gtm.gms : International Gas Trade Model
The Gas Trade Model (GTM) models interrelated gas markets.
Prices may be free to move as to equilibrate supplies and
demand. Disequilibria can be introduced with controls over
prices and/or quantities traded.
Reference:
- Manne, A S, and Beltramo, M A, GTM: An International Gas Trade Model ,International Energy Program Report. Stanford University, 1984.
Small Model of Type: NLP
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$Title An International Gas Trade Model (GTM,SEQ=53)
$Ontext
The Gas Trade Model (GTM) models interrelated gas markets.
Prices may be free to move as to equilibrate supplies and
demand. Disequilibria can be introduced with controls over
prices and/or quantities traded.
Manne, A S, and Beltramo, M A, GTM: An International Gas Trade Model ,
International Energy Program Report. Stanford University, 1984.
$Offtext
Sets i supply regions / mexico, alberta-bc, atlantic, appalacia, us-gulf, mid-cont, permian-b, rockies, pacific
alaska /
j demand regions / mexico, west-can, ont-quebec, atlantic, new-engl, ny-nj, mid-atl, south-atl, midwest
south-west, central, n-central, west, n-west /
jfx(j) regions with fixed demand / mexico, west-can, ont-quebec, atlantic /
ij(i,j) feasible links
Table sdat(i,*) supply data
ref-p1 ref-q1 ref-p2 ref-q2 limit
* ($/mcf) (tcf) ($/mcf) (tcf) (tcf)
mexico 2.0 .5 2.5
alberta-bc 3.0 1.6 3.75
atlantic .25 .03 .3
appalacia 3.5 .58 7.0 .65 .72
us-gulf 3.5 7.88 7.0 8.82 9.75
mid-cont 3.5 2.07 7.0 2.31 2.55
permian-b 3.5 1.39 7.0 1.55 1.72
rockies 3.5 1.16 7.0 1.30 1.44
pacific 3.5 .42 7.0 .47 .52
alaska 2.0 .80 2.0 .1 inf
Table ddat(j,*) demand data
ref-p ref-q elas tax ex-dem
* ($/mcf) (tcf) ($/mcf) (tcf)
mexico 1.0 2.2 -.5
west-can 3.0 1.47 -.5
ont-quebec 3.5 1.38 -.5
atlantic 3.5 .20 -.5
new-engl 9.37 .76 -.60
ny-nj 8.33 1.18 -.66
mid-atl 8.26 .89 -.65
south-atl 8.07 1.62 -.89
midwest 8.01 2.96 -.65
south-west 7.29 6.04 -.84
central 7.79 1.17 -.67
n-central 8.06 1.51 -.54
west 8.18 2.10 -.43
n-west 9.39 .36 -.57
$Eject
Parameters supa(i) supply constant a
supb(i) supply constant b
supc(i) supply capacity
dema(j) demand constant a
demb(j) demand constant b ;
supc(i) = sdat(i,"limit");
supb(i) = ((sdat(i,"ref-p1")-sdat(i,"ref-p2"))/(1/(supc(i)-sdat(i,"ref-q1"))-1/(supc(i)-sdat(i,"ref-q2"))))
$(supc(i) ne inf);
supa(i) = sdat(i,"ref-p1") - supb(i)/(supc(i)-sdat(i,"ref-q1"));
* we rely on supa(i) evaluating to exactly zero in some cases
supa(i) = round(supa(i),4);
supc(i)$(supc(i) eq inf) = 100;
sdat(i,"sup-a") = supa(i); sdat(i,"sup-b") = supb(i); display sdat;
demb(j) = 1/ddat(j,"elas") + 1;
dema(j) = ddat(j,"ref-p")/demb(j)/ddat(j,"ref-q")**(demb(j)-1);
ddat(j,"dem-a") = dema(j); ddat(j,"dem-b") = demb(j); display ddat;
Table utc(i,j) unit transport cost ($ per mcf)
mexico west-can ont-quebec atlantic new-engl ny-nj mid-atl south-atl midwest south-west
mexico .25 2.29 2.22 2.03 1.96 1.25
alberta-bc .40 .90 1.15 1.10 1.10 1.55 .80 1.25
atlantic 1.50
appalacia .72 .46
us-gulf 2.12 1.08 1.01 .82 .75 .04
mid-cont .86 .14
permian-b .83 .77 .05
rockies .53
alaska 6.0
+ central n-central west n-west
mexico 2.13
alberta-bc .80 .65 .70 .65
us-gulf .54
mid-cont .64
permian-b .55 .94
rockies .31 .58 .70 1.91
pacific .43
$Eject
Table pc(i,j) pipeline capacities (tcf)
mexico west-can ont-quebec atlantic new-engl ny-nj mid-atl south-atl midwest south-west
mexico inf .067 .067 .067 .067
alberta-bc inf inf .30 .150 .10 inf
atlantic inf inf
appalacia .34 .35
us-gulf inf 1.390 1.060 2.0 2.62 3.73
mid-cont .62 2.30
permian-b .12 1.45
rockies .48
alaska .80
+ central n-central west n-west
mexico .033
alberta-bc inf inf inf inf
mid-cont 1.03
permian-b 1.46
rockies .14 inf .10 inf
pacific .48
Sets check1(i,j) supply links with zero cost and non-zero capacity
check2(i,j) supply links with nonzero cost but zero capacity ;
check1(i,j) = yes$(utc(i,j) eq 0 and pc(i,j) ne 0);
check2(i,j) = yes$(utc(i,j) ne 0 and pc(i,j) eq 0);
ij(i,j) = yes$pc(i,j);
Display check1, check2;
Variables x(i,j) shipment of natural gas (tcf)
s(i) regional supply (tcf)
d(j) regional demand (tcf)
benefit consumers benefits minus cost
Positive Variables x, s, d;
Equations sb(i) supply balance (tcf)
db(j) demand balance (tcf)
bdef benefit definition ;
sb(i).. sum(j$ij(i,j), x(i,j)) =l= s(i) ;
db(j).. sum(i$ij(i,j), x(i,j)) =g= d(j) ;
bdef.. benefit =e= sum(j, dema(j)*d(j)**demb(j)) - sum(i, supa(i)*s(i) - supb(i)*log((supc(i)-s(i))/supc(i)))
- sum((i,j)$ij(i,j), utc(i,j)*x(i,j));
x.up(i,j) = pc(i,j); d.lo(j) = .2; d.fx(jfx) = ddat(jfx,"ref-q"); s.up(i) = 0.99*supc(i);
Model gtm gas transport model / all /; solve gtm maximizing benefit using nlp;
$Eject
Parameter report1(i,*) supply summary report
report2(j,*) demand summary report ;
report1(i,"supply") = s.l(i); report1(i,"capacity") = s.up(i); report1(i,"price") = sb.m(i);
report2(j,"demand") = d.l(j); report2(j,"price") = -db.m(j);
Display report1, report2, x.l;
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