##############################################################################
# Institute for the Design of Advanced Energy Systems Process Systems
# Engineering Framework (IDAES PSE Framework) Copyright (c) 2018-2019, by the
# software owners: The Regents of the University of California, through
# Lawrence Berkeley National Laboratory, National Technology & Engineering
# Solutions of Sandia, LLC, Carnegie Mellon University, West Virginia
# University Research Corporation, et al. All rights reserved.
#
# Please see the files COPYRIGHT.txt and LICENSE.txt for full copyright and
# license information, respectively. Both files are also available online
# at the URL "https://github.com/IDAES/idaes-pse".
##############################################################################
"""
Steam turbine inlet stage model. This model is based on:
Liese, (2014). "Modeling of a Steam Turbine Including Partial Arc Admission
for Use in a Process Simulation Software Environment." Journal of Engineering
for Gas Turbines and Power. v136.
"""
__Author__ = "John Eslick"
import logging
_log = logging.getLogger(__name__)
from pyomo.common.config import In
from pyomo.environ import (Var, Expression, Constraint, sqrt, SolverFactory,
value, Param)
from pyomo.opt import TerminationCondition
from idaes.core import declare_process_block_class
from idaes.unit_models.pressure_changer import (PressureChangerData,
ThermodynamicAssumption)
from idaes.core.util import from_json, to_json, StoreSpec
from idaes.core.util.model_statistics import degrees_of_freedom
[docs]@declare_process_block_class("TurbineInletStage",
doc="Inlet stage steam turbine model")
class TurbineInletStageData(PressureChangerData):
# Same settings as the default pressure changer, but force to expander with
# isentropic efficiency
CONFIG = PressureChangerData.CONFIG()
CONFIG.compressor = False
CONFIG.get('compressor')._default = False
CONFIG.get('compressor')._domain = In([False])
CONFIG.thermodynamic_assumption = ThermodynamicAssumption.isentropic
CONFIG.get('thermodynamic_assumption')._default = \
ThermodynamicAssumption.isentropic
CONFIG.get('thermodynamic_assumption')._domain = \
In([ThermodynamicAssumption.isentropic])
[docs] def build(self):
super(TurbineInletStageData, self).build()
self.flow_coeff = Var(self.flowsheet().config.time,
initialize=1.053/3600.0,
doc="Turbine flow coefficient [kg*C^0.5/Pa/s]")
self.delta_enth_isentropic = Var(self.flowsheet().config.time,
initialize=-1000,
doc="Specific enthalpy change of isentropic process [J/mol]")
self.blade_reaction = Var(initialize=0.9,
doc="Blade reaction parameter")
self.blade_velocity = Var(initialize=110.0,
doc="Design blade velocity [m/s]")
self.eff_nozzle = Var(initialize=0.95, bounds=(0.0, 1.0),
doc="Nozzel efficiency (typically 0.90 to 0.95)")
self.efficiency_mech = Var(initialize=0.98,
doc="Turbine mechanical efficiency")
self.flow_scale = Param(mutable=True, default=1e3, doc=
"Scaling factor for pressure flow relation should be approximatly"
" the same order of magnitude as the expected flow.")
self.eff_nozzle.fix()
self.blade_reaction.fix()
self.flow_coeff.fix()
self.blade_velocity.fix()
self.efficiency_mech.fix()
self.ratioP[:] = 1 # make sure these have a number value
self.deltaP[:] = 0 # to avoid an error later in initialize
@self.Expression(self.flowsheet().config.time,
doc="Entering steam velocity calculation [m/s]")
def steam_entering_velocity(b, t):
# 1.414 = 44.72/sqrt(1000) for SI if comparing to Liese (2014)
# b.delta_enth_isentropic[t] = -(hin - hiesn), the mw converts
# enthalpy to a mass basis
return 1.414*sqrt(-(1-b.blade_reaction)*b.delta_enth_isentropic[t]/
b.control_volume.properties_in[t].mw*self.eff_nozzle)
@self.Constraint(self.flowsheet().config.time,
doc="Equation: Turbine inlet flow")
def inlet_flow_constraint(b, t):
# Some local vars to make the equation more readable
g = b.control_volume.properties_in[t].heat_capacity_ratio
mw = b.control_volume.properties_in[t].mw
flow = b.control_volume.properties_in[t].flow_mol
Tin = b.control_volume.properties_in[t].temperature
cf = b.flow_coeff[t]
Pin = b.control_volume.properties_in[t].pressure
Pratio = b.ratioP[t]
return ((1/b.flow_scale**2)*flow**2*mw**2*(Tin - 273.15) ==
(1/b.flow_scale**2)*cf**2*Pin**2*
(g/(g - 1)*(Pratio**(2.0/g) - Pratio**((g + 1)/g))))
@self.Constraint(self.flowsheet().config.time,
doc="Equation: Isentropic enthalpy change")
def isentropic_enthalpy(b, t):
return b.work_isentropic[t] == (b.delta_enth_isentropic[t]*
b.control_volume.properties_in[t].flow_mol)
@self.Constraint(self.flowsheet().config.time,
doc="Equation: Efficiency")
def efficiency_correlation(b, t):
Vr = b.blade_velocity/b.steam_entering_velocity[t]
eff = b.efficiency_isentropic[t]
R = b.blade_reaction
return eff == 2*Vr*((sqrt(1 - R) - Vr) +
sqrt((sqrt(1 - R) - Vr)**2 + R))
@self.Expression(self.flowsheet().config.time,
doc="Thermodynamic power [J/s]")
def power_thermo(b, t):
return b.control_volume.work[t]
@self.Expression(self.flowsheet().config.time, doc="Shaft power [J/s]")
def power_shaft(b, t):
return b.power_thermo[t]*b.efficiency_mech
def _get_performance_contents(self, time_point=0):
pc = super()._get_performance_contents(time_point=time_point)
pc["vars"]["Mechanical Efficiency"] = self.efficiency_mech
pc["vars"]["Flow Coefficient"] = self.flow_coeff[time_point]
pc["vars"]["Isentropic Specific Enthalpy"] = \
self.delta_enth_isentropic[time_point]
pc["vars"]["Blade Reaction"] = self.blade_reaction
pc["vars"]["Blade Velocity"] = self.blade_velocity
pc["vars"]["Nozzel Efficiency"] = self.eff_nozzle
pc["exprs"] = {}
pc["exprs"]["Thermodynamic Power"] = self.power_thermo[time_point]
pc["exprs"]["Shaft Power"] = self.power_shaft[time_point]
pc["exprs"]["Inlet Steam Velocity"] = \
self.steam_entering_velocity[time_point]
pc["params"] = {}
pc["params"]["Flow Scaling"] = self.flow_scale
return pc
[docs] def initialize(self, state_args={}, outlvl=0, solver='ipopt',
optarg={'tol': 1e-6, 'max_iter':30}):
"""
Initialize the inlet turbine stage model. This deactivates the
specialized constraints, then does the isentropic turbine initialization,
then reactivates the constraints and solves.
Args:
state_args (dict): Initial state for property initialization
outlvl (int): Amount of output (0 to 3) 0 is lowest
solver (str): Solver to use for initialization
optarg (dict): Solver arguments dictionary
"""
stee = True if outlvl >= 3 else False
# sp is what to save to make sure state after init is same as the start
# saves value, fixed, and active state, doesn't load originally free
# values, this makes sure original problem spec is same but initializes
# the values of free vars
sp = StoreSpec.value_isfixed_isactive(only_fixed=True)
istate = to_json(self, return_dict=True, wts=sp)
# Deactivate special constraints
self.inlet_flow_constraint.deactivate()
self.isentropic_enthalpy.deactivate()
self.efficiency_correlation.deactivate()
self.deltaP.unfix()
self.ratioP.unfix()
# Fix turbine parameters + eff_isen
self.eff_nozzle.fix()
self.blade_reaction.fix()
self.flow_coeff.fix()
self.blade_velocity.fix()
# fix inlet and free outlet
for t in self.flowsheet().config.time:
for k, v in self.inlet.vars.items():
v[t].fix()
for k, v in self.outlet.vars.items():
v[t].unfix()
# If there isn't a good guess for efficeny or outlet pressure
# provide something reasonable.
eff = self.efficiency_isentropic[t]
eff.fix(eff.value if value(eff) > 0.3 and value(eff) < 1.0 else 0.8)
# for outlet pressure try outlet pressure, pressure ratio, delta P,
# then if none of those look reasonable use a pressure ratio of 0.8
# to calculate outlet pressure
Pout = self.outlet.pressure[t]
Pin = self.inlet.pressure[t]
prdp = value((self.deltaP[t] - Pin)/Pin)
if value(Pout/Pin) > 0.98 or value(Pout/Pin) < 0.3:
if value(self.ratioP[t]) < 0.98 and value(self.ratioP[t]) > 0.3:
Pout.fix(value(Pin*self.ratioP))
elif prdp < 0.98 and prdp > 0.3:
Pout.fix(value(prdp*Pin))
else:
Pout.fix(value(Pin*0.8))
else:
Pout.fix()
self.deltaP[:] = value(Pout - Pin)
self.ratioP[:] = value(Pout/Pin)
for t in self.flowsheet().config.time:
self.properties_isentropic[t].pressure.value = \
value(self.outlet.pressure[t])
self.properties_isentropic[t].flow_mol.value = \
value(self.inlet.flow_mol[t])
self.properties_isentropic[t].enth_mol.value = \
value(self.inlet.enth_mol[t]*0.95)
self.outlet.flow_mol[t].value = \
value(self.inlet.flow_mol[t])
self.outlet.enth_mol[t].value = \
value(self.inlet.enth_mol[t]*0.95)
# Make sure the initialization problem has no degrees of freedom
# This shouldn't happen here unless there is a bug in this
dof = degrees_of_freedom(self)
try:
assert(dof == 0)
except:
_log.exception("degrees_of_freedom = {}".format(dof))
raise
# one bad thing about reusing this is that the log messages aren't
# really compatible with being nested inside another initialization
super(TurbineInletStageData, self).initialize(state_args=state_args,
outlvl=outlvl, solver=solver, optarg=optarg)
# Free eff_isen and activate sepcial constarints
self.efficiency_isentropic.unfix()
self.outlet.pressure.unfix()
self.inlet_flow_constraint.activate()
self.isentropic_enthalpy.activate()
self.efficiency_correlation.activate()
slvr = SolverFactory(solver)
slvr.options = optarg
res = slvr.solve(self, tee=stee)
if outlvl > 0:
if res.solver.termination_condition == TerminationCondition.optimal:
_log.info("{} Initialization Complete.".format(self.name))
else:
_log.warning(
"""{} Initialization Failed. The most likely cause of initialization failure for
the Turbine inlet stages model is that the flow coefficient is not compatible
with flow rate guess.""".format(self.name))
# reload original spec
from_json(self, sd=istate, wts=sp)