$(branch(bus,node,'limit') and branch(node,bus,'limit')) = 1;
conex(bus,node)$(conex(node,bus)) = 1;
Parameter data (k, Gen ,*) ;
data(k,Gen,'DP')=(GD(Gen ,"Pmax")-GD( Gen ,"Pmin")) / card ( k ) ;
data (k , Gen , 'Pini')= ( ord (k)-1)*data( k , Gen , 'DP' ) + GD( Gen , "Pmin" ) ;
data ( k , Gen , 'Pfin' ) = data( k , Gen , 'Pini' ) + data( k , Gen , 'DP' ) ;
data (k, Gen , 'Cini')=GD (Gen ,"a")*( data (k , Gen , 'Pini' ))*( data (k , Gen , 'Pini' ))
+GD (Gen ,"b")*data (k, Gen , 'Pini')+GD (Gen ,"c") ;
data (k, Gen , 'Cfin')=GD (Gen ,"a")*(data (k , Gen , 'Pfin' ))*(data(k , Gen , 'Pfin' ))
+GD (Gen ,"b")*data (k, Gen , 'Pfin')+GD (Gen ,"c") ;
data (k , Gen , 's') =( data (k , Gen , 'Cfin')-data( k , Gen , 'Cini' ) ) / data ( k , Gen , 'DP' ) ;
Pk.up ( Gen , t , k ) = data ( k , Gen , 'DP' ) ;
Pk.lo ( Gen , t , k ) =0;
Equation const1, const2, const3,const4,const5;
const1.. OF =e=sum ((bus,Gen,t)$GB(bus,Gen) , GD (Gen , 'a')*GD( Gen ,"Pmin")*GD( Gen ,"Pmin")
+GD (Gen , 'b')*GD ( Gen ,"Pmin") +GD ( Gen , 'c' )
+ sum (k, data (k, Gen , 's')*pk ( Gen , t , k) ) ) ;
*const1.. OF =e= sum((bus,Gen,t)$GB(bus,Gen), Pg(Gen,t)*Pg(Gen,t)*GD(Gen,'a')*Sbase+Pg(Gen,t)*GD(Gen,'b')*Sbase+GD(Gen,'c')) ;
const2(Gen,t).. pg(Gen,t+1) - pg(Gen,t) =l= GD(Gen,'RU')/Sbase;
const3(Gen,t).. pg(Gen,t-1) - pg(Gen,t) =l= GD(Gen,'RD')/Sbase;
const4(bus,t).. sum(Gen,pg(Gen,t)) =g= WD(t,'d')*BusData(bus,'pd')/Sbase;
const5(gen,t).. suc(Gen,t)=e= GD (Gen , 'Scost')*(sum(t,u(Gen,t)));
Pg.lo(Gen,t) = GD(Gen,'Pmin')/Sbase;
Pg.up(Gen,t) = GD(Gen,'Pmax')/Sbase;
Model loadflow /all/;
Option LP = Cplex;
solve loadflow us mip min OF;
