def test_init():
m, solver = blr.main()
# initialize each unit at the time
blr.initialize(m)
blr.unfix_inlets(m)
# check that the model solved properly and has 0 degrees of freedom
assert(degrees_of_freedom(m)==0)
def test_boiler():
m, solver = blr.main()
# initialize each unit at the time
blr.initialize(m)
# unfix inlets to build arcs at the flowsheet level
blr.unfix_inlets(m)
m.fs.ATMP1.outlet.enth_mol[0].fix(62710.01)
m.fs.ATMP1.SprayWater.flow_mol[0].unfix()
result = solver.solve(m, tee=False)
assert result.solver.termination_condition == \
pyo.TerminationCondition.optimal
assert result.solver.status == pyo.SolverStatus.ok
assert pyo.value(m.fs.ECON.side_1.properties_out[0].temperature) == \
pytest.approx(521.009,1)
def main():
# import steam cycle and build concrete model
m, solver = import_steam_cycle()
print(degrees_of_freedom(m))
# at this point we have a flowsheet with "steam cycle" that solves
# correctly, with 0 degrees of freedom.
# next step is to import and build the boiler heat exchanger network
# importing the boiler heat exchanger network
# from (boiler_subflowsheet_build.py)
# this step appends all the boiler unit models into our model ("m")
# model "m" has been created a few lines above
import idaes.power_generation.flowsheets.\
supercritical_power_plant.boiler_subflowsheet_build as blr
# import the models (ECON, WW, PrSH, PlSH, FSH, Spliter, Mixer, Reheater)
# see boiler_subflowhseet_build.py for a beter description
blr.build_boiler(m.fs)
# initialize boiler network models (one by one)
blr.initialize(m)
# at this point we have both flowsheets (steam cycle + boiler network)
# in the same model/concrete object ("m"), however they are disconnected.
# Here we want to solve them at the same time
# this is a square problem (i.e. degrees of freedom = 0)
print('solving square problem disconnected')
results = solver.solve(m, tee=True)
# at this point we want to connect the units in both flowsheets
# Economizer inlet = Feed water heater 8 outlet (water)
# HP inlet = Attemperator outlet (steam)
# Reheater inlet (steam) = HP split 7 outlet (last stage of HP turbine)
# IP inlet = Reheater outlet steam7
blr.unfix_inlets(m)
print('unfix inlet conditions, degreeso of freedom = ' +
str(degrees_of_freedom(m)))
# user can save the initialization to a json file (uncomment next line)
# MS.to_json(m, fname = 'SCPC_full.json')
# later user can use the json file to initialize the model
# if this is the case comment out previous MS.to_json and uncomment next line
# MS.from_json(m, fname = 'SCPC_full.json')
# deactivate constraints linking the FWH8 to HP turbine
m.fs.boiler_pressure_drop.deactivate()
m.fs.close_flow.deactivate()
m.fs.turb.constraint_reheat_flow.deactivate()
m.fs.turb.constraint_reheat_press.deactivate()
m.fs.turb.constraint_reheat_temp.deactivate()
m.fs.turb.inlet_split.inlet.enth_mol.unfix()
m.fs.turb.inlet_split.inlet.pressure.unfix()
# user can fix the boiler feed water pump pressure (uncomenting next line)
# m.fs.bfp.outlet.pressure[:].fix(26922222.222))
m.fs.FHWtoECON = Arc(source=m.fs.fwh8.desuperheat.outlet_2,
destination=m.fs.ECON.side_1_inlet)
m.fs.Att2HP = Arc(source=m.fs.ATMP1.outlet,
destination=m.fs.turb.inlet_split.inlet)
m.fs.HPout2RH = Arc(source=m.fs.turb.hp_split[7].outlet_1,
destination=m.fs.RH.side_1_inlet)
m.fs.RHtoIP = Arc(source=m.fs.RH.side_1_outlet,
destination=m.fs.turb.ip_stages[1].inlet)
pyo.TransformationFactory("network.expand_arcs").apply_to(m)
# unfix boiler connections
m.fs.ECON.side_1_inlet.flow_mol.unfix()
m.fs.ECON.side_1_inlet.enth_mol[0].unfix()
m.fs.ECON.side_1_inlet.pressure[0].unfix()
m.fs.RH.side_1_inlet.flow_mol.unfix()
m.fs.RH.side_1_inlet.enth_mol[0].unfix()
m.fs.RH.side_1_inlet.pressure[0].unfix()
m.fs.hotwell.makeup.flow_mol[:].setlb(-1.0)
# if user has trouble with infeasible solutions, an easy test
# is to deactivate the link to HP turbine
# (m.fs.Att2HP_expanded "enth_mol and pressure" equalities)
# and fix inlet pressure and enth_mol to turbine
# (m.fs.turb.inlet_split.inlet)
# (then double check the values from m.fs.ATMP1.outlet)
# m.fs.Att2HP_expanded.enth_mol_equality.deactivate()
# m.fs.Att2HP_expanded.pressure_equality.deactivate()
m.fs.turb.inlet_split.inlet.pressure.fix(2.423e7)
# m.fs.turb.inlet_split.inlet.enth_mol.fix(62710.01)
# finally, since we want to maintain High Pressure (HP) inlet temperature
# constant (~866 K), we need to fix Attemperator enthalpy outlet
# and unfix heat duty to Platen superheater, note that fixing enthalpy
# to control temperature is only valid because pressure is also fixed
m.fs.ATMP1.outlet.enth_mol[0].fix(62710.01)
m.fs.PlSH.heat_duty[:].unfix() # fix(5.5e7)
# m.fs.ATMP1.SprayWater.flow_mol[0].unfix()
print('connecting flowsheets, degrees of freedom = ' +
str(degrees_of_freedom(m)))
print('solving full plant model')
solver.options = {
"tol": 1e-6,
"linear_solver": "ma27",
"max_iter": 40,
}
# square problems tend to work better without bounds
strip_bounds = pyo.TransformationFactory('contrib.strip_var_bounds')
strip_bounds.apply_to(m, reversible=True)
# this is the final solve with both flowsheets connected
results = solver.solve(m, tee=True)
return m, results
def test_init(boiler):
# initialize each unit at the time
blr.initialize(boiler)
blr.unfix_inlets(boiler)
# check that the model solved properly and has 0 degrees of freedom
assert (degrees_of_freedom(boiler) == 0)
def boiler_flowsheet():
"""
Make the flowsheet object, fix some variables, and solve the problem
"""
import idaes.power_generation.flowsheets.\
supercritical_power_plant.boiler_subflowsheet_build as blr
# First, we import the boler model from boiler_subflowsheet_build
m, solver = blr.main()
# initialize boiler flowsheet
blr.initialize(m)
# unfix inlet values to each unit and build the flowsheet connectivity
blr.unfix_inlets(m)
results = solver.solve(m, tee=True)
print(results)
# adding boiler block
# The model solved in line 116 considers heat to platen superheater,
# heat to water wall, and flue gas inlet to finishing superheater as fixed
# variables. This code uses simplified surrogate models for these inputs.
# Therefore, in the new model, these variables will change with plant load,
# More details regarding this methodology can be found in Zamarripa et al.,
# FOCAPD 2 page paper included in this directory as FOCAPD_paper.pdf
m.fs.SR = pyo.Var(initialize=1.15, doc='stoichiometric ratio')
m.fs.SR.setlb(1.0)
m.fs.SR.setub(1.25)
m.fs.SR.fix(1.15)
m.fs.coal_flow = pyo.Var(initialize=54.01, doc='coal flowrate kg.s')
m.fs.FGET = pyo.Var(initialize=1300.00, doc='flue gas exit temperature K')
m.fs.FG_flow = pyo.Var(m.fs.prop_fluegas.component_list,
initialize=2000,
domain=pyo.Reals,
doc='component molar flow rate')
init_fg = {
"H2O": (8.69 / 100),
"CO2": (14.49 / 100),
"N2": (0.6999),
"O2": (2.47 / 100),
"NO": 0.0006,
"SO2": (0.002)
}
m.fs.fg_frac = pyo.Var(m.fs.prop_fluegas.component_list,
initialize=init_fg,
doc='flue gas molar fraction')
# surrogate models valid for coal flowrate (30 to 70 kg/s) and SR (1-2.5)
def fg_mol_frac_rule(b, i):
if i == 'CO2':
return m.fs.fg_frac[i] == 0.23235491508307534735955\
* m.fs.SR**-0.5
elif i == 'H2O':
return m.fs.fg_frac[i] == 0.45009703293861530459807E-001 \
* m.fs.SR
elif i == 'N2':
return m.fs.fg_frac[i] == 1 - (
m.fs.fg_frac['CO2'] + m.fs.fg_frac['H2O'] +
m.fs.fg_frac['NO'] + m.fs.fg_frac['O2'] + m.fs.fg_frac['SO2'])
elif i == 'NO':
return m.fs.fg_frac[i] == 0.38148020722713599076938E-005 \
* m.fs.coal_flow
elif i == 'O2':
return m.fs.fg_frac[i] == 0.60149266916011525155317E-003 \
* m.fs.coal_flow
elif i == 'SO2':
return m.fs.fg_frac[i] == 0.21991717807021016347323E-004 \
* m.fs.coal_flow
m.fs.fg_mol_cn = pyo.Constraint(m.fs.prop_fluegas.component_list,
rule=fg_mol_frac_rule)
def fg_flow_rule(b, i):
mass_flow = 0.87757407893140026988732 * m.fs.coal_flow \
- 0.68240933480416252066014E-001 * m.fs.SR + 8.6386912890637752582\
* m.fs.coal_flow*m.fs.SR - 0.11737247790640543564002E-003 \
* (m.fs.coal_flow/m.fs.SR)**2 # ~ 28.3876e3 kg/s
# flow mol component in mol/s = kg/s/kg/mol
return m.fs.FSH.side_2.properties_in[0].flow_mol_comp[i] == \
(mass_flow / sum(m.fs.fg_frac[c]*m.fs.prop_fluegas.mw_comp[c]
for c in m.fs.prop_fluegas.component_list))\
* m.fs.fg_frac[i]
m.fs.fg_flow_cn = pyo.Constraint(m.fs.prop_fluegas.component_list,
rule=fg_flow_rule)
def fg_temp_rule(b):
return m.fs.FSH.side_2.properties_in[0].temperature == \
59836.381548557488713413 * m.fs.coal_flow**-0.5 \
+ 791.74814907302368283126 * m.fs.coal_flow**0.5 \
+ 0.60200443235342349090899 * m.fs.coal_flow**1.5 \
+ 285.74858049626226375040 * m.fs.SR**3 - 29865.27413896147845662\
* (m.fs.coal_flow*m.fs.SR)**-.5 - 518.58090213915738786454 \
* (m.fs.coal_flow*m.fs.SR)**0.5 - 0.86351166781748790735040E-002 \
* (m.fs.coal_flow*m.fs.SR)**2 - 30141.308801694875000976 \
* (m.fs.SR/m.fs.coal_flow)**0.5 - 18.109911868067683826666 \
* m.fs.coal_flow/m.fs.SR + 1017.0807559525446777116 \
* m.fs.SR/m.fs.coal_flow
m.fs.fg_temp_cn = pyo.Constraint(rule=fg_temp_rule)
def heat_2_PLSH_rule(b):
return m.fs.PlSH.heat_duty[0] == - 42149808.046329699456692 \
* pyo.log(m.fs.coal_flow) + 13125913.817196270450950 \
* pyo.exp(m.fs.SR) - 82168941.403612509369850 \
* m.fs.coal_flow**-.5 - 20751.165176131220505340 \
* (m.fs.coal_flow*m.fs.SR)**1.5 + 35303843.583323523402214 \
* (m.fs.coal_flow/m.fs.SR)**0.5
m.fs.heat_2_PLSH_cn = pyo.Constraint(rule=heat_2_PLSH_rule)
def heat_2_ww_rule(b):
heat_total = 15383517.068522246554494 * m.fs.coal_flow \
- 145195958.70188459753990 * m.fs.SR**0.5 + 91548063.4268338829278\
* (m.fs.coal_flow*m.fs.SR)**0.5 - 11732787.822234204038978 \
* m.fs.coal_flow*m.fs.SR - 19639.552666366322227987 \
* (m.fs.coal_flow/m.fs.SR)**2
return m.fs.Water_wall.heat_duty[0] == heat_total \
- m.fs.PlSH.heat_duty[0]
m.fs.heat_2_ww_cn = pyo.Constraint(rule=heat_2_ww_rule)
# unfix variables to build flowsheet connections
m.fs.PlSH.heat_duty.unfix()
m.fs.Water_wall.heat_duty.unfix()
m.fs.FSH.side_2.properties_in[:].flow_mol_comp.unfix()
m.fs.FSH.side_2.properties_in[:].temperature.unfix()
m.fs.coal_flow.fix(50.15)
print('degrees of freedom = ' + str(degrees_of_freedom(m)))
# initialize surrogate models (better initial point before solve)
calculate_variable_from_constraint(m.fs.PlSH.heat_duty[0],
m.fs.heat_2_PLSH_cn)
calculate_variable_from_constraint(m.fs.Water_wall.heat_duty[0],
m.fs.heat_2_ww_cn)
# set scaling parameters
iscale.calculate_scaling_factors(m)
# final solve
results = solver.solve(m, tee=False)
return m
# import steam cycle and build concrete model
m, solver = import_steam_cycle()
print(degrees_of_freedom(m))
#at this point we have a flowsheet with "steam cycle" that solves
# correctly, with 0 degrees of freedom.
# next step is to import and build the boiler heat exchanger network
# importing the boiler heat exchanger network from (boiler_subflowsheet_build.py)
# will basically append all the unit models into our model ("m")
# model "m" has been created a few lines above
import idaes.power_generation.flowsheets.supercritical_power_plant.boiler_subflowsheet_build as blr
# import the models (ECON, WW, PrSH, PlSH, FSH, Spliter, Mixer, Reheater)
# see boiler_subflowhseet_build.py for a beter description
blr.build_boiler(m.fs)
#initialize boiler network models (one by one)
blr.initialize(m)
# at this point we have both flowsheets (steam cycle + boiler network)
# in the same model/concrete object ("m")
# however they are disconnected. Here we want to solve them at the same time
# this is a square problem (i.e. degrees of freedom = 0)
print('solving square problem disconnected')
results = solver.solve(m, tee=True)
# at this point we want to connect the units in both flowsheets
# Economizer inlet = Feed water heater 8 outlet (water)
# HP inlet = Attemperator outlet (steam)
# Reheater inlet (steam) = HP split 7 outlet (last stage of HP turbine)
# IP inlet = Reheater outlet steam7
blr.unfix_inlets(m)
print('unfix inlet conditions, degreeso of freedom = ' +
str(degrees_of_freedom(m)))
def test_power_plan():
# import steam cycle and build concrete model
m, solver = steam_cycle.main()
print(degrees_of_freedom(m))
#at this point we have a flowsheet with "steam cycle" that solves
# correctly, with 0 degrees of freedom.
# next step is to import and build the boiler heat exchanger network
# importing the boiler heat exchanger network from (boiler_subflowsheet_build.py)
# will basically append all the unit models into our model ("m")
# model "m" has been created a few lines above
# import the models (ECON, WW, PrSH, PlSH, FSH, Spliter, Mixer, Reheater)
# see boiler_subflowhseet_build.py for a beter description
blr.build_boiler(m.fs)
#initialize boiler network models (one by one)
blr.initialize(m)
# at this point we have both flowsheets (steam cycle + boiler network)
# in the same model/concrete object ("m")
# however they are disconnected. Here we want to solve them at the same time
# this is a square problem (i.e. degrees of freedom = 0)
# print('solving square problem disconnected')
results = solver.solve(m, tee=True)
# at this point we want to connect the units in both flowsheets
# Economizer inlet = Feed water heater 8 outlet (water)
# HP inlet = Attemperator outlet (steam)
# Reheater inlet (steam) = HP split 7 outlet (last stage of HP turbine)
# IP inlet = Reheater outlet steam7
blr.unfix_inlets(m)
# deactivate constraints linking the FWH8 to HP turbine
m.fs.boiler_pressure_drop.deactivate()
m.fs.close_flow.deactivate()
m.fs.turb.constraint_reheat_flow.deactivate()
m.fs.turb.constraint_reheat_press.deactivate()
m.fs.turb.constraint_reheat_temp.deactivate()
m.fs.turb.inlet_split.inlet.enth_mol.unfix()
m.fs.turb.inlet_split.inlet.pressure.unfix()
m.fs.FHWtoECON = Arc(source = m.fs.fwh8.desuperheat.outlet_2,
destination = m.fs.ECON.side_1_inlet)
m.fs.Att2HP = Arc(source = m.fs.ATMP1.outlet,
destination = m.fs.turb.inlet_split.inlet)
m.fs.HPout2RH = Arc(source = m.fs.turb.hp_split[7].outlet_1,
destination = m.fs.RH.side_1_inlet)
m.fs.RHtoIP = Arc(source = m.fs.RH.side_1_outlet,
destination =m.fs.turb.ip_stages[1].inlet)
pyo.TransformationFactory("network.expand_arcs").apply_to(m)
#unfix boiler connections
m.fs.ECON.side_1_inlet.flow_mol.unfix()
m.fs.ECON.side_1_inlet.enth_mol[0].unfix()
m.fs.ECON.side_1_inlet.pressure[0].unfix()
m.fs.RH.side_1_inlet.flow_mol.unfix()
m.fs.RH.side_1_inlet.enth_mol[0].unfix()
m.fs.RH.side_1_inlet.pressure[0].unfix()
m.fs.hotwell.makeup.flow_mol[:].setlb(-1.0)
# if user has trouble with infeasible solutions, an easy test
# is to deactivate the link to HP turbine (m.fs.Att2HP_expanded "enth_mol and pressure" equalities)
# and fix inlet pressure and enth_mol to turbine (m.fs.turb.inlet_split.inlet)
m.fs.turb.inlet_split.inlet.pressure.fix(2.423e7)
# finally, since we want to maintain High Pressure (HP) inlet temperature constant (~866 K)
# we need to fix Attemperator enthalpy outlet and unfix heat duty to Platen superheater
# note fixing enthalpy to control temperature is only valid because pressure is also fixed
m.fs.ATMP1.outlet.enth_mol[0].fix(62710.01)
m.fs.PlSH.heat_duty[:].unfix()
# print(degrees_of_freedom(m))
solver.options = {
"tol": 1e-6,
"linear_solver": "ma27",
"max_iter": 40,
}
#square problems tend to work better without bounds
strip_bounds = pyo.TransformationFactory('contrib.strip_var_bounds')
strip_bounds.apply_to(m, reversible=True)
# this is the final solve with both flowsheets connected
results = solver.solve(m, tee=True)
strip_bounds.revert(m)