##############################################################################
# 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 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"
from pyomo.environ import Var, Param, sqrt, value, SolverFactory, units as pyunits
from idaes.core import declare_process_block_class
from idaes.power_generation.unit_models.helm.turbine import HelmIsentropicTurbineData
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
import idaes.core.util.scaling as iscale
_log = idaeslog.getLogger(__name__)
[docs]@declare_process_block_class(
"HelmTurbineInletStage",
doc="Inlet stage steam turbine model",
)
class HelmTurbineInletStageData(HelmIsentropicTurbineData):
CONFIG = HelmIsentropicTurbineData.CONFIG()
[docs] def build(self):
super().build()
self.flow_coeff = Var(
self.flowsheet().config.time,
initialize=1.053 / 3600.0,
doc="Turbine flow coefficient [kg*C^0.5/Pa/s]",
units=pyunits.kg*pyunits.K**0.5/pyunits.Pa/pyunits.s
)
self.blade_reaction = Var(
initialize=0.9,
doc="Blade reaction parameter"
)
self.blade_velocity = Var(
initialize=110.0,
doc="Design blade velocity [m/s]",
units=pyunits.m/pyunits.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=1.0,
doc="Turbine mechanical efficiency"
)
self.eff_nozzle.fix()
self.blade_reaction.fix()
self.flow_coeff.fix()
self.blade_velocity.fix()
self.efficiency_mech.fix()
self.efficiency_isentropic.unfix()
self.ratioP[:] = 0.9 # 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(
(b.blade_reaction - 1)*b.delta_enth_isentropic[t]*self.eff_nozzle
/ b.control_volume.properties_in[t].mw
)
@self.Expression(self.flowsheet().config.time, doc="Efficiency expression")
def efficiency_isentropic_expr(b, t):
Vr = b.blade_velocity / b.steam_entering_velocity[t]
R = b.blade_reaction
return 2*Vr*((sqrt(1 - R) - Vr) + sqrt((sqrt(1 - R) - Vr)**2 + R))
@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 flow ** 2 * mw ** 2 * Tin == (
cf ** 2 * Pin ** 2 * g / (g - 1)
* (Pratio ** (2.0 / g) - Pratio ** ((g + 1) / g)))
@self.Constraint(self.flowsheet().config.time, doc="Equation: Efficiency")
def efficiency_correlation(b, t):
return b.efficiency_isentropic[t] == b.efficiency_isentropic_expr[t]
@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
[docs] def initialize(
self,
state_args={},
outlvl=idaeslog.NOTSET,
solver="ipopt",
optarg={"tol": 1e-6, "max_iter": 30},
calculate_cf=False,
):
"""
Initialize the inlet turbine stage model. This deactivates the
specialized constraints, then does the isentropic turbine initialization,
then reactivates the constraints and solves. This initializtion uses a
flow value guess, so some reasonable flow guess should be sepecified prior
to initializtion.
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
calculate_cf (bool): If True, use the flow and pressure ratio to
calculate the flow coefficient.
"""
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
sp = StoreSpec.value_isfixed_isactive(only_fixed=True)
istate = to_json(self, return_dict=True, wts=sp)
# Setup for initializtion step 1
self.inlet_flow_constraint.deactivate()
self.efficiency_correlation.deactivate()
self.eff_nozzle.fix()
self.blade_reaction.fix()
self.flow_coeff.fix()
self.blade_velocity.fix()
self.inlet.fix()
self.outlet.unfix()
for t in self.flowsheet().config.time:
self.efficiency_isentropic[t] = 0.9
super().initialize(outlvl=outlvl, solver=solver, optarg=optarg)
# Free eff_isen and activate sepcial constarints
self.inlet_flow_constraint.activate()
self.efficiency_correlation.activate()
if calculate_cf:
self.ratioP.fix()
self.flow_coeff.unfix()
for t in self.flowsheet().config.time:
g = self.control_volume.properties_in[t].heat_capacity_ratio
mw = self.control_volume.properties_in[t].mw
flow = self.control_volume.properties_in[t].flow_mol
Tin = self.control_volume.properties_in[t].temperature
Pin = self.control_volume.properties_in[t].pressure
Pratio = self.ratioP[t]
self.flow_coeff[t].value = value(
flow * mw * sqrt(
Tin/(g/(g - 1) *(Pratio**(2.0/g) - Pratio**((g + 1)/g)))
)/Pin
)
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: {}".format(idaeslog.condition(res)))
# reload original spec
if calculate_cf:
cf = {}
for t in self.flowsheet().config.time:
cf[t] = value(self.flow_coeff[t])
from_json(self, sd=istate, wts=sp)
if calculate_cf:
# cf was probably fixed, so will have to set the value agian here
# if you ask for it to be calculated.
for t in self.flowsheet().config.time:
self.flow_coeff[t] = cf[t]
def calculate_scaling_factors(self):
super().calculate_scaling_factors()
for t, c in self.inlet_flow_constraint.items():
s = iscale.get_scaling_factor(
self.control_volume.properties_in[t].flow_mol)**2
iscale.constraint_scaling_transform(c, s)