def add_cut(self, it):
_,branch,_,Binv, _,_,_,_,winds,sigma,_ = self.data + self.aux
p, a, D, t, m, s = self.var
index = self.worst['line']
ID = branch[index]['id']
i,j = branch[index]['ij']
y = branch[index]['y']
if self.solver == 'cplex':
Di, Dj = self.sol.get_values([D[i], D[j]])
sij = 's{}'.format(ID)
Bij = {k: Binv[k][i]-Binv[k][j] for k in winds}
rhs = y**2*sum([sigma[k]**2*Bij[k]*(Bij[k]-Di+Dj) for k in winds])
coeff = y**2*sum([sigma[k]**2*(Bij[k]-Di+Dj) for k in winds])
x = arr([y*(Bij[k]-Di+Dj)*sigma[k] for k in winds])
#self.M.linear_constraints.add(lin_expr = [sp(ind = [sij], val = [1.0])],
#rhs = [0], names=['cut_help%d'%it], senses='G')
self.M.linear_constraints.add(lin_expr =
[sp(ind = [sij, D[i], D[j]], val = [norm(x), coeff, -coeff])],
rhs = [rhs], names=['cut_%d'%it], senses='G')
else:
x = arr([y*(Binv[k][i]-Binv[k][j]-D[i].x+D[j].x)*sigma[k] for k in winds])
self.M.addConstr(s[ID] >= 0, 'cut_%d_help'%(it+1))
self.M.addConstr(qs(x[l]*y*(Binv[k][i]-Binv[k][j]-D[i]+D[j])*sigma[k]
for l,k in enumerate(winds)) <= s[ID]*norm(x), 'cut_%d'%it)
def addCons(self):
bus,branch,Bbus,_, line_nu,gen_nu, n,_,d,mu,winds,sigma,gens = self.data + \
[self.line_nu, self.gen_nu] + self.aux
if self.verbose: print 'defining constraints'
p, a, D, t, m, s = self.var
sumvar = sum(sigma[b]**2 for b in winds)
if self.solver == 'cplex':
ng = len(gens)
self.M.linear_constraints.add(lin_expr = [sp(ind = a, val = [1.0]*ng)],
rhs = [1.0], names=['sum_alpha'])
self.M.linear_constraints.add(lin_expr = [sp(ind = p, val = [1.0]*ng)],
rhs = [sum(d)-sum(mu)], names=['power_balance'])
for i in xrange(n-1):
Bi = Bbus[i,:-1].tocoo()
J,V = Bi.col, Bi.data
if i in gens:
pi, ai, Di, ti = 'p_%d'%i, 'a_%d'%i, 'delta_%d'%i, 'theta_%d'%i
self.M.linear_constraints.add(lin_expr =
[sp(ind = list(D[J])+[ai], val = list(V)+[-1]),
sp(ind = list(t[J])+[pi], val = list(V)+[-1])],
rhs=[0, mu[i]-d[i]], names=[Di, ti], senses='EE')
self.M.linear_constraints.add(lin_expr =
[sp(ind = [pi,ai], val = [1, sumvar**.5*gen_nu]),
sp(ind = [pi,ai], val = [1, -sumvar**.5*gen_nu])],
rhs=[bus[i]['pmax'], bus[i]['pmin']],
names=['gen+_%d'%i, 'gen-_%d'%i], senses='LG')
else:
self.M.linear_constraints.add(lin_expr =
[sp(ind = D[J], val = V), sp(ind = t[J], val = V)],
rhs=[0, mu[i]-d[i]], names=['delta_%d'%i, 'theta_%d'%i],
senses='EE')
self.M.linear_constraints.add(lin_expr =
[sp(ind = [D[n-1]], val = [1.0]), sp(ind = [t[n-1]], val = [1.0])],
rhs = [0,0], names=['delta_%d'%(n-1), 'theta_%d'%(n-1)], senses='EE')
for line in branch:
ID = line['id']
ij = line['ij']
i,j = ij
mij, sij = 'm{}'.format(ID), 's{}'.format(ID)
self.M.linear_constraints.add(lin_expr =
[sp(ind = [mij, t[i], t[j]], val = [1.0, -line['y'], line['y']])],
rhs = [0], names=['line_avg_{}'.format(ID)], senses='E')
self.M.linear_constraints.add(lin_expr =
[sp(ind = [mij, sij], val = [-1.0, line_nu]),
sp(ind = [mij, sij], val = [1.0, line_nu])],
names=['line+_{}'.format(ID), 'line-_{}'.format(ID)],
rhs = [line['fmax'], line['fmax']], senses='LL')
else: # gurobi is much nicer
self.M.addConstr(qs(a[i] for i in gens) == 1, 'sum_alpha_1')
self.M.addConstr(qs(p[i] for i in gens) + sum(mu) == sum(d), 'power_balance')
for i in xrange(n-1):
Bi = Bbus[i,:-1].tocoo()
Bi = zip(Bi.col, Bi.data)
if i in gens:
self.M.addConstr(qs(v*D[j] for j,v in Bi) == a[i], 'delta_%d'%i)
self.M.addConstr(qs(v*t[j] for j,v in Bi) == p[i]+mu[i]-d[i],
'theta_%d'%i)
self.M.addConstr(sumvar**.5*a[i]*gen_nu <= bus[i]['pmax']-p[i],
'gen+_%d'%i)
self.M.addConstr(sumvar**.5*a[i]*gen_nu <= -bus[i]['pmin']+p[i],
'gen-_%d'%i)
else:
self.M.addConstr(qs(v*D[j] for j,v in Bi) == 0, 'delta_%d'%i)
self.M.addConstr(qs(v*t[j] for j,v in Bi) == mu[i]-d[i], 'theta_%d'%i)
self.M.addConstr(D[n-1] == 0, 'delta')
self.M.addConstr(t[n-1] == 0, 'theta')
for line in branch:
ID = line['id']
ij = line['ij']
i,j = ij
self.M.addConstr(m[ID] == line['y']*(t[i]-t[j]),
'line_avg_{}'.format(ID))
self.M.addConstr(s[ID]*line_nu <= line['fmax'] - m[ID],
'line+_{}'.format(ID))
self.M.addConstr(s[ID]*line_nu <= line['fmax'] + m[ID],
'line-_{}'.format(ID))