def declare_eq_branch_power_btheta_approx(model, index_set, branches, approximation_type=ApproximationType.BTHETA):
"""
Create the equality constraints for power (from BTHETA approximation)
in the branch
"""
m = model
con_set = decl.declare_set("_con_eq_branch_power_btheta_approx_set", model, index_set)
m.eq_pf_branch = pe.Constraint(con_set)
for branch_name in con_set:
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
tau = 1.0
shift = 0.0
if branch['branch_type'] == 'transformer':
tau = branch['transformer_tap_ratio']
shift = math.radians(branch['transformer_phase_shift'])
if approximation_type == ApproximationType.BTHETA:
x = branch['reactance']
b = -1/(tau*x)
elif approximation_type == ApproximationType.BTHETA_LOSSES:
b = tx_calc.calculate_susceptance(branch)/tau
m.eq_pf_branch[branch_name] = \
m.pf[branch_name] == \
b * (m.va[from_bus] - m.va[to_bus] + shift)
def power_flow_through_branch(Vi,
Vj,
delta,
branch,
bus_type="from_bus",
power_type="Reactive"):
if not (power_type == "Active" or power_type == "Reactive"):
raise ValueError(
'Power type must be "Active" (for p) or "Reactive" (for q)')
if not (bus_type == "from_bus" or bus_type == "to_bus"):
raise ValueError(
'Bus type must be "from_bus" (for f) or "to_bus" (for t)')
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
if power_type == "Active":
if bus_type == "from_bus":
return Vi**2 * g - Vi * Vj * g * pe.cos(
delta) - Vi * Vj * b * pe.sin(delta)
else:
return Vj**2 * g - Vi * Vj * g * pe.cos(
delta) - Vi * Vj * b * pe.sin(delta)
else:
if bus_type == "from_bus":
return -Vi**2 * b + Vi * Vj * b * pe.cos(
delta) - Vi * Vj * g * pe.sin(delta)
else:
return -Vj**2 * b + Vi * Vj * b * pe.cos(
delta) - Vi * Vj * g * pe.sin(delta)
def declare_eq_branch_current(model,
index_set,
branches,
coordinate_type=CoordinateType.RECTANGULAR):
"""
Create the equality constraints for the real and imaginary current
in the branch
"""
assert (coordinate_type != CoordinateType.POLAR
and "Branch current in polar coordinates not implemented.")
m = model
con_set = decl.declare_set("_con_eq_branch_current_set", model, index_set)
m.eq_ifr_branch = pe.Constraint(con_set)
m.eq_ifj_branch = pe.Constraint(con_set)
m.eq_itr_branch = pe.Constraint(con_set)
m.eq_itj_branch = pe.Constraint(con_set)
for branch_name in con_set:
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
bc = branch['charging_susceptance']
tau = 1.0
shift = 0.0
if branch['branch_type'] == 'transformer':
tau = branch['transformer_tap_ratio']
shift = math.radians(branch['transformer_phase_shift'])
g11 = g / tau**2
g12 = (g * math.cos(shift) - b * math.sin(shift)) / tau
g21 = (g * math.cos(shift) + b * math.sin(shift)) / tau
g22 = g
b11 = (b + bc / 2) / tau**2
b12 = (b * math.cos(shift) + g * math.sin(shift)) / tau
b21 = (b * math.cos(shift) - g * math.sin(shift)) / tau
b22 = b + bc / 2
m.eq_ifr_branch[branch_name] = \
m.ifr[branch_name] == \
g11 * m.vr[from_bus] - g12 * m.vr[to_bus] - (b11 * m.vj[from_bus] - b12 * m.vj[to_bus])
m.eq_ifj_branch[branch_name] = \
m.ifj[branch_name] == \
g11 * m.vj[from_bus] - g12 * m.vj[to_bus] + (b11 * m.vr[from_bus] - b12 * m.vr[to_bus])
m.eq_itr_branch[branch_name] = \
m.itr[branch_name] == \
-(g21 * m.vr[from_bus] - g22 * m.vr[to_bus] - (b21 * m.vj[from_bus] - b22 * m.vj[to_bus]))
m.eq_itj_branch[branch_name] = \
m.itj[branch_name] == \
-(g21 * m.vj[from_bus] - g22 * m.vj[to_bus] + (b21 * m.vr[from_bus] - b22 * m.vr[to_bus]))
def declare_eq_branch_power_ptdf_approx(model, index_set, branches, buses, bus_p_loads, gens_by_bus,
bus_gs_fixed_shunts, ptdf_tol = 1e-10,
approximation_type = ApproximationType.PTDF):
"""
Create the equality constraints for power (from PTDF approximation)
in the branch
"""
m = model
con_set = decl.declare_set("_con_eq_branch_power_ptdf_approx_set", model, index_set)
m.eq_pf_branch = pe.Constraint(con_set)
for branch_name in con_set:
branch = branches[branch_name]
expr = 0
tau = 1.0
shift = 0.0
if branch['branch_type'] == 'transformer':
tau = branch['transformer_tap_ratio']
shift = math.radians(branch['transformer_phase_shift'])
if approximation_type == ApproximationType.PTDF:
ptdf = branch['ptdf']
if shift != 0.:
b = -(1 / branch['reactance'])
expr += b * (shift / tau)
elif approximation_type == ApproximationType.PTDF_LOSSES:
ptdf = branch['ptdf_r']
if shift != 0.:
b = tx_calc.calculate_susceptance(branch)
expr += b * (shift / tau)
for bus_name, coef in ptdf.items():
if ptdf_tol and abs(coef) < ptdf_tol:
continue
bus = buses[bus_name]
phi_from = bus['phi_from']
phi_to = bus['phi_to']
if bus_gs_fixed_shunts[bus_name] != 0.0:
expr += coef * bus_gs_fixed_shunts[bus_name]
if bus_p_loads[bus_name] != 0.0:
expr += coef * m.pl[bus_name]
for gen_name in gens_by_bus[bus_name]:
expr -= coef * m.pg[gen_name]
for _, phi in phi_from.items():
expr += coef * phi
for _, phi in phi_to.items():
expr -= coef * phi
m.eq_pf_branch[branch_name] = \
m.pf[branch_name] == expr
def pwl_active_from_ub_rule(model, branch_name, i):
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
coeffs = branch_dict["Active_from_bus"][branch_name]['boxes']['coefficients'][i-1]
#M = 10*(g+b) + 4*(coeffs[0]+coeffs[1]+coeffs[2]+coeffs[3])
M = 2*s_max[branch_name] + 10*(np.abs(coeffs[0])+np.abs(coeffs[1])+np.abs(coeffs[2])+np.abs(coeffs[3]))
return -model.pf[branch_name] + coeffs[0]*model.vm[from_bus] + coeffs[1]*model.vm[to_bus] + coeffs[2]*model.dva_branch[branch_name, i, 0] + coeffs[3] <= M*(1-model.u_branch[branch_name, i, 0])
def _calculate_phase_shift(self):
phase_shift_array = np.array([
tx_calc.calculate_susceptance(branch) *
(radians(branch['transformer_phase_shift']) /
branch['transformer_tap_ratio']) if
(branch['branch_type'] == 'transformer') else 0.
for branch in (self._branches[bn] for bn in self.branches_keys)
])
## protect the array using numpy
phase_shift_array.flags.writeable = False
self.phase_shift_array = phase_shift_array
def declare_eq_branch_power(model, index_set, branches):
"""
Create the equality constraints for the real and reactive power
in the branch
"""
m = model
con_set = decl.declare_set("_con_eq_branch_power_set", model, index_set)
m.eq_pf_branch = pe.Constraint(con_set)
m.eq_pt_branch = pe.Constraint(con_set)
m.eq_qf_branch = pe.Constraint(con_set)
m.eq_qt_branch = pe.Constraint(con_set)
for branch_name in con_set:
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
vmsq_from_bus = m.vmsq[from_bus]
vmsq_to_bus = m.vmsq[to_bus]
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
bc = branch['charging_susceptance']
tau = 1.0
shift = 0.0
if branch['branch_type'] == 'transformer':
tau = branch['transformer_tap_ratio']
shift = math.radians(branch['transformer_phase_shift'])
g11 = g / tau**2
g12 = g * math.cos(shift) / tau
g21 = g * math.sin(shift) / tau
g22 = g
b11 = (b + bc / 2) / tau**2
b12 = b * math.cos(shift) / tau
b21 = b * math.sin(shift) / tau
b22 = b + bc / 2
m.eq_pf_branch[branch_name] = \
m.pf[branch_name] == \
g11 * vmsq_from_bus - \
(g12 * m.c[(from_bus,to_bus)] +
g21 * m.s[(from_bus,to_bus)] +
b12 * m.s[(from_bus,to_bus)] -
b21 * m.c[(from_bus,to_bus)])
m.eq_pt_branch[branch_name] = \
m.pt[branch_name] == \
g22 * vmsq_to_bus - \
(g12 * m.c[(from_bus,to_bus)] +
g21 * m.s[(from_bus,to_bus)] -
b12 * m.s[(from_bus,to_bus)] +
b21 * m.c[(from_bus,to_bus)])
m.eq_qf_branch[branch_name] = \
m.qf[branch_name] == \
-b11 * vmsq_from_bus + \
(b12 * m.c[(from_bus,to_bus)] +
b21 * m.s[(from_bus,to_bus)] -
g12 * m.s[(from_bus,to_bus)] +
g21 * m.c[(from_bus,to_bus)])
m.eq_qt_branch[branch_name] = \
m.qt[branch_name] == \
-b22 * vmsq_to_bus + \
(b12 * m.c[(from_bus,to_bus)] +
b21 * m.s[(from_bus,to_bus)] +
g12 * m.s[(from_bus,to_bus)] -
g21 * m.c[(from_bus,to_bus)])
def declare_eq_branch_power(model,
index_set,
branches,
branch_attrs,
coordinate_type=CoordinateType.POLAR):
"""
Create the equality constraints for the real and reactive power
in the branch
"""
m = model
bus_pairs = zip_items(branch_attrs['from_bus'], branch_attrs['to_bus'])
unique_bus_pairs = list(set([val for idx, val in bus_pairs.items()]))
declare_expr_c(model, unique_bus_pairs, coordinate_type)
declare_expr_s(model, unique_bus_pairs, coordinate_type)
con_set = decl.declare_set("_con_eq_branch_power_set", model, index_set)
m.eq_pf_branch = pe.Constraint(con_set)
m.eq_pt_branch = pe.Constraint(con_set)
m.eq_qf_branch = pe.Constraint(con_set)
m.eq_qt_branch = pe.Constraint(con_set)
for branch_name in con_set:
branch = branches[branch_name]
if not branch['in_service']:
continue
from_bus = branch['from_bus']
to_bus = branch['to_bus']
if coordinate_type == CoordinateType.POLAR:
vmsq_from_bus = m.vm[from_bus]**2
vmsq_to_bus = m.vm[to_bus]**2
elif coordinate_type == CoordinateType.RECTANGULAR:
vmsq_from_bus = m.vr[from_bus]**2 + m.vj[from_bus]**2
vmsq_to_bus = m.vr[to_bus]**2 + m.vj[to_bus]**2
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
bc = branch['charging_susceptance']
tau = 1.0
shift = 0.0
if branch['branch_type'] == 'transformer':
tau = branch['transformer_tap_ratio']
shift = math.radians(branch['transformer_phase_shift'])
g11 = g / tau**2
g12 = g * math.cos(shift) / tau
g21 = g * math.sin(shift) / tau
g22 = g
b11 = (b + bc / 2) / tau**2
b12 = b * math.cos(shift) / tau
b21 = b * math.sin(shift) / tau
b22 = b + bc / 2
m.eq_pf_branch[branch_name] = \
m.pf[branch_name] == \
g11 * vmsq_from_bus - \
(g12 * m.c[(from_bus,to_bus)] +
g21 * m.s[(from_bus,to_bus)] +
b12 * m.s[(from_bus,to_bus)] -
b21 * m.c[(from_bus,to_bus)])
m.eq_pt_branch[branch_name] = \
m.pt[branch_name] == \
g22 * vmsq_to_bus - \
(g12 * m.c[(from_bus,to_bus)] +
g21 * m.s[(from_bus,to_bus)] -
b12 * m.s[(from_bus,to_bus)] +
b21 * m.c[(from_bus,to_bus)])
m.eq_qf_branch[branch_name] = \
m.qf[branch_name] == \
-b11 * vmsq_from_bus + \
(b12 * m.c[(from_bus,to_bus)] +
b21 * m.s[(from_bus,to_bus)] -
g12 * m.s[(from_bus,to_bus)] +
g21 * m.c[(from_bus,to_bus)])
m.eq_qt_branch[branch_name] = \
m.qt[branch_name] == \
-b22 * vmsq_to_bus + \
(b12 * m.c[(from_bus,to_bus)] +
b21 * m.s[(from_bus,to_bus)] +
g12 * m.s[(from_bus,to_bus)] -
g21 * m.c[(from_bus,to_bus)])
def create_hot_start_lpac_model(model_data,
voltages,
lower_bound=-pi / 3,
upper_bound=pi / 3,
cosine_segment_count=20,
include_feasibility_slack=False,
mode="uniform"):
"""
The hot start LPAC model assumes that voltages are known, e.g. from an AC base point solution.
"""
###Grid data
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')
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 voltage magnitudes and squares of voltage magnitudes
bus_voltage_magnitudes = voltages #Assumes voltages is given as a dictionary
libbus.declare_var_vm(model,
bus_attrs['names'],
initialize=bus_voltage_magnitudes)
model.vm.fix()
libbus.declare_var_vmsq(
model=model,
index_set=bus_attrs['names'],
initialize={k: v**2
for k, v in bus_attrs['vm'].items()},
bounds=zip_items({k: v**2
for k, v in bus_attrs['v_min'].items()},
{k: v**2
for k, v in bus_attrs['v_max'].items()}))
### declare the polar voltages
libbus.declare_var_va(model,
bus_attrs['names'],
initialize=bus_attrs['va'])
### declare the cosine approximation variables
cos_hat_bounds = {k: (0, 1) for k in branch_attrs['names']}
decl.declare_var('cos_hat',
model,
branch_attrs['names'],
bounds=cos_hat_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(0.0))
### declare the fixed shunts at the buses
bus_bs_fixed_shunts, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(
buses, shunts)
### declare (and fix) the loads at the buses
bus_p_loads, bus_q_loads = tx_utils.dict_of_bus_loads(buses, loads)
libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads)
libbus.declare_var_ql(model, bus_attrs['names'], initialize=bus_q_loads)
model.pl.fix()
model.ql.fix()
### include the feasibility slack for the bus balances
p_rhs_kwargs = {}
q_rhs_kwargs = {}
if include_feasibility_slack:
p_rhs_kwargs, q_rhs_kwargs, penalty_expr = _include_feasibility_slack(
model, bus_attrs, gen_attrs, bus_p_loads, bus_q_loads)
### declare the generator real and reactive 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']))
qg_init = {
k: (gen_attrs['q_min'][k] + gen_attrs['q_max'][k]) / 2.0
for k in gen_attrs['qg']
}
libgen.declare_var_qg(model,
gen_attrs['names'],
initialize=qg_init,
bounds=zip_items(gen_attrs['q_min'],
gen_attrs['q_max']))
### declare the current flows in the branches
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(bus_attrs['va'][k])
for k in bus_attrs['vm']
}
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(bus_attrs['va'][k])
for k in bus_attrs['vm']
}
s_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
s_lbub = dict()
for k in branches.keys():
if s_max[k] is None:
s_lbub[k] = (None, None)
else:
s_lbub[k] = (-s_max[k], s_max[k])
pf_bounds = s_lbub
pt_bounds = s_lbub
qf_bounds = s_lbub
qt_bounds = s_lbub
pf_init = dict()
pt_init = dict()
qf_init = dict()
qt_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)
itr_init = tx_calc.calculate_itr(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
itj_init = tx_calc.calculate_itj(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])
pt_init[branch_name] = tx_calc.calculate_p(itr_init, itj_init,
vr_init[to_bus],
vj_init[to_bus])
qf_init[branch_name] = tx_calc.calculate_q(ifr_init, ifj_init,
vr_init[from_bus],
vj_init[from_bus])
qt_init[branch_name] = tx_calc.calculate_q(itr_init, itj_init,
vr_init[to_bus],
vj_init[to_bus])
libbranch.declare_var_pf(model=model,
index_set=branch_attrs['names'],
initialize=pf_init,
bounds=pf_bounds)
libbranch.declare_var_pt(model=model,
index_set=branch_attrs['names'],
initialize=pt_init,
bounds=pt_bounds)
libbranch.declare_var_qf(model=model,
index_set=branch_attrs['names'],
initialize=qf_init,
bounds=qf_bounds)
libbranch.declare_var_qt(model=model,
index_set=branch_attrs['names'],
initialize=qt_init,
bounds=qt_bounds)
####################
#Constraints
####################
###Balance equations in a bus
#p balance
libbus.declare_eq_p_balance(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,
**p_rhs_kwargs)
#q balance
libbus.declare_eq_q_balance(model=model,
index_set=bus_attrs['names'],
bus_q_loads=bus_q_loads,
gens_by_bus=gens_by_bus,
bus_bs_fixed_shunts=bus_bs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
**q_rhs_kwargs)
### Power in a branch
branch_con_set = decl.declare_set('_con_eq_p_q_lpac_branch_power', model,
branch_attrs['names'])
model.eq_pf_branch_t = pe.Constraint(branch_con_set)
model.eq_pt_branch_t = pe.Constraint(branch_con_set)
model.eq_qf_branch_t = pe.Constraint(branch_con_set)
model.eq_qt_branch_t = pe.Constraint(branch_con_set)
for branch_name in branch_con_set:
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
model.eq_pf_branch_t[branch_name] = \
model.pf[branch_name] == \
g*model.vmsq[from_bus] - model.vm[from_bus]*model.vm[to_bus]*(g * model.cos_hat[branch_name] + b * (model.va[from_bus] - model.va[to_bus]))
model.eq_pt_branch_t[branch_name] = \
model.pt[branch_name] == \
g*model.vmsq[to_bus] - model.vm[from_bus]*model.vm[to_bus]*(g * model.cos_hat[branch_name] + b * (model.va[to_bus] - model.va[from_bus]))
model.eq_qf_branch_t[branch_name] = \
model.qf[branch_name] == \
-b*model.vmsq[from_bus] - model.vm[from_bus]*model.vm[to_bus]*(g*(model.va[from_bus] - model.va[to_bus]) - b*model.cos_hat[branch_name])
model.eq_qt_branch_t[branch_name] = \
model.qt[branch_name] == \
-b*model.vmsq[to_bus] - model.vm[from_bus]*model.vm[to_bus]*(g*(model.va[to_bus] - model.va[from_bus]) - b*model.cos_hat[branch_name])
### Piecewise linear cosine constraints
model.N = pe.Set(initialize=list(range(cosine_segment_count + 1)))
declare_pwl_cosine_bounds(model=model,
index_set=branch_attrs['names'],
branches=branches,
lower_bound=lower_bound,
upper_bound=upper_bound,
cosine_segment_count=cosine_segment_count,
mode=mode)
### Objective is to maximize cosine hat variables
obj_expr = sum(model.cos_hat[branch_name]
for branch_name in branch_attrs['names'])
if include_feasibility_slack:
obj_expr += penalty_expr
model.obj = pe.Objective(expr=obj_expr)
return model, md
def create_cold_start_lpac_model(model_data,
cosine_segment_count=20,
lower_bound=-pi / 3,
upper_bound=pi / 3,
include_feasibility_slack=False,
mode="uniform"):
"""
The cold start LPAC model assumes that no target voltages are available and that all voltages are initially approximated as 1 pu.
"""
###Grid data
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')
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 the polar voltages
libbus.declare_var_va(model,
bus_attrs['names'],
initialize=bus_attrs['va'])
libbus.declare_var_vmsq(
model=model,
index_set=bus_attrs['names'],
initialize={k: v**2
for k, v in bus_attrs['vm'].items()},
bounds=zip_items({k: v**2
for k, v in bus_attrs['v_min'].items()},
{k: v**2
for k, v in bus_attrs['v_max'].items()}))
### declare the voltage change variables
decl.declare_var('phi', model, bus_attrs['names'])
### declare the cosine approximation variables
cos_hat_bounds = {k: (0, 1) for k in branch_attrs['names']}
decl.declare_var('cos_hat',
model,
branch_attrs['names'],
bounds=cos_hat_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(0.0))
### declare (and fix) the loads at the buses
bus_p_loads, bus_q_loads = tx_utils.dict_of_bus_loads(buses, loads)
libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads)
libbus.declare_var_ql(model, bus_attrs['names'], initialize=bus_q_loads)
model.pl.fix()
model.ql.fix()
### declare the fixed shunts at the buses
bus_bs_fixed_shunts, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(
buses, shunts)
### include the feasibility slack for the bus balances
p_rhs_kwargs = {}
q_rhs_kwargs = {}
if include_feasibility_slack:
p_rhs_kwargs, q_rhs_kwargs, penalty_expr = _include_feasibility_slack(
model, bus_attrs, gen_attrs, bus_p_loads, bus_q_loads)
### declare the generator real and reactive 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']))
qg_init = {
k: (gen_attrs['q_min'][k] + gen_attrs['q_max'][k]) / 2.0
for k in gen_attrs['qg']
}
libgen.declare_var_qg(model,
gen_attrs['names'],
initialize=qg_init,
bounds=zip_items(gen_attrs['q_min'],
gen_attrs['q_max']))
### declare the current flows in the branches
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(bus_attrs['va'][k])
for k in bus_attrs['vm']
}
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(bus_attrs['va'][k])
for k in bus_attrs['vm']
}
s_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
s_lbub = dict()
for k in branches.keys():
if s_max[k] is None:
s_lbub[k] = (None, None)
else:
s_lbub[k] = (-s_max[k], s_max[k])
pf_bounds = s_lbub
pt_bounds = s_lbub
qf_bounds = s_lbub
qt_bounds = s_lbub
pf_init = dict()
pt_init = dict()
qf_init = dict()
qt_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)
itr_init = tx_calc.calculate_itr(vr_init[from_bus], vj_init[from_bus],
vr_init[to_bus], vj_init[to_bus],
y_matrix)
itj_init = tx_calc.calculate_itj(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])
pt_init[branch_name] = tx_calc.calculate_p(itr_init, itj_init,
vr_init[to_bus],
vj_init[to_bus])
qf_init[branch_name] = tx_calc.calculate_q(ifr_init, ifj_init,
vr_init[from_bus],
vj_init[from_bus])
qt_init[branch_name] = tx_calc.calculate_q(itr_init, itj_init,
vr_init[to_bus],
vj_init[to_bus])
libbranch.declare_var_pf(model=model,
index_set=branch_attrs['names'],
initialize=pf_init,
bounds=pf_bounds)
libbranch.declare_var_pt(model=model,
index_set=branch_attrs['names'],
initialize=pt_init,
bounds=pt_bounds)
libbranch.declare_var_qf(model=model,
index_set=branch_attrs['names'],
initialize=qf_init,
bounds=qf_bounds)
libbranch.declare_var_qt(model=model,
index_set=branch_attrs['names'],
initialize=qt_init,
bounds=qt_bounds)
################################
#Constraints
################################
### Balance equations at a bus (based on Kirchhoff Current Law)
#Should be able to just use DC OPF approximation of B-theta type?
### declare the p balance
libbus.declare_eq_p_balance(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,
**p_rhs_kwargs)
#Need one also for q balance
libbus.declare_eq_q_balance(model=model,
index_set=bus_attrs['names'],
bus_q_loads=bus_q_loads,
gens_by_bus=gens_by_bus,
bus_bs_fixed_shunts=bus_bs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
**q_rhs_kwargs)
### Constraints for power in a branch
branch_con_set = decl.declare_set('_con_eq_p_q_lpac_branch_power', model,
branch_attrs['names'])
model.eq_pf_branch_t = pe.Constraint(branch_con_set)
model.eq_pt_branch_t = pe.Constraint(branch_con_set)
model.eq_qf_branch_t = pe.Constraint(branch_con_set)
model.eq_qt_branch_t = pe.Constraint(branch_con_set)
for branch_name in branch_con_set:
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
model.eq_pf_branch_t[branch_name] = \
model.pf[branch_name] == \
g - g * model.cos_hat[branch_name] - b * (model.va[from_bus] - model.va[to_bus])
model.eq_pt_branch_t[branch_name] = \
model.pt[branch_name] == \
g - g * model.cos_hat[branch_name] - b * (model.va[to_bus] - model.va[from_bus])
model.eq_qf_branch_t[branch_name] = \
model.qf[branch_name] == \
-b - g*(model.va[from_bus] - model.va[to_bus]) + b*model.cos_hat[branch_name] - b*(model.phi[from_bus] - model.phi[to_bus])
model.eq_qt_branch_t[branch_name] = \
model.qt[branch_name] == \
-b - g*(model.va[to_bus] - model.va[from_bus]) +b*model.cos_hat[branch_name] - b*(model.phi[to_bus] - model.phi[from_bus])
### Piecewise linear cosine constraints
model.N = pe.Set(initialize=list(range(cosine_segment_count + 1)))
declare_pwl_cosine_bounds(model=model,
index_set=branch_attrs['names'],
branches=branches,
lower_bound=lower_bound,
upper_bound=upper_bound,
cosine_segment_count=cosine_segment_count,
mode=mode)
### Objective is to maximize cosine hat variables
# obj_expr = sum(model.cos_hat[branch_name] for branch_name in branch_attrs['names'])
# if include_feasibility_slack:
# obj_expr += penalty_expr
# model.obj = pe.Objective(expr=obj_expr)
###Objective to match with acopf.py
### declare the generator cost objective
libgen.declare_expression_pgqg_operating_cost(model=model,
index_set=gen_attrs['names'],
p_costs=gen_attrs['p_cost'],
q_costs=gen_attrs.get(
'q_cost', None))
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
if hasattr(model, 'qg_operating_cost'):
obj_expr += sum(model.qg_operating_cost[gen_name]
for gen_name in model.qg_operating_cost)
model.obj = pe.Objective(expr=obj_expr)
return model, md
