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opf.py
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opf.py
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## Copyright 2015-2018 Tom Brown (FIAS), Jonas Hoersch (FIAS), David
## Schlachtberger (FIAS)
## This program is free software; you can redistribute it and/or
## modify it under the terms of the GNU General Public License as
## published by the Free Software Foundation; either version 3 of the
## License, or (at your option) any later version.
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
"""Optimal Power Flow functions.
"""
# make the code as Python 3 compatible as possible
from __future__ import division, absolute_import
from six import iteritems, itervalues, string_types
__author__ = "Tom Brown (FIAS), Jonas Hoersch (FIAS), David Schlachtberger (FIAS)"
__copyright__ = "Copyright 2015-2017 Tom Brown (FIAS), Jonas Hoersch (FIAS), David Schlachtberger (FIAS), GNU GPL 3"
import numpy as np
import pandas as pd
from scipy.sparse.linalg import spsolve
from pyomo.environ import (ConcreteModel, Var, Objective,
NonNegativeReals, Constraint, Reals,
Suffix, Expression, Binary, SolverFactory)
try:
from pyomo.solvers.plugins.solvers.persistent_solver import PersistentSolver
except ImportError:
# Only used in conjunction with isinstance, so we mock it to be backwards compatible
class PersistentSolver(): pass
from itertools import chain
import logging
logger = logging.getLogger(__name__)
from distutils.version import StrictVersion, LooseVersion
try:
_pd_version = StrictVersion(pd.__version__)
except ValueError:
_pd_version = LooseVersion(pd.__version__)
from .pf import (calculate_dependent_values, find_slack_bus,
find_bus_controls, calculate_B_H, calculate_PTDF, find_tree,
find_cycles, _as_snapshots)
from .opt import (l_constraint, l_objective, LExpression, LConstraint,
patch_optsolver_free_model_before_solving,
patch_optsolver_record_memusage_before_solving,
empty_network, free_pyomo_initializers)
from .descriptors import (get_switchable_as_dense, get_switchable_as_iter,
allocate_series_dataframes, zsum, ind_operational)
pd.Series.zsum = zsum
def network_opf(network,snapshots=None):
"""Optimal power flow for snapshots."""
raise NotImplementedError("Non-linear optimal power flow not supported yet")
def define_generator_variables_constraints(network,snapshots):
extendable_gens_i = network.generators.index[network.generators.p_nom_extendable]
fixed_gens_i = network.generators.index[~network.generators.p_nom_extendable & ~network.generators.committable]
fixed_committable_gens_i = network.generators.index[~network.generators.p_nom_extendable & network.generators.committable]
if (network.generators.p_nom_extendable & network.generators.committable).any():
logger.warning("The following generators have both investment optimisation and unit commitment:\n{}\nCurrently PyPSA cannot do both these functions, so PyPSA is choosing investment optimisation for these generators.".format(network.generators.index[network.generators.p_nom_extendable & network.generators.committable]))
p_min_pu = get_switchable_as_dense(network, 'Generator', 'p_min_pu', snapshots)
p_max_pu = get_switchable_as_dense(network, 'Generator', 'p_max_pu', snapshots)
## Define generator dispatch variables ##
gen_p_bounds = {(gen,sn) : (None,None)
for gen in extendable_gens_i | fixed_committable_gens_i
for sn in snapshots}
if len(fixed_gens_i):
var_lower = p_min_pu.loc[:,fixed_gens_i].multiply(network.generators.loc[fixed_gens_i, 'p_nom'])
var_upper = p_max_pu.loc[:,fixed_gens_i].multiply(network.generators.loc[fixed_gens_i, 'p_nom'])
gen_p_bounds.update({(gen,sn) : (var_lower[gen][sn],var_upper[gen][sn])
for gen in fixed_gens_i
for sn in snapshots})
def gen_p_bounds_f(model,gen_name,snapshot):
return gen_p_bounds[gen_name,snapshot]
network.model.generator_p = Var(list(network.generators.index), snapshots,
domain=Reals, bounds=gen_p_bounds_f)
free_pyomo_initializers(network.model.generator_p)
## Define generator capacity variables if generator is extendable ##
def gen_p_nom_bounds(model, gen_name):
return (network.generators.at[gen_name,"p_nom_min"],
network.generators.at[gen_name,"p_nom_max"])
network.model.generator_p_nom = Var(list(extendable_gens_i),
domain=NonNegativeReals, bounds=gen_p_nom_bounds)
free_pyomo_initializers(network.model.generator_p_nom)
## Define generator dispatch constraints for extendable generators ##
gen_p_lower = {(gen,sn) :
[[(1,network.model.generator_p[gen,sn]),
(-p_min_pu.at[sn, gen],
network.model.generator_p_nom[gen])],">=",0.]
for gen in extendable_gens_i for sn in snapshots}
l_constraint(network.model, "generator_p_lower", gen_p_lower,
list(extendable_gens_i), snapshots)
gen_p_upper = {(gen,sn) :
[[(1,network.model.generator_p[gen,sn]),
(-p_max_pu.at[sn, gen],
network.model.generator_p_nom[gen])],"<=",0.]
for gen in extendable_gens_i for sn in snapshots}
l_constraint(network.model, "generator_p_upper", gen_p_upper,
list(extendable_gens_i), snapshots)
## Define committable generator statuses ##
network.model.generator_status = Var(list(fixed_committable_gens_i), snapshots,
within=Binary)
var_lower = p_min_pu.loc[:,fixed_committable_gens_i].multiply(network.generators.loc[fixed_committable_gens_i, 'p_nom'])
var_upper = p_max_pu.loc[:,fixed_committable_gens_i].multiply(network.generators.loc[fixed_committable_gens_i, 'p_nom'])
committable_gen_p_lower = {(gen,sn) : LConstraint(LExpression([(var_lower[gen][sn],network.model.generator_status[gen,sn]),(-1.,network.model.generator_p[gen,sn])]),"<=") for gen in fixed_committable_gens_i for sn in snapshots}
l_constraint(network.model, "committable_gen_p_lower", committable_gen_p_lower,
list(fixed_committable_gens_i), snapshots)
committable_gen_p_upper = {(gen,sn) : LConstraint(LExpression([(var_upper[gen][sn],network.model.generator_status[gen,sn]),(-1.,network.model.generator_p[gen,sn])]),">=") for gen in fixed_committable_gens_i for sn in snapshots}
l_constraint(network.model, "committable_gen_p_upper", committable_gen_p_upper,
list(fixed_committable_gens_i), snapshots)
## Deal with minimum up time ##
up_time_gens = fixed_committable_gens_i[network.generators.loc[fixed_committable_gens_i,"min_up_time"] > 0]
for gen_i, gen in enumerate(up_time_gens):
min_up_time = network.generators.loc[gen,"min_up_time"]
initial_status = network.generators.loc[gen,"initial_status"]
blocks = max(1,len(snapshots)-min_up_time+1)
gen_up_time = {}
for i in range(blocks):
lhs = LExpression([(1,network.model.generator_status[gen,snapshots[j]]) for j in range(i,i+min_up_time)])
if i == 0:
rhs = LExpression([(min_up_time,network.model.generator_status[gen,snapshots[i]])],-min_up_time*initial_status)
else:
rhs = LExpression([(min_up_time,network.model.generator_status[gen,snapshots[i]]),(-min_up_time,network.model.generator_status[gen,snapshots[i-1]])])
gen_up_time[i] = LConstraint(lhs,">=",rhs)
l_constraint(network.model, "gen_up_time_{}".format(gen_i), gen_up_time,
range(blocks))
## Deal with minimum down time ##
down_time_gens = fixed_committable_gens_i[network.generators.loc[fixed_committable_gens_i,"min_down_time"] > 0]
for gen_i, gen in enumerate(down_time_gens):
min_down_time = network.generators.loc[gen,"min_down_time"]
initial_status = network.generators.loc[gen,"initial_status"]
blocks = max(1,len(snapshots)-min_down_time+1)
gen_down_time = {}
for i in range(blocks):
#sum of 1-status
lhs = LExpression([(-1,network.model.generator_status[gen,snapshots[j]]) for j in range(i,i+min_down_time)],min_down_time)
if i == 0:
rhs = LExpression([(-min_down_time,network.model.generator_status[gen,snapshots[i]])],min_down_time*initial_status)
else:
rhs = LExpression([(-min_down_time,network.model.generator_status[gen,snapshots[i]]),(min_down_time,network.model.generator_status[gen,snapshots[i-1]])])
gen_down_time[i] = LConstraint(lhs,">=",rhs)
l_constraint(network.model, "gen_down_time_{}".format(gen_i), gen_down_time,
range(blocks))
## Deal with start up costs ##
suc_gens = fixed_committable_gens_i[network.generators.loc[fixed_committable_gens_i,"start_up_cost"] > 0]
network.model.generator_start_up_cost = Var(list(suc_gens),snapshots,
domain=NonNegativeReals)
sucs = {}
for gen in suc_gens:
suc = network.generators.loc[gen,"start_up_cost"]
initial_status = network.generators.loc[gen,"initial_status"]
for i,sn in enumerate(snapshots):
if i == 0:
rhs = LExpression([(suc, network.model.generator_status[gen,sn])],-suc*initial_status)
else:
rhs = LExpression([(suc, network.model.generator_status[gen,sn]),(-suc,network.model.generator_status[gen,snapshots[i-1]])])
lhs = LExpression([(1,network.model.generator_start_up_cost[gen,sn])])
sucs[gen,sn] = LConstraint(lhs,">=",rhs)
l_constraint(network.model, "generator_start_up", sucs, list(suc_gens), snapshots)
## Deal with shut down costs ##
sdc_gens = fixed_committable_gens_i[network.generators.loc[fixed_committable_gens_i,"shut_down_cost"] > 0]
network.model.generator_shut_down_cost = Var(list(sdc_gens),snapshots,
domain=NonNegativeReals)
sdcs = {}
for gen in sdc_gens:
sdc = network.generators.loc[gen,"shut_down_cost"]
initial_status = network.generators.loc[gen,"initial_status"]
for i,sn in enumerate(snapshots):
if i == 0:
rhs = LExpression([(-sdc, network.model.generator_status[gen,sn])],sdc*initial_status)
else:
rhs = LExpression([(-sdc, network.model.generator_status[gen,sn]),(sdc,network.model.generator_status[gen,snapshots[i-1]])])
lhs = LExpression([(1,network.model.generator_shut_down_cost[gen,sn])])
sdcs[gen,sn] = LConstraint(lhs,">=",rhs)
l_constraint(network.model, "generator_shut_down", sdcs, list(sdc_gens), snapshots)
## Deal with ramp limits without unit commitment ##
ru_gens = network.generators.index[network.generators.ramp_limit_up.notnull()]
ru = {}
for gen in ru_gens:
for sn, sn_prev in zip(snapshots[1:], snapshots[:-1]):
if network.generators.at[gen, "p_nom_extendable"]:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev]),
(-network.generators.at[gen, "ramp_limit_up"],
network.model.generator_p_nom[gen])])
elif not network.generators.at[gen, "committable"]:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev])],
-network.generators.at[gen, "ramp_limit_up"]*network.generators.at[gen, "p_nom"])
else:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev]),
((network.generators.at[gen, "ramp_limit_start_up"] - network.generators.at[gen, "ramp_limit_up"])*network.generators.at[gen, "p_nom"],
network.model.generator_status[gen,sn_prev]),
(-network.generators.at[gen, "ramp_limit_start_up"]*network.generators.at[gen, "p_nom"],
network.model.generator_status[gen,sn])])
ru[gen,sn] = LConstraint(lhs,"<=")
l_constraint(network.model, "ramp_up", ru, list(ru_gens), snapshots[1:])
rd_gens = network.generators.index[network.generators.ramp_limit_down.notnull()]
rd = {}
for gen in rd_gens:
for sn, sn_prev in zip(snapshots[1:], snapshots[:-1]):
if network.generators.at[gen, "p_nom_extendable"]:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev]),
(network.generators.at[gen, "ramp_limit_down"],
network.model.generator_p_nom[gen])])
elif not network.generators.at[gen, "committable"]:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev])],
network.generators.loc[gen, "ramp_limit_down"]*network.generators.at[gen, "p_nom"])
else:
lhs = LExpression([(1, network.model.generator_p[gen,sn]),
(-1, network.model.generator_p[gen,sn_prev]),
((network.generators.at[gen, "ramp_limit_down"] - network.generators.at[gen, "ramp_limit_shut_down"])*network.generators.at[gen, "p_nom"],
network.model.generator_status[gen,sn]),
(network.generators.at[gen, "ramp_limit_shut_down"]*network.generators.at[gen, "p_nom"],
network.model.generator_status[gen,sn_prev])])
rd[gen,sn] = LConstraint(lhs,">=")
l_constraint(network.model, "ramp_down", rd, list(rd_gens), snapshots[1:])
def define_storage_variables_constraints(network,snapshots):
sus = network.storage_units
ext_sus_i = sus.index[sus.p_nom_extendable]
fix_sus_i = sus.index[~ sus.p_nom_extendable]
model = network.model
## Define storage dispatch variables ##
p_max_pu = get_switchable_as_dense(network, 'StorageUnit', 'p_max_pu', snapshots)
p_min_pu = get_switchable_as_dense(network, 'StorageUnit', 'p_min_pu', snapshots)
bounds = {(su,sn) : (0,None) for su in ext_sus_i for sn in snapshots}
bounds.update({(su,sn) :
(0,sus.at[su,"p_nom"]*p_max_pu.at[sn, su])
for su in fix_sus_i for sn in snapshots})
def su_p_dispatch_bounds(model,su_name,snapshot):
return bounds[su_name,snapshot]
network.model.storage_p_dispatch = Var(list(network.storage_units.index), snapshots,
domain=NonNegativeReals, bounds=su_p_dispatch_bounds)
free_pyomo_initializers(network.model.storage_p_dispatch)
bounds = {(su,sn) : (0,None) for su in ext_sus_i for sn in snapshots}
bounds.update({(su,sn) :
(0,-sus.at[su,"p_nom"]*p_min_pu.at[sn, su])
for su in fix_sus_i
for sn in snapshots})
def su_p_store_bounds(model,su_name,snapshot):
return bounds[su_name,snapshot]
network.model.storage_p_store = Var(list(network.storage_units.index), snapshots,
domain=NonNegativeReals, bounds=su_p_store_bounds)
free_pyomo_initializers(network.model.storage_p_store)
## Define spillage variables only for hours with inflow>0. ##
inflow = get_switchable_as_dense(network, 'StorageUnit', 'inflow', snapshots)
spill_sus_i = sus.index[inflow.max()>0] #skip storage units without any inflow
inflow_gt0_b = inflow>0
spill_bounds = {(su,sn) : (0,inflow.at[sn,su])
for su in spill_sus_i
for sn in snapshots
if inflow_gt0_b.at[sn,su]}
spill_index = spill_bounds.keys()
def su_p_spill_bounds(model,su_name,snapshot):
return spill_bounds[su_name,snapshot]
network.model.storage_p_spill = Var(list(spill_index),
domain=NonNegativeReals, bounds=su_p_spill_bounds)
free_pyomo_initializers(network.model.storage_p_spill)
## Define generator capacity variables if generator is extendable ##
def su_p_nom_bounds(model, su_name):
return (sus.at[su_name,"p_nom_min"],
sus.at[su_name,"p_nom_max"])
network.model.storage_p_nom = Var(list(ext_sus_i), domain=NonNegativeReals,
bounds=su_p_nom_bounds)
free_pyomo_initializers(network.model.storage_p_nom)
## Define generator dispatch constraints for extendable generators ##
def su_p_upper(model,su_name,snapshot):
return (model.storage_p_dispatch[su_name,snapshot] <=
model.storage_p_nom[su_name]*p_max_pu.at[snapshot, su_name])
network.model.storage_p_upper = Constraint(list(ext_sus_i),snapshots,rule=su_p_upper)
free_pyomo_initializers(network.model.storage_p_upper)
def su_p_lower(model,su_name,snapshot):
return (model.storage_p_store[su_name,snapshot] <=
-model.storage_p_nom[su_name]*p_min_pu.at[snapshot, su_name])
network.model.storage_p_lower = Constraint(list(ext_sus_i),snapshots,rule=su_p_lower)
free_pyomo_initializers(network.model.storage_p_lower)
## Now define state of charge constraints ##
network.model.state_of_charge = Var(list(network.storage_units.index), snapshots,
domain=NonNegativeReals, bounds=(0,None))
upper = {(su,sn) : [[(1,model.state_of_charge[su,sn]),
(-sus.at[su,"max_hours"],model.storage_p_nom[su])],"<=",0.]
for su in ext_sus_i for sn in snapshots}
upper.update({(su,sn) : [[(1,model.state_of_charge[su,sn])],"<=",
sus.at[su,"max_hours"]*sus.at[su,"p_nom"]]
for su in fix_sus_i for sn in snapshots})
l_constraint(model, "state_of_charge_upper", upper,
list(network.storage_units.index), snapshots)
#this builds the constraint previous_soc + p_store - p_dispatch + inflow - spill == soc
#it is complicated by the fact that sometimes previous_soc and soc are floats, not variables
soc = {}
#store the combinations with a fixed soc
fixed_soc = {}
state_of_charge_set = get_switchable_as_dense(network, 'StorageUnit', 'state_of_charge_set', snapshots)
for su in sus.index:
for i,sn in enumerate(snapshots):
soc[su,sn] = [[],"==",0.]
elapsed_hours = network.snapshot_weightings[sn]
if i == 0 and not sus.at[su,"cyclic_state_of_charge"]:
previous_state_of_charge = sus.at[su,"state_of_charge_initial"]
soc[su,sn][2] -= ((1-sus.at[su,"standing_loss"])**elapsed_hours
* previous_state_of_charge)
else:
previous_state_of_charge = model.state_of_charge[su,snapshots[i-1]]
soc[su,sn][0].append(((1-sus.at[su,"standing_loss"])**elapsed_hours,
previous_state_of_charge))
state_of_charge = state_of_charge_set.at[sn,su]
if pd.isnull(state_of_charge):
state_of_charge = model.state_of_charge[su,sn]
soc[su,sn][0].append((-1,state_of_charge))
else:
soc[su,sn][2] += state_of_charge
#make sure the variable is also set to the fixed state of charge
fixed_soc[su,sn] = [[(1,model.state_of_charge[su,sn])],"==",state_of_charge]
soc[su,sn][0].append((sus.at[su,"efficiency_store"]
* elapsed_hours,model.storage_p_store[su,sn]))
soc[su,sn][0].append((-(1/sus.at[su,"efficiency_dispatch"]) * elapsed_hours,
model.storage_p_dispatch[su,sn]))
soc[su,sn][2] -= inflow.at[sn,su] * elapsed_hours
for su,sn in spill_index:
elapsed_hours = network.snapshot_weightings.at[sn]
storage_p_spill = model.storage_p_spill[su,sn]
soc[su,sn][0].append((-1.*elapsed_hours,storage_p_spill))
l_constraint(model,"state_of_charge_constraint",
soc,list(network.storage_units.index), snapshots)
l_constraint(model, "state_of_charge_constraint_fixed",
fixed_soc, list(fixed_soc.keys()))
def define_store_variables_constraints(network,snapshots):
stores = network.stores
ext_stores = stores.index[stores.e_nom_extendable]
fix_stores = stores.index[~ stores.e_nom_extendable]
e_max_pu = get_switchable_as_dense(network, 'Store', 'e_max_pu', snapshots)
e_min_pu = get_switchable_as_dense(network, 'Store', 'e_min_pu', snapshots)
model = network.model
## Define store dispatch variables ##
network.model.store_p = Var(list(stores.index), snapshots, domain=Reals)
## Define store energy variables ##
bounds = {(store,sn) : (None,None) for store in ext_stores for sn in snapshots}
bounds.update({(store,sn) :
(stores.at[store,"e_nom"]*e_min_pu.at[sn,store],stores.at[store,"e_nom"]*e_max_pu.at[sn,store])
for store in fix_stores for sn in snapshots})
def store_e_bounds(model,store,snapshot):
return bounds[store,snapshot]
network.model.store_e = Var(list(stores.index), snapshots, domain=Reals,
bounds=store_e_bounds)
free_pyomo_initializers(network.model.store_e)
## Define energy capacity variables if store is extendable ##
def store_e_nom_bounds(model, store):
return (stores.at[store,"e_nom_min"],
stores.at[store,"e_nom_max"])
network.model.store_e_nom = Var(list(ext_stores), domain=Reals,
bounds=store_e_nom_bounds)
free_pyomo_initializers(network.model.store_e_nom)
## Define energy capacity constraints for extendable generators ##
def store_e_upper(model,store,snapshot):
return (model.store_e[store,snapshot] <=
model.store_e_nom[store]*e_max_pu.at[snapshot,store])
network.model.store_e_upper = Constraint(list(ext_stores), snapshots, rule=store_e_upper)
free_pyomo_initializers(network.model.store_e_upper)
def store_e_lower(model,store,snapshot):
return (model.store_e[store,snapshot] >=
model.store_e_nom[store]*e_min_pu.at[snapshot,store])
network.model.store_e_lower = Constraint(list(ext_stores), snapshots, rule=store_e_lower)
free_pyomo_initializers(network.model.store_e_lower)
## Builds the constraint previous_e - p == e ##
e = {}
for store in stores.index:
for i,sn in enumerate(snapshots):
e[store,sn] = LConstraint(sense="==")
e[store,sn].lhs.variables.append((-1,model.store_e[store,sn]))
elapsed_hours = network.snapshot_weightings[sn]
if i == 0 and not stores.at[store,"e_cyclic"]:
previous_e = stores.at[store,"e_initial"]
e[store,sn].lhs.constant += ((1-stores.at[store,"standing_loss"])**elapsed_hours
* previous_e)
else:
previous_e = model.store_e[store,snapshots[i-1]]
e[store,sn].lhs.variables.append(((1-stores.at[store,"standing_loss"])**elapsed_hours,
previous_e))
e[store,sn].lhs.variables.append((-elapsed_hours, model.store_p[store,sn]))
l_constraint(model,"store_constraint", e, list(stores.index), snapshots)
def define_branch_extension_variables(network,snapshots):
passive_branches = network.passive_branches()
extendable_passive_branches = passive_branches[passive_branches.s_nom_extendable]
bounds = {b : (extendable_passive_branches.at[b,"s_nom_min"],
extendable_passive_branches.at[b,"s_nom_max"])
for b in extendable_passive_branches.index}
def branch_s_nom_bounds(model, branch_type, branch_name):
return bounds[branch_type,branch_name]
network.model.passive_branch_s_nom = Var(list(extendable_passive_branches.index),
domain=NonNegativeReals, bounds=branch_s_nom_bounds)
free_pyomo_initializers(network.model.passive_branch_s_nom)
extendable_links = network.links[network.links.p_nom_extendable]
bounds = {b : (extendable_links.at[b,"p_nom_min"],
extendable_links.at[b,"p_nom_max"])
for b in extendable_links.index}
def branch_p_nom_bounds(model, branch_name):
return bounds[branch_name]
network.model.link_p_nom = Var(list(extendable_links.index),
domain=NonNegativeReals, bounds=branch_p_nom_bounds)
free_pyomo_initializers(network.model.link_p_nom)
def define_link_flows(network,snapshots):
extendable_links_i = network.links.index[network.links.p_nom_extendable]
fixed_links_i = network.links.index[~ network.links.p_nom_extendable]
p_max_pu = get_switchable_as_dense(network, 'Link', 'p_max_pu', snapshots)
p_min_pu = get_switchable_as_dense(network, 'Link', 'p_min_pu', snapshots)
fixed_lower = p_min_pu.loc[:,fixed_links_i].multiply(network.links.loc[fixed_links_i, 'p_nom'])
fixed_upper = p_max_pu.loc[:,fixed_links_i].multiply(network.links.loc[fixed_links_i, 'p_nom'])
network.model.link_p = Var(list(network.links.index), snapshots)
p_upper = {(cb, sn) : LConstraint(LExpression([(1, network.model.link_p[cb, sn])],
-fixed_upper.at[sn, cb]),"<=")
for cb in fixed_links_i for sn in snapshots}
p_upper.update({(cb,sn) : LConstraint(LExpression([(1, network.model.link_p[cb, sn]),
(-p_max_pu.at[sn, cb], network.model.link_p_nom[cb])]),
"<=")
for cb in extendable_links_i for sn in snapshots})
l_constraint(network.model, "link_p_upper", p_upper,
list(network.links.index), snapshots)
p_lower = {(cb, sn) : LConstraint(LExpression([(1, network.model.link_p[cb, sn])],
-fixed_lower.at[sn, cb]),">=")
for cb in fixed_links_i for sn in snapshots}
p_lower.update({(cb,sn) : LConstraint(LExpression([(1, network.model.link_p[cb, sn]),
(-p_min_pu.at[sn, cb], network.model.link_p_nom[cb])]),
">=")
for cb in extendable_links_i for sn in snapshots})
l_constraint(network.model, "link_p_lower", p_lower,
list(network.links.index), snapshots)
def define_passive_branch_flows(network,snapshots,formulation="angles",ptdf_tolerance=0.):
if formulation == "angles":
define_passive_branch_flows_with_angles(network,snapshots)
elif formulation == "ptdf":
define_passive_branch_flows_with_PTDF(network,snapshots,ptdf_tolerance)
elif formulation == "cycles":
define_passive_branch_flows_with_cycles(network,snapshots)
elif formulation == "kirchhoff":
define_passive_branch_flows_with_kirchhoff(network,snapshots)
def define_passive_branch_flows_with_angles(network,snapshots):
network.model.voltage_angles = Var(list(network.buses.index), snapshots)
slack = {(sub,sn) :
[[(1,network.model.voltage_angles[network.sub_networks.slack_bus[sub],sn])], "==", 0.]
for sub in network.sub_networks.index for sn in snapshots}
l_constraint(network.model,"slack_angle",slack,list(network.sub_networks.index),snapshots)
passive_branches = network.passive_branches()
network.model.passive_branch_p = Var(list(passive_branches.index), snapshots)
flows = {}
for branch in passive_branches.index:
bus0 = passive_branches.at[branch,"bus0"]
bus1 = passive_branches.at[branch,"bus1"]
bt = branch[0]
bn = branch[1]
sub = passive_branches.at[branch,"sub_network"]
attribute = "r_pu_eff" if network.sub_networks.at[sub,"carrier"] == "DC" else "x_pu_eff"
y = 1/ passive_branches.at[ branch, attribute]
for sn in snapshots:
lhs = LExpression([(y,network.model.voltage_angles[bus0,sn]),
(-y,network.model.voltage_angles[bus1,sn]),
(-1,network.model.passive_branch_p[bt,bn,sn])],
-y*(passive_branches.at[branch,"phase_shift"]*np.pi/180. if bt == "Transformer" else 0.))
flows[bt,bn,sn] = LConstraint(lhs,"==",LExpression())
l_constraint(network.model, "passive_branch_p_def", flows,
list(passive_branches.index), snapshots)
def define_passive_branch_flows_with_PTDF(network,snapshots,ptdf_tolerance=0.):
passive_branches = network.passive_branches()
network.model.passive_branch_p = Var(list(passive_branches.index), snapshots)
flows = {}
for sub_network in network.sub_networks.obj:
find_bus_controls(sub_network)
branches_i = sub_network.branches_i()
if len(branches_i) > 0:
calculate_PTDF(sub_network)
#kill small PTDF values
sub_network.PTDF[abs(sub_network.PTDF) < ptdf_tolerance] = 0
for i,branch in enumerate(branches_i):
bt = branch[0]
bn = branch[1]
for sn in snapshots:
lhs = sum(sub_network.PTDF[i,j]*network._p_balance[bus,sn]
for j,bus in enumerate(sub_network.buses_o)
if sub_network.PTDF[i,j] != 0)
rhs = LExpression([(1,network.model.passive_branch_p[bt,bn,sn])])
flows[bt,bn,sn] = LConstraint(lhs,"==",rhs)
l_constraint(network.model, "passive_branch_p_def", flows,
list(passive_branches.index), snapshots)
def define_sub_network_cycle_constraints( subnetwork, snapshots, passive_branch_p, attribute):
""" Constructs cycle_constraints for a particular subnetwork
"""
sub_network_cycle_constraints = {}
sub_network_cycle_index = []
matrix = subnetwork.C.tocsc()
branches = subnetwork.branches()
for col_j in range( matrix.shape[1] ):
cycle_is = matrix.getcol(col_j).nonzero()[0]
if len(cycle_is) == 0: continue
sub_network_cycle_index.append((subnetwork.name, col_j))
branch_idx_attributes = []
for cycle_i in cycle_is:
branch_idx = branches.index[cycle_i]
attribute_value = 1e5 * branches.at[ branch_idx, attribute] * subnetwork.C[ cycle_i, col_j]
branch_idx_attributes.append( (branch_idx, attribute_value))
for snapshot in snapshots:
expression_list = [ (attribute_value,
passive_branch_p[branch_idx[0], branch_idx[1], snapshot]) for (branch_idx, attribute_value) in branch_idx_attributes]
lhs = LExpression(expression_list)
sub_network_cycle_constraints[subnetwork.name,col_j,snapshot] = LConstraint(lhs,"==",LExpression())
return( sub_network_cycle_index, sub_network_cycle_constraints)
def define_passive_branch_flows_with_cycles(network,snapshots):
for sub_network in network.sub_networks.obj:
find_tree(sub_network)
find_cycles(sub_network)
#following is necessary to calculate angles post-facto
find_bus_controls(sub_network)
if len(sub_network.branches_i()) > 0:
calculate_B_H(sub_network)
passive_branches = network.passive_branches()
network.model.passive_branch_p = Var(list(passive_branches.index), snapshots)
cycle_index = []
cycle_constraints = {}
for subnetwork in network.sub_networks.obj:
branches = subnetwork.branches()
attribute = "r_pu_eff" if network.sub_networks.at[subnetwork.name,"carrier"] == "DC" else "x_pu_eff"
sub_network_cycle_index, sub_network_cycle_constraints = define_sub_network_cycle_constraints( subnetwork,
snapshots,
network.model.passive_branch_p, attribute)
cycle_index.extend( sub_network_cycle_index)
cycle_constraints.update( sub_network_cycle_constraints)
l_constraint(network.model, "cycle_constraints", cycle_constraints,
cycle_index, snapshots)
network.model.cycles = Var(cycle_index, snapshots, domain=Reals, bounds=(None,None))
flows = {}
for subnetwork in network.sub_networks.obj:
branches = subnetwork.branches()
buses = subnetwork.buses()
for i,branch in enumerate(branches.index):
bt = branch[0]
bn = branch[1]
cycle_is = subnetwork.C[i,:].nonzero()[1]
tree_is = subnetwork.T[i,:].nonzero()[1]
if len(cycle_is) + len(tree_is) == 0: logger.error("The cycle formulation does not support infinite impedances, yet.")
for snapshot in snapshots:
expr = LExpression([(subnetwork.C[i,j], network.model.cycles[subnetwork.name,j,snapshot])
for j in cycle_is])
lhs = expr + sum(subnetwork.T[i,j]*network._p_balance[buses.index[j],snapshot]
for j in tree_is)
rhs = LExpression([(1,network.model.passive_branch_p[bt,bn,snapshot])])
flows[bt,bn,snapshot] = LConstraint(lhs,"==",rhs)
l_constraint(network.model, "passive_branch_p_def", flows,
list(passive_branches.index), snapshots)
def define_passive_branch_flows_with_kirchhoff(network,snapshots,skip_vars=False):
""" define passive branch flows with the kirchoff method """
for sub_network in network.sub_networks.obj:
find_tree(sub_network)
find_cycles(sub_network)
#following is necessary to calculate angles post-facto
find_bus_controls(sub_network)
if len(sub_network.branches_i()) > 0:
calculate_B_H(sub_network)
passive_branches = network.passive_branches()
if not skip_vars:
network.model.passive_branch_p = Var(list(passive_branches.index), snapshots)
cycle_index = []
cycle_constraints = {}
for subnetwork in network.sub_networks.obj:
branches = subnetwork.branches()
attribute = "r_pu_eff" if network.sub_networks.at[subnetwork.name,"carrier"] == "DC" else "x_pu_eff"
sub_network_cycle_index, sub_network_cycle_constraints = define_sub_network_cycle_constraints( subnetwork,
snapshots,
network.model.passive_branch_p, attribute)
cycle_index.extend( sub_network_cycle_index)
cycle_constraints.update( sub_network_cycle_constraints)
l_constraint(network.model, "cycle_constraints", cycle_constraints,
cycle_index, snapshots)
def define_passive_branch_constraints(network,snapshots):
passive_branches = network.passive_branches()
extendable_branches = passive_branches[passive_branches.s_nom_extendable]
fixed_branches = passive_branches[~ passive_branches.s_nom_extendable]
s_max_pu = pd.concat({c : get_switchable_as_dense(network, c, 's_max_pu', snapshots)
for c in network.passive_branch_components}, axis=1, sort=False)
flow_upper = {(b[0],b[1],sn) : [[(1,network.model.passive_branch_p[b[0],b[1],sn])],
"<=", s_max_pu.at[sn,b]*fixed_branches.at[b,"s_nom"]]
for b in fixed_branches.index
for sn in snapshots}
flow_upper.update({(b[0],b[1],sn) : [[(1,network.model.passive_branch_p[b[0],b[1],sn]),
(-s_max_pu.at[sn,b],network.model.passive_branch_s_nom[b[0],b[1]])],"<=",0]
for b in extendable_branches.index
for sn in snapshots})
l_constraint(network.model, "flow_upper", flow_upper,
list(passive_branches.index), snapshots)
flow_lower = {(b[0],b[1],sn) : [[(1,network.model.passive_branch_p[b[0],b[1],sn])],
">=", -s_max_pu.at[sn,b]*fixed_branches.at[b,"s_nom"]]
for b in fixed_branches.index
for sn in snapshots}
flow_lower.update({(b[0],b[1],sn): [[(1,network.model.passive_branch_p[b[0],b[1],sn]),
(s_max_pu.at[sn,b],network.model.passive_branch_s_nom[b[0],b[1]])],">=",0]
for b in extendable_branches.index
for sn in snapshots})
l_constraint(network.model, "flow_lower", flow_lower,
list(passive_branches.index), snapshots)
def define_nodal_balances(network,snapshots):
"""Construct the nodal balance for all elements except the passive
branches.
Store the nodal balance expression in network._p_balance.
"""
#dictionary for constraints
network._p_balance = {(bus,sn) : LExpression()
for bus in network.buses.index
for sn in snapshots}
efficiency = get_switchable_as_dense(network, 'Link', 'efficiency', snapshots)
for cb in network.links.index:
bus0 = network.links.at[cb,"bus0"]
bus1 = network.links.at[cb,"bus1"]
for sn in snapshots:
network._p_balance[bus0,sn].variables.append((-1,network.model.link_p[cb,sn]))
network._p_balance[bus1,sn].variables.append((efficiency.at[sn,cb],network.model.link_p[cb,sn]))
#Add any other buses to which the links are attached
for i in [int(col[3:]) for col in network.links.columns if col[:3] == "bus" and col not in ["bus0","bus1"]]:
efficiency = get_switchable_as_dense(network, 'Link', 'efficiency{}'.format(i), snapshots)
for cb in network.links.index[network.links["bus{}".format(i)] != ""]:
bus = network.links.at[cb, "bus{}".format(i)]
for sn in snapshots:
network._p_balance[bus,sn].variables.append((efficiency.at[sn,cb],network.model.link_p[cb,sn]))
for gen in network.generators.index:
bus = network.generators.at[gen,"bus"]
sign = network.generators.at[gen,"sign"]
for sn in snapshots:
network._p_balance[bus,sn].variables.append((sign,network.model.generator_p[gen,sn]))
load_p_set = get_switchable_as_dense(network, 'Load', 'p_set', snapshots)
for load in network.loads.index:
bus = network.loads.at[load,"bus"]
sign = network.loads.at[load,"sign"]
for sn in snapshots:
network._p_balance[bus,sn].constant += sign*load_p_set.at[sn,load]
for su in network.storage_units.index:
bus = network.storage_units.at[su,"bus"]
sign = network.storage_units.at[su,"sign"]
for sn in snapshots:
network._p_balance[bus,sn].variables.append((sign,network.model.storage_p_dispatch[su,sn]))
network._p_balance[bus,sn].variables.append((-sign,network.model.storage_p_store[su,sn]))
for store in network.stores.index:
bus = network.stores.at[store,"bus"]
sign = network.stores.at[store,"sign"]
for sn in snapshots:
network._p_balance[bus,sn].variables.append((sign,network.model.store_p[store,sn]))
def define_nodal_balance_constraints(network,snapshots):
passive_branches = network.passive_branches()
for branch in passive_branches.index:
bus0 = passive_branches.at[branch,"bus0"]
bus1 = passive_branches.at[branch,"bus1"]
bt = branch[0]
bn = branch[1]
for sn in snapshots:
network._p_balance[bus0,sn].variables.append((-1,network.model.passive_branch_p[bt,bn,sn]))
network._p_balance[bus1,sn].variables.append((1,network.model.passive_branch_p[bt,bn,sn]))
power_balance = {k: LConstraint(v,"==",LExpression()) for k,v in iteritems(network._p_balance)}
l_constraint(network.model, "power_balance", power_balance,
list(network.buses.index), snapshots)
def define_sub_network_balance_constraints(network,snapshots):
sn_balance = {}
for sub_network in network.sub_networks.obj:
for sn in snapshots:
sn_balance[sub_network.name,sn] = LConstraint(LExpression(),"==",LExpression())
for bus in sub_network.buses().index:
sn_balance[sub_network.name,sn].lhs.variables.extend(network._p_balance[bus,sn].variables)
sn_balance[sub_network.name,sn].lhs.constant += network._p_balance[bus,sn].constant
l_constraint(network.model,"sub_network_balance_constraint", sn_balance,
list(network.sub_networks.index), snapshots)
def define_global_constraints(network,snapshots):
global_constraints = {}