PBUC : Price based Unit commitment

Reference

  • Alireza Soroudi, Power System Optimization Modelling in GAMS, Model PBUC (Gcode5.5) in chapter Unit commitment, 2017

Category : GAMS PSOPT library


Mainfile : PBUC.gms

$title Price based Unit commitment

$onText
For more details please refer to Chapter 5 (Gcode5.5), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: MIP
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Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
$offText

Set
   t 'time'               / t1*t24   /
   i 'generators indices' / g1*g10   /
   k 'cost segments'      / sg1*sg20 /
   char                   / ch1*ch2  /;

Alias (t,h);

Table gendata(i,*) 'generator cost characteristics and limits'
        a       b     c    CostsD  costst  RU   RD   UT  DT  SD   SU   Pmin  Pmax  U0  Uini  S0
   g1   0.0148  12.1  82   42.6    42.6    40   40   3   2   90   110  80    200   1   0     1
   g2   0.0289  12.6  49   50.6    50.6    64   64   4   2   130  140  120   320   2   0     0
   g3   0.0135  13.2  100  57.1    57.1    30   30   3   2   70   80   50    150   3   0     3
   g4   0.0127  13.9  105  47.1    47.9    104  104  5   3   240  250  250   520   1   1     0
   g5   0.0261  13.5  72   56.6    56.9    56   56   4   2   110  130  80    280   1   1     0
   g6   0.0212  15.4  29   141.5  141.5    30   30   3   2   60   80   50    150   0   0     0
   g7   0.0382  14.0  32   113.5  113.5    24   24   3   2   50   60   30    120   0   1     0
   g8   0.0393  13.5  40   42.6    42.6    22   22   3   2   45   55   30    110   0   0     0
   g9   0.0396  15.0  25   50.6    50.6    16   16   0   0   35   45   20    80    0   0     0
   g10  0.0510  14.3  15   57.1    57.1    12   12   0   0   30   40   20    60    0   0     0;
* -----------------------------------------------------

Parameter data(k,i,*);
data(k,i,'DP')       =(gendata(i,"Pmax") - gendata(i,"Pmin"))/card(k);
data(k,i,'Pini')     =(ord(k) - 1)*data(k,i,'DP') + gendata(i,"Pmin");
data(k,i,'Pfin')     = data(k,i,'Pini') + data(k,i,'DP');
data(k,i,'Cini')     = gendata(i,"a")*power(data(k,i,'Pini'),2)
                     + gendata(i,"b")*data(k,i,'Pini') + gendata(i,"c");
data(k,i,'Cfin')     = gendata(i,"a")*power(data(k,i,'Pfin'),2)
                     + gendata(i,"b")*data(k,i,'Pfin') + gendata(i,"c");
data(k,i,'s')        =(data(k,i,'Cfin') - data(k,i,'Cini'))/data(k,i,'DP');
gendata(i,'Mincost') = gendata(i,'a')*power(gendata(i,"Pmin"),2)
                     + gendata(i,'b')*gendata(i,"Pmin") + gendata(i,'c');
* -----------------------------------------------------

Table dataLP(t,*)
        lambda  load
   t1   14.72   883
   t2   15.62   915
   t3   14.72   1010
   t4   14.73   1149
   t5   14.83   1236
   t6   15.72   1331
   t7   20.21   1397
   t8   23.40   1419
   t9   23.86   1455
   t10  21.27   1455
   t11  19.83   1441
   t12  17.38   1419
   t13  17.96   1397
   t14  17.75   1339
   t15  18.51   1368
   t16  17.65   1339
   t17  23.45   1236
   t18  18.38   1105
   t19  18.54   1038
   t20  18.52   959
   t21  20.59   922
   t22  20.52   885
   t23  20.50   915
   t24  15.62   834;

Parameter unit(i,char);
unit(i,'ch1') = 24;
unit(i,'ch2') =(gendata(i,'UT') - gendata(i,'U0'))*gendata(i,'Uini');

Parameter unit2(i,char);
unit2(i,'ch1')  = 24;
unit2(i,'ch2')  =(gendata(i,'DT') - gendata(i,'S0'))*(1 - gendata(i,'Uini'));
gendata(i,'Lj') = smin(char,unit(i,char));
gendata(i,'Fj') = smin(char,unit2(i,char));

Variable costThermal, OF;
Positive Variable pu(i,t), p(i,t), StC(i,t), SDC(i,t), Pk(i,t,k);
Binary   Variable u(i,t), y(i,t), z(i,t);

p.up(i,t)    = gendata(i,"Pmax");
p.lo(i,t)    = 0;
Pk.up(i,t,k) = data(k,i,'DP');
Pk.lo(i,t,k) = 0;
p.up(i,t)    = gendata(i,"Pmax");
pu.up(i,h)   = gendata(i,"Pmax");

Equation
   Uptime1, Uptime2, Uptime3, Dntime1, Dntime2, Dntime3, Ramp1, Ramp2, Ramp3, Ramp4,
   startc, shtdnc, genconst1, Genconst2, Genconst3, Genconst4, balance, benefitcalc;

Uptime1(i)$(gendata(i,"Lj")>0)..
   sum(t$(ord(t)<(gendata(i,"Lj")+1)), 1-U(i,t)) =e= 0;

Uptime2(i)$(gendata(i,"UT")>1)..
   sum(t$(ord(t)>24-gendata(i,"UT")+1), U(i,t) - y(i,t)) =g= 0;

Uptime3(i,t)$(ord(t)>gendata(i,"Lj") and ord(t)<24-gendata(i,"UT")+2 and not(gendata(i,"Lj")>24-gendata(i,"UT")))..
   sum(h$((ord(h)>ord(t)-1) and (ord(h)<ord(t) + gendata(i,"UT"))), U(i,h)) =g= gendata(i,"UT")*y(i,t);

Dntime1(i)$(gendata(i,"Fj")>0)..
   sum(t$(ord(t)<(gendata(i,"Fj")+1)), U(i,t)) =e= 0;

Dntime2(i)$(gendata(i,"DT")>1)..
   sum(t$(ord(t)>24-gendata(i,"DT")+1), 1 - U(i,t) - z(i,t)) =g= 0;

Dntime3(i,t)$(ord(t)>gendata(i,"Fj") and ord(t)<24-gendata(i,"DT")+2 and not(gendata(i,"Fj")>24-gendata(i,"DT")))..
   sum(h$((ord(h)>ord(t)-1) and (ord(h)<ord(t)+gendata(i,"DT"))),1-U(i,h)) =g= gendata(i,"DT")*z(i,t);

startc(i,t).. StC(i,t) =g= gendata(i,"costst")*y(i,t);
shtdnc(i,t).. SDC(i,t) =g= gendata(i,"CostsD")*z(i,t);

genconst1(i,h)..
   p(i,h)      =e= u(i,h)*gendata(i,"Pmin") + sum(k, Pk(i,h,k));

Genconst2(i,h)$(ord(h)>0)..
   U(i,h)      =e= U(i,h-1)$(ord(h)>1) + gendata(i,"Uini")$(ord(h)=1) + y(i,h) - z(i,h);

Genconst3(i,t,k)..
   Pk(i,t,k)   =l= U(i,t)*data(k,i,'DP');

Genconst4..
   costThermal =e= sum((i,t), StC(i,t)+SDC(i,t))
                +  sum((t,i), u(i,t)*gendata(i,'Mincost') + sum(k, data(k,i,'s')*pk(i,t,k)));

Ramp1(i,t)..             p(i,t-1) - p(i,t) =l= U(i,t)*gendata(i,'RD') + z(i,t)*gendata(i,"SD");
Ramp2(i,t)..             p(i,t)  =l= pu(i,t);
Ramp3(i,t)$(ord(t)<24).. pu(i,t) =l= (u(i,t) - z(i,t+1))*gendata(i,"Pmax") + z(i,t+1)*gendata(i,"SD");
Ramp4(i,t)$(ord(t)>1)..  pu(i,t) =l= p(i,t-1) + U(i,t-1)*gendata(i,'RU') + y(i,t)*gendata(i,"SU");

balance(t)..  sum(i, p(i,t)) =l= dataLP(t,'load');
benefitcalc.. OF =e= sum((i,t), dataLP(t,'lambda')*p(i,t)) - costThermal

Model UCLP / all /;
option optCr = 0.0;
solve UCLP maximizing OF using mip;
display p.l;

Parameter report(*);
report('FC') = costThermal.l - sum((i,t), StC.l(i,t) + SDC.l(i,t));
report('SC') = sum((i,t), StC.l(i,t));
report('SD') = sum((i,t), SDC.l(i,t));
report('OF') = OF.l;
display report;

$ifI %system.fileSys%==Unix $exit
$call MSAppAvail Excel
$ifThen not errorLevel 1
   execute_unload "UC.gdx" P.l
   execute 'gdxxrw.exe UC.gdx Var=P rng=PB!a1'
$endIf