def create_psv_acpf_model(model_data):
model, md = _create_base_acpf_model(model_data)
gens = dict(md.elements(element_type='generator'))
buses = dict(md.elements(element_type='bus'))
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
gens_by_bus = tx_utils.gens_by_bus(buses, gens)
buses_with_gens = _buses_with_gens(gens)
bus_pairs = zip_items(branch_attrs['from_bus'], branch_attrs['to_bus'])
unique_bus_pairs = list(OrderedDict((val, None) for idx, val in bus_pairs.items()).keys())
# declare the polar voltages
libbranch.declare_var_dva(model=model,
index_set=unique_bus_pairs,
initialize=0
)
libbus.declare_var_vm(model,
bus_attrs['names'],
initialize=bus_attrs['vm']
)
libbus.declare_var_va(model,
bus_attrs['names'],
initialize=tx_utils.radians_from_degrees_dict(bus_attrs['va'])
)
### In a system with N buses and G generators, there are then 2(N-1)-(G-1) unknowns.
### fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
model.va[ref_bus].fix(radians(ref_angle))
model.vm[ref_bus].fixed = True
# if there is more than one generator at the reference
# bus, then we fix the pg for all but one
for i,g in enumerate(gens_by_bus[ref_bus]):
if i > 0:
model.pg[g].fixed = True
for bus_name in bus_attrs['names']:
if bus_name != ref_bus and bus_name in buses_with_gens:
model.vm[bus_name].fixed = True
for gen_name in gens_by_bus[bus_name]:
model.pg[gen_name].fixed = True
# relate c, s, and vmsq to vm and va
libbranch.declare_eq_delta_va(model=model,
index_set=unique_bus_pairs)
libbus.declare_eq_vmsq(model=model,
index_set=bus_attrs['names'],
coordinate_type=CoordinateType.POLAR)
libbranch.declare_eq_c(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.POLAR)
libbranch.declare_eq_s(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.POLAR)
return model, md
def create_psv_acopf_model(model_data,
include_feasibility_slack=False,
pw_cost_model='delta'):
model, md = _create_base_power_ac_model(
model_data,
include_feasibility_slack=include_feasibility_slack,
pw_cost_model=pw_cost_model)
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
bus_pairs = zip_items(branch_attrs['from_bus'], branch_attrs['to_bus'])
unique_bus_pairs = list(
OrderedDict((val, None) for idx, val in bus_pairs.items()).keys())
# declare the polar voltages
libbranch.declare_var_dva(model=model,
index_set=unique_bus_pairs,
initialize=0,
bounds=(-pi / 2, pi / 2))
libbus.declare_var_vm(model,
bus_attrs['names'],
initialize=bus_attrs['vm'],
bounds=zip_items(bus_attrs['v_min'],
bus_attrs['v_max']))
va_bounds = {k: (-pi, pi) for k in bus_attrs['va']}
libbus.declare_var_va(model,
bus_attrs['names'],
initialize=tx_utils.radians_from_degrees_dict(
bus_attrs['va']),
bounds=va_bounds)
# fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
model.va[ref_bus].fix(radians(ref_angle))
# relate c, s, and vmsq to vm and va
libbranch.declare_eq_delta_va(model=model, index_set=unique_bus_pairs)
libbus.declare_eq_vmsq(model=model,
index_set=bus_attrs['names'],
coordinate_type=CoordinateType.POLAR)
libbranch.declare_eq_c(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.POLAR)
libbranch.declare_eq_s(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.POLAR)
return model, md
def create_gdp_subproblem(model, model_data, include_angle_diff_limits=False):
md = model_data
tx_utils.scale_ModelData_to_pu(md, inplace=True)
gens = dict(md.elements(element_type='generator'))
buses = dict(md.elements(element_type='bus'))
branches = dict(md.elements(element_type='branch'))
loads = dict(md.elements(element_type='load'))
shunts = dict(md.elements(element_type='shunt'))
gen_attrs = md.attributes(element_type='generator')
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
inlet_branches_by_bus, outlet_branches_by_bus = \
tx_utils.inlet_outlet_branches_by_bus(branches, buses)
gens_by_bus = tx_utils.gens_by_bus(buses, gens)
model.subproblem = bi.SubModel(fixed=(model.u, model.v, model.w))
### declare (and fix) the loads at the buses
bus_p_loads, _ = tx_utils.dict_of_bus_loads(buses, loads)
buses_with_loads = list(k for k in bus_p_loads.keys()
if bus_p_loads[k] != 0.)
libbus.declare_var_pl(model.subproblem,
bus_attrs['names'],
initialize=bus_p_loads)
model.subproblem.pl.fix()
### declare the fixed shunts at the buses
_, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(buses, shunts)
### declare the polar voltages
va_bounds = {k: (-pi, pi) for k in bus_attrs['va']}
libbus.declare_var_va(model.subproblem,
bus_attrs['names'],
initialize=tx_utils.radians_from_degrees_dict(
bus_attrs['va']),
bounds=va_bounds)
### fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
model.subproblem.va[ref_bus].fix(radians(ref_angle))
### declare the generator real power
pg_init = {
k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0
for k in gen_attrs['pg']
}
libgen.declare_var_pg(model.subproblem,
gen_attrs['names'],
initialize=pg_init,
bounds=zip_items(gen_attrs['p_min'],
gen_attrs['p_max']))
### declare the current flows in the branches
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
p_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
p_lbub = {k: (-p_max[k], p_max[k]) for k in branches.keys()}
pf_bounds = p_lbub
pf_init = dict()
for branch_name, branch in branches.items():
from_bus = branch['from_bus']
to_bus = branch['to_bus']
y_matrix = tx_calc.calculate_y_matrix_from_branch(branch)
ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init,
vr_init[from_bus],
vj_init[from_bus])
libbranch.declare_var_pf(model=model.subproblem,
index_set=branch_attrs['names'],
initialize=pf_init,
bounds=pf_bounds)
# need to include variable references on subproblem to variables, which exist on the master block
bi.components.varref(model.subproblem)
### declare the branch power flow disjuncts (LHS is status quo, RHS is compromised)
libbranch.declare_eq_branch_power_btheta_approx(
model=model.subproblem,
index_set=branch_attrs['names'],
branches=branches)
subcons.declare_eq_branch_power_off(model=model.subproblem,
index_set=branch_attrs['names'],
branches=branches)
subcons.disjunctify(model=model.subproblem,
indicator_name='pf_branch_indicator',
disjunct_name='pf_branch_disjunct',
LHS_disjunct_set=model.subproblem.eq_pf_branch,
RHS_disjunct_set=model.subproblem.eq_pf_branch_off)
### declare the load shed disjuncts (LHS is status quo, RHS is compromised)
subcons.declare_ineq_load_shed_ub(model=model.subproblem,
index_set=buses_with_loads)
subcons.declare_ineq_load_shed_lb(model=model.subproblem,
index_set=buses_with_loads)
subcons.declare_ineq_load_shed_lb_off(model=model.subproblem,
index_set=buses_with_loads)
subcons.disjunctify(
model=model.subproblem,
indicator_name='load_shed_indicator',
disjunct_name='load_shed_disjunct',
LHS_disjunct_set=model.subproblem.ineq_load_shed_lb,
RHS_disjunct_set=model.subproblem.ineq_load_shed_lb_off)
### declare the generator disjuncts (LHS is status quo, RHS is compromised)
subcons.declare_ineq_gen_on(model=model.subproblem,
index_set=gen_attrs['names'],
gens=gens)
subcons.declare_ineq_gen_off(model=model.subproblem,
index_set=gen_attrs['names'],
gens=gens)
subcons.disjunctify(model=model.subproblem,
indicator_name='gen_indicator',
disjunct_name='gen_disjunct',
LHS_disjunct_set=model.subproblem.ineq_gen,
RHS_disjunct_set=model.subproblem.ineq_gen_off)
### declare the p balance
rhs_kwargs = {'include_feasibility_slack_neg': 'load_shed'}
libbus.declare_eq_p_balance_dc_approx(
model=model.subproblem,
index_set=bus_attrs['names'],
bus_p_loads=bus_p_loads,
gens_by_bus=gens_by_bus,
bus_gs_fixed_shunts=bus_gs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
approximation_type=ApproximationType.BTHETA,
**rhs_kwargs)
### declare the real power flow limits
libbranch.declare_ineq_p_branch_thermal_lbub(
model=model.subproblem,
index_set=branch_attrs['names'],
branches=branches,
p_thermal_limits=p_max,
approximation_type=ApproximationType.BTHETA)
### declare angle difference limits on interconnected buses
if include_angle_diff_limits:
libbranch.declare_ineq_angle_diff_branch_lbub(
model=model.subproblem,
index_set=branch_attrs['names'],
branches=branches,
coordinate_type=CoordinateType.POLAR)
model.subproblem.obj = pe.Objective(expr=sum(model.load_shed[l]
for l in buses_with_loads),
sense=pe.minimize)
return model, md
def create_explicit_subproblem(model,
subproblem,
model_data,
omega_key,
include_angle_diff_limits=False,
include_bigm=False):
### power system data
md = model_data
### create dictionaries of object sets
gens = dict(md.elements(element_type='generator'))
buses = dict(md.elements(element_type='bus'))
branches = dict(md.elements(element_type='branch'))
loads = dict(md.elements(element_type='load'))
shunts = dict(md.elements(element_type='shunt'))
### create dictionaries across object attributes for an object of the same set type
gen_attrs = md.attributes(element_type='generator')
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
inlet_branches_by_bus, outlet_branches_by_bus = \
tx_utils.inlet_outlet_branches_by_bus(branches, buses)
gens_by_bus = tx_utils.gens_by_bus(buses, gens)
### declare (and fix) the loads at the buses
bus_p_loads, _ = tx_utils.dict_of_bus_loads(buses, loads)
buses_with_loads = list(k for k in bus_p_loads.keys()
if bus_p_loads[k] != 0.)
#libbus.declare_var_pl(model.subproblem, bus_attrs['names'], initialize=bus_p_loads)
#model.subproblem.pl.fix()
subproblem.pl = bus_p_loads
### declare the fixed shunts at the buses
_, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(buses, shunts)
### declare the polar voltages
va_bounds = {k: (-pi, pi) for k in bus_attrs['va']}
libbus.declare_var_va(subproblem,
bus_attrs['names'],
initialize=tx_utils.radians_from_degrees_dict(
bus_attrs['va']),
bounds=va_bounds)
### fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
subproblem.va[ref_bus].fix(radians(ref_angle))
### declare the generator real power
pg_init = {
k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0
for k in gen_attrs['pg']
}
libgen.declare_var_pg(subproblem, gen_attrs['names'], initialize=pg_init)
### declare the current flows in the branches
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
pf_init = dict()
for branch_name, branch in branches.items():
from_bus = branch['from_bus']
to_bus = branch['to_bus']
y_matrix = tx_calc.calculate_y_matrix_from_branch(branch)
ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init,
vr_init[from_bus],
vj_init[from_bus])
libbranch.declare_var_pf(model=subproblem,
index_set=branch_attrs['names'],
initialize=pf_init)
# need to include variable references on subproblem to variables, which exist on the master block
bi.components.varref(subproblem)
if include_bigm:
# create big-M
_create_bigm(subproblem, md)
### declare the branch power flow disjuncts
subcons.declare_eq_branch_power_btheta_approx_bigM(
model=subproblem,
index_set=branch_attrs['names'],
branches=branches)
### declare the real power flow limits
p_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
subcons.declare_ineq_p_branch_thermal_lbub_switch(
model=subproblem,
index_set=branch_attrs['names'],
p_thermal_limits=p_max)
else:
### declare the branch power flow with indicator variable in the bilinear term
subcons.declare_eq_branch_power_btheta_approx_nonlin(
model=subproblem,
index_set=branch_attrs['names'],
branches=branches)
### declare the real power flow limits
p_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
libbranch.declare_ineq_p_branch_thermal_lbub(
model=subproblem,
index_set=branch_attrs['names'],
branches=branches,
p_thermal_limits=p_max,
approximation_type=ApproximationType.BTHETA)
### declare the load shed
subcons.declare_ineq_load_shed_stochastic(model=subproblem,
index_set=buses_with_loads,
scenario=omega_key)
### declare the generator compromised
subcons.declare_ineq_gen(model=subproblem,
index_set=gen_attrs['names'],
gens=gens)
### declare the p balance
rhs_kwargs = {'include_feasibility_slack_neg': ('load_shed', omega_key)}
libbus.declare_eq_p_balance_dc_approx(
model=subproblem,
index_set=bus_attrs['names'],
bus_p_loads=bus_p_loads,
gens_by_bus=gens_by_bus,
bus_gs_fixed_shunts=bus_gs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
approximation_type=ApproximationType.BTHETA,
**rhs_kwargs)
### declare angle difference limits on interconnected buses
if include_angle_diff_limits:
libbranch.declare_ineq_angle_diff_branch_lbub(
model=subproblem,
index_set=branch_attrs['names'],
branches=branches,
coordinate_type=CoordinateType.POLAR)
### lower-level objective for interdiction problem (opposite to upper-level objective)
subproblem.obj = pe.Objective(expr=sum(model.load_shed[omega_key, l]
for l in buses_with_loads),
sense=pe.minimize)
return model, md
def create_btheta_losses_dcopf_model(model_data,
relaxation_type=RelaxationType.SOC,
include_angle_diff_limits=False,
include_feasibility_slack=False,
pw_cost_model='delta'):
md = model_data.clone_in_service()
tx_utils.scale_ModelData_to_pu(md, inplace=True)
gens = dict(md.elements(element_type='generator'))
buses = dict(md.elements(element_type='bus'))
branches = dict(md.elements(element_type='branch'))
loads = dict(md.elements(element_type='load'))
shunts = dict(md.elements(element_type='shunt'))
gen_attrs = md.attributes(element_type='generator')
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
load_attrs = md.attributes(element_type='load')
shunt_attrs = md.attributes(element_type='shunt')
inlet_branches_by_bus, outlet_branches_by_bus = \
tx_utils.inlet_outlet_branches_by_bus(branches, buses)
gens_by_bus = tx_utils.gens_by_bus(buses, gens)
model = pe.ConcreteModel()
### declare (and fix) the loads at the buses
bus_p_loads, _ = tx_utils.dict_of_bus_loads(buses, loads)
libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads)
model.pl.fix()
### declare the fixed shunts at the buses
_, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(buses, shunts)
### declare the polar voltages
va_bounds = {k: (-pi, pi) for k in bus_attrs['va']}
libbus.declare_var_va(model,
bus_attrs['names'],
initialize=tx_utils.radians_from_degrees_dict(
bus_attrs['va']),
bounds=va_bounds)
dva_initialize = {k: 0.0 for k in branch_attrs['names']}
libbranch.declare_var_dva(model,
branch_attrs['names'],
initialize=dva_initialize)
### include the feasibility slack for the bus balances
p_rhs_kwargs = {}
penalty_expr = None
if include_feasibility_slack:
p_marginal_slack_penalty = _validate_and_extract_slack_penalty(md)
p_rhs_kwargs, penalty_expr = _include_feasibility_slack(
model, bus_attrs['names'], bus_p_loads, gens_by_bus, gen_attrs,
p_marginal_slack_penalty)
### fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
model.va[ref_bus].fix(radians(ref_angle))
### declare the generator real power
pg_init = {
k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0
for k in gen_attrs['pg']
}
libgen.declare_var_pg(model,
gen_attrs['names'],
initialize=pg_init,
bounds=zip_items(gen_attrs['p_min'],
gen_attrs['p_max']))
### declare the current flows in the branches
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
p_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
pf_bounds = {k: (-p_max[k], p_max[k]) for k in branches.keys()}
pf_init = dict()
for branch_name, branch in branches.items():
from_bus = branch['from_bus']
to_bus = branch['to_bus']
y_matrix = tx_calc.calculate_y_matrix_from_branch(branch)
ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init,
vr_init[from_bus],
vj_init[from_bus])
pfl_bounds = {k: (0, p_max[k]**2) for k in branches.keys()}
pfl_init = {k: 0 for k in branches.keys()}
libbranch.declare_var_pf(model=model,
index_set=branch_attrs['names'],
initialize=pf_init,
bounds=pf_bounds)
libbranch.declare_var_pfl(model=model,
index_set=branch_attrs['names'],
initialize=pfl_init,
bounds=pfl_bounds)
### declare the angle difference constraint
libbranch.declare_eq_branch_dva(model=model,
index_set=branch_attrs['names'],
branches=branches)
### declare the branch power flow approximation constraints
libbranch.declare_eq_branch_power_btheta_approx(
model=model,
index_set=branch_attrs['names'],
branches=branches,
approximation_type=ApproximationType.BTHETA_LOSSES)
### declare the branch power loss approximation constraints
libbranch.declare_eq_branch_loss_btheta_approx(
model=model,
index_set=branch_attrs['names'],
branches=branches,
relaxation_type=relaxation_type)
### declare the p balance
libbus.declare_eq_p_balance_dc_approx(
model=model,
index_set=bus_attrs['names'],
bus_p_loads=bus_p_loads,
gens_by_bus=gens_by_bus,
bus_gs_fixed_shunts=bus_gs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
approximation_type=ApproximationType.BTHETA_LOSSES,
**p_rhs_kwargs)
### declare the real power flow limits
libbranch.declare_ineq_p_branch_thermal_lbub(
model=model,
index_set=branch_attrs['names'],
branches=branches,
p_thermal_limits=p_max,
approximation_type=ApproximationType.BTHETA)
### declare angle difference limits on interconnected buses
if include_angle_diff_limits:
libbranch.declare_ineq_angle_diff_branch_lbub(
model=model,
index_set=branch_attrs['names'],
branches=branches,
coordinate_type=CoordinateType.POLAR)
### declare the generator cost objective
p_costs = gen_attrs['p_cost']
pw_pg_cost_gens = list(
libgen.pw_gen_generator(gen_attrs['names'], costs=p_costs))
if len(pw_pg_cost_gens) > 0:
if pw_cost_model == 'delta':
libgen.declare_var_delta_pg(model=model,
index_set=pw_pg_cost_gens,
p_costs=p_costs)
libgen.declare_pg_delta_pg_con(model=model,
index_set=pw_pg_cost_gens,
p_costs=p_costs)
else:
libgen.declare_var_pg_cost(model=model,
index_set=pw_pg_cost_gens,
p_costs=p_costs)
libgen.declare_piecewise_pg_cost_cons(model=model,
index_set=pw_pg_cost_gens,
p_costs=p_costs)
libgen.declare_expression_pg_operating_cost(model=model,
index_set=gen_attrs['names'],
p_costs=p_costs,
pw_formulation=pw_cost_model)
obj_expr = sum(model.pg_operating_cost[gen_name]
for gen_name in model.pg_operating_cost)
if include_feasibility_slack:
obj_expr += penalty_expr
model.obj = pe.Objective(expr=obj_expr)
return model, md