##############################################################################
# Institute for the Design of Advanced Energy Systems Process Systems
# Engineering Framework (IDAES PSE Framework) Copyright (c) 2018-2020, 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 outlet 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"
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.generic_models.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
import idaes.logger as idaeslog
_log = idaeslog.getLogger(__name__)
[docs]@declare_process_block_class(
"TurbineOutletStage", doc="Outlet stage steam turbine model"
)
class TurbineOutletStageData(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(TurbineOutletStageData, self).build()
self.flow_coeff = Var(
initialize=0.0333, doc="Turbine flow coefficient [kg*C^0.5/s/Pa]"
)
self.eff_dry = Var(initialize=0.87, doc="Turbine dry isentropic efficiency")
self.design_exhaust_flow_vol = Var(
initialize=6000.0, doc="Design exit volumetirc flowrate [m^3/s]"
)
self.efficiency_mech = Var(initialize=0.98, doc="Turbine mechanical efficiency")
self.flow_scale = Param(
mutable=True,
default=1e-4,
doc="Scaling factor for pressure flow relation should be approximatly"
" the same order of magnitude as the expected flow.",
)
self.eff_dry.fix()
self.design_exhaust_flow_vol.fix()
self.flow_coeff.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="Efficiency factor correlation"
)
def tel(b, t):
f = b.control_volume.properties_out[t].flow_vol / b.design_exhaust_flow_vol
return 1e6 * (
-0.0035 * f ** 5
+ 0.022 * f ** 4
- 0.0542 * f ** 3
+ 0.0638 * f ** 2
- 0.0328 * f
+ 0.0064
)
@self.Constraint(
self.flowsheet().config.time, doc="Equation: Stodola, for choked flow"
)
def stodola_equation(b, t):
flow = b.control_volume.properties_in[t].flow_mol
mw = b.control_volume.properties_in[t].mw
Tin = b.control_volume.properties_in[t].temperature
Pin = b.control_volume.properties_in[t].pressure
Pr = b.ratioP[t]
cf = b.flow_coeff
return (b.flow_scale ** 2) * flow ** 2 * mw ** 2 * (Tin - 273.15) == (
b.flow_scale ** 2
) * cf ** 2 * Pin ** 2 * (1 - Pr ** 2)
@self.Expression(
self.flowsheet().config.time,
doc="Equation: isentropic specific enthalpy change",
)
def delta_enth_isentropic(b, t):
flow = b.control_volume.properties_in[t].flow_mol
work_isen = b.work_isentropic[t]
return work_isen / flow
@self.Constraint(
self.flowsheet().config.time, doc="Equation: Efficiency correlation"
)
def efficiency_correlation(b, t):
x = b.control_volume.properties_out[t].vapor_frac
eff = b.efficiency_isentropic[t]
dh_isen = b.delta_enth_isentropic[t]
tel = b.tel[t]
return eff == b.eff_dry * x * (1 - 0.65 * (1 - x)) * (1 + tel / dh_isen)
@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
pc["vars"]["Isentropic Efficieincy (Dry)"] = self.eff_dry
pc["vars"]["Design Exhaust Flow"] = self.design_exhaust_flow_vol
pc["exprs"] = {}
pc["exprs"]["Thermodynamic Power"] = self.power_thermo[time_point]
pc["exprs"]["Shaft Power"] = self.power_shaft[time_point]
pc["params"] = {}
pc["params"]["Flow Scaling"] = self.flow_scale
return pc
[docs] def initialize(
self,
state_args={},
outlvl=idaeslog.NOTSET,
solver="ipopt",
optarg={"tol": 1e-6, "max_iter": 30},
):
"""
Initialize the outlet 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 : sets output level of initialization routine
solver (str): Solver to use for initialization
optarg (dict): Solver arguments dictionary
"""
init_log = idaeslog.getInitLogger(self.name, outlvl, tag="unit")
solve_log = idaeslog.getSolveLogger(self.name, outlvl, tag="unit")
# 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.stodola_equation.deactivate()
self.efficiency_correlation.deactivate()
self.deltaP.unfix()
self.ratioP.unfix()
# Fix turbine parameters + eff_isen
self.eff_dry.fix()
self.design_exhaust_flow_vol.fix()
self.flow_coeff.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 efficiency 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) > 0.95 or value(Pout / Pin) < 0.003:
if value(self.ratioP[t]) < 0.9 and value(self.ratioP[t]) > 0.01:
Pout.fix(value(Pin * self.ratioP))
elif prdp < 0.9 and prdp > 0.01:
Pout.fix(value(prdp * Pin))
else:
Pout.fix(value(Pin * 0.3))
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 AssertionError:
init_log.error("Degrees of freedom not 0, ({})".format(dof))
raise
mw = self.control_volume.properties_in[0].mw
Tin = self.control_volume.properties_in[0].temperature
Pin = self.control_volume.properties_in[0].pressure
Pr = self.ratioP[0]
cf = self.flow_coeff
self.inlet.flow_mol.fix(
value(cf * Pin * sqrt(1 - Pr ** 2) / mw / sqrt(Tin - 273.15))
)
# one bad thing about reusing this is that the log messages aren't
# really compatible with being nested inside another initialization
super().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.fix()
self.inlet.flow_mol.unfix()
self.stodola_equation.activate()
self.efficiency_correlation.activate()
slvr = SolverFactory(solver)
slvr.options = optarg
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = slvr.solve(self, tee=slc.tee)
init_log.info(
"Initialization Complete (Outlet Stage): {}".format(idaeslog.condition(res))
)
# reload original spec
from_json(self, sd=istate, wts=sp)