| $ontext
network of energy suppliers
Reference:
Steven A. Gabriel, Antonio J. Conejo, J. David Fuller,
Benjamin F. Hobbs, Carlos Ruiz
Complementarity Modeling in Energy Markets
Springer 2012
$offtext
Sets
s 'producers (supplier)' /A,B,C,D/
n 'nodes in network' /node1,node2/
sn(s,n) 'network topology' /
(A,B).node1
(C,D).node2
/
exports(s,n,n) 'export links' /(A,B).node1.node2/
exporter(s) 'exporters are subset of suppliers'
link(n,n) 'export flow'
;
alias(n,n1,n2);
* interesting: the next rhs are the same nut the calculate something
* different
exporter(s) = sum(exports(s,n1,n2),1);
link(n1,n2) = sum(exports(s,n1,n2),1);
display sn,exports,exporter,link;
parameters
tau_reg(n,n) 'regulated tariff for export (exogenous)' /node1.node2 0.5/
gamma(s) 'unit production cost for each supplier'
/ A 10, B 12, C 15, D 18 /
a(n) 'coefficient for demand function'
/node1 20, node2 40/
b(n) 'coefficient for demand function'
/node1 1, node2 2/
q_max(s) 'upper bound on production (capacity)'
/A 10, B 10, C 5, D 5 /
g_max(n,n) 'max flow over link (capacity)' /node1.node2 5/
gamma_TSO 'unit cost for TSO' /1/
;
positive variables
sell(s,n) 'quantity sold'
q(s,n) 'quantity produced'
f(s,n,n) 'quantity exported'
lambda(s,n) 'dual on upper bound production'
g(n,n) 'flows'
veps(n,n) 'dual on transportation capacity condition'
;
free variables
delta(s,n) 'dual on sell=production-export'
pi(n) 'prices'
tau(n,n) 'congestion tariff (endogenous)'
;
equations
FOC_supplier_sell(s,n) 'derivative of Lagrangian wrt variable sell'
FOC_supplier_q(s,n) 'derivative of Lagrangian wrt variable q'
FOC_supplier_exp(s,n,n) 'derivative of Lagrangian wrt variable f'
supplier_max_prod(s,n) 'capacity constraint'
supplier_supply(s,n) 'supply is locally sold or exported'
MC(n) 'market clearing'
FOC_TSO_g(n,n) 'derivative of Lagragian wrt variable g'
TSO_max(n,n) 'capacity constraint'
TSO_sum(n,n) 'summation of flows'
;
FOC_supplier_sell(sn(s,n))..
-pi(n)+delta(s,n) =g= 0;
FOC_supplier_q(sn(s,n))..
gamma(s)+lambda(s,n)-delta(s,n) =g= 0;
FOC_supplier_exp(exports(s,n1,n2))..
-pi(n2)+(tau_reg(n1,n2)+tau(n1,n2))+delta(s,n1) =g= 0;
supplier_max_prod(sn(s,n))..
q_max(s)-q(s,n) =g= 0;
supplier_supply(sn(s,n))..
sell(s,n)-q(s,n)+sum(exports(s,n,n2),f(s,n,n2))=e=0;
MC(n)..
sum(sn(s,n),sell(s,n)) + sum(exports(s,n1,n),f(s,n1,n)) -(a(n)-b(n)*pi(n)) =e= 0;
FOC_TSO_g(link(n1,n2))..
-tau_reg(n1,n2) - tau(n1,n2) + gamma_TSO + veps(n1,n2) =g= 0;
TSO_max(link(n1,n2))..
g_max(n1,n2) - g(n1,n2) =g= 0;
TSO_sum(link(n1,n2))..
g(n1,n2) - sum(exports(s,n1,n2),f(s,n1,n2)) =e= 0;
MODEL compl1 /
FOC_supplier_sell.sell
FOC_supplier_q.q
FOC_supplier_exp.f
supplier_max_prod.lambda
supplier_supply.delta
MC.pi
FOC_TSO_g.g
TSO_max.veps
TSO_sum.tau
/;
solve compl1 using mcp;
parameter results(*,*,*);
$macro report(a) \
results(a,'unit cost', s) = gamma(s); \
results(a,'sell', s) = sum(n, sell.l(s,n)); \
results(a,'q', s) = sum(n, q.l(s,n)); \
results(a,'qmax', s) = q_max(s); \
results(a,'export',s) = sum((n1,n2),f.l(s,n1,n2)); \
results(a,'flow', n) = sum(n2, g.l(n,n2)); \
results(a,'maxflow',n) = sum(n2, g_max(n,n2)); \
results(a,'price', n) = pi.l(n); \
results(a,'exo.tariff',n) = sum(n2,tau_reg(n,n2)); \
results(a,'end.tariff',n) = sum(n2,tau.l(n,n2)); \
display results;
report('base case')
* make A,B more expensive
gamma('A') = 15;
gamma('B') = 17;
solve compl1 using mcp;
report('A,B expensive')
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