def __init__(self, paramfile):
for row in paramfile:
if row[0]=='BIAS_COMBINE': self.BIAS_COMBINE = row[1]
if row[0]=='COMP_COMBINE': self.COMP_COMBINE = row[1]
if row[0]=='FLAT_COMBINE': self.FLAT_COMBINE = row[1]
if row[0]=='FIBER_TRACE': self.FIBER_TRACE = row[1]
if row[0]=='BIAS_SUBTRACT': self.BIAS_SUBTRACT = row[1]
if row[0]=='LAMBDA_SOLVE': self.LAMBDA_SOLVE = row[1]
if row[0]=='COSMIC_RAYS': self.COSMIC_RAYS = row[1]
if row[0]=='SKY_SUBTRACT': self.SKY_SUBTRACT = row[1]
if row[0]=='WRITE_SPECTRA': self.WRITE_SPECTRA = row[1]
if row[0]=='FIBERS_TOTAL': self.FIBERS_TOTAL = int(row[1])
if row[0]=='FIBERS_EXCLUDE':
fibs = np.array( [ int(i) for i in row[1].split(',') ] )
fibs.sort()
fibs = fibs[ np.find( 0<fibs ) ]
fibs = fibs[ np.find( fibs<self.FIBERS_TOTAL+1 ) ]
self.FIBERS_EXCLUDE = fibs
if row[0]=='FIBER_WIDTH': self.FIBER_WIDTH = int(row[1])
if row[0]=='FIBER_SEP': self.FIBER_SEP = int(row[1])
if row[0]=='LO_BUFFER': self.LO_BUFFER = int(row[1])
if row[0]=='HI_BUFFER': self.HI_BUFFER = int(row[1])
if row[0]=='LINE_LIST': self.LINE_LIST = row[1]
if row[0]=='COMP_HEADER': self.COMP_HEADER = row[1]
if row[0]=='COMP_NAME': self.COMP_NAME = row[1]
if row[0]=='POLYFIT_ORDER': self.POLYFIT_ORDER = int(row[1])
if row[0]=='CR_SCAN_DX': self.CR_SCAN_DX = int(row[1])
def bustypes(bus, gen):
"""Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
"""
# get generator status
nb = bus.shape[0]
ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
Cg = sparse((gen[:, GEN_STATUS] > 0, (gen[:, GEN_BUS], range(ng))),
(nb, ng))
# number of generators at each bus that are ON
bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF) & bus_gen_status) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV) & bus_gen_status) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ) | ~bus_gen_status) # PQ bus indices
# pick a new reference bus if for some reason there is none (may have been
# shut down)
if len(ref) == 0:
ref = pv[0] # use the first PV bus
pv = pv[1:] # take it off PV list
return ref, pv, pq
def bustypes(bus, gen):
"""Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
changes by Uni Kassel (Florian Schaefer): If new ref bus is chosen -> Init as numpy array
"""
# get generator status
# nb = bus.shape[0]
# ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
#Cg = sparse((gen[:, GEN_STATUS] > 0,
# (gen[:, GEN_BUS], range(ng))), (nb, ng))
# number of generators at each bus that are ON
#bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF)) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV)) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ)) # PQ bus indices
return ref, pv, pq
def makePTDF(baseMVA, bus, branch, slack=None):
"""Builds the DC PTDF matrix for a given choice of slack.
Returns the DC PTDF matrix for a given choice of slack. The matrix is
C{nbr x nb}, where C{nbr} is the number of branches and C{nb} is the
number of buses. The C{slack} can be a scalar (single slack bus) or an
C{nb x 1} column vector of weights specifying the proportion of the
slack taken up at each bus. If the C{slack} is not specified the
reference bus is used by default.
For convenience, C{slack} can also be an C{nb x nb} matrix, where each
column specifies how the slack should be handled for injections
at that bus.
@see: L{makeLODF}
@author: Ray Zimmerman (PSERC Cornell)
"""
## use reference bus for slack by default
if slack is None:
slack = find(bus[:, BUS_TYPE] == REF)
slack = slack[0]
## set the slack bus to be used to compute initial PTDF
if isscalar(slack):
slack_bus = slack
else:
slack_bus = 0 ## use bus 1 for temp slack bus
nb = bus.shape[0]
nbr = branch.shape[0]
noref = arange(1, nb) ## use bus 1 for voltage angle reference
noslack = find(arange(nb) != slack_bus)
## check that bus numbers are equal to indices to bus (one set of bus numbers)
if any(bus[:, BUS_I] != arange(nb)):
stderr.write('makePTDF: buses must be numbered consecutively')
## compute PTDF for single slack_bus
Bbus, Bf, _, _ = makeBdc(baseMVA, bus, branch)
Bbus, Bf = Bbus.todense(), Bf.todense()
H = zeros((nbr, nb))
H[:, noslack] = solve( Bbus[ix_(noslack, noref)].T, Bf[:, noref].T ).T
# = Bf[:, noref] * inv(Bbus[ix_(noslack, noref)])
## distribute slack, if requested
if not isscalar(slack):
if len(slack.shape) == 1: ## slack is a vector of weights
slack = slack / sum(slack) ## normalize weights
## conceptually, we want to do ...
## H = H * (eye(nb, nb) - slack * ones((1, nb)))
## ... we just do it more efficiently
v = dot(H, slack)
for k in range(nb):
H[:, k] = H[:, k] - v
else:
H = dot(H, slack)
return H
def ppci_to_pfsoln(ppci, options):
internal = ppci["internal"]
if options["only_v_results"]:
# time series relevant hack which ONLY saves V from ppci
_update_v(internal["bus"], internal["V"])
return internal["bus"], internal["gen"], internal["branch"]
else:
# reads values from internal ppci storage to bus, gen, branch and returns it
if options['distributed_slack']:
# consider buses with non-zero slack weights as if they were slack buses,
# and gens with non-zero slack weights as if they were reference machines
# this way, the function pfsoln will extract results for distributed slack gens, too
# also, the function pfsoln will extract results for the PQ buses for xwards
gens_with_slack_weights = find(internal["gen"][:, SL_FAC] != 0)
# gen_buses_with_slack_weights = internal["gen"][gens_with_slack_weights, GEN_BUS].astype(int32)
buses_with_slack_weights = internal["bus"][find(
internal["bus"][:, SL_FAC_BUS] != 0), BUS_I].astype(int32)
# buses_with_slack_weights = union1d(gen_buses_with_slack_weights, buses_with_slack_weights)
ref = union1d(internal["ref"], buses_with_slack_weights)
ref_gens = union1d(internal["ref_gens"], gens_with_slack_weights)
else:
ref = internal["ref"]
ref_gens = internal["ref_gens"]
_, pfsoln = _get_numba_functions(ppci, options)
result_pfsoln = pfsoln(internal["baseMVA"], internal["bus"],
internal["gen"], internal["branch"],
internal["Ybus"], internal["Yf"],
internal["Yt"], internal["V"], ref, ref_gens)
return result_pfsoln
def bustypes(bus, gen):
"""Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
"""
# get generator status
nb = bus.shape[0]
ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
Cg = sparse((gen[:, GEN_STATUS] > 0,
(gen[:, GEN_BUS], range(ng))), (nb, ng))
# number of generators at each bus that are ON
bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF) & bus_gen_status) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV) & bus_gen_status) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ) | ~bus_gen_status) # PQ bus indices
# pick a new reference bus if for some reason there is none (may have been
# shut down)
if len(ref) == 0:
ref = pv[0] # use the first PV bus
pv = pv[1:] # take it off PV list
return ref, pv, pq
def sumAnyNBinom(p, anyN=1):
"""Returns probability of a positive outcome given that
a positive outcome requires at least anyN events,
and given that the independent probability of each event is in vector p.
Parameters
----------
p : list or 1darray
Vector of probabilities of each independent event.
anyN : int
Minimum number of events required to be considered a positive outcome.
Returns
-------
tot : float
Overall probability of a positive outcome."""
if isinstance(p, list):
p = np.asarray(p)
n = len(p)
tmp = np.zeros(n)
tot = np.zeros(2**n)
for eventi, event in enumerate(itertools.product(*tuple([[0, 1]] * n))):
event = np.array(event)
if np.sum(event) >= anyN:
tmp[np.find(event == 1)] = p[np.find(event == 1)]
tmp[np.find(event == 0)] = 1 - p[np.find(event == 0)]
tot[eventi] = np.prod(tmp)
return tot.sum()
def _sys_event(self, C):
sysdef = self.sysdef
row, col = C.shape
if self.systype.lower() == "series":
self.cutset = 1 - np.prod(np.ones((row, col)) - C, axis=1, dtype=int)
ncutsets = []
elif self.systype.lower() == "parallel":
self.cutset = np.prod(C, axis=1, dtype=int)
ncutsets = []
else:
if self.sysdef[1].lower() == "link":
self.sysdef = -self.sysdef
self.sysdef[0] = np.hstack((0, self.sysdef[0], 0))
sysnonzero = np.find(self.sysdef[0] != 0)[0]
syszero = np.find(self.sysdef[0] == 0)[0]
int1 = syszero - np.hstack((0, syszero[:-1]))
sizeCutSets = int1[int1 > 1] - 1
ncutsets = sizeCutSets.shape[0]
for i in xrange(ncutsets):
cCutSet = np.ones(row, 1)
for j in xrange(sizeCutSets[i]):
comp = self.sysdef[0][sysnonzero[np.sum(sizeCutSets[:i]) + j]]
if comp < 0:
cCutSet = cCutSet * (np.ones((row, 1)) - C.T[:, abs(comp)])
else:
cCutSet = cCutSet * C.T[:, comp]
cCutSets[:, i] = cCutSet
self.cutset = np.ones(row, 1) - np.prod(np.ones(row, ncutsets) - cCutSets, axis=1)
def rhoa( snd, cal=260e-9, corrramp=True ):
''' compute apparent resistivity from sounding '''
Tx = np.prod( [float(a) for a in snd['LOOP_SIZE'].split()] )
if 'COIL_SIZE' in snd:
Rx = snd['COIL_SIZE']
else:
Rx = Tx
v = snd['VOLTAGE']
istart, istop = 0, len(v) # default: take all
mav = np.find( v == max(v) )
if len(mav) > 1: #several equal big ones: start after
istart = max(mav)+1
if min(v) < 0.0: # negative values: stop at first
istop = min( np.find( v < 0.0 ) )
v = v[istart:istop]
dv = snd['ST_DEV'][istart:istop] #/ snd['CURRENT']
t = snd['TIME'][istart:istop]
if corrramp and 'RAMP_TIME' in snd:
t = t - snd['RAMP_TIME']
if Rx == 1: # apparently B-field
rhoa = rhoafromB( v * cal, t, Tx )
else:
rhoa = rhoafromU( v, t, Tx, Rx )
rhoaerr = dv / v * (2./3.)
return rhoa, t, rhoaerr
def bustypes(bus, gen, Sbus):
"""
Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
"""
# flag to indicate that it is impossible to solve the grid
the_grid_is_disabled = False
# get generator status
nb = bus.shape[0]
ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
Cg = sparse((gen[:, GEN_STATUS] > 0, (gen[:, GEN_BUS], range(ng))),
(nb, ng))
# number of generators at each bus that are ON
bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF) & bus_gen_status) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV) & bus_gen_status) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ) | ~bus_gen_status) # PQ bus indices
# pick a new reference bus if for some reason there is none (may have been
# shut down)
if len(ref) == 0:
if len(pv) > 0:
ref = [pv[0]] # use the first PV bus
pv = pv[1:] # take it off PV list
else: # look for positive power injections to take the largest as the slack
positive_power_injections = Sbus.real[where(Sbus.real > 0)[0]]
if len(positive_power_injections) > 0:
idx = where(Sbus.real == max(positive_power_injections))[0]
if len(idx) == 1:
ref = idx
i = where(pq == idx[0])[0][0]
pq = delete(pq, i)
else:
warn('It was not possible to find a slack bus')
the_grid_is_disabled = True
else:
warn('It was not possible to find a slack bus')
the_grid_is_disabled = True
# create the types array
types = zeros(nb)
types[ref] = 3
types[pv] = 2
types[pq] = 1
return ref, pv, pq, types, the_grid_is_disabled
def bustypes(bus, gen, Sbus):
"""
Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
"""
# flag to indicate that it is impossible to solve the grid
the_grid_is_disabled = False
# get generator status
nb = bus.shape[0]
ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
Cg = sparse((gen[:, GEN_STATUS] > 0,
(gen[:, GEN_BUS], range(ng))), (nb, ng))
# number of generators at each bus that are ON
bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF) & bus_gen_status) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV) & bus_gen_status) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ) | ~bus_gen_status) # PQ bus indices
# pick a new reference bus if for some reason there is none (may have been
# shut down)
if len(ref) == 0:
if len(pv) > 0:
ref = [pv[0]] # use the first PV bus
pv = pv[1:] # take it off PV list
else: # look for positive power injections to take the largest as the slack
positive_power_injections = Sbus.real[where(Sbus.real > 0)[0]]
if len(positive_power_injections) > 0:
idx = where(Sbus.real == max(positive_power_injections))[0]
if len(idx) == 1:
ref = idx
i = where(pq == idx[0])[0][0]
pq = delete(pq, i)
else:
warn('It was not possible to find a slack bus')
the_grid_is_disabled = True
else:
warn('It was not possible to find a slack bus')
the_grid_is_disabled = True
# create the types array
types = zeros(nb)
types[ref] = 3
types[pv] = 2
types[pq] = 1
return ref, pv, pq, types, the_grid_is_disabled
def userfcn_reserves_ext2int(ppc, *args):
"""This is the 'ext2int' stage userfcn callback that prepares the input
data for the formulation stage. It expects to find a 'reserves' field
in ppc as described above. The optional args are not currently used.
"""
## initialize some things
r = ppc['reserves']
o = ppc['order']
ng0 = o['ext']['gen'].shape[0] ## number of original gens (+ disp loads)
nrz = r['req'].shape[0] ## number of reserve zones
if nrz > 1:
ppc['reserves']['rgens'] = any(r['zones'], 0) ## mask of gens available to provide reserves
else:
ppc['reserves']['rgens'] = r['zones']
igr = find(ppc['reserves']['rgens']) ## indices of gens available to provide reserves
ngr = len(igr) ## number of gens available to provide reserves
## check data for consistent dimensions
if r['zones'].shape[0] != nrz:
stderr.write('userfcn_reserves_ext2int: the number of rows in ppc[\'reserves\'][\'req\'] (%d) and ppc[\'reserves\'][\'zones\'] (%d) must match\n' % (nrz, r['zones'].shape[0]))
if (r['cost'].shape[0] != ng0) & (r['cost'].shape[0] != ngr):
stderr.write('userfcn_reserves_ext2int: the number of rows in ppc[\'reserves\'][\'cost\'] (%d) must equal the total number of generators (%d) or the number of generators able to provide reserves (%d)\n' % (r['cost'].shape[0], ng0, ngr))
if 'qty' in r:
if r['qty'].shape[0] != r['cost'].shape[0]:
stderr.write('userfcn_reserves_ext2int: ppc[\'reserves\'][\'cost\'] (%d x 1) and ppc[\'reserves\'][\'qty\'] (%d x 1) must be the same dimension\n' % (r['cost'].shape[0], r['qty'].shape[0]))
## convert both cost and qty from ngr x 1 to full ng x 1 vectors if necessary
if r['cost'].shape[0] < ng0:
if 'original' not in ppc['reserves']:
ppc['reserves']['original'] = {}
ppc['reserves']['original']['cost'] = r['cost'].copy() ## save original
cost = zeros(ng0)
cost[igr] = r['cost']
ppc['reserves']['cost'] = cost
if 'qty' in r:
ppc['reserves']['original']['qty'] = r['qty'].copy() ## save original
qty = zeros(ng0)
qty[igr] = r['qty']
ppc['reserves']['qty'] = qty
##----- convert stuff to internal indexing -----
## convert all reserve parameters (zones, costs, qty, rgens)
if 'qty' in r:
ppc = e2i_field(ppc, ['reserves', 'qty'], 'gen')
ppc = e2i_field(ppc, ['reserves', 'cost'], 'gen')
ppc = e2i_field(ppc, ['reserves', 'zones'], 'gen', 1)
ppc = e2i_field(ppc, ['reserves', 'rgens'], 'gen', 1)
## save indices of gens available to provide reserves
ppc['order']['ext']['reserves']['igr'] = igr ## external indexing
ppc['reserves']['igr'] = find(ppc['reserves']['rgens']) ## internal indexing
return ppc
def getHNR(y, Fs, F0, Nfreqs):
print('holla')
NBins = len(y)
N0 = round(Fs / F0)
N0_delta = round(N0 * 0.1)
y = [x * z for x, z in zip(np.hamming(len(y)), y)]
fftY = np.fft(y, NBins)
aY = np.log10(abs(fftY))
ay = np.ifft(aY)
peakinx = np.zeros(np.floor(len(y)) / 2 / N0)
for k in range(1, len(peakinx)):
ayseg = ay[(k * N0 - N0_delta):(k * N0 + N0_delta)]
val, inx = max(
abs(ayseg)) # MAX does not behave the same - doesn't return inx??
peakinx[k] = inx + (k * N0) - N0_delta - 1
s_ayseg = np.sign(np.diff(ayseg))
l_inx = inx - np.find(
(np.sign(s_ayseg[inx - 1:-1:1]) != np.sign(inx)))[0] + 1
r_inx = inx + np.find(np.sign(s_ayseg[inx + 1:]) == np.sign(inx))[0]
l_inx = l_inx + k * N0 - N0_delta - 1
r_inx = r_inx + k * N0 - N0_delta - 1
for num in range(l_inx, r_inx):
ay[num] = 0
midL = round(len(y) / 2) + 1
ay[midL:] = ay[(midL - 1):-1:(midL - 1 - (len(ay) - midL))]
Nap = np.real(np.fft(ay))
N = Nap # ???? why?
Ha = aY - Nap # change these names ffs
Hdelta = F0 / Fs * len(y)
for f in [
num + 0.0001 for num in range(Hdelta, round(len(y) / 2), Hdelta)
]:
fstart = np.ceil(f - Hdelta)
Bdf = abs(min(Ha[fstart:round(f)]))
N[fstart:round(f)] = N[fstart:round(f)] - Bdf
H = aY - N
n = np.zeros(len(Nfreqs))
for k in range(1, len(Nfreqs)):
Ef = round(Nfreqs[k] / Fs * len(y))
n[k] = (20 * np.mean(H[1:Ef])) - (20 * np.mean(N[1:Ef]))
return n
def get_influence_matrix(self):
"""
:return: binary matrix showing influence of input to output
"""
m = None
for layer in self.modules():
if isinstance(layer, nn.Linear):
if m is None:
m = np.find(layer.weight)
else:
m = m* np.find(layer.weight)
return m
def pfsoln(baseMVA,
bus0,
gen0,
branch0,
Ybus,
Yf,
Yt,
V,
ref,
ref_gens,
Ibus=None):
"""Updates bus, gen, branch data structures to match power flow soln.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
# initialize return values
bus = bus0
gen = gen0
branch = branch0
# ----- update Qg for all gens and Pg for slack bus(es) -----
# generator info
on = find(gen[:, GEN_STATUS] > 0) # which generators are on?
gbus = gen[on, GEN_BUS].astype(int) # what buses are they at?
# xward: add ref buses that are not at the generators
xbus = setdiff1d(ref, gbus)
# compute total injected bus powers
Ibus = zeros(len(V)) if Ibus is None else Ibus
Sbus = V[gbus] * conj(Ybus[gbus, :] * V - Ibus[gbus])
Sbus_xw = V[xbus] * conj(Ybus[xbus, :] * V - Ibus[xbus])
_update_v(bus, V)
_update_q(baseMVA, bus, gen, gbus, Sbus, on)
_update_p(baseMVA, bus, gen, ref, gbus, on, r_[Sbus, Sbus_xw], ref_gens)
# ----- update/compute branch power flows -----
out = find(branch[:, BR_STATUS] == 0) # out-of-service branches
br = find(branch[:, BR_STATUS]).astype(int) # in-service branches
if len(out):
raise RuntimeError
# complex power at "from" bus
Sf = V[real(branch[br, F_BUS]).astype(int)] * conj(Yf[br, :] * V) * baseMVA
# complex power injected at "to" bus
St = V[real(branch[br, T_BUS]).astype(int)] * conj(Yt[br, :] * V) * baseMVA
branch[ix_(br, [PF, QF, PT, QT])] = c_[Sf.real, Sf.imag, St.real, St.imag]
branch[ix_(out, [PF, QF, PT, QT])] = zeros((len(out), 4))
return bus, gen, branch
def modcost(gencost, alpha, modtype='SCALE_F'):
"""Modifies generator costs by shifting or scaling (F or X).
For each generator cost F(X) (for real or reactive power) in
C{gencost}, this function modifies the cost by scaling or shifting
the function by C{alpha}, depending on the value of C{modtype}, and
and returns the modified C{gencost}. Rows of C{gencost} can be a mix
of polynomial or piecewise linear costs.
C{modtype} takes one of the 4 possible values (let F_alpha(X) denote the
the modified function)::
SCALE_F (default) : F_alpha(X) == F(X) * ALPHA
SCALE_X : F_alpha(X * ALPHA) == F(X)
SHIFT_F : F_alpha(X) == F(X) + ALPHA
SHIFT_X : F_alpha(X + ALPHA) == F(X)
@author: Ray Zimmerman (PSERC Cornell)
"""
gencost = gencost.copy()
ng, m = gencost.shape
if ng != 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
ipol = find(gencost[:, MODEL] == POLYNOMIAL)
c = gencost[ipol, COST:m]
if modtype == 'SCALE_F':
gencost[ipol, COST:m] = alpha * c
gencost[ipwl, COST + 1:m:2] = alpha * gencost[ipwl, COST + 1:m:2]
elif modtype == 'SCALE_X':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
for i in range(n):
gencost[ipol[k], COST + i] = c[k, i] / alpha**(n - i - 1)
gencost[ipwl, COST:m - 1:2] = alpha * gencost[ipwl, COST:m - 1:2]
elif modtype == 'SHIFT_F':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
gencost[ipol[k], COST + n - 1] = alpha + c[k, n - 1]
gencost[ipwl, COST + 1:m:2] = alpha + gencost[ipwl, COST + 1:m:2]
elif modtype == 'SHIFT_X':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
gencost[ipol[k], COST:COST + n] = \
polyshift(c[k, :n].T, alpha).T
gencost[ipwl, COST:m - 1:2] = alpha + gencost[ipwl, COST:m - 1:2]
else:
sys.stderr.write('modcost: "%s" is not a valid modtype\n' %
modtype)
return gencost
def modcost(gencost, alpha, modtype='SCALE_F'):
"""Modifies generator costs by shifting or scaling (F or X).
For each generator cost F(X) (for real or reactive power) in
C{gencost}, this function modifies the cost by scaling or shifting
the function by C{alpha}, depending on the value of C{modtype}, and
and returns the modified C{gencost}. Rows of C{gencost} can be a mix
of polynomial or piecewise linear costs.
C{modtype} takes one of the 4 possible values (let F_alpha(X) denote the
the modified function)::
SCALE_F (default) : F_alpha(X) == F(X) * ALPHA
SCALE_X : F_alpha(X * ALPHA) == F(X)
SHIFT_F : F_alpha(X) == F(X) + ALPHA
SHIFT_X : F_alpha(X + ALPHA) == F(X)
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
gencost = gencost.copy()
ng, m = gencost.shape
if ng != 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
ipol = find(gencost[:, MODEL] == POLYNOMIAL)
c = gencost[ipol, COST:m]
if modtype == 'SCALE_F':
gencost[ipol, COST:m] = alpha * c
gencost[ipwl, COST+1:m:2] = alpha * gencost[ipwl, COST + 1:m:2]
elif modtype == 'SCALE_X':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
for i in range(n):
gencost[ipol[k], COST + i] = c[k, i] / alpha**(n - i - 1)
gencost[ipwl, COST:m - 1:2] = alpha * gencost[ipwl, COST:m - 1:2]
elif modtype == 'SHIFT_F':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
gencost[ipol[k], COST + n - 1] = alpha + c[k, n - 1]
gencost[ipwl, COST+1:m:2] = alpha + gencost[ipwl, COST + 1:m:2]
elif modtype == 'SHIFT_X':
for k in range(len(ipol)):
n = gencost[ipol[k], NCOST].astype(int)
gencost[ipol[k], COST:COST + n] = \
polyshift(c[k, :n].T, alpha).T
gencost[ipwl, COST:m - 1:2] = alpha + gencost[ipwl, COST:m - 1:2]
else:
sys.stderr.write('modcost: "%s" is not a valid modtype\n' % modtype)
return gencost
def getHNR(y, Fs, F0, Nfreqs):
print 'holla'
NBins = len(y)
N0 = round(Fs/F0)
N0_delta = round(N0 * 0.1)
y = [x*z for x,z in zip(np.hamming(len(y)),y)]
fftY = np.fft(y, NBins)
aY = np.log10(abs(fftY))
ay = np.ifft(aY)
peakinx = np.zeros(np.floor(len(y))/2/N0)
for k in range(1, len(peakinx)):
ayseg = ay[k*N0 - N0_delta : k*N0 + N0_delta]
val, inx = max(abs(ayseg)) #MAX does not behave the same - doesn't return inx??
peakinx[k] = inx + (k * N0) - N0_delta - 1
s_ayseg = np.sign(np.diff(ayseg))
l_inx = inx - np.find((np.sign(s_ayseg[inx-1:-1:1]) != np.sign(inx)))[0] + 1
r_inx = inx + np.find(np.sign(s_ayseg[inx+1:]) == np.sign(inx))[0]
l_inx = l_inx + k*N0 - N0_delta - 1
r_inx = r_inx + k*N0 - N0_delta - 1
for num in range(l_inx, r_inx):
ay[num] = 0
midL = round(len(y)/2)+1
ay[midL:] = ay[midL-1: -1 : midL-1-(len(ay)-midL)]
Nap = np.real(np.fft(ay))
N = Nap #???? why?
Ha = aY - Nap #change these names ffs
Hdelta = F0/Fs * len(y)
for f in [num+0.0001 for num in range(Hdelta, round(len(y)/2), Hdelta)]:
fstart = np.ceil(f - Hdelta)
Bdf = abs(min(Ha[fstart:round(f)]))
N[fstart:round(f)] = N[fstart:round(f)] - Bdf
H = aY - N
n = np.zeros(len(Nfreqs))
for k in range(1, len(Nfreqs)):
Ef = round(Nfreqs[k] / Fs * len(y))
n[k] = (20 * np.mean(H[1:Ef])) - (20 * np.mean(N[1:Ef]))
return n
def makeSbus(baseMVA, bus, gen):
"""Builds the vector of complex bus power injections.
Returns the vector of complex bus power injections, that is, generation
minus load. Power is expressed in per unit.
@see: L{makeYbus}
kk
@author: Ray Zimmerman (PSERC Cornell)
"""
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS] ## what buses are they at?
## form net complex bus power injection vector
nb = bus.shape[0]
ngon = on.shape[0]
## connection matrix, element i, j is 1 if gen on(j) at bus i is ON
Cg = sparse((ones(ngon), (gbus, range(ngon))), (nb, ngon))
## power injected by gens plus power injected by loads converted to p.u.
Sbus = (Cg * (gen[on, PG] + 1j * gen[on, QG]) -
(bus[:, PD] + 1j * bus[:, QD])) / baseMVA
return Sbus
def makeSbus(baseMVA, bus, gen):
"""Builds the vector of complex bus power injections.
Returns the vector of complex bus power injections, that is, generation
minus load. Power is expressed in per unit.
@see: L{makeYbus}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS] ## what buses are they at?
## form net complex bus power injection vector
nb = bus.shape[0]
ngon = on.shape[0]
## connection matrix, element i, j is 1 if gen on(j) at bus i is ON
Cg = sparse((ones(ngon), (gbus, range(ngon))), (nb, ngon))
## power injected by gens plus power injected by loads converted to p.u.
Sbus = ( Cg * (gen[on, PG] + 1j * gen[on, QG]) -
(bus[:, PD] + 1j * bus[:, QD]) ) / baseMVA
return Sbus
def Theta_abs_mean(dc_bus_sol):
dc_bus_sol = dc_bus_sol.copy()
Theta_slack = dc_bus_sol[find(dc_bus_sol[:, 5] == 1)[0], 2]
dc_bus_sol[:, 2] -= Theta_slack
dc_ThetaMean = np.mean(abs(dc_bus_sol[:, 2]))
return dc_ThetaMean
def fix_entsoe(dic, limit=10):
""" Handle DST shift and interpolate remaining nans.
Error if time starts with last sunday in october 02:00..."""
time = dic[list(dic)[0]].index
month, day, wd, hour = time.month, time.day, time.weekday, time.hour
shift = find((month == 10) & (wd == 6) & (hour == 2) &
(day > 24)) # DST shift hours in October
for i, df in dic.items():
if i in self.bidz:
# DST shift in October
for s in shift:
if sum(np.isnan(df.iloc[s, :])) > 0 and sum(df.iloc[
s - 1, :]) / sum(df.iloc[s - 2, :]) > 1.5:
df.iloc[s - 1, :] /= 2
df.iloc[s, :] = df.iloc[s - 1, :]
# Remaining nans
df.interpolate(
limit=limit,
inplace=True) # interpolate up to limit samples
if np.sum(arr(np.isnan(df))) > 0:
print(
'Too many nans in Entso-e data for %s, might not work properly.'
% i)
return dic
def quick_gci(g,
fmin=20,
fmax=1000,
fs=20000,
theta=0,
reps=2,
reps2=None,
gamma=1,
inside=False):
""" Return GCIs using QuickGCI algorithm. """
Bh, Ah = butter1(fmin / (fs / 2), 'high')
Bl, Al = butter1(fmax / (fs / 2), 'low')
for i in range(reps):
g = sig.filtfilt(Bh, Ah, g)
g = sig.filtfilt(Bl, Al, g)
x = fasthilbert(g) * exp(1j * theta)
q = abs(x)**gamma * imag(-x)
for i in range(reps if reps2 is None else reps2):
q = sig.filtfilt(Bl, Al, q)
r = fasthilbert(q)
dphi = der(angle(r))
gci = find(dphi < -1.5 * pi)
if not inside: return gci
else: return gci, locals()
def gadfli(g,
fmin=20,
fmax=1000,
fs=20000,
m=0.25,
tau=-0.25,
theta=0,
reps=2,
inside=False):
""" Return GCIs using GADFLI algorithm. """
Bh, Ah = butter1(fmin / (fs / 2), 'high')
Bl, Al = butter1(fmax / (fs / 2), 'low')
for i in range(reps):
g = sig.filtfilt(Bh, Ah, g)
g = sig.filtfilt(Bl, Al, g)
dg = der(g)
h = fasthilbert(dg) * exp(1j * theta)
dphi = der(angle(h))
gci_c = find(dphi < -1.5 * pi) # candidates
rh = real(h)
kept = inlier_elim(rh, m)
scale = kept.std()
gci = array([i for i in gci_c if rh[i] < tau * scale])
if not inside: return gci
else: return gci, locals()
def makeSbus(baseMVA, bus, gen, vm=None):
"""Builds the vector of complex bus power injections.
Returns the vector of complex bus power injections, that is, generation
minus load. Power is expressed in per unit.
@see: L{makeYbus}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS] ## what buses are they at?
## form net complex bus power injection vector
nb = bus.shape[0]
ngon = on.shape[0]
## connection matrix, element i, j is 1 if gen on(j) at bus i is ON
Cg = sparse((ones(ngon), (gbus, range(ngon))), (nb, ngon))
S_load = bus[:, PD] + 1j * bus[:, QD]
if vm is not None:
ci = bus[:, CID]
cz = bus[:, CZD]
cp = (1 - ci - cz)
volt_depend = cp + ci * vm + cz * vm ** 2
S_load *= volt_depend
## power injected by gens plus power injected by loads converted to p.u.
Sbus = (Cg * (gen[on, PG] + 1j * gen[on, QG])
- S_load) / baseMVA
return Sbus
def userfcn_iflims_ext2int(ppc, *args):
"""This is the 'ext2int' stage userfcn callback that prepares the input
data for the formulation stage. It expects to find an 'if' field in
ppc as described above. The optional args are not currently used.
"""
## initialize some things
ifmap = ppc['if']['map']
o = ppc['order']
nl0 = o['ext']['branch'].shape[0] ## original number of branches
nl = ppc['branch'].shape[0] ## number of on-line branches
## save if.map for external indexing
ppc['order']['ext']['ifmap'] = ifmap
##----- convert stuff to internal indexing -----
e2i = zeros(nl0)
e2i[o['branch']['status']['on']] = arange(nl) ## ext->int branch index mapping
d = sign(ifmap[:, 1])
br = abs(ifmap[:, 1]).astype(int)
ifmap[:, 1] = d * e2i[br]
ifmap = delete(ifmap, find(ifmap[:, 1] == 0), 0) ## delete branches that are out
ppc['if']['map'] = ifmap
return ppc
def _update_p(baseMVA, bus, gen, ref, gbus, on, Sbus, ref_gens):
# update Pg for slack bus(es)
# inj P + local Pd
for slack_bus in ref:
gens_at_bus = find(
gbus == slack_bus) # which is(are) the reference gen(s)?
# xward results come at the PQ buses and not at the PV buses:
if len(gens_at_bus) == 0:
bus[slack_bus, PD] = -Sbus[
slack_bus].real * baseMVA # negative because it is a PQ bus
continue
p_bus = Sbus[gens_at_bus[0]].real * baseMVA + bus[slack_bus, PD]
if len(gens_at_bus) > 1: # more than one generator at this ref bus
# subtract off what is generated by other gens at this bus
ext_grids = intersect1d(gens_at_bus, ref_gens)
pv_gens = setdiff1d(gens_at_bus, ext_grids)
p_ext_grids = p_bus - sum(gen[pv_gens, PG])
slack_weights = gen[ext_grids, SL_FAC]
sum_slack_weights = sum(slack_weights)
if sum_slack_weights > 0:
# distribute bus slack power according to the distributed slack contribution factors
gen[ext_grids, PG] = gen[ext_grids, PG] + (p_ext_grids - sum(
gen[ext_grids, PG])) * slack_weights / sum_slack_weights
else:
gen[ext_grids, PG] = p_ext_grids / len(ext_grids)
else:
gen[on[gens_at_bus[0]], PG] = p_bus
def _update_q(baseMVA, bus, gen, gbus, Sbus, on):
# update Qg for all generators
gen[:, QG] = zeros(gen.shape[0]) # zero out all Qg
gen[on, QG] = Sbus.imag * baseMVA + bus[gbus, QD] # inj Q + local Qd
# ... at this point any buses with more than one generator will have
# the total Q dispatch for the bus assigned to each generator. This
# must be split between them. We do it first equally, then in proportion
# to the reactive range of the generator.
if len(on) > 1:
# build connection matrix, element i, j is 1 if gen on(i) at bus j is ON
nb = bus.shape[0]
ngon = on.shape[0]
Cg = csr_matrix((ones(ngon), (range(ngon), gbus)), (ngon, nb))
# divide Qg by number of generators at the bus to distribute equally
ngg = Cg * Cg.sum(0).T # ngon x 1, number of gens at this gen's bus
ngg = asarray(ngg).flatten() # 1D array
gen[on, QG] = gen[on, QG] / ngg
# divide proportionally
Cmin = csr_matrix((gen[on, QMIN], (range(ngon), gbus)), (ngon, nb))
Cmax = csr_matrix((gen[on, QMAX], (range(ngon), gbus)), (ngon, nb))
Qg_tot = Cg.T * gen[on, QG] # nb x 1 vector of total Qg at each bus
Qg_min = Cmin.sum(0).T # nb x 1 vector of min total Qg at each bus
Qg_max = Cmax.sum(0).T # nb x 1 vector of max total Qg at each bus
Qg_min = asarray(Qg_min).flatten() # 1D array
Qg_max = asarray(Qg_max).flatten() # 1D array
# gens at buses with Qg range = 0
ig = find(Cg * Qg_min == Cg * Qg_max)
Qg_save = gen[on[ig], QG]
gen[on, QG] = gen[on, QMIN] + (Cg * ((Qg_tot - Qg_min) / (Qg_max - Qg_min + EPS))) * \
(gen[on, QMAX] - gen[on, QMIN]) # ^ avoid div by 0
gen[on[ig], QG] = Qg_save # (terms are mult by 0 anyway)
def pfsoln(baseMVA, bus, gen, branch, Ybus, Yf, Yt, V, ref, ref_gens, Ibus=None):
"""Updates bus, gen, branch data structures to match power flow soln.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
# generator info
on = find(gen[:, GEN_STATUS] > 0) # which generators are on?
gbus = gen[on, GEN_BUS].astype(int) # what buses are they at?
# xward: add ref buses that are not at the generators
xbus = setdiff1d(ref, gbus)
# compute total injected bus powers
Ibus = zeros(len(V)) if Ibus is None else Ibus
Sbus = V[gbus] * conj(Ybus[gbus, :] * V - Ibus[gbus])
Sbus_xw = V[xbus] * conj(Ybus[xbus, :] * V - Ibus[xbus])
_update_v(bus, V)
# update gen results
_update_q(baseMVA, bus, gen, gbus, Sbus, on)
_update_p(baseMVA, bus, gen, ref, gbus, on, r_[Sbus, Sbus_xw], ref_gens)
# ----- update/compute branch power flows -----
branch = _update_branch_flows(Yf, Yt, V, baseMVA, branch)
return bus, gen, branch
def line_walk(self, p):
NC = self.number_of_cells()
NP = p.shape[0]
cell = self.entity('cell')
cidx = np.random.randint(0, NC, NP)
isNotOK = np.ones(NP, dtype=np.bool)
while isNotOK.sum() > 0:
idx0, = np.find(isNotOK)
cidx0 = cidx[isNotOK]
pp = p[isNotOK]
a = np.zeros((len(cidx0), 3), dtype=self.ftype)
p0 = cell[cidx0, 0]
p1 = cell[cidx0, 1]
p2 = cell[cidx0, 2]
v0 = p0 - pp
v1 = p1 - pp
v2 = p2 - pp
a[:, 0] = np.cross(v1, v2)
a[:, 1] = np.cross(v2, v0)
a[:, 2] = np.cross(v0, v1)
idx = np.argmin(a, axis=-1)
isOK = a[range(a.shape[0]), idx] >= 0
def userfcn_iflims_ext2int(ppc, *args):
"""This is the 'ext2int' stage userfcn callback that prepares the input
data for the formulation stage. It expects to find an 'if' field in
ppc as described above. The optional args are not currently used.
"""
## initialize some things
ifmap = ppc['if']['map']
o = ppc['order']
nl0 = o['ext']['branch'].shape[0] ## original number of branches
nl = ppc['branch'].shape[0] ## number of on-line branches
## save if.map for external indexing
ppc['order']['ext']['ifmap'] = ifmap
##----- convert stuff to internal indexing -----
e2i = zeros(nl0)
e2i[o['branch']['status']['on']] = arange(
nl) ## ext->int branch index mapping
d = sign(ifmap[:, 1])
br = abs(ifmap[:, 1]).astype(int)
ifmap[:, 1] = d * e2i[br]
ifmap = delete(ifmap, find(ifmap[:, 1] == 0),
0) ## delete branches that are out
ppc['if']['map'] = ifmap
return ppc
def optimal_power_flow_energy_reserve(*args):
casedata = args[0] # Target power flow modelling
beta = args[1] # The reserve level
mpc = loadcase(casedata) # Import the power flow modelling
## convert to internal indexing
mpc = ext2int(mpc)
baseMVA, bus, gen, branch,gencost = mpc["baseMVA"], mpc["bus"], mpc["gen"], mpc["branch"],mpc["gencost"] #
nb = shape(mpc['bus'])[0] ## number of buses
nl = shape(mpc['branch'])[0] ## number of branches
ng = shape(mpc['gen'])[0] ## number of dispatchable injections
## Formualte the
stat = branch[:, BR_STATUS] ## ones at in-service branches
b = stat / branch[:, BR_X] ## series susceptance
tap = ones(nl) ## default tap ratio = 1
i = find(branch[:, TAP]) ## indices of non-zero tap ratios
tap[i] = branch[i, TAP] ## assign non-zero tap ratios
## build connection matrix Cft = Cf - Ct for line and from - to buses
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = r_[range(nl), range(nl)] ## double set of row indices
## connection matrix
Cft = sparse((r_[ones(nl), -ones(nl)], (i, r_[f, t])), (nl, nb))
## build Bf such that Bf * Va is the vector of real branch powers injected
## at each branch's "from" bus
Bf = sparse((r_[b, -b], (i, r_[f, t])), shape=(nl, nb)) ## = spdiags(b, 0, nl, nl) * Cft
## build Bbus
Bbus = Cft.T * Bf
# The distribution factor
Distribution_factor = sparse(Bf*inv(Bbus))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], arange(ng))), (nb, ng)) # Sparse index generation method is different from the way of matlab
Cd = sparse((ones(nb), (bus[:, BUS_I], arange(nb))), (nb, nb)) # Sparse index load
Pd = sum(bus[:,PD]) # Total power demand
# Formulate the problem
lb = concatenate((gen[:,PMIN],zeros(ng))) # extend the
ub = concatenate((gen[:,PMAX],gen[:,PMAX]))
Aeq = sparse(concatenate((ones(ng),zeros(ng))))
beq = [Pd]
Aineq = sparse(hstack([Distribution_factor * Cg,zeros((nl,ng))]))
Aineq = vstack([Aineq, -Aineq])
# The ramp reserve requirement
Aineq = vstack([Aineq, sparse((r_[ones(ng), ones(ng)], (r_[arange(ng), arange(ng)], r_[arange(ng), ng+arange(ng)])), (ng, 2*ng))])
Aineq = vstack([Aineq, sparse((r_[-ones(ng), ones(ng)], (r_[arange(ng), arange(ng)], r_[arange(ng), ng+arange(ng)])), (ng, 2*ng))])
bineq = concatenate((branch[:, RATE_A] + Distribution_factor * Cd * bus[:, PD], branch[:, RATE_A] - Distribution_factor * Cd * bus[:, PD]))
bineq = concatenate((bineq, gen[:, PMAX]))
bineq = concatenate((bineq, -gen[:, PMIN]))
c = concatenate((gencost[:,5],zeros(ng)))
Q = diag(concatenate((gencost[:,4],zeros(ng))))
(Pg,obj) = miqp_gurobi(c = c,Q = Q, Aeq = Aeq, beq = beq, A = Aineq, b = bineq, xmin = lb,xmax = ub)
obj = obj + sum(gencost[:,6])
return Pg, obj
def makeAang(baseMVA, branch, nb, ppopt):
"""Construct constraints for branch angle difference limits.
Constructs the parameters for the following linear constraint limiting
the voltage angle differences across branches, where C{Va} is the vector
of bus voltage angles. C{nb} is the number of buses::
lang <= Aang * Va <= uang
C{iang} is the vector of indices of branches with angle difference limits.
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
## options
ignore_ang_lim = ppopt['OPF_IGNORE_ANG_LIM']
if ignore_ang_lim:
Aang = zeros((0, nb))
lang = array([])
uang = array([])
iang = array([])
else:
iang = find(((branch[:, ANGMIN] != 0) & (branch[:, ANGMIN] > -360)) |
((branch[:, ANGMAX] != 0) & (branch[:, ANGMAX] < 360)))
iangl = find(branch[iang, ANGMIN])
iangh = find(branch[iang, ANGMAX])
nang = len(iang)
if nang > 0:
ii = r_[arange(nang), arange(nang)]
jj = r_[branch[iang, F_BUS], branch[iang, T_BUS]]
Aang = sparse((r_[ones(nang), -ones(nang)],
(ii, jj)), (nang, nb))
uang = Inf * ones(nang)
lang = -uang
lang[iangl] = branch[iang[iangl], ANGMIN] * pi / 180
uang[iangh] = branch[iang[iangh], ANGMAX] * pi / 180
else:
Aang = zeros((0, nb))
lang = array([])
uang = array([])
return Aang, lang, uang, iang
def makeAang(baseMVA, branch, nb, ppopt):
"""Construct constraints for branch angle difference limits.
Constructs the parameters for the following linear constraint limiting
the voltage angle differences across branches, where C{Va} is the vector
of bus voltage angles. C{nb} is the number of buses::
lang <= Aang * Va <= uang
C{iang} is the vector of indices of branches with angle difference limits.
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
## options
ignore_ang_lim = ppopt['OPF_IGNORE_ANG_LIM']
if ignore_ang_lim:
Aang = zeros((0, nb))
lang = array([])
uang = array([])
iang = array([])
else:
iang = find(((branch[:, ANGMIN] != 0) & (branch[:, ANGMIN] > -360)) |
((branch[:, ANGMAX] != 0) & (branch[:, ANGMAX] < 360)))
iangl = find(branch[iang, ANGMIN])
iangh = find(branch[iang, ANGMAX])
nang = len(iang)
if nang > 0:
ii = r_[arange(nang), arange(nang)]
jj = r_[branch[iang, F_BUS], branch[iang, T_BUS]]
Aang = sparse((r_[ones(nang), -ones(nang)],
(ii, jj)), (nang, nb))
uang = Inf * ones(nang)
lang = -uang
lang[iangl] = branch[iang[iangl], ANGMIN] * pi / 180
uang[iangh] = branch[iang[iangh], ANGMAX] * pi / 180
else:
Aang = zeros((0, nb))
lang = array([])
uang = array([])
return Aang, lang, uang, iang
def userfcn_reserves_formulation(om, *args):
"""This is the 'formulation' stage userfcn callback that defines the
user costs and constraints for fixed reserves. It expects to find
a 'reserves' field in the ppc stored in om, as described above.
By the time it is passed to this callback, ppc['reserves'] should
have two additional fields:
- C{igr} C{1 x ngr}, indices of generators available for reserves
- C{rgens} C{1 x ng}, 1 if gen avaiable for reserves, 0 otherwise
It is also assumed that if cost or qty were C{ngr x 1}, they have been
expanded to C{ng x 1} and that everything has been converted to
internal indexing, i.e. all gens are on-line (by the 'ext2int'
callback). The optional args are not currently used.
"""
## initialize some things
ppc = om.get_ppc()
r = ppc['reserves']
igr = r['igr'] ## indices of gens available to provide reserves
ngr = len(igr) ## number of gens available to provide reserves
ng = ppc['gen'].shape[0] ## number of on-line gens (+ disp loads)
## variable bounds
Rmin = zeros(ngr) ## bound below by 0
Rmax = Inf * ones(ngr) ## bound above by ...
k = find(ppc['gen'][igr, RAMP_10])
Rmax[k] = ppc['gen'][igr[k], RAMP_10] ## ... ramp rate and ...
if 'qty' in r:
k = find(r['qty'][igr] < Rmax)
Rmax[k] = r['qty'][igr[k]] ## ... stated max reserve qty
Rmax = Rmax / ppc['baseMVA']
## constraints
I = speye(ngr, ngr, format='csr') ## identity matrix
Ar = hstack([sparse((ones(ngr), (arange(ngr), igr)), (ngr, ng)), I], 'csr')
ur = ppc['gen'][igr, PMAX] / ppc['baseMVA']
lreq = r['req'] / ppc['baseMVA']
## cost
Cw = r['cost'][igr] * ppc['baseMVA'] ## per unit cost coefficients
## add them to the model
om.add_vars('R', ngr, [], Rmin, Rmax)
om.add_constraints('Pg_plus_R', Ar, [], ur, ['Pg', 'R'])
om.add_constraints('Rreq', sparse(r['zones'][:, igr]), lreq, [], ['R'])
om.add_costs('Rcost', {'N': I, 'Cw': Cw}, ['R'])
return om
def userfcn_reserves_formulation(om, *args):
"""This is the 'formulation' stage userfcn callback that defines the
user costs and constraints for fixed reserves. It expects to find
a 'reserves' field in the ppc stored in om, as described above.
By the time it is passed to this callback, ppc['reserves'] should
have two additional fields:
- C{igr} C{1 x ngr}, indices of generators available for reserves
- C{rgens} C{1 x ng}, 1 if gen avaiable for reserves, 0 otherwise
It is also assumed that if cost or qty were C{ngr x 1}, they have been
expanded to C{ng x 1} and that everything has been converted to
internal indexing, i.e. all gens are on-line (by the 'ext2int'
callback). The optional args are not currently used.
"""
## initialize some things
ppc = om.get_ppc()
r = ppc['reserves']
igr = r['igr'] ## indices of gens available to provide reserves
ngr = len(igr) ## number of gens available to provide reserves
ng = ppc['gen'].shape[0] ## number of on-line gens (+ disp loads)
## variable bounds
Rmin = zeros(ngr) ## bound below by 0
Rmax = Inf * ones(ngr) ## bound above by ...
k = find(ppc['gen'][igr, RAMP_10])
Rmax[k] = ppc['gen'][igr[k], RAMP_10] ## ... ramp rate and ...
if 'qty' in r:
k = find(r['qty'][igr] < Rmax)
Rmax[k] = r['qty'][igr[k]] ## ... stated max reserve qty
Rmax = Rmax / ppc['baseMVA']
## constraints
I = speye(ngr, ngr, format='csr') ## identity matrix
Ar = hstack([sparse((ones(ngr), (arange(ngr), igr)), (ngr, ng)), I], 'csr')
ur = ppc['gen'][igr, PMAX] / ppc['baseMVA']
lreq = r['req'] / ppc['baseMVA']
## cost
Cw = r['cost'][igr] * ppc['baseMVA'] ## per unit cost coefficients
## add them to the model
om.add_vars('R', ngr, [], Rmin, Rmax)
om.add_constraints('Pg_plus_R', Ar, [], ur, ['Pg', 'R'])
om.add_constraints('Rreq', sparse( r['zones'][:, igr] ), lreq, [], ['R'])
om.add_costs('Rcost', {'N': I, 'Cw': Cw}, ['R'])
return om
def userfcn_dcline_int2ext(results, args):
"""This is the 'int2ext' stage userfcn callback that converts everything
back to external indexing and packages up the results. It expects to
find a 'dcline' field in the results struct as described for ppc
above. It also expects that the last 2*ndc entries in the gen and
gencost matrices correspond to the in-service DC lines (where ndc is
the number of rows in MPC.dcline. These extra rows are removed from
gen and gencost and the flow is taken from the PG of these gens and
placed in the flow column of the appropiate dcline row. The
optional args are not currently used.
"""
c = idx_dcline.c
## initialize some things
o = results['order']
k = find(o['ext']['dcline'][:, c['BR_STATUS']])
ndc = len(k) ## number of in-service DC lines
ng = results['gen'].shape[0] - 2*ndc; ## number of original gens/disp loads
## extract dummy gens
fg = results['gen'][ng:ng + ndc, :]
tg = results['gen'][ng + ndc:ng + 2 * ndc, :]
## remove dummy gens
#results['gen'] = results['gen'][:ng + 1, :]
#results['gencost'] = results['gencost'][:ng + 1, :]
results['gen'] = results['gen'][:ng, :]
results['gencost'] = results['gencost'][:ng, :]
## get the solved flows
results['dcline'][:, c['PF']] = -fg[:, PG]
results['dcline'][:, c['PT']] = tg[:, PG]
results['dcline'][:, c['QF']] = fg[:, QG]
results['dcline'][:, c['QT']] = tg[:, QG]
results['dcline'][:, c['VF']] = fg[:, VG]
results['dcline'][:, c['VT']] = tg[:, VG]
if fg.shape[1] >= MU_QMIN:
results['dcline'] = c_[results['dcline'], zeros((ndc, 6))]
results['dcline'][:, c['MU_PMIN'] ] = fg[:, MU_PMAX] + tg[:, MU_PMIN]
results['dcline'][:, c['MU_PMAX'] ] = fg[:, MU_PMIN] + tg[:, MU_PMAX]
results['dcline'][:, c['MU_QMINF']] = fg[:, MU_QMIN]
results['dcline'][:, c['MU_QMAXF']] = fg[:, MU_QMAX]
results['dcline'][:, c['MU_QMINT']] = tg[:, MU_QMIN]
results['dcline'][:, c['MU_QMAXT']] = tg[:, MU_QMAX]
results['order']['int'] = {}
##----- convert stuff back to external indexing -----
results['order']['int']['dcline'] = results['dcline'] ## save internal version
## copy results to external version
o['ext']['dcline'][k, c['PF']:c['VT'] + 1] = results['dcline'][:, c['PF']:c['VT'] + 1]
if results['dcline'].shape[1] == c['MU_QMAXT'] + 1:
o['ext']['dcline'] = c_[o['ext']['dcline'], zeros((ndc, 6))]
o['ext']['dcline'][k, c['MU_PMIN']:c['MU_QMAXT'] + 1] = \
results['dcline'][:, c['MU_PMIN']:c['MU_QMAXT'] + 1]
results['dcline'] = o['ext']['dcline'] ## use external version
return results
def inlier_elim(b, m):
""" Apply inlier elimination, return remaining samples. """
while True:
s = b.std()
idx = find(abs(b) >= m * s)
if len(idx) != len(b):
b = b[idx]
else:
return b
def findTieline(bus, branch):
tl = find(bus[branch[:, F_BUS].astype(int), BUS_AREA] != \
bus[branch[:, T_BUS].astype(int), BUS_AREA])
ntl = len(tl)
busBD = branch[ix_(tl, [F_BUS, T_BUS])].astype(int)
busBDregion = hstack((bus[ix_(busBD[:, 0], [BUS_AREA])], \
bus[ix_(busBD[:, 1], [BUS_AREA])])).astype(int)
tieline = hstack((busBD, busBDregion, tl.reshape((ntl, 1))))
return tieline, ntl
def userfcn_dcline_int2ext(results, args):
"""This is the 'int2ext' stage userfcn callback that converts everything
back to external indexing and packages up the results. It expects to
find a 'dcline' field in the results struct as described for ppc
above. It also expects that the last 2*ndc entries in the gen and
gencost matrices correspond to the in-service DC lines (where ndc is
the number of rows in MPC.dcline. These extra rows are removed from
gen and gencost and the flow is taken from the PG of these gens and
placed in the flow column of the appropiate dcline row. The
optional args are not currently used.
"""
c = idx_dcline.c
## initialize some things
o = results['order']
k = find(o['ext']['dcline'][:, c.BR_STATUS])
ndc = len(k) ## number of in-service DC lines
ng = results['gen'].shape[0] - 2 * ndc
## number of original gens/disp loads
## extract dummy gens
fg = results['gen'][ng + range(ndc + 1), :]
tg = results['gen'][ng + ndc + range(ndc + 1), :]
## remove dummy gens
results['gen'] = results['gen'][:ng + 1, :]
results['gencost'] = results['gencost'][:ng + 1, :]
## get the solved flows
results['dcline'][:, c.PF] = -fg[:, PG]
results['dcline'][:, c.PT] = tg[:, PG]
results['dcline'][:, c.QF] = fg[:, QG]
results['dcline'][:, c.QT] = tg[:, QG]
results['dcline'][:, c.VF] = fg[:, VG]
results['dcline'][:, c.VT] = tg[:, VG]
if fg.shape[1] >= MU_QMIN:
results['dcline'][:, c.MU_PMIN] = fg[:, MU_PMAX] + tg[:, MU_PMIN]
results['dcline'][:, c.MU_PMAX] = fg[:, MU_PMIN] + tg[:, MU_PMAX]
results['dcline'][:, c.MU_QMINF] = fg[:, MU_QMIN]
results['dcline'][:, c.MU_QMAXF] = fg[:, MU_QMAX]
results['dcline'][:, c.MU_QMINT] = tg[:, MU_QMIN]
results['dcline'][:, c.MU_QMAXT] = tg[:, MU_QMAX]
##----- convert stuff back to external indexing -----
results['order']['int']['dcline'] = results[
'dcline'] ## save internal version
## copy results to external version
o['ext']['dcline'][k, c.PF:c.VT + 1] = results['dcline'][:, c.PF:c.VT + 1]
if results['dcline'].shape[1] == c.MU_QMAXT:
o['ext']['dcline'][k, c.MU_PMIN:c.MU_QMAXT + 1] = \
results['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1]
results['dcline'] = o['ext']['dcline'] ## use external version
return results
def plot_settings(self):
""" Plotting settings (colors, linewidths etc.), possibly depending on bus variable.
"""
var = 'Vbase' # base colors etc on Vbase
var_lim = [380, 300,
0] # different categories of Vbase, should be a list
# bus settings
self.sets_variable_lim = var_lim
var = self.bus.loc[:, var]
self.bus_set = arr([
find(v >= arr(var_lim))[0] if v >= var_lim[-1] else -1 for v in var
])
self.bus_color = ['r', (230. / 255, 152. / 255, 0), 'g']
self.bus_name_color = ['k'] * 3
self.bus_lw = [1.5, 1, 1]
self.bus_name_fs = [0, 0, 0]
# line settings
var_line = var.loc[self.line.bus0]
self.line_set = arr([
find(v >= arr(var_lim))[0] if v >= var_lim[-1] else -1
for v in var_line
])
self.line_lw = [1, 1, 1]
self.line_color = ['r', (230. / 255, 152. / 255, 0), 'g']
# Link
self.link_lw = 1
self.link_color = 'b'
# Interactive plot
self.interactive = True # interactive map mode
self.picker_node = 7 # tolerance for interactive picking
self.picker_arc = 3
self.significant_figures = 3 # when info is displayed
self.info_fc = [213. / 255, 230. / 255, 1] # color for info box
self.info_ec = 'k' # color info-box edge
self.info_lw = 1 # info-box edge width
self.equal_aspect = False
def bustypes(bus, gen):
"""Builds index lists of each type of bus (C{REF}, C{PV}, C{PQ}).
Generators with "out-of-service" status are treated as L{PQ} buses with
zero generation (regardless of C{Pg}/C{Qg} values in gen). Expects C{bus}
and C{gen} have been converted to use internal consecutive bus numbering.
@param bus: bus data
@param gen: generator data
@return: index lists of each bus type
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
changes by Uni Kassel (Florian Schaefer): If new ref bus is chosen -> Init as numpy array
"""
# get generator status
nb = bus.shape[0]
ng = gen.shape[0]
# gen connection matrix, element i, j is 1 if, generator j at bus i is ON
Cg = sparse((gen[:, GEN_STATUS] > 0, (gen[:, GEN_BUS], range(ng))),
(nb, ng))
# number of generators at each bus that are ON
bus_gen_status = (Cg * ones(ng, int)).astype(bool)
# form index lists for slack, PV, and PQ buses
ref = find((bus[:, BUS_TYPE] == REF) & bus_gen_status) # ref bus index
pv = find((bus[:, BUS_TYPE] == PV) & bus_gen_status) # PV bus indices
pq = find((bus[:, BUS_TYPE] == PQ) | ~bus_gen_status) # PQ bus indices
# throw an error since no reference bus is defined
if len(ref) == 0:
raise KeyError(
"No reference bus (ext_grid) is available. Abort power flow calculation. Please add an ext_grid"
)
# bugfix Pypower: must be an numpy array!
# ref = zeros(1, dtype=int)
# ref[0] = pv[0] # use the first PV bus
# pv = pv[1:] # take it off PV list
return ref, pv, pq
def totcost(gencost, Pg):
"""Computes total cost for generators at given output level.
Computes total cost for generators given a matrix in gencost format and
a column vector or matrix of generation levels. The return value has the
same dimensions as PG. Each row of C{gencost} is used to evaluate the
cost at the points specified in the corresponding row of C{Pg}.
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
ng, m = gencost.shape
totalcost = zeros(ng)
if len(gencost) > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
ipol = find(gencost[:, MODEL] == POLYNOMIAL)
if len(ipwl) > 0:
p = gencost[:, COST:(m-1):2]
c = gencost[:, (COST+1):m:2]
for i in ipwl:
ncost = gencost[i, NCOST]
for k in arange(ncost - 1):
p1, p2 = p[i, k], p[i, k+1]
c1, c2 = c[i, k], c[i, k+1]
m = (c2 - c1) / (p2 - p1)
b = c1 - m * p1
Pgen = Pg[i]
if Pgen < p2:
totalcost[i] = m * Pgen + b
break
totalcost[i] = m * Pgen + b
if len(ipol) > 0:
totalcost[ipol] = polycost(gencost[ipol, :], Pg[ipol])
return totalcost
def totcost(gencost, Pg):
"""Computes total cost for generators at given output level.
Computes total cost for generators given a matrix in gencost format and
a column vector or matrix of generation levels. The return value has the
same dimensions as PG. Each row of C{gencost} is used to evaluate the
cost at the points specified in the corresponding row of C{Pg}.
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
ng, m = gencost.shape
totalcost = zeros(ng)
if len(gencost) > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
ipol = find(gencost[:, MODEL] == POLYNOMIAL)
if len(ipwl) > 0:
p = gencost[:, COST:(m-1):2]
c = gencost[:, (COST+1):m:2]
for i in ipwl:
ncost = gencost[i, NCOST]
for k in arange(ncost - 1):
p1, p2 = p[i, k], p[i, k+1]
c1, c2 = c[i, k], c[i, k+1]
m = (c2 - c1) / (p2 - p1)
b = c1 - m * p1
Pgen = Pg[i]
if Pgen < p2:
totalcost[i] = m * Pgen + b
break
totalcost[i] = m * Pgen + b
if len(ipol) > 0:
totalcost[ipol] = polycost(gencost[ipol, :], Pg[ipol])
return totalcost
def polycost(gencost, Pg, der=0):
"""Evaluates polynomial generator cost & derivatives.
C{f = polycost(gencost, Pg)} returns the vector of costs evaluated at C{Pg}
C{df = polycost(gencost, Pg, 1)} returns the vector of first derivatives
of costs evaluated at C{Pg}
C{d2f = polycost(gencost, Pg, 2)} returns the vector of second derivatives
of costs evaluated at C{Pg}
C{gencost} must contain only polynomial costs
C{Pg} is in MW, not p.u. (works for C{Qg} too)
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
if any(gencost[:, MODEL] == PW_LINEAR):
sys.stderr.write('polycost: all costs must be polynomial\n')
ng = len(Pg)
maxN = max( gencost[:, NCOST].astype(int) )
minN = min( gencost[:, NCOST].astype(int) )
## form coefficient matrix where 1st column is constant term, 2nd linear, etc.
c = zeros((ng, maxN))
for n in arange(minN, maxN + 1):
k = find(gencost[:, NCOST] == n) ## cost with n coefficients
c[k, :n] = gencost[k, (COST + n - 1):COST - 1:-1]
## do derivatives
for d in range(1, der + 1):
if c.shape[1] >= 2:
c = c[:, 1:maxN - d + 1]
else:
c = zeros((ng, 1))
break
for k in range(2, maxN - d + 1):
c[:, k-1] = c[:, k-1] * k
## evaluate polynomial
if len(c) == 0:
f = zeros(Pg.shape)
else:
f = c[:, :1].flatten() ## constant term
for k in range(1, c.shape[1]):
f = f + c[:, k] * Pg**k
return f
def despike(datax,datay,threshold=3.0,interpolate=False):
"""
Remove spikes larger than threshold*(standard deviation of diffs in datay).
interpolate=False (default) just removes the points;
interpolate=True will just make them equal to the point to the left
(if you need to keep array length constant, say).
"""
d = np.diff(datay)
spikes = np.find(abs(d)>threshold*std(d))
if (len(spikes)>0.1*len(d)):
print 'Did not remove spikes because it wanted to remove too many.'
return datax,datay # if we're trying to remove a lot of points, just send it back...
spikes=np.delete(spikes,find(diff(spikes)==1)+1) # if spike is one point, don't delete point after as well.
if interpolate==False:
datax = np.delete(datax,spikes+1)
datay = np.delete(datay,spikes+1)
else:
# don't actually 'interpolate', just set it equal to the previous point
# (actual interpolation could get messy in the case of a two-point spike, for example)
for i in spikes+1: datay[i] = datay[i-3]
if (np.any(np.abs(diff(datay))>threshold*np.std(d))): datax,datay = despike(datax,datay,threshold,interpolate)
return datax, datay
def pipsopf_solver(om, ppopt, out_opt=None):
"""Solves AC optimal power flow using PIPS.
Inputs are an OPF model object, a PYPOWER options vector and
a dict containing keys (can be empty) for each of the desired
optional output fields.
outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (ppc) with the usual baseMVA, bus
branch, gen, gencost fields, along with the following additional
fields:
- C{order} see 'help ext2int' for details of this field
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{nln}
- C{l} lower bounds on nonlinear constraints
- C{u} upper bounds on nonlinear constraints
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
C{success} is C{True} if solver converged successfully, C{False} otherwise
C{raw} is a raw output dict in form returned by MINOS
- xr final value of optimization variables
- pimul constraint multipliers
- info solver specific termination code
- output solver specific output information
@see: L{opf}, L{pips}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
##----- initialization -----
## optional output
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
step_control = (ppopt['OPF_ALG'] == 565) ## OPF_ALG == 565, PIPS-sc
if feastol == 0:
feastol = ppopt['OPF_VIOLATION']
opt = { 'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'step_control': step_control,
'cost_mult': 1e-4,
'verbose': verbose }
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
vv, _, nn, _ = om.get_idx()
## problem dimensions
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
ny = om.getN('var', 'y') ## number of piece-wise linear costs
## linear constraints
A, l, u = om.linear_constraints()
## bounds on optimization vars
_, xmin, xmax = om.getv()
## build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
## try to select an interior initial point
ll, uu = xmin.copy(), xmax.copy()
ll[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
uu[xmax == Inf] = 1e10
x0 = (ll + uu) / 2
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180)
## angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# PQ = r_[gen[:, PMAX], gen[:, QMAX]]
# c = totcost(gencost[ipwl, :], PQ[ipwl])
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl, NCOST+2*gencost[ipwl, NCOST])] ## largest y-value in CCV data
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
# x0[vv["i1"]["y"]:vv["iN"]["y"]] = c + 0.1 * abs(c)
## find branches with flow limits
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
nl2 = len(il) ## number of constrained lines
##----- run opf -----
f_fcn = lambda x, return_hessian=False: opf_costfcn(x, om, return_hessian)
gh_fcn = lambda x: opf_consfcn(x, om, Ybus, Yf[il, :], Yt[il,:], ppopt, il)
hess_fcn = lambda x, lmbda, cost_mult: opf_hessfcn(x, lmbda, om, Ybus, Yf[il, :], Yt[il, :], ppopt, il, cost_mult)
solution = pips(f_fcn, x0, A, l, u, xmin, xmax, gh_fcn, hess_fcn, opt)
x, f, info, lmbda, output = solution["x"], solution["f"], \
solution["eflag"], solution["lmbda"], solution["output"]
success = (info > 0)
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Vm = x[vv["i1"]["Vm"]:vv["iN"]["Vm"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
Qg = x[vv["i1"]["Qg"]:vv["iN"]["Qg"]]
V = Vm * exp(1j * Va)
##----- calculate return values -----
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
bus[:, VM] = Vm
gen[:, PG] = Pg * baseMVA
gen[:, QG] = Qg * baseMVA
gen[:, VG] = Vm[ gen[:, GEN_BUS].astype(int) ]
## compute branch flows
Sf = V[ branch[:, F_BUS].astype(int) ] * conj(Yf * V) ## cplx pwr at "from" bus, p["u"].
St = V[ branch[:, T_BUS].astype(int) ] * conj(Yt * V) ## cplx pwr at "to" bus, p["u"].
branch[:, PF] = Sf.real * baseMVA
branch[:, QF] = Sf.imag * baseMVA
branch[:, PT] = St.real * baseMVA
branch[:, QT] = St.imag * baseMVA
## line constraint is actually on square of limit
## so we must fix multipliers
muSf = zeros(nl)
muSt = zeros(nl)
if len(il) > 0:
muSf[il] = \
2 * lmbda["ineqnonlin"][:nl2] * branch[il, RATE_A] / baseMVA
muSt[il] = \
2 * lmbda["ineqnonlin"][nl2:nl2+nl2] * branch[il, RATE_A] / baseMVA
## update Lagrange multipliers
bus[:, MU_VMAX] = lmbda["upper"][vv["i1"]["Vm"]:vv["iN"]["Vm"]]
bus[:, MU_VMIN] = lmbda["lower"][vv["i1"]["Vm"]:vv["iN"]["Vm"]]
gen[:, MU_PMAX] = lmbda["upper"][vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMIN] = lmbda["lower"][vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_QMAX] = lmbda["upper"][vv["i1"]["Qg"]:vv["iN"]["Qg"]] / baseMVA
gen[:, MU_QMIN] = lmbda["lower"][vv["i1"]["Qg"]:vv["iN"]["Qg"]] / baseMVA
bus[:, LAM_P] = \
lmbda["eqnonlin"][nn["i1"]["Pmis"]:nn["iN"]["Pmis"]] / baseMVA
bus[:, LAM_Q] = \
lmbda["eqnonlin"][nn["i1"]["Qmis"]:nn["iN"]["Qmis"]] / baseMVA
branch[:, MU_SF] = muSf / baseMVA
branch[:, MU_ST] = muSt / baseMVA
## package up results
nlnN = om.getN('nln')
## extract multipliers for nonlinear constraints
kl = find(lmbda["eqnonlin"] < 0)
ku = find(lmbda["eqnonlin"] > 0)
nl_mu_l = zeros(nlnN)
nl_mu_u = r_[zeros(2*nb), muSf, muSt]
nl_mu_l[kl] = -lmbda["eqnonlin"][kl]
nl_mu_u[ku] = lmbda["eqnonlin"][ku]
mu = {
'var': {'l': lmbda["lower"], 'u': lmbda["upper"]},
'nln': {'l': nl_mu_l, 'u': nl_mu_u},
'lin': {'l': lmbda["mu_l"], 'u': lmbda["mu_u"]} }
results = ppc
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
pimul = r_[
results["mu"]["nln"]["l"] - results["mu"]["nln"]["u"],
results["mu"]["lin"]["l"] - results["mu"]["lin"]["u"],
-ones(ny > 0),
results["mu"]["var"]["l"] - results["mu"]["var"]["u"],
]
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw
def makeBdc(baseMVA, bus, branch):
"""Builds the B matrices and phase shift injections for DC power flow.
Returns the B matrices and phase shift injection vectors needed for a
DC power flow.
The bus real power injections are related to bus voltage angles by::
P = Bbus * Va + PBusinj
The real power flows at the from end the lines are related to the bus
voltage angles by::
Pf = Bf * Va + Pfinj
Does appropriate conversions to p.u.
@see: L{dcpf}
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
## constants
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of lines
## check that bus numbers are equal to indices to bus (one set of bus nums)
if any(bus[:, BUS_I] != range(nb)):
stderr.write('makeBdc: buses must be numbered consecutively in '
'bus matrix\n')
## for each branch, compute the elements of the branch B matrix and the phase
## shift "quiescent" injections, where
##
## | Pf | | Bff Bft | | Vaf | | Pfinj |
## | | = | | * | | + | |
## | Pt | | Btf Btt | | Vat | | Ptinj |
##
stat = branch[:, BR_STATUS] ## ones at in-service branches
b = stat / branch[:, BR_X] ## series susceptance
tap = ones(nl) ## default tap ratio = 1
i = find(branch[:, TAP]) ## indices of non-zero tap ratios
tap[i] = branch[i, TAP] ## assign non-zero tap ratios
b = b / tap
## build connection matrix Cft = Cf - Ct for line and from - to buses
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = r_[range(nl), range(nl)] ## double set of row indices
## connection matrix
Cft = sparse((r_[ones(nl), -ones(nl)], (i, r_[f, t])), (nl, nb))
## build Bf such that Bf * Va is the vector of real branch powers injected
## at each branch's "from" bus
Bf = sparse((r_[b, -b], (i, r_[f, t])))## = spdiags(b, 0, nl, nl) * Cft
## build Bbus
Bbus = Cft.T * Bf
## build phase shift injection vectors
Pfinj = b * (-branch[:, SHIFT] * pi / 180) ## injected at the from bus ...
# Ptinj = -Pfinj ## and extracted at the to bus
Pbusinj = Cft.T * Pfinj ## Pbusinj = Cf * Pfinj + Ct * Ptinj
return Bbus, Bf, Pbusinj, Pfinj
def ext2int(ppc, val_or_field=None, ordering=None, dim=0):
"""Converts external to internal indexing.
This function has two forms, the old form that operates on
and returns individual matrices and the new form that operates
on and returns an entire PYPOWER case dict.
1. C{ppc = ext2int(ppc)}
If the input is a single PYPOWER case dict, then all isolated
buses, off-line generators and branches are removed along with any
generators, branches or areas connected to isolated buses. Then the
buses are renumbered consecutively, beginning at 0, and the
generators are sorted by increasing bus number. Any 'ext2int'
callback routines registered in the case are also invoked
automatically. All of the related
indexing information and the original data matrices are stored under
the 'order' key of the dict to be used by C{int2ext} to perform
the reverse conversions. If the case is already using internal
numbering it is returned unchanged.
Example::
ppc = ext2int(ppc)
@see: L{int2ext}, L{e2i_field}, L{e2i_data}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
ppc = deepcopy(ppc)
if val_or_field is None: # nargin == 1
first = 'order' not in ppc
if first or ppc["order"]["state"] == 'e':
## initialize order
if first:
o = {
'ext': {
'bus': None,
'branch': None,
'gen': None
},
'bus': { 'e2i': None,
'i2e': None,
'status': {} },
'gen': { 'e2i': None,
'i2e': None,
'status': {} },
'branch': { 'status': {} }
}
else:
o = ppc["order"]
## sizes
nb = ppc["bus"].shape[0]
ng = ppc["gen"].shape[0]
ng0 = ng
if 'A' in ppc:
dc = True if ppc["A"].shape[1] < (2 * nb + 2 * ng) else False
elif 'N' in ppc:
dc = True if ppc["N"].shape[1] < (2 * nb + 2 * ng) else False
else:
dc = False
## save data matrices with external ordering
if 'ext' not in o: o['ext'] = {}
o["ext"]["bus"] = ppc["bus"].copy()
o["ext"]["branch"] = ppc["branch"].copy()
o["ext"]["gen"] = ppc["gen"].copy()
if 'areas' in ppc:
if len(ppc["areas"]) == 0: ## if areas field is empty
del ppc['areas'] ## delete it (so it's ignored)
else: ## otherwise
o["ext"]["areas"] = ppc["areas"].copy() ## save it
## check that all buses have a valid BUS_TYPE
bt = ppc["bus"][:, BUS_TYPE]
err = find(~((bt == PQ) | (bt == PV) | (bt == REF) | (bt == NONE)))
if len(err) > 0:
sys.stderr.write('ext2int: bus %d has an invalid BUS_TYPE\n' % err)
## determine which buses, branches, gens are connected and
## in-service
n2i = sparse((range(nb), (ppc["bus"][:, BUS_I], zeros(nb))),
shape=(max(ppc["bus"][:, BUS_I]) + 1, 1))
n2i = array( n2i.todense().flatten() )[0, :] # as 1D array
bs = (bt != NONE) ## bus status
o["bus"]["status"]["on"] = find( bs ) ## connected
o["bus"]["status"]["off"] = find( ~bs ) ## isolated
gs = ( (ppc["gen"][:, GEN_STATUS] > 0) & ## gen status
bs[ n2i[ppc["gen"][:, GEN_BUS].astype(int)] ] )
o["gen"]["status"]["on"] = find( gs ) ## on and connected
o["gen"]["status"]["off"] = find( ~gs ) ## off or isolated
brs = ( ppc["branch"][:, BR_STATUS].astype(int) & ## branch status
bs[n2i[ppc["branch"][:, F_BUS].astype(int)]] &
bs[n2i[ppc["branch"][:, T_BUS].astype(int)]] ).astype(bool)
o["branch"]["status"]["on"] = find( brs ) ## on and conn
o["branch"]["status"]["off"] = find( ~brs )
if 'areas' in ppc:
ar = bs[ n2i[ppc["areas"][:, PRICE_REF_BUS].astype(int)] ]
o["areas"] = {"status": {}}
o["areas"]["status"]["on"] = find( ar )
o["areas"]["status"]["off"] = find( ~ar )
## delete stuff that is "out"
if len(o["bus"]["status"]["off"]) > 0:
# ppc["bus"][o["bus"]["status"]["off"], :] = array([])
ppc["bus"] = ppc["bus"][o["bus"]["status"]["on"], :]
if len(o["branch"]["status"]["off"]) > 0:
# ppc["branch"][o["branch"]["status"]["off"], :] = array([])
ppc["branch"] = ppc["branch"][o["branch"]["status"]["on"], :]
if len(o["gen"]["status"]["off"]) > 0:
# ppc["gen"][o["gen"]["status"]["off"], :] = array([])
ppc["gen"] = ppc["gen"][o["gen"]["status"]["on"], :]
if 'areas' in ppc and (len(o["areas"]["status"]["off"]) > 0):
# ppc["areas"][o["areas"]["status"]["off"], :] = array([])
ppc["areas"] = ppc["areas"][o["areas"]["status"]["on"], :]
## update size
nb = ppc["bus"].shape[0]
## apply consecutive bus numbering
o["bus"]["i2e"] = ppc["bus"][:, BUS_I].copy()
o["bus"]["e2i"] = zeros(max(o["bus"]["i2e"]) + 1)
o["bus"]["e2i"][o["bus"]["i2e"].astype(int)] = arange(nb)
ppc["bus"][:, BUS_I] = \
o["bus"]["e2i"][ ppc["bus"][:, BUS_I].astype(int) ].copy()
ppc["gen"][:, GEN_BUS] = \
o["bus"]["e2i"][ ppc["gen"][:, GEN_BUS].astype(int) ].copy()
ppc["branch"][:, F_BUS] = \
o["bus"]["e2i"][ ppc["branch"][:, F_BUS].astype(int) ].copy()
ppc["branch"][:, T_BUS] = \
o["bus"]["e2i"][ ppc["branch"][:, T_BUS].astype(int) ].copy()
if 'areas' in ppc:
ppc["areas"][:, PRICE_REF_BUS] = \
o["bus"]["e2i"][ ppc["areas"][:,
PRICE_REF_BUS].astype(int) ].copy()
## reorder gens in order of increasing bus number
o["gen"]["e2i"] = argsort(ppc["gen"][:, GEN_BUS])
o["gen"]["i2e"] = argsort(o["gen"]["e2i"])
ppc["gen"] = ppc["gen"][o["gen"]["e2i"].astype(int), :]
if 'int' in o:
del o['int']
o["state"] = 'i'
ppc["order"] = o
## update gencost, A and N
if 'gencost' in ppc:
ordering = ['gen'] ## Pg cost only
if ppc["gencost"].shape[0] == (2 * ng0):
ordering.append('gen') ## include Qg cost
ppc = e2i_field(ppc, 'gencost', ordering)
if 'A' in ppc or 'N' in ppc:
if dc:
ordering = ['bus', 'gen']
else:
ordering = ['bus', 'bus', 'gen', 'gen']
if 'A' in ppc:
ppc = e2i_field(ppc, 'A', ordering, 1)
if 'N' in ppc:
ppc = e2i_field(ppc, 'N', ordering, 1)
## execute userfcn callbacks for 'ext2int' stage
if 'userfcn' in ppc:
ppc = run_userfcn(ppc['userfcn'], 'ext2int', ppc)
else: ## convert extra data
if isinstance(val_or_field, str) or isinstance(val_or_field, list):
## field
warn('Calls of the form ppc = ext2int(ppc, '
'\'field_name\', ...) have been deprecated. Please '
'replace ext2int with e2i_field.', DeprecationWarning)
gen, branch = val_or_field, ordering
ppc = e2i_field(ppc, gen, branch, dim)
else:
## value
warn('Calls of the form val = ext2int(ppc, val, ...) have been '
'deprecated. Please replace ext2int with e2i_data.',
DeprecationWarning)
gen, branch = val_or_field, ordering
ppc = e2i_data(ppc, gen, branch, dim)
return ppc
def qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt):
"""Quadratic Program Solver based on IPOPT.
Uses IPOPT to solve the following QP (quadratic programming) problem::
min 1/2 x'*H*x + c'*x
x
subject to::
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except C{H}, C{C}, C{A} and C{L}):
- C{H} : matrix (possibly sparse) of quadratic cost coefficients
- C{C} : vector of linear cost coefficients
- C{A, l, u} : define the optional linear constraints. Default
values for the elements of C{l} and C{u} are -Inf and Inf,
respectively.
- C{xmin, xmax} : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
- C{x0} : optional starting value of optimization vector C{x}
- C{opt} : optional options structure with the following fields,
all of which are also optional (default values shown in parentheses)
- C{verbose} (0) - controls level of progress output displayed
- 0 = no progress output
- 1 = some progress output
- 2 = verbose progress output
- C{max_it} (0) - maximum number of iterations allowed
- 0 = use algorithm default
- C{ipopt_opt} - options struct for IPOPT, values in
C{verbose} and C{max_it} override these options
- C{problem} : The inputs can alternatively be supplied in a single
C{problem} dict with fields corresponding to the input arguments
described above: C{H, c, A, l, u, xmin, xmax, x0, opt}
Outputs:
- C{x} : solution vector
- C{f} : final objective function value
- C{exitflag} : exit flag
- 1 = first order optimality conditions satisfied
- 0 = maximum number of iterations reached
- -1 = numerically failed
- C{output} : output struct with the following fields:
- C{iterations} - number of iterations performed
- C{hist} - dict list with trajectories of the following:
C{feascond}, C{gradcond}, C{compcond}, C{costcond}, C{gamma},
C{stepsize}, C{obj}, C{alphap}, C{alphad}
- message - exit message
- C{lmbda} : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
- C{mu_l} - lower (left-hand) limit on linear constraints
- C{mu_u} - upper (right-hand) limit on linear constraints
- C{lower} - lower bound on optimization variables
- C{upper} - upper bound on optimization variables
Calling syntax options::
x, f, exitflag, output, lmbda = \
qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(H, c, A, l, u)
x = qps_ipopt(H, c, A, l, u, xmin, xmax)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(problem), where problem is a struct with fields:
H, c, A, l, u, xmin, xmax, x0, opt
all fields except 'c', 'A' and 'l' or 'u' are optional
x = qps_ipopt(...)
x, f = qps_ipopt(...)
x, f, exitflag = qps_ipopt(...)
x, f, exitflag, output = qps_ipopt(...)
x, f, exitflag, output, lmbda = qps_ipopt(...)
Example::
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ]
c = zeros((4, 1))
A = [ 1 1 1 1
0.17 0.11 0.10 0.18 ]
l = [1, 0.10]
u = [1, Inf]
xmin = zeros((4, 1))
x0 = [1, 0, 0, 1]
opt = {'verbose': 2)
x, f, s, out, lambda = qps_ipopt(H, c, A, l, u, xmin, [], x0, opt)
Problem from U{http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm}
@see: C{pyipopt}, L{ipopt_options}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
if 'opt' in p: opt = p['opt']
if 'x0' in p: x0 = p['x0']
if 'xmax' in p: xmax = p['xmax']
if 'xmin' in p: xmin = p['xmin']
if 'u' in p: u = p['u']
if 'l' in p: l = p['l']
if 'A' in p: A = p['A']
if 'c' in p: c = p['c']
if 'H' in p: H = p['H']
else: ## individual args
assert H is not None
assert c is not None
assert A is not None
assert l is not None
if opt is None:
opt = {}
# if x0 is None:
# x0 = array([])
# if xmax is None:
# xmax = array([])
# if xmin is None:
# xmin = array([])
## define nx, set default values for missing optional inputs
if len(H) == 0 or not any(any(H)):
if len(A) == 0 and len(xmin) == 0 and len(xmax) == 0:
stderr.write('qps_ipopt: LP problem must include constraints or variable bounds\n')
else:
if len(A) > 0:
nx = shape(A)[1]
elif len(xmin) > 0:
nx = len(xmin)
else: # if len(xmax) > 0
nx = len(xmax)
H = sparse((nx, nx))
else:
nx = shape(H)[0]
if len(c) == 0:
c = zeros(nx)
if len(A) > 0 and (len(l) == 0 or all(l == -Inf)) and \
(len(u) == 0 or all(u == Inf)):
A = None ## no limits => no linear constraints
nA = shape(A)[0] ## number of original linear constraints
if nA:
if len(u) == 0: ## By default, linear inequalities are ...
u = Inf * ones(nA) ## ... unbounded above and ...
if len(l) == 0:
l = -Inf * ones(nA) ## ... unbounded below.
if len(x0) == 0:
x0 = zeros(nx)
## default options
if 'verbose' in opt:
verbose = opt['verbose']
else:
verbose = 0
if 'max_it' in opt:
max_it = opt['max_it']
else:
max_it = 0
## make sure args are sparse/full as expected by IPOPT
if len(H) > 0:
if not issparse(H):
H = sparse(H)
if not issparse(A):
A = sparse(A)
##----- run optimization -----
## set options dict for IPOPT
options = {}
if 'ipopt_opt' in opt:
options['ipopt'] = ipopt_options(opt['ipopt_opt'])
else:
options['ipopt'] = ipopt_options()
options['ipopt']['jac_c_constant'] = 'yes'
options['ipopt']['jac_d_constant'] = 'yes'
options['ipopt']['hessian_constant'] = 'yes'
options['ipopt']['least_square_init_primal'] = 'yes'
options['ipopt']['least_square_init_duals'] = 'yes'
# options['ipopt']['mehrotra_algorithm'] = 'yes' ## default 'no'
if verbose:
options['ipopt']['print_level'] = min(12, verbose * 2 + 1)
else:
options['ipopt']['print_level = 0']
if max_it:
options['ipopt']['max_iter'] = max_it
## define variable and constraint bounds, if given
if nA:
options['cu'] = u
options['cl'] = l
if len(xmin) > 0:
options['lb'] = xmin
if len(xmax) > 0:
options['ub'] = xmax
## assign function handles
funcs = {}
funcs['objective'] = lambda x: 0.5 * x.T * H * x + c.T * x
funcs['gradient'] = lambda x: H * x + c
funcs['constraints'] = lambda x: A * x
funcs['jacobian'] = lambda x: A
funcs['jacobianstructure'] = lambda : A
funcs['hessian'] = lambda x, sigma, lmbda: tril(H)
funcs['hessianstructure'] = lambda : tril(H)
## run the optimization
x, info = pyipopt(x0, funcs, options)
if info['status'] == 0 | info['status'] == 1:
eflag = 1
else:
eflag = 0
output = {}
if 'iter' in info:
output['iterations'] = info['iter']
output['info'] = info['status']
f = funcs['objective'](x)
## repackage lmbdas
kl = find(info['lmbda'] < 0) ## lower bound binding
ku = find(info['lmbda'] > 0) ## upper bound binding
mu_l = zeros(nA)
mu_l[kl] = -info['lmbda'][kl]
mu_u = zeros(nA)
mu_u[ku] = info['lmbda'][ku]
lmbda = {
'mu_l': mu_l,
'mu_u': mu_u,
'lower': info['zl'],
'upper': info['zu']
}
return x, f, eflag, output, lmbda
def pfsoln(baseMVA, bus0, gen0, branch0, Ybus, Yf, Yt, V, ref, pv, pq):
"""Updates bus, gen, branch data structures to match power flow soln.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
## initialize return values
bus = bus0
gen = gen0
branch = branch0
##----- update bus voltages -----
bus[:, VM] = abs(V)
bus[:, VA] = angle(V) * 180 / pi
##----- update Qg for all gens and Pg for slack bus(es) -----
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS].astype(int) ## what buses are they at?
## compute total injected bus powers
Sbus = V[gbus] * conj(Ybus[gbus, :] * V)
## update Qg for all generators
gen[:, QG] = zeros(gen.shape[0]) ## zero out all Qg
gen[on, QG] = Sbus.imag * baseMVA + bus[gbus, QD] ## inj Q + local Qd
## ... at this point any buses with more than one generator will have
## the total Q dispatch for the bus assigned to each generator. This
## must be split between them. We do it first equally, then in proportion
## to the reactive range of the generator.
if len(on) > 1:
## build connection matrix, element i, j is 1 if gen on(i) at bus j is ON
nb = bus.shape[0]
ngon = on.shape[0]
Cg = csr_matrix((ones(ngon), (range(ngon), gbus)), (ngon, nb))
## divide Qg by number of generators at the bus to distribute equally
ngg = Cg * Cg.sum(0).T ## ngon x 1, number of gens at this gen's bus
ngg = asarray(ngg).flatten() # 1D array
gen[on, QG] = gen[on, QG] / ngg
## divide proportionally
Cmin = csr_matrix((gen[on, QMIN], (range(ngon), gbus)), (ngon, nb))
Cmax = csr_matrix((gen[on, QMAX], (range(ngon), gbus)), (ngon, nb))
Qg_tot = Cg.T * gen[on, QG]## nb x 1 vector of total Qg at each bus
Qg_min = Cmin.sum(0).T ## nb x 1 vector of min total Qg at each bus
Qg_max = Cmax.sum(0).T ## nb x 1 vector of max total Qg at each bus
Qg_min = asarray(Qg_min).flatten() # 1D array
Qg_max = asarray(Qg_max).flatten() # 1D array
## gens at buses with Qg range = 0
ig = find(Cg * Qg_min == Cg * Qg_max)
Qg_save = gen[on[ig], QG]
gen[on, QG] = gen[on, QMIN] + \
(Cg * ((Qg_tot - Qg_min) / (Qg_max - Qg_min + EPS))) * \
(gen[on, QMAX] - gen[on, QMIN]) ## ^ avoid div by 0
gen[on[ig], QG] = Qg_save ## (terms are mult by 0 anyway)
## update Pg for slack bus(es)
## inj P + local Pd
for k in range(len(ref)):
refgen = find(gbus == ref[k]) ## which is(are) the reference gen(s)?
gen[on[refgen[0]], PG] = \
Sbus[refgen[0]].real * baseMVA + bus[ref[k], PD]
if len(refgen) > 1: ## more than one generator at this ref bus
## subtract off what is generated by other gens at this bus
gen[on[refgen[0]], PG] = \
gen[on[refgen[0]], PG] - sum(gen[on[refgen[1:len(refgen)]], PG])
##----- update/compute branch power flows -----
out = find(branch[:, BR_STATUS] == 0) ## out-of-service branches
br = find(branch[:, BR_STATUS]).astype(int) ## in-service branches
## complex power at "from" bus
Sf = V[ branch[br, F_BUS].astype(int) ] * conj(Yf[br, :] * V) * baseMVA
## complex power injected at "to" bus
St = V[ branch[br, T_BUS].astype(int) ] * conj(Yt[br, :] * V) * baseMVA
branch[ ix_(br, [PF, QF, PT, QT]) ] = c_[Sf.real, Sf.imag, St.real, St.imag]
branch[ ix_(out, [PF, QF, PT, QT]) ] = zeros((len(out), 4))
return bus, gen, branch
def ipoptopf_solver(om, ppopt):
"""Solves AC optimal power flow using IPOPT.
Inputs are an OPF model object and a PYPOWER options vector.
Outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (ppc) with the usual C{baseMVA}, C{bus}
C{branch}, C{gen}, C{gencost} fields, along with the following additional
fields:
- C{order} see 'help ext2int' for details of this field
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{nln}
- C{l} lower bounds on nonlinear constraints
- C{u} upper bounds on nonlinear constraints
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
C{success} is C{True} if solver converged successfully, C{False} otherwise
C{raw} is a raw output dict in form returned by MINOS
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
@see: L{opf}, L{pips}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
import pyipopt
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc['baseMVA'], ppc['bus'], ppc['gen'], ppc['branch'], ppc['gencost']
vv, _, nn, _ = om.get_idx()
## problem dimensions
nb = shape(bus)[0] ## number of buses
ng = shape(gen)[0] ## number of gens
nl = shape(branch)[0] ## number of branches
ny = om.getN('var', 'y') ## number of piece-wise linear costs
## linear constraints
A, l, u = om.linear_constraints()
## bounds on optimization vars
_, xmin, xmax = om.getv()
## build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
## try to select an interior initial point
ll = xmin.copy(); uu = xmax.copy()
ll[xmin == -Inf] = -2e19 ## replace Inf with numerical proxies
uu[xmax == Inf] = 2e19
x0 = (ll + uu) / 2
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180)
x0[vv['i1']['Va']:vv['iN']['Va']] = Varefs[0] ## angles set to first reference angle
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# PQ = r_[gen[:, PMAX], gen[:, QMAX]]
# c = totcost(gencost[ipwl, :], PQ[ipwl])
## largest y-value in CCV data
c = gencost.flatten('F')[sub2ind(shape(gencost), ipwl, NCOST + 2 * gencost[ipwl, NCOST])]
x0[vv['i1']['y']:vv['iN']['y']] = max(c) + 0.1 * abs(max(c))
# x0[vv['i1']['y']:vv['iN']['y']) = c + 0.1 * abs(c)
## find branches with flow limits
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
nl2 = len(il) ## number of constrained lines
##----- run opf -----
## build Jacobian and Hessian structure
if A is not None and issparse(A):
nA = A.shape[0] ## number of original linear constraints
else:
nA = 0
nx = len(x0)
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
Cf = sparse((ones(nl), (arange(nl), f)), (nl, nb)) ## connection matrix for line & from buses
Ct = sparse((ones(nl), (arange(nl), t)), (nl, nb)) ## connection matrix for line & to buses
Cl = Cf + Ct
Cb = Cl.T * Cl + speye(nb, nb)
Cl2 = Cl[il, :]
Cg = sparse((ones(ng), (gen[:, GEN_BUS], arange(ng))), (nb, ng))
nz = nx - 2 * (nb + ng)
nxtra = nx - 2 * nb
if nz > 0:
Js = vstack([
hstack([Cb, Cb, Cg, sparse((nb, ng)), sparse((nb, nz))]),
hstack([Cb, Cb, sparse((nb, ng)), Cg, sparse((nb, nz))]),
hstack([Cl2, Cl2, sparse((nl2, 2 * ng)), sparse((nl2, nz))]),
hstack([Cl2, Cl2, sparse((nl2, 2 * ng)), sparse((nl2, nz))])
], 'coo')
else:
Js = vstack([
hstack([Cb, Cb, Cg, sparse((nb, ng))]),
hstack([Cb, Cb, sparse((nb, ng)), Cg, ]),
hstack([Cl2, Cl2, sparse((nl2, 2 * ng)), ]),
hstack([Cl2, Cl2, sparse((nl2, 2 * ng)), ])
], 'coo')
if A is not None and issparse(A):
Js = vstack([Js, A], 'coo')
f, _, d2f = opf_costfcn(x0, om, True)
Hs = tril(d2f + vstack([
hstack([Cb, Cb, sparse((nb, nxtra))]),
hstack([Cb, Cb, sparse((nb, nxtra))]),
sparse((nxtra, nx))
]), format='coo')
## set options struct for IPOPT
# options = {}
# options['ipopt'] = ipopt_options([], ppopt)
## extra data to pass to functions
userdata = {
'om': om,
'Ybus': Ybus,
'Yf': Yf[il, :],
'Yt': Yt[il, :],
'ppopt': ppopt,
'il': il,
'A': A,
'nA': nA,
'neqnln': 2 * nb,
'niqnln': 2 * nl2,
'Js': Js,
'Hs': Hs
}
## check Jacobian and Hessian structure
#xr = rand(x0.shape)
#lmbda = rand( 2 * nb + 2 * nl2)
#Js1 = eval_jac_g(x, flag, userdata) #(xr, options.auxdata)
#Hs1 = eval_h(xr, 1, lmbda, userdata)
#i1, j1, s = find(Js)
#i2, j2, s = find(Js1)
#if (len(i1) != len(i2)) | (norm(i1 - i2) != 0) | (norm(j1 - j2) != 0):
# raise ValueError, 'something''s wrong with the Jacobian structure'
#
#i1, j1, s = find(Hs)
#i2, j2, s = find(Hs1)
#if (len(i1) != len(i2)) | (norm(i1 - i2) != 0) | (norm(j1 - j2) != 0):
# raise ValueError, 'something''s wrong with the Hessian structure'
## define variable and constraint bounds
# n is the number of variables
n = x0.shape[0]
# xl is the lower bound of x as bounded constraints
xl = xmin
# xu is the upper bound of x as bounded constraints
xu = xmax
neqnln = 2 * nb
niqnln = 2 * nl2
# number of constraints
m = neqnln + niqnln + nA
# lower bound of constraint
gl = r_[zeros(neqnln), -Inf * ones(niqnln), l]
# upper bound of constraints
gu = r_[zeros(neqnln), zeros(niqnln), u]
# number of nonzeros in Jacobi matrix
nnzj = Js.nnz
# number of non-zeros in Hessian matrix, you can set it to 0
nnzh = Hs.nnz
eval_hessian = True
if eval_hessian:
hessian = lambda x, lagrange, obj_factor, flag, user_data=None: \
eval_h(x, lagrange, obj_factor, flag, userdata)
nlp = pyipopt.create(n, xl, xu, m, gl, gu, nnzj, nnzh,
eval_f, eval_grad_f, eval_g, eval_jac_g, hessian)
else:
nnzh = 0
nlp = pyipopt.create(n, xl, xu, m, gl, gu, nnzj, nnzh,
eval_f, eval_grad_f, eval_g, eval_jac_g)
nlp.int_option('print_level', 5)
nlp.num_option('tol', 1.0000e-12)
nlp.int_option('max_iter', 250)
nlp.num_option('dual_inf_tol', 0.10000)
nlp.num_option('constr_viol_tol', 1.0000e-06)
nlp.num_option('compl_inf_tol', 1.0000e-05)
nlp.num_option('acceptable_tol', 1.0000e-08)
nlp.num_option('acceptable_constr_viol_tol', 1.0000e-04)
nlp.num_option('acceptable_compl_inf_tol', 0.0010000)
nlp.str_option('mu_strategy', 'adaptive')
iter = 0
def intermediate_callback(algmod, iter_count, obj_value, inf_pr, inf_du,
mu, d_norm, regularization_size, alpha_du, alpha_pr, ls_trials,
user_data=None):
iter = iter_count
return True
nlp.set_intermediate_callback(intermediate_callback)
## run the optimization
# returns final solution x, upper and lower bound for multiplier, final
# objective function obj and the return status of ipopt
x, zl, zu, obj, status, zg = nlp.solve(x0, m, userdata)
info = {'x': x, 'zl': zl, 'zu': zu, 'obj': obj, 'status': status, 'lmbda': zg}
nlp.close()
success = (status == 0) | (status == 1)
output = {'iterations': iter}
f, _ = opf_costfcn(x, om)
## update solution data
Va = x[vv['i1']['Va']:vv['iN']['Va']]
Vm = x[vv['i1']['Vm']:vv['iN']['Vm']]
Pg = x[vv['i1']['Pg']:vv['iN']['Pg']]
Qg = x[vv['i1']['Qg']:vv['iN']['Qg']]
V = Vm * exp(1j * Va)
##----- calculate return values -----
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
bus[:, VM] = Vm
gen[:, PG] = Pg * baseMVA
gen[:, QG] = Qg * baseMVA
gen[:, VG] = Vm[gen[:, GEN_BUS].astype(int)]
## compute branch flows
f_br = branch[:, F_BUS].astype(int)
t_br = branch[:, T_BUS].astype(int)
Sf = V[f_br] * conj(Yf * V) ## cplx pwr at "from" bus, p.u.
St = V[t_br] * conj(Yt * V) ## cplx pwr at "to" bus, p.u.
branch[:, PF] = Sf.real * baseMVA
branch[:, QF] = Sf.imag * baseMVA
branch[:, PT] = St.real * baseMVA
branch[:, QT] = St.imag * baseMVA
## line constraint is actually on square of limit
## so we must fix multipliers
muSf = zeros(nl)
muSt = zeros(nl)
if len(il) > 0:
muSf[il] = 2 * info['lmbda'][2 * nb + arange(nl2)] * branch[il, RATE_A] / baseMVA
muSt[il] = 2 * info['lmbda'][2 * nb + nl2 + arange(nl2)] * branch[il, RATE_A] / baseMVA
## update Lagrange multipliers
bus[:, MU_VMAX] = info['zu'][vv['i1']['Vm']:vv['iN']['Vm']]
bus[:, MU_VMIN] = info['zl'][vv['i1']['Vm']:vv['iN']['Vm']]
gen[:, MU_PMAX] = info['zu'][vv['i1']['Pg']:vv['iN']['Pg']] / baseMVA
gen[:, MU_PMIN] = info['zl'][vv['i1']['Pg']:vv['iN']['Pg']] / baseMVA
gen[:, MU_QMAX] = info['zu'][vv['i1']['Qg']:vv['iN']['Qg']] / baseMVA
gen[:, MU_QMIN] = info['zl'][vv['i1']['Qg']:vv['iN']['Qg']] / baseMVA
bus[:, LAM_P] = info['lmbda'][nn['i1']['Pmis']:nn['iN']['Pmis']] / baseMVA
bus[:, LAM_Q] = info['lmbda'][nn['i1']['Qmis']:nn['iN']['Qmis']] / baseMVA
branch[:, MU_SF] = muSf / baseMVA
branch[:, MU_ST] = muSt / baseMVA
## package up results
nlnN = om.getN('nln')
## extract multipliers for nonlinear constraints
kl = find(info['lmbda'][:2 * nb] < 0)
ku = find(info['lmbda'][:2 * nb] > 0)
nl_mu_l = zeros(nlnN)
nl_mu_u = r_[zeros(2 * nb), muSf, muSt]
nl_mu_l[kl] = -info['lmbda'][kl]
nl_mu_u[ku] = info['lmbda'][ku]
## extract multipliers for linear constraints
lam_lin = info['lmbda'][2 * nb + 2 * nl2 + arange(nA)] ## lmbda for linear constraints
kl = find(lam_lin < 0) ## lower bound binding
ku = find(lam_lin > 0) ## upper bound binding
mu_l = zeros(nA)
mu_l[kl] = -lam_lin[kl]
mu_u = zeros(nA)
mu_u[ku] = lam_lin[ku]
mu = {
'var': {'l': info['zl'], 'u': info['zu']},
'nln': {'l': nl_mu_l, 'u': nl_mu_u}, \
'lin': {'l': mu_l, 'u': mu_u}
}
results = ppc
results['bus'], results['branch'], results['gen'], \
results['om'], results['x'], results['mu'], results['f'] = \
bus, branch, gen, om, x, mu, f
pimul = r_[
results['mu']['nln']['l'] - results['mu']['nln']['u'],
results['mu']['lin']['l'] - results['mu']['lin']['u'],
-ones(ny > 0),
results['mu']['var']['l'] - results['mu']['var']['u']
]
raw = {'xr': x, 'pimul': pimul, 'info': info['status'], 'output': output}
return results, success, raw
def makeAvl(baseMVA, gen):
"""Construct linear constraints for constant power factor var loads.
Constructs parameters for the following linear constraint enforcing a
constant power factor constraint for dispatchable loads::
lvl <= Avl * [Pg, Qg] <= uvl
C{ivl} is the vector of indices of generators representing variable loads.
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
## data dimensions
ng = gen.shape[0] ## number of dispatchable injections
Pg = gen[:, PG] / baseMVA
Qg = gen[:, QG] / baseMVA
Pmin = gen[:, PMIN] / baseMVA
Qmin = gen[:, QMIN] / baseMVA
Qmax = gen[:, QMAX] / baseMVA
# Find out if any of these "generators" are actually dispatchable loads.
# (see 'help isload' for details on what constitutes a dispatchable load)
# Dispatchable loads are modeled as generators with an added constant
# power factor constraint. The power factor is derived from the original
# value of Pmin and either Qmin (for inductive loads) or Qmax (for
# capacitive loads). If both Qmin and Qmax are zero, this implies a unity
# power factor without the need for an additional constraint.
ivl = find( isload(gen) & ((Qmin != 0) | (Qmax != 0)) )
nvl = ivl.shape[0] ## number of dispatchable loads
## at least one of the Q limits must be zero (corresponding to Pmax == 0)
if any( (Qmin[ivl] != 0) & (Qmax[ivl] != 0) ):
stderr.write('makeAvl: either Qmin or Qmax must be equal to zero for '
'each dispatchable load.\n')
# Initial values of PG and QG must be consistent with specified power
# factor This is to prevent a user from unknowingly using a case file which
# would have defined a different power factor constraint under a previous
# version which used PG and QG to define the power factor.
Qlim = (Qmin[ivl] == 0) * Qmax[ivl] + (Qmax[ivl] == 0) * Qmin[ivl]
if any( abs( Qg[ivl] - Pg[ivl] * Qlim / Pmin[ivl] ) > 1e-6 ):
stderr.write('makeAvl: For a dispatchable load, PG and QG must be '
'consistent with the power factor defined by PMIN and '
'the Q limits.\n')
# make Avl, lvl, uvl, for lvl <= Avl * [Pg Qg] <= uvl
if nvl > 0:
xx = Pmin[ivl]
yy = Qlim
pftheta = arctan2(yy, xx)
pc = sin(pftheta)
qc = -cos(pftheta)
ii = r_[ arange(nvl), arange(nvl) ]
jj = r_[ ivl, ivl + ng ]
Avl = sparse((r_[pc, qc], (ii, jj)), (nvl, 2 * ng))
lvl = zeros(nvl)
uvl = lvl
else:
Avl = zeros((0, 2*ng))
lvl = array([])
uvl = array([])
return Avl, lvl, uvl, ivl
def total_load(bus, gen=None, load_zone=None, which_type=None):
"""Returns vector of total load in each load zone.
@param bus: standard C{bus} matrix with C{nb} rows, where the fixed active
and reactive loads are specified in columns C{PD} and C{QD}
@param gen: (optional) standard C{gen} matrix with C{ng} rows, where the
dispatchable loads are specified by columns C{PG}, C{QG}, C{PMIN},
C{QMIN} and C{QMAX} (in rows for which C{isload(GEN)} returns C{True}).
If C{gen} is empty, it assumes there are no dispatchable loads.
@param load_zone: (optional) C{nb} element vector where the value of
each element is either zero or the index of the load zone
to which the corresponding bus belongs. If C{load_zone(b) = k}
then the loads at bus C{b} will added to the values of C{Pd[k]} and
C{Qd[k]}. If C{load_zone} is empty, the default is defined as the areas
specified in the C{bus} matrix, i.e. C{load_zone = bus[:, BUS_AREA]}
and load will have dimension C{= max(bus[:, BUS_AREA])}. If
C{load_zone = 'all'}, the result is a scalar with the total system
load.
@param which_type: (default is 'BOTH' if C{gen} is provided, else 'FIXED')
- 'FIXED' : sum only fixed loads
- 'DISPATCHABLE' : sum only dispatchable loads
- 'BOTH' : sum both fixed and dispatchable loads
@see: L{scale_load}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
nb = bus.shape[0] ## number of buses
if gen is None:
gen = array([])
if load_zone is None:
load_zone = array([], int)
## fill out and check which_type
if len(gen) == 0:
which_type = 'FIXED'
if (which_type == None) and (len(gen) > 0):
which_type = 'BOTH' ## 'FIXED', 'DISPATCHABLE' or 'BOTH'
if (which_type[0] != 'F') and (which_type[0] != 'D') and (which_type[0] != 'B'):
stderr.write("total_load: which_type should be 'FIXED, 'DISPATCHABLE or 'BOTH'\n")
want_Q = True
want_fixed = (which_type[0] == 'B') | (which_type[0] == 'F')
want_disp = (which_type[0] == 'B') | (which_type[0] == 'D')
## initialize load_zone
if isinstance(load_zone, basestring) and (load_zone == 'all'):
load_zone = ones(nb, int) ## make a single zone of all buses
elif len(load_zone) == 0:
load_zone = bus[:, BUS_AREA].astype(int) ## use areas defined in bus data as zones
nz = max(load_zone) ## number of load zones
## fixed load at each bus, & initialize dispatchable
if want_fixed:
Pdf = bus[:, PD] ## real power
if want_Q:
Qdf = bus[:, QD] ## reactive power
else:
Pdf = zeros(nb) ## real power
if want_Q:
Qdf = zeros(nb) ## reactive power
## dispatchable load at each bus
if want_disp: ## need dispatchable
ng = gen.shape[0]
is_ld = isload(gen) and (gen[:, GEN_STATUS] > 0)
ld = find(is_ld)
## create map of external bus numbers to bus indices
i2e = bus[:, BUS_I].astype(int)
e2i = zeros(max(i2e) + 1)
e2i[i2e] = arange(nb)
gbus = gen[:, GEN_BUS].astype(int)
Cld = sparse((is_ld, (e2i[gbus], arange(ng))), (nb, ng))
Pdd = -Cld * gen[:, PMIN] ## real power
if want_Q:
Q = zeros(ng)
Q[ld] = (gen[ld, QMIN] == 0) * gen[ld, QMAX] + \
(gen[ld, QMAX] == 0) * gen[ld, QMIN]
Qdd = -Cld * Q ## reactive power
else:
Pdd = zeros(nb)
if want_Q:
Qdd = zeros(nb)
## compute load sums
Pd = zeros(nz)
if want_Q:
Qd = zeros(nz)
for k in range(1, nz + 1):
idx = find(load_zone == k)
Pd[k - 1] = sum(Pdf[idx]) + sum(Pdd[idx])
if want_Q:
Qd[k - 1] = sum(Qdf[idx]) + sum(Qdd[idx])
return Pd, Qd
z = scipy.io.loadmat('tmp2');
mi = z['mi']
sx,sy = mi.shape
#im = plt.imshow(mi, interpolation='bilinear',
# origin='lower', extent=[1,sx,1,sx])
#plt.savefig('mi.pdf')
#plt.show()
print "MI Loaded"
mi = np.triu(mi)
a = mi.ravel();
print a
level = ss.scoreatpercentile(a,99.)
indexes = np.transpose(np.find(mi<level))
#mi[mi<level]=0
plt.savefig('mi2.pdf')
exit()
print level
print "MI prunned"
G = nx.Graph();
for r in indexes:
#for i in xrange(sx):
#if i % 100 == 0:
# print i
#for j in xrange(i):
# z = mi[i][j]
# if z > 0:
def t_auction_pips(quiet=False):
"""Tests for code in auction.py, using PIPS solver.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
n_tests = 183
t_begin(n_tests, quiet)
try:
from pypower.extras.smartmarket import runmkt
except ImportError:
t_skip(n_tests, 'smartmarket code not available')
return
ppopt = ppoption
ppopt['OPF_VIOLATION'] = 1e-7
ppopt['PDIPM_GRADTOL'] = 1e-6
ppopt['PDIPM_COMPTOL'] = 1e-7
ppopt['PDIPM_COSTTOL'] = 5e-9
ppopt['OPF_ALG'] = 560
ppopt['OUT_ALL_LIM'] = 1
ppopt['OUT_BRANCH'] = 0
ppopt['OUT_SYS_SUM'] = 0
ppopt['OUT_ALL'] = 0
ppopt['VERBOSE'] = 0
q = array([
[12, 24, 24],
[12, 24, 24],
[12, 24, 24],
[12, 24, 24],
[12, 24, 24],
[12, 24, 24],
[10, 10, 10],
[10, 10, 10],
[10, 10, 10],
])
##----- one offer block marginal @ $50 -----
p = array([
[20, 50, 60],
[20, 40, 70],
[20, 42, 80],
[20, 44, 90],
[20, 46, 75],
[20, 48, 60],
[100, 70, 60],
[100, 50, 20],
[100, 60, 50]
])
t = 'one marginal offer @ $50, auction_type = 5'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1150, 100, [], [], mpopt)
cq5 = cq.copy()
cp5 = cp.copy()
i2e = bus.bus_i
e2i = sparse((max(i2e), 1))
e2i[i2e] = range(bus.size())
G = find( isload(gen) == False ) ## real generators
L = find( isload(gen) ) ## dispatchable loads
Gbus = e2i[gen.gen_bus[G]]
Lbus = e2i[gen.gen_bus[L]]
Qfudge = zeros(p.shape)
Qfudge[L, :] = \
diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L :].shape)
t_is( cq[G[0], 1:3], [23.32, 0], 2, t )
t_is( cp[G[0], :], 50, 4, t )
t_is( cq[L[1], 0:2], [10, 0], 2, t )
t_is( cp[L[1], :], 54.0312, 4, t )
t_is( cp[G, 0], bus.lam_P[Gbus], 8, [t, ' : gen prices'] )
t_is( cp[L, 0], bus.lam_P[Lbus] + Qfudge[L, 0], 8, [t, ' : load prices'] )
lao_X = p(G[0], 1) / bus.lam_P[Gbus[0], LAM_P]
fro_X = p(G(5), 2) / bus.lam_P[Gbus[5], LAM_P]
lab_X = p(L(2), 1) / (bus.lam_P[Lbus[2]] + Qfudge[L[2], 0])
frb_X = p(L(1), 1) / (bus.lam_P[Lbus[1]] + Qfudge[L[1], 0])
t_is( lao_X, 1, 4, 'lao_X')
t_is( fro_X, 1.1324, 4, 'fro_X')
t_is( lab_X, 1.0787, 4, 'lab_X')
t_is( frb_X, 0.9254, 4, 'frb_X')
t = 'one marginal offer @ $50, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1110, 100, [], [], mpopt)
cp1 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 6, [t, ' : prices'] )
t = 'one marginal offer @ $50, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1120, 100, [], [], mpopt)
cp2 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :] * fro_X, 8, [t, ' : gen prices'] )
t_is( cp[L[0:1], :], cp5[L[0:1], :] * fro_X, 8, [t, ' : load 1,2 prices'] )
t_is( cp[L[2], :], 60, 5, [t, ' : load 3 price'] ) ## clipped by accepted bid
t = 'one marginal offer @ $50, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1130, 100, [], [], mpopt)
cp3 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5 * lab_X, 8, [t, ' : prices'] )
t = 'one marginal offer @ $50, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1140, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], p[G[0], 1], 8, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp5[G[1:6], :] * frb_X, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp5[L, :] * frb_X, 8, [t, ' : load prices'] )
t = 'one marginal offer @ $50, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp3, 8, [t, ' : prices'] )
p2 = p.copy()
p2[L, :] = array([
[100, 100, 100],
[100, 0, 0],
[100, 100, 0]
])
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 5, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :] * fro_X, 4, [t, ' : gen prices'] )
t_is( cp[L, :], cp5[L, :] * fro_X, 4, [t, ' : load prices'] ) ## load 3 not clipped as in FRO
t = 'one marginal offer @ $50, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1170, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5 * (lao_X + lab_X) / 2, 8, [t, ' : prices'] )
t_is( cp, (cp1 + cp3) / 2, 8, [t, ' : prices'] )
t = 'one marginal offer @ $50, auction_type = 8'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1180, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp1[G, :], 8, [t, ' : gen prices'] )
t_is( cp[L, :], cp3[L, :], 8, [t, ' : load prices'] )
t = 'one marginal offer @ $50, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1100, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, p, 8, [t, ' : prices'] )
##----- one bid block marginal @ $55 -----
p[L[1], 1] = 55
t = 'one marginal bid @ $55, auction_type = 5'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1150, 100, [], [], mpopt)
cq5 = cq.copy()
cp5 = cp.copy()
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is( cq[G[0], 1:3], [24, 0], 2, t )
t_is( cp[G[0], :], 50.016, 3, t )
t_is( cq[L[1], 0:2], [10, 0.63], 2, t )
t_is( cp[L[1], :], 55, 4, t )
t_is( cp[G, 0], bus.lam_P[Gbus], 8, [t, ' : gen prices'] )
t_is( cp[L, 0], bus.lam_P[Lbus] + Qfudge[L, 0], 8, [t, ' : load prices'] )
lao_X = p[G[0], 1] / bus.lam_P[Gbus[0]]
fro_X = p[G[5], 2] / bus.lam_P[Gbus[5]]
lab_X = p[L[1], 1] / (bus.lam_P[Lbus[1]] + Qfudge[L[1], 0])
frb_X = p[L[2], 2] / (bus.lam_P[Lbus[2]] + Qfudge[L[2], 0])
t_is( lao_X, 0.9997, 4, 'lao_X')
t_is( fro_X, 1.1111, 4, 'fro_X')
t_is( lab_X, 1, 4, 'lab_X')
t_is( frb_X, 0.8960, 4, 'frb_X')
t = 'one marginal bid @ $55, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1110, 100, [], [], mpopt)
cp1 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5 * lao_X, 8, [t, ' : prices'] )
t = 'one marginal bid @ $55, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1120, 100, [], [], mpopt)
cp2 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :] * fro_X, 8, [t, ' : gen prices'] )
t_is( cp[L[0], :], cp5[L[0], :] * fro_X, 8, [t, ' : load 1 price'] )
t_is( cp[L[1], :], 55, 5, [t, ' : load 2 price'] )
t_is( cp[L[2], :], 60, 5, [t, ' : load 3 price'] )
t = 'one marginal bid @ $55, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1130, 100, [], [], mpopt)
cp3 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 7, [t, ' : prices'] )
t = 'one marginal bid @ $55, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1140, 100, [], [], mpopt)
cp4 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 50, 5, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp5[G[1:6], :] * frb_X, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp5[L, :] * frb_X, 8, [t, ' : load prices'] )
t = 'one marginal bid @ $55, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp1, 8, [t, ' : prices'] )
p2 = p.copy()
p2[G, :] = array([
[0, 0, 100],
[0, 0, 100],
[0, 0, 100],
[0, 0, 100],
[0, 0, 100],
[0, 0, 100]
])
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 3, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :] * frb_X, 3, [t, ' : gen prices'] ) ## gen 1, not clipped this time
t_is( cp[L, :], cp4[L, :], 3, [t, ' : load prices'] )
t = 'one marginal bid @ $55, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1170, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5 * (lao_X + lab_X) / 2, 8, [t, ' : prices'] )
t_is( cp, (cp1 + cp3) / 2, 8, [t, ' : prices'] )
t = 'one marginal bid @ $55, auction_type = 8'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1180, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp1[G, :], 8, [t, ' : gen prices'] )
t_is( cp[L, :], cp3[L, :], 8, [t, ' : load prices'] )
t = 'one marginal bid @ $55, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1100, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, p, 8, [t, ' : prices'] )
##----- one bid block marginal @ $54.50 and one offer block marginal @ $50 -----
p[L[1], 1] = 54.5
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 5'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1150, 100, [], [], mpopt)
cq5 = cq.copy()
cp5 = cp.copy()
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is( cq[G[0], 1:3], [23.74, 0], 2, t )
t_is( cp[G[0], :], 50, 4, t )
t_is( cq[L[1], 0:2], [10, 0.39], 2, t )
t_is( cp[L[1], :], 54.5, 4, t )
t_is( cp[G, 0], bus.lam_P[Gbus], 8, [t, ' : gen prices'] )
t_is( cp[L, 0], bus.lam_P[Lbus] + Qfudge[L, 0], 8, [t, ' : load prices'] )
lao_X = p[G[0], 1] / bus.lam_P[Gbus[0]]
fro_X = p[G[5], 2] / bus.lam_P[Gbus[5]]
lab_X = p[L[1], 1] / (bus.lam_P[Lbus[1]] + Qfudge[L[1], 0])
frb_X = p[L[2], 2] / (bus.lam_P[Lbus[2]] + Qfudge[L[2], 0])
t_is( lao_X, 1, 4, 'lao_X')
t_is( fro_X, 1.1221, 4, 'fro_X')
t_is( lab_X, 1, 4, 'lab_X')
t_is( frb_X, 0.8976, 4, 'frb_X')
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1110, 100, [], [], mpopt)
cp1 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 4, [t, ' : prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1120, 100, [], [], mpopt)
cp2 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :] * fro_X, 5, [t, ' : gen prices'] )
t_is( cp[L[0], :], cp5[L[0], :] * fro_X, 5, [t, ' : load 1 price'] )
t_is( cp[L[1], :], 54.5, 5, [t, ' : load 2 price'] )
t_is( cp[L[2], :], 60, 5, [t, ' : load 3 price'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1130, 100, [], [], mpopt)
cp3 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 6, [t, ' : prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1140, 100, [], [], mpopt)
cp4 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 50, 5, [t, ' : gen 1 price'] )
t_is( cp[G[1:5], :], cp5[G[1:5], :] * frb_X, 8, [t, ' : gen 2-5 prices'] )
t_is( cp[G[5], :], 48, 5, [t, ' : gen 6 price'] )
t_is( cp[L, :], cp5[L, :] * frb_X, 8, [t, ' : load prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 4, [t, ' : prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1170, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 4, [t, ' : prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 8'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1180, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 4, [t, ' : prices'] )
t = 'marginal offer @ $50, bid @ $54.50, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1100, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, p, 8, [t, ' : prices'] )
##----- gen 1 at Pmin, load 3 block 2 marginal @ $60 -----
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 5'
p[L[1], 1] = 50 ## undo previous change
p2 = p.copy()
p2[G[0], 1:3] = [65, 65]
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1150, 100, [], [], mpopt)
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is( cp[G[0], :], 65, 4, [t, ' : gen 1 price'] )
t_is( cp[G[1], :], 54.2974, 4, [t, ' : gen 2 price'] )
cq5 = cq.copy()
cp5 = cp.copy()
cp_lam = cp5.copt()
cp_lam[0, :] = bus.lam_P[Gbus[0]] ## unclipped
lao_X = p2[G[5], 1] / bus.lam_P[Gbus[5]]
fro_X = p2[G[5], 2] / bus.lam_P[Gbus[5]]
lab_X = p2[L[2], 1] / (bus.lam_P[Lbus[2]] + Qfudge[L[2], 0])
frb_X = p2[L[1], 1] / (bus.lam_P[Lbus[1]] + Qfudge[L[1], 0])
t_is( lao_X, 0.8389, 4, 'lao_X')
t_is( fro_X, 1.0487, 4, 'fro_X')
t_is( lab_X, 1, 4, 'lab_X')
t_is( frb_X, 0.8569, 4, 'frb_X')
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1110, 100, [], [], mpopt)
cp1 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 65, 8, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp_lam[G[1:6], :] * lao_X, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp_lam[L, :] * lao_X, 8, [t, ' : load prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1120, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 65, 8, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp_lam[G[1:6], :] * fro_X, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L[0:2], :], cp_lam[L[0:2], :] * fro_X, 8, [t, ' : load 1-2 prices'] )
t_is( cp[L[2], :], 60, 8, [t, ' : load 3 price'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1130, 100, [], [], mpopt)
cp3 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 65, 8, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp_lam[G[1:6], :], 6, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp_lam[L, :], 6, [t, ' : load prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1140, 100, [], [], mpopt)
cp4 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 65, 5, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp5[G[1:6], :] * frb_X, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp5[L, :] * frb_X, 8, [t, ' : load prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp4, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1170, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G[0], :], 65, 4, [t, ' : gen 1 price'] )
t_is( cp[G[1:6], :], cp_lam[G[1:6], :] * (lao_X + lab_X) / 2, 8, [t, ' : gen 2-6 prices'] )
t_is( cp[L, :], cp_lam[L, :] * (lao_X + lab_X) / 2, 8, [t, ' : load prices'] )
t_is( cp, (cp1 + cp3) / 2, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 8'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1180, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp1[G, :], 8, [t, ' : prices'] )
t_is( cp[L, :], cp3[L, :], 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal bid @ $60, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1100, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, p2, 8, [t, ' : prices'] )
##----- gen 1 at Pmin, gen 6 block 3 marginal @ $60 -----
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 5'
p2[L, :] = array([
[100, 100, 100],
[100, 0, 0],
[100, 100, 0]
])
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1150, 100, [], [], mpopt)
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is( cp[G[0], :], 65, 4, [t, ' : gen 1 price'] )
t_is( cp[G[1], :], 57.1612, 4, [t, ' : gen 2 price'] )
cq5 = cq.copy()
cp5 = cp.copy()
cp_lam = cp5.copy()
cp_lam[0, :] = bus.lamP[Gbus[0]] ## unclipped
lao_X = p2[G[5], 2] / bus.lam_P[Gbus[5]]
fro_X = p2[G[0], 2] / bus.lam_P[Gbus[0]]
lab_X = p2[L[2], 1] / (bus.lam_P[Lbus[2]] + Qfudge[L[2], 0])
frb_X = p2[L[1], 1] / (bus.lam_P[Lbus[1]] + Qfudge[L[1], 0])
t_is( lao_X, 1, 4, 'lao_X')
t_is( fro_X, 1.1425, 4, 'fro_X')
t_is( lab_X, 1.5813, 4, 'lab_X')
t_is( frb_X, 0, 4, 'frb_X')
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1110, 100, [], [], mpopt)
cp1 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp5, 6, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1120, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp_lam * fro_X, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1130, 100, [], [], mpopt)
cp3 = cp.copy()
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp_lam * lab_X, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1140, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, 0], [654042444660], 4, [t, ' : gen prices'] )
t_is( cp[L, :], cp_lam[L, :] * frb_X, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1160, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp_lam * fro_X, 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1170, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, cp_lam * (lao_X + lab_X) / 2, 8, [t, ' : prices'] )
t_is( cp, (cp_lam + cp3) / 2, 7, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 8'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1180, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp[G, :], cp5[G, :], 7, [t, ' : prices'] )
t_is( cp[L, :], cp3[L, :], 8, [t, ' : prices'] )
t = 'gen 1 @ Pmin, marginal offer @ $60, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p2, 1100, 100, [], [], mpopt)
t_is( cq, cq5, 8, [t, ' : quantities'] )
t_is( cp, p2, 8, [t, ' : prices'] )
##----- gen 2 decommitted, one offer block marginal @ $60 -----
p[G[1], :] = p[G[1], :] + 100
t = 'price of decommited gen, auction_type = 5'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1150, 200, [], [], mpopt)
cp5 = cp.copy()
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is(sum(cq[1, :]), 0, 8, t)
t_is(cp[1, 0], 59.194, 3, t)
# Xo = p[0:6, :] / (diag(bus.lam_P[Gbus]) * ones(p[G, :].shape))
# ao = (cq[0:6, :] != 0)
# ro = (cq[0:6, :] == 0)
# Xb = p[6:9, :] / (diag(bus.lam_P[Lbus] + gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape))
# ab = (cq[6:9, :] != 0)
# rb = (cq[6:9, :] == 0)
# aXo = ao * Xo
# rXo = ro * Xo
# aXb = ab * Xb
# rXb = rb * Xb
lao_X = p[G[5], 2] / bus.lam_P[Gbus[5]]
fro_X = p[G[0], 2] / bus.lam_P[Gbus[0]]
lab_X = p[L[0], 1] / (bus.lam_P[Lbus[0]] + Qfudge[L[0], 0])
frb_X = p[L[0], 2] / (bus.lam_P[Lbus[0]] + Qfudge[L[0], 0])
t_is( lao_X, 1, 4, 'lao_X')
t_is( fro_X, 1.0212, 4, 'fro_X')
t_is( lab_X, 1.1649, 4, 'lab_X')
t_is( frb_X, 0.9985, 4, 'frb_X')
t = 'price of decommited gen, auction_type = 1'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1110, 200, [], [], mpopt)
t_is(cp[1, 0], 59.194, 3, t)
t = 'price of decommited gen, auction_type = 2'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1120, 200, [], [], mpopt)
t_is(cp[1, 0], cp5[1, 0] * fro_X, 3, t)
t = 'price of decommited gen, auction_type = 3'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1130, 200, [], [], mpopt)
t_is(cp[1, 0], cp5[1, 0] * lab_X, 3, t)
t = 'price of decommited gen, auction_type = 4'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1140, 200, [], [], mpopt)
t_is(cp[1, 0], cp5[1, 0] * frb_X, 3, t)
t = 'price of decommited gen, auction_type = 6'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1160, 200, [], [], mpopt)
t_is(cp[1, 0], cp5[1, 0] * fro_X, 3, t)
t = 'price of decommited gen, auction_type = 7'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1170, 200, [], [], mpopt)
t_is(cp[1, 0], cp5[1, 0] * (lao_X + lab_X) / 2, 3, t)
t = 'price of decommited gen, auction_type = 0'
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1100, 200, [], [], mpopt)
t_is(cp[1, 0], 120, 3, t)
t = 'single block, marginal offer @ $50, auction_type = 5'
q = array([
[60],
[36],
[36],
[36],
[36],
[36],
[30],
[10],
[20]
])
p = array([
[50],
[40],
[42],
[44],
[46],
[48],
[100],
[100],
[100]
])
MVAbase, cq, cp, bus, gen, gencost, branch, f, dispatch, success, et = \
runmkt('t_auction_case', q, p, 1150, 100, [], [], mpopt)
t_is( cq[G[0]], 35.32, 2, t )
t_is( cq[G[1:6]], q[G[1:6]], 8, [t, ' : gen qtys'] )
t_is( cp[G[0]], 50, 4, t )
t_is( cq[L], q[L], 8, [t, ' : load qtys'] )
t_is( cp[L[1], :], 54.03, 2, t )
t_is( cp[G], bus.lam_P[Gbus], 8, [t, ' : gen prices'] )
Qfudge = zeros(p.shape)
Qfudge[L, :] = diag(gen.Qg[L] / gen.Pg[L] * bus.lam_Q[Lbus]) * ones(p[L, :].shape)
t_is( cp[L], bus.lam_P[Lbus] + Qfudge[L, 0], 8, [t, ' : load prices'] )
t_end()
def qps_gurobi(H, c, A, l, u, xmin, xmax, x0, opt):
"""Quadratic Program Solver based on GUROBI.
A wrapper function providing a PYPOWER standardized interface for using
gurobipy to solve the following QP (quadratic programming)
problem:
min 1/2 x'*H*x + c'*x
x
subject to
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except H, c, A and l):
H : matrix (possibly sparse) of quadratic cost coefficients
c : vector of linear cost coefficients
A, l, u : define the optional linear constraints. Default
values for the elements of l and u are -Inf and Inf,
respectively.
xmin, xmax : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
x0 : optional starting value of optimization vector C{x}
opt : optional options structure with the following fields,
all of which are also optional (default values shown in
parentheses)
verbose (0) - controls level of progress output displayed
0 = no progress output
1 = some progress output
2 = verbose progress output
grb_opt - options dict for Gurobi, value in
verbose overrides these options
problem : The inputs can alternatively be supplied in a single
PROBLEM dict with fields corresponding to the input arguments
described above: H, c, A, l, u, xmin, xmax, x0, opt
Outputs:
x : solution vector
f : final objective function value
exitflag : gurobipy exit flag
1 = converged
0 or negative values = negative of GUROBI_MEX exit flag
(see gurobipy documentation for details)
output : gurobipy output dict
(see gurobipy documentation for details)
lmbda : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
mu_l - lower (left-hand) limit on linear constraints
mu_u - upper (right-hand) limit on linear constraints
lower - lower bound on optimization variables
upper - upper bound on optimization variables
Note the calling syntax is almost identical to that of QUADPROG
from MathWorks' Optimization Toolbox. The main difference is that
the linear constraints are specified with A, l, u instead of
A, b, Aeq, beq.
Calling syntax options:
x, f, exitflag, output, lmbda = ...
qps_gurobi(H, c, A, l, u, xmin, xmax, x0, opt)
r = qps_gurobi(H, c, A, l, u)
r = qps_gurobi(H, c, A, l, u, xmin, xmax)
r = qps_gurobi(H, c, A, l, u, xmin, xmax, x0)
r = qps_gurobi(H, c, A, l, u, xmin, xmax, x0, opt)
r = qps_gurobi(problem), where problem is a dict with fields:
H, c, A, l, u, xmin, xmax, x0, opt
all fields except 'c', 'A' and 'l' or 'u' are optional
Example: (problem from from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm)
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ]
c = zeros((4, 1))
A = [ [1 1 1 1]
[0.17 0.11 0.10 0.18] ]
l = [1; 0.10]
u = [1; Inf]
xmin = zeros((4, 1))
x0 = [1; 0; 0; 1]
opt = {'verbose': 2}
x, f, s, out, lmbda = qps_gurobi(H, c, A, l, u, xmin, [], x0, opt)
@see: L{gurobipy}.
"""
import gurobipy
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
if 'opt' in p: opt = p['opt']
if 'x0' in p: x0 = p['x0']
if 'xmax' in p: xmax = p['xmax']
if 'xmin' in p: xmin = p['xmin']
if 'u' in p: u = p['u']
if 'l' in p: l = p['l']
if 'A' in p: A = p['A']
if 'c' in p: c = p['c']
if 'H' in p: H = p['H']
else: ## individual args
assert H is not None
assert c is not None
assert A is not None
assert l is not None
if opt is None:
opt = {}
# if x0 is None:
# x0 = array([])
# if xmax is None:
# xmax = array([])
# if xmin is None:
# xmin = array([])
## define nx, set default values for missing optional inputs
if len(H) == 0 or not any(any(H)):
if len(A) == 0 and len(xmin) == 0 and len(xmax) == 0:
stderr.write('qps_gurobi: LP problem must include constraints or variable bounds\n')
else:
if len(A) > 0:
nx = shape(A)[1]
elif len(xmin) > 0:
nx = len(xmin)
else: # if len(xmax) > 0
nx = len(xmax)
H = sparse((nx, nx))
else:
nx = shape(H)[0]
if len(c) == 0:
c = zeros(nx)
if len(A) > 0 and (len(l) == 0 or all(l == -Inf)) and \
(len(u) == 0 or all(u == Inf)):
A = None ## no limits => no linear constraints
nA = shape(A)[0] ## number of original linear constraints
if nA:
if len(u) == 0: ## By default, linear inequalities are ...
u = Inf * ones(nA) ## ... unbounded above and ...
if len(l) == 0:
l = -Inf * ones(nA) ## ... unbounded below.
if len(x0) == 0:
x0 = zeros(nx)
## default options
if 'verbose' in opt:
verbose = opt['verbose']
else:
verbose = 0
# if 'max_it' in opt:
# max_it = opt['max_it']
# else:
# max_it = 0
## set up options struct for Gurobi
if 'grb_opt' in opt:
g_opt = gurobi_options(opt['grb_opt'])
else:
g_opt = gurobi_options()
g_opt['Display'] = min(verbose, 3)
if verbose:
g_opt['DisplayInterval'] = 1
else:
g_opt['DisplayInterval'] = Inf
if not issparse(A):
A = sparse(A)
## split up linear constraints
ieq = find( abs(u-l) <= EPS ) ## equality
igt = find( u >= 1e10 & l > -1e10 ) ## greater than, unbounded above
ilt = find( l <= -1e10 & u < 1e10 ) ## less than, unbounded below
ibx = find( (abs(u-l) > EPS) & (u < 1e10) & (l > -1e10) )
## grab some dimensions
nlt = len(ilt) ## number of upper bounded linear inequalities
ngt = len(igt) ## number of lower bounded linear inequalities
nbx = len(ibx) ## number of doubly bounded linear inequalities
neq = len(ieq) ## number of equalities
niq = nlt + ngt + 2 * nbx ## number of inequalities
AA = [ A[ieq, :], A[ilt, :], -A[igt, :], A[ibx, :], -A[ibx, :] ]
bb = [ u[ieq], u[ilt], -l[igt], u[ibx], -l[ibx] ]
contypes = '=' * neq + '<' * niq
## call the solver
if len(H) == 0 or not any(any(H)):
lpqp = 'LP'
else:
lpqp = 'QP'
rr, cc, vv = find(H)
g_opt['QP']['qrow'] = int(rr.T - 1)
g_opt['QP']['qcol'] = int(cc.T - 1)
g_opt['QP']['qval'] = 0.5 * vv.T
if verbose:
methods = [
'primal simplex',
'dual simplex',
'interior point',
'concurrent',
'deterministic concurrent'
]
print('Gurobi Version %s -- %s %s solver\n'
'<unknown>' % (methods[g_opt['Method'] + 1], lpqp))
x, f, eflag, output, lmbda = \
gurobipy(c.T, 1, AA, bb, contypes, xmin, xmax, 'C', g_opt)
pi = lmbda['Pi']
rc = lmbda['RC']
output['flag'] = eflag
if eflag == 2:
eflag = 1 ## optimal solution found
else:
eflag = -eflag ## failed somehow
## check for empty results (in case optimization failed)
lam = {}
if len(x) == 0:
x = NaN(nx, 1);
lam['lower'] = NaN(nx)
lam['upper'] = NaN(nx)
else:
lam['lower'] = zeros(nx)
lam['upper'] = zeros(nx)
if len(f) == 0:
f = NaN
if len(pi) == 0:
pi = NaN(len(bb))
kl = find(rc > 0); ## lower bound binding
ku = find(rc < 0); ## upper bound binding
lam['lower'][kl] = rc[kl]
lam['upper'][ku] = -rc[ku]
lam['eqlin'] = pi[:neq + 1]
lam['ineqlin'] = pi[neq + range(niq + 1)]
mu_l = zeros(nA)
mu_u = zeros(nA)
## repackage lmbdas
kl = find(lam['eqlin'] > 0) ## lower bound binding
ku = find(lam['eqlin'] < 0) ## upper bound binding
mu_l[ieq[kl]] = lam['eqlin'][kl]
mu_l[igt] = -lam['ineqlin'][nlt + range(ngt + 1)]
mu_l[ibx] = -lam['ineqlin'][nlt + ngt + nbx + range(nbx)]
mu_u[ieq[ku]] = -lam['eqlin'][ku]
mu_u[ilt] = -lam['ineqlin'][:nlt + 1]
mu_u[ibx] = -lam['ineqlin'][nlt + ngt + range(nbx + 1)]
lmbda = {
'mu_l': mu_l,
'mu_u': mu_u,
'lower': lam['lower'],
'upper': lam['upper']
}
return x, f, eflag, output, lmbda
def t_dcline(quiet=False):
"""Tests for DC line extension in L{{toggle_dcline}.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
num_tests = 50
t_begin(num_tests, quiet)
tdir = dirname(__file__)
casefile = join(tdir, 't_case9_dcline')
if quiet:
verbose = False
else:
verbose = False
t0 = ''
ppopt = ppoption(OPF_VIOLATION=1e-6, PDIPM_GRADTOL=1e-8,
PDIPM_COMPTOL=1e-8, PDIPM_COSTTOL=1e-9)
ppopt = ppoption(ppopt, OPF_ALG=560, OPF_ALG_DC=200)
ppopt = ppoption(ppopt, OUT_ALL=0, VERBOSE=verbose)
## set up indices
ib_data = r_[arange(BUS_AREA + 1), arange(BASE_KV, VMIN + 1)]
ib_voltage = arange(VM, VA + 1)
ib_lam = arange(LAM_P, LAM_Q + 1)
ib_mu = arange(MU_VMAX, MU_VMIN + 1)
ig_data = r_[[GEN_BUS, QMAX, QMIN], arange(MBASE, APF + 1)]
ig_disp = array([PG, QG, VG])
ig_mu = arange(MU_PMAX, MU_QMIN + 1)
ibr_data = arange(ANGMAX + 1)
ibr_flow = arange(PF, QT + 1)
ibr_mu = array([MU_SF, MU_ST])
ibr_angmu = array([MU_ANGMIN, MU_ANGMAX])
## load case
ppc0 = loadcase(casefile)
del ppc0['dclinecost']
ppc = ppc0
ppc = toggle_dcline(ppc, 'on')
ppc = toggle_dcline(ppc, 'off')
ndc = ppc['dcline'].shape[0]
## run AC OPF w/o DC lines
t = ''.join([t0, 'AC OPF (no DC lines) : '])
r0 = runopf(ppc0, ppopt)
success = r0['success']
t_ok(success, [t, 'success'])
r = runopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
t_is(r['f'], r0['f'], 8, [t, 'f'])
t_is( r['bus'][:,ib_data ], r0['bus'][:,ib_data ], 10, [t, 'bus data'])
t_is( r['bus'][:,ib_voltage], r0['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
t_is( r['bus'][:,ib_lam ], r0['bus'][:,ib_lam ], 3, [t, 'bus lambda'])
t_is( r['bus'][:,ib_mu ], r0['bus'][:,ib_mu ], 2, [t, 'bus mu'])
t_is( r['gen'][:,ig_data ], r0['gen'][:,ig_data ], 10, [t, 'gen data'])
t_is( r['gen'][:,ig_disp ], r0['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is( r['gen'][:,ig_mu ], r0['gen'][:,ig_mu ], 3, [t, 'gen mu'])
t_is(r['branch'][:,ibr_data ], r0['branch'][:,ibr_data ], 10, [t, 'branch data'])
t_is(r['branch'][:,ibr_flow ], r0['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
t_is(r['branch'][:,ibr_mu ], r0['branch'][:,ibr_mu ], 2, [t, 'branch mu'])
t = ''.join([t0, 'AC PF (no DC lines) : '])
ppc1 = {'baseMVA': r['baseMVA'],
'bus': r['bus'][:, :VMIN + 1].copy(),
'gen': r['gen'][:, :APF + 1].copy(),
'branch': r['branch'][:, :ANGMAX + 1].copy(),
'gencost': r['gencost'].copy(),
'dcline': r['dcline'][:, :c.LOSS1 + 1].copy()}
ppc1['bus'][:, VM] = 1
ppc1['bus'][:, VA] = 0
rp = runpf(ppc1, ppopt)
success = rp['success']
t_ok(success, [t, 'success'])
t_is( rp['bus'][:,ib_voltage], r['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
t_is( rp['gen'][:,ig_disp ], r['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is(rp['branch'][:,ibr_flow ], r['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
## run with DC lines
t = ''.join([t0, 'AC OPF (with DC lines) : '])
ppc = toggle_dcline(ppc, 'on')
r = runopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
expected = array([
[10, 8.9, -10, 10, 1.0674, 1.0935],
[2.2776, 2.2776, 0, 0, 1.0818, 1.0665],
[0, 0, 0, 0, 1.0000, 1.0000],
[10, 9.5, 0.0563, -10, 1.0778, 1.0665]
])
t_is(r['dcline'][:, c.PF:c.VT + 1], expected, 4, [t, 'P Q V'])
expected = array([
[0, 0.8490, 0.6165, 0, 0, 0.2938],
[0, 0, 0, 0.4290, 0.0739, 0],
[0, 0, 0, 0, 0, 0],
[0, 7.2209, 0, 0, 0.0739, 0]
])
t_is(r['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1], expected, 3, [t, 'mu'])
t = ''.join([t0, 'AC PF (with DC lines) : '])
ppc1 = {'baseMVA': r['baseMVA'],
'bus': r['bus'][:, :VMIN + 1].copy(),
'gen': r['gen'][:, :APF + 1].copy(),
'branch': r['branch'][:, :ANGMAX + 1].copy(),
'gencost': r['gencost'].copy(),
'dcline': r['dcline'][:, :c.LOSS1 + 1].copy()}
ppc1 = toggle_dcline(ppc1, 'on')
ppc1['bus'][:, VM] = 1
ppc1['bus'][:, VA] = 0
rp = runpf(ppc1, ppopt)
success = rp['success']
t_ok(success, [t, 'success'])
t_is( rp['bus'][:,ib_voltage], r['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
#t_is( rp['gen'][:,ig_disp ], r['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is( rp['gen'][:2,ig_disp ], r['gen'][:2,ig_disp ], 3, [t, 'gen dispatch'])
t_is( rp['gen'][2,PG ], r['gen'][2,PG ], 3, [t, 'gen dispatch'])
t_is( rp['gen'][2,QG]+rp['dcline'][0,c.QF], r['gen'][2,QG]+r['dcline'][0,c.QF], 3, [t, 'gen dispatch'])
t_is(rp['branch'][:,ibr_flow ], r['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
## add appropriate P and Q injections and check angles and generation when running PF
t = ''.join([t0, 'AC PF (with equivalent injections) : '])
ppc1 = {'baseMVA': r['baseMVA'],
'bus': r['bus'][:, :VMIN + 1].copy(),
'gen': r['gen'][:, :APF + 1].copy(),
'branch': r['branch'][:, :ANGMAX + 1].copy(),
'gencost': r['gencost'].copy(),
'dcline': r['dcline'][:, :c.LOSS1 + 1].copy()}
ppc1['bus'][:, VM] = 1
ppc1['bus'][:, VA] = 0
for k in range(ndc):
if ppc1['dcline'][k, c.BR_STATUS]:
ff = find(ppc1['bus'][:, BUS_I] == ppc1['dcline'][k, c.F_BUS])
tt = find(ppc1['bus'][:, BUS_I] == ppc1['dcline'][k, c.T_BUS])
ppc1['bus'][ff, PD] = ppc1['bus'][ff, PD] + r['dcline'][k, c.PF]
ppc1['bus'][ff, QD] = ppc1['bus'][ff, QD] - r['dcline'][k, c.QF]
ppc1['bus'][tt, PD] = ppc1['bus'][tt, PD] - r['dcline'][k, c.PT]
ppc1['bus'][tt, QD] = ppc1['bus'][tt, QD] - r['dcline'][k, c.QT]
ppc1['bus'][ff, VM] = r['dcline'][k, c.VF]
ppc1['bus'][tt, VM] = r['dcline'][k, c.VT]
ppc1['bus'][ff, BUS_TYPE] = PV
ppc1['bus'][tt, BUS_TYPE] = PV
rp = runpf(ppc1, ppopt)
success = rp['success']
t_ok(success, [t, 'success'])
t_is( rp['bus'][:,ib_voltage], r['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
t_is( rp['gen'][:,ig_disp ], r['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is(rp['branch'][:,ibr_flow ], r['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
## test DC OPF
t = ''.join([t0, 'DC OPF (with DC lines) : '])
ppc = ppc0.copy()
ppc['gen'][0, PMIN] = 10
ppc['branch'][4, RATE_A] = 100
ppc = toggle_dcline(ppc, 'on')
r = rundcopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
expected = array([
[10, 8.9, 0, 0, 1.01, 1],
[2, 2, 0, 0, 1, 1],
[0, 0, 0, 0, 1, 1],
[10, 9.5, 0, 0, 1, 0.98]
])
t_is(r['dcline'][:, c.PF:c.VT + 1], expected, 4, [t, 'P Q V'])
expected = array([
[0, 1.8602, 0, 0, 0, 0],
[1.8507, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0.2681, 0, 0, 0, 0]
])
t_is(r['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1], expected, 3, [t, 'mu'])
t = ''.join([t0, 'DC PF (with DC lines) : '])
ppc1 = {'baseMVA': r['baseMVA'],
'bus': r['bus'][:, :VMIN + 1].copy(),
'gen': r['gen'][:, :APF + 1].copy(),
'branch': r['branch'][:, :ANGMAX + 1].copy(),
'gencost': r['gencost'].copy(),
'dcline': r['dcline'][:, :c.LOSS1 + 1].copy()}
ppc1 = toggle_dcline(ppc1, 'on')
ppc1['bus'][:, VA] = 0
rp = rundcpf(ppc1, ppopt)
success = rp['success']
t_ok(success, [t, 'success'])
t_is( rp['bus'][:,ib_voltage], r['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
t_is( rp['gen'][:,ig_disp ], r['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is(rp['branch'][:,ibr_flow ], r['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
## add appropriate P injections and check angles and generation when running PF
t = ''.join([t0, 'DC PF (with equivalent injections) : '])
ppc1 = {'baseMVA': r['baseMVA'],
'bus': r['bus'][:, :VMIN + 1].copy(),
'gen': r['gen'][:, :APF + 1].copy(),
'branch': r['branch'][:, :ANGMAX + 1].copy(),
'gencost': r['gencost'].copy(),
'dcline': r['dcline'][:, :c.LOSS1 + 1].copy()}
ppc1['bus'][:, VA] = 0
for k in range(ndc):
if ppc1['dcline'][k, c.BR_STATUS]:
ff = find(ppc1['bus'][:, BUS_I] == ppc1['dcline'][k, c.F_BUS])
tt = find(ppc1['bus'][:, BUS_I] == ppc1['dcline'][k, c.T_BUS])
ppc1['bus'][ff, PD] = ppc1['bus'][ff, PD] + r['dcline'][k, c.PF]
ppc1['bus'][tt, PD] = ppc1['bus'][tt, PD] - r['dcline'][k, c.PT]
ppc1['bus'][ff, BUS_TYPE] = PV
ppc1['bus'][tt, BUS_TYPE] = PV
rp = rundcpf(ppc1, ppopt)
success = rp['success']
t_ok(success, [t, 'success'])
t_is( rp['bus'][:,ib_voltage], r['bus'][:,ib_voltage], 3, [t, 'bus voltage'])
t_is( rp['gen'][:,ig_disp ], r['gen'][:,ig_disp ], 3, [t, 'gen dispatch'])
t_is(rp['branch'][:,ibr_flow ], r['branch'][:,ibr_flow ], 3, [t, 'branch flow'])
## run with DC lines
t = ''.join([t0, 'AC OPF (with DC lines + poly cost) : '])
ppc = loadcase(casefile)
ppc = toggle_dcline(ppc, 'on')
r = runopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
expected1 = array([
[10, 8.9, -10, 10, 1.0663, 1.0936],
[7.8429, 7.8429, 0, 0, 1.0809, 1.0667],
[0, 0, 0, 0, 1.0000, 1.0000],
[6.0549, 5.7522, -0.5897, -10, 1.0778, 1.0667]
])
t_is(r['dcline'][:, c.PF:c.VT + 1], expected1, 4, [t, 'P Q V'])
expected2 = array([
[0, 0.7605, 0.6226, 0, 0, 0.2980],
[0, 0, 0, 0.4275, 0.0792, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0.0792, 0]
])
t_is(r['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1], expected2, 3, [t, 'mu'])
ppc['dclinecost'][3, :8] = array([2, 0, 0, 4, 0, 0, 7.3, 0])
r = runopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
t_is(r['dcline'][:, c.PF:c.VT + 1], expected1, 4, [t, 'P Q V'])
t_is(r['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1], expected2, 3, [t, 'mu'])
t = ''.join([t0, 'AC OPF (with DC lines + pwl cost) : '])
ppc['dclinecost'][3, :8] = array([1, 0, 0, 2, 0, 0, 10, 73])
r = runopf(ppc, ppopt)
success = r['success']
t_ok(success, [t, 'success'])
t_is(r['dcline'][:, c.PF:c.VT + 1], expected1, 4, [t, 'P Q V'])
t_is(r['dcline'][:, c.MU_PMIN:c.MU_QMAXT + 1], expected2, 3, [t, 'mu'])
t_end()
def dcopf_solver(om, ppopt, out_opt=None):
"""Solves a DC optimal power flow.
Inputs are an OPF model object, a PYPOWER options dict and
a dict containing fields (can be empty) for each of the desired
optional output fields.
Outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (ppc) with the usual baseMVA, bus
branch, gen, gencost fields, along with the following additional
fields:
- C{order} see 'help ext2int' for details of this field
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
- C{g} (optional) constraint values
- C{dg} (optional) constraint 1st derivatives
- C{df} (optional) obj fun 1st derivatives (not yet implemented)
- C{d2f} (optional) obj fun 2nd derivatives (not yet implemented)
C{success} is C{True} if solver converged successfully, C{False} otherwise.
C{raw} is a raw output dict in form returned by MINOS
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
@see: L{opf}, L{qps_pypower}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
"""
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
alg = ppopt['OPF_ALG_DC']
if alg == 0:
if have_fcn('cplex'): ## use CPLEX by default, if available
alg = 500
elif have_fcn('mosek'): ## if not, then MOSEK, if available
alg = 600
elif have_fcn('gurobi'): ## if not, then Gurobi, if available
alg = 700
else: ## otherwise PIPS
alg = 200
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
cp = om.get_cost_params()
N, H, Cw = cp["N"], cp["H"], cp["Cw"]
fparm = array(c_[cp["dd"], cp["rh"], cp["kk"], cp["mm"]])
Bf = om.userdata('Bf')
Pfinj = om.userdata('Pfinj')
vv, ll, _, _ = om.get_idx()
## problem dimensions
ipol = find(gencost[:, MODEL] == POLYNOMIAL) ## polynomial costs
ipwl = find(gencost[:, MODEL] == PW_LINEAR) ## piece-wise linear costs
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
nw = N.shape[0] ## number of general cost vars, w
ny = om.getN('var', 'y') ## number of piece-wise linear costs
nxyz = om.getN('var') ## total number of control vars of all types
## linear constraints & variable bounds
A, l, u = om.linear_constraints()
x0, xmin, xmax = om.getv()
## set up objective function of the form: f = 1/2 * X'*HH*X + CC'*X
## where X = [x;y;z]. First set up as quadratic function of w,
## f = 1/2 * w'*HHw*w + CCw'*w, where w = diag(M) * (N*X - Rhat). We
## will be building on the (optionally present) user supplied parameters.
## piece-wise linear costs
any_pwl = int(ny > 0)
if any_pwl:
# Sum of y vars.
Npwl = sparse((ones(ny), (zeros(ny), arange(vv["i1"]["y"], vv["iN"]["y"]))), (1, nxyz))
Hpwl = sparse((1, 1))
Cpwl = array([1])
fparm_pwl = array([[1, 0, 0, 1]])
else:
Npwl = None#zeros((0, nxyz))
Hpwl = None#array([])
Cpwl = array([])
fparm_pwl = zeros((0, 4))
## quadratic costs
npol = len(ipol)
if any(find(gencost[ipol, NCOST] > 3)):
stderr.write('DC opf cannot handle polynomial costs with higher '
'than quadratic order.\n')
iqdr = find(gencost[ipol, NCOST] == 3)
ilin = find(gencost[ipol, NCOST] == 2)
polycf = zeros((npol, 3)) ## quadratic coeffs for Pg
if len(iqdr) > 0:
polycf[iqdr, :] = gencost[ipol[iqdr], COST:COST + 3]
if npol:
polycf[ilin, 1:3] = gencost[ipol[ilin], COST:COST + 2]
polycf = dot(polycf, diag([ baseMVA**2, baseMVA, 1])) ## convert to p.u.
if npol:
Npol = sparse((ones(npol), (arange(npol), vv["i1"]["Pg"] + ipol)),
(npol, nxyz)) # Pg vars
Hpol = sparse((2 * polycf[:, 0], (arange(npol), arange(npol))),
(npol, npol))
else:
Npol = None
Hpol = None
Cpol = polycf[:, 1]
fparm_pol = ones((npol, 1)) * array([[1, 0, 0, 1]])
## combine with user costs
NN = vstack([n for n in [Npwl, Npol, N] if n is not None and n.shape[0] > 0], "csr")
# FIXME: Zero dimension sparse matrices.
if (Hpwl is not None) and any_pwl and (npol + nw):
Hpwl = hstack([Hpwl, sparse((any_pwl, npol + nw))])
if Hpol is not None:
if any_pwl and npol:
Hpol = hstack([sparse((npol, any_pwl)), Hpol])
if npol and nw:
Hpol = hstack([Hpol, sparse((npol, nw))])
if (H is not None) and nw and (any_pwl + npol):
H = hstack([sparse((nw, any_pwl + npol)), H])
HHw = vstack([h for h in [Hpwl, Hpol, H] if h is not None and h.shape[0] > 0], "csr")
CCw = r_[Cpwl, Cpol, Cw]
ffparm = r_[fparm_pwl, fparm_pol, fparm]
## transform quadratic coefficients for w into coefficients for X
nnw = any_pwl + npol + nw
M = sparse((ffparm[:, 3], (range(nnw), range(nnw))))
MR = M * ffparm[:, 1]
HMR = HHw * MR
MN = M * NN
HH = MN.T * HHw * MN
CC = MN.T * (CCw - HMR)
C0 = 0.5 * dot(MR, HMR) + sum(polycf[:, 2]) # Constant term of cost.
## set up input for QP solver
opt = {'alg': alg, 'verbose': verbose}
if (alg == 200) or (alg == 250):
## try to select an interior initial point
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180.0)
lb, ub = xmin.copy(), xmax.copy()
lb[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
ub[xmax == Inf] = 1e10
x0 = (lb + ub) / 2;
# angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# largest y-value in CCV data
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl,
NCOST + 2 * gencost[ipwl, NCOST])]
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
## set up options
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
if feastol == 0:
feastol = ppopt['OPF_VIOLATION'] ## = OPF_VIOLATION by default
opt["pips_opt"] = { 'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'cost_mult': 1 }
elif alg == 400:
opt['ipopt_opt'] = ipopt_options([], ppopt)
elif alg == 500:
opt['cplex_opt'] = cplex_options([], ppopt)
elif alg == 600:
opt['mosek_opt'] = mosek_options([], ppopt)
elif alg == 700:
opt['grb_opt'] = gurobi_options([], ppopt)
else:
raise ValueError("Unrecognised solver [%d]." % alg)
##----- run opf -----
x, f, info, output, lmbda = \
qps_pypower(HH, CC, A, l, u, xmin, xmax, x0, opt)
success = (info == 1)
##----- calculate return values -----
if not any(isnan(x)):
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
f = f + C0
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
gen[:, PG] = Pg * baseMVA
## compute branch flows
branch[:, [QF, QT]] = zeros((nl, 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
## package up results
mu_l = lmbda["mu_l"]
mu_u = lmbda["mu_u"]
muLB = lmbda["lower"]
muUB = lmbda["upper"]
## update Lagrange multipliers
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
bus[:, [LAM_P, LAM_Q, MU_VMIN, MU_VMAX]] = zeros((nb, 4))
gen[:, [MU_PMIN, MU_PMAX, MU_QMIN, MU_QMAX]] = zeros((gen.shape[0], 4))
branch[:, [MU_SF, MU_ST]] = zeros((nl, 2))
bus[:, LAM_P] = (mu_u[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]] -
mu_l[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]]) / baseMVA
branch[il, MU_SF] = mu_u[ll["i1"]["Pf"]:ll["iN"]["Pf"]] / baseMVA
branch[il, MU_ST] = mu_u[ll["i1"]["Pt"]:ll["iN"]["Pt"]] / baseMVA
gen[:, MU_PMIN] = muLB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMAX] = muUB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
pimul = r_[
mu_l - mu_u,
-ones(int(ny > 0)), ## dummy entry corresponding to linear cost row in A
muLB - muUB
]
mu = { 'var': {'l': muLB, 'u': muUB},
'lin': {'l': mu_l, 'u': mu_u} }
results = deepcopy(ppc)
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw