Turbine (Multistage)

pair: idaes.power_generation.unit_models.helm.turbine_multistage;HelmTurbineMultistage

idaes.power_generation.unit_models.helm.turbine_multistage

This is a composite model for a power plant turbine with high, intermediate and low pressure sections. This model contains an inlet stage with throttle valves for partial arc admission and optional splitters for steam extraction.

The figure below shows the layout of the mutistage turbine model. Optional splitters provide for steam extraction. The splitters can have two or more outlets (one being the main steam outlet). The streams that connect one stage to the next can also be omitted. This allows for connecting additional unit models (usually reheaters) between stages.

MultiStage Turbine Model

Example

This example sets up a turbine multistage turbine model similar to what could be found in a power plant steam cycle. There are 7 high-pressure stages, 14 intermediate-pressure stages, and 11 low-pressure stages. Steam extractions are provided after stages hp4, hp7, ip5, ip14, lp4, lp7, lp9, lp11. The extraction at ip14 uses a splitter with three outlets, one for the main steam, one for the boiler feed pump, and one for a feedwater heater. There is a disconnection between the HP and IP sections so that steam can be sent to a reheater. In this example, a heater block is a stand-in for a reheater model.

from pyomo.environ import (ConcreteModel, SolverFactory, TransformationFactory,
                           Constraint, value)
from pyomo.network import Arc

from idaes.core import FlowsheetBlock
from idaes.unit_models import Heater
from idaes.power_generation.unit_models.helm import HelmTurbineMultistage
from idaes.generic_models.properties import iapws95

solver = SolverFactory('ipopt')
solver.options = {'tol': 1e-6}

m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.turb = HelmTurbineMultistage(default={
    "property_package": m.fs.properties,
    "num_hp": 7,
    "num_ip": 14,
    "num_lp": 11,
    "hp_split_locations": [4,7],
    "ip_split_locations": [5, 14],
    "lp_split_locations": [4,7,9,11],
    "hp_disconnect": [7], # 7 is last stage in hp so disconnect hp from ip
    "ip_split_num_outlets": {14:3}})
# Add reheater (for example using a simple heater block)
m.fs.reheat = Heater(default={"property_package": m.fs.properties})
# Add Arcs (streams) to connect the HP and IP sections through reheater
m.fs.hp_to_reheat = Arc(source=m.fs.turb.hp_split[7].outlet_1,
                        destination=m.fs.reheat.inlet)
m.fs.reheat_to_ip = Arc(source=m.fs.reheat.outlet,
                        destination=m.fs.turb.ip_stages[1].inlet)
# Set the turbine inlet conditions and an initial flow guess
p = 2.4233e7
hin = iapws95.htpx(T=880, P=p)
m.fs.turb.inlet_split.inlet.enth_mol[0].fix(hin)
m.fs.turb.inlet_split.inlet.flow_mol[0].fix(26000)
m.fs.turb.inlet_split.inlet.pressure[0].fix(p)

# Set the inlet of the ip section for initialization, since it is disconnected
p = 7.802e+06
hin = iapws95.htpx(T=880, P=p)
m.fs.turb.ip_stages[1].inlet.enth_mol[0].value = hin
m.fs.turb.ip_stages[1].inlet.flow_mol[0].value = 25220.0
m.fs.turb.ip_stages[1].inlet.pressure[0].value = p
# Set the efficency and pressure ratios of stages other than inlet and outlet
for i, s in turb.hp_stages.items():
    s.ratioP[:] = 0.88
    s.efficiency_isentropic[:] = 0.9
for i, s in turb.ip_stages.items():
    s.ratioP[:] = 0.85
    s.efficiency_isentropic[:] = 0.9
for i, s in turb.lp_stages.items():
    s.ratioP[:] = 0.82
    s.efficiency_isentropic[:] = 0.9
# Usually these fractions would be determined by the boiler feed water heater
# network. Since this example doesn't include them, just fix split fractions
turb.hp_split[4].split_fraction[0,"outlet_2"].fix(0.03)
turb.hp_split[7].split_fraction[0,"outlet_2"].fix(0.03)
turb.ip_split[5].split_fraction[0,"outlet_2"].fix(0.04)
turb.ip_split[14].split_fraction[0,"outlet_2"].fix(0.04)
turb.ip_split[14].split_fraction[0,"outlet_3"].fix(0.15)
turb.lp_split[4].split_fraction[0,"outlet_2"].fix(0.04)
turb.lp_split[7].split_fraction[0,"outlet_2"].fix(0.04)
turb.lp_split[9].split_fraction[0,"outlet_2"].fix(0.04)
turb.lp_split[11].split_fraction[0,"outlet_2"].fix(0.04)
# unfix inlet flow for pressure driven simulation
turb.inlet_split.inlet.flow_mol.unfix()
# Set the inlet steam mixer to use the constraints that the pressures of all
# inlet streams are equal
turb.inlet_mix.use_equal_pressure_constraint()
# Initialize turbine
turb.initialize(outlvl=1)
# Copy conditions out of turbine to initialize the reheater
for t in m.fs.time:
    m.fs.reheat.inlet.flow_mol[t].value = \
        value(turb.hp_split[7].outlet_1_state[t].flow_mol)
    m.fs.reheat.inlet.enth_mol[t].value = \
        value(turb.hp_split[7].outlet_1_state[t].enth_mol)
    m.fs.reheat.inlet.pressure[t].value = \
        value(turb.hp_split[7].outlet_1_state[t].pressure)
# initialize the reheater
m.fs.reheat.initialize(outlvl=4)
# Add constraint to the reheater to result in 880K outlet temperature
def reheat_T_rule(b, t):
    return m.fs.reheat.control_volume.properties_out[t].temperature == 880
m.fs.reheat.temperature_out_equation = Constraint(m.fs.reheat.time_ref,
    rule=reheat_T_rule)
# Expand the Arcs connecting the turbine to the reheater
TransformationFactory("network.expand_arcs").apply_to(m)
# Fix the outlet pressure (usually determined by condenser)
m.fs.turb.outlet_stage.control_volume.properties_out[0].pressure.fix()

# Solve the pressure driven flow model with reheat
solver.solve(m, tee=True)

Unit Models

The multistage turbine model contains the models in the table below. The splitters for steam extraction are not present if a turbine section contains no steam extractions.

Unit	Index Sets	Doc
`inlet_split`	None	Splitter to split the main steam feed into steams for each arc (`Separator <technical_specs/model_libraries/generic/unit_models/separator:Separator>`)
`throttle_valve`	Admission Arcs	Throttle valves for each admission arc (`HelmValve <technical_specs/model_libraries/power_generation/unit_models/steam_valve:HelmValve>`)
`inlet_stage`	Admission Arcs	Parallel inlet turbine stages that represent admission arcs (`TurbineInlet <technical_specs/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Inlet Stage)>`)
`inlet_mix`	None	Mixer to combine the streams from each arc back to one stream (`Mixer <technical_specs/model_libraries/generic/unit_models/mixer:Mixer>`)
`hp_stages`	HP stages	Turbine stages in the high-pressure section (`TurbineStage <technical_specs/model_libraries/power_generation/unit_models/turbine_stage:Turbine (Stage)>`)
`ip_stages`	IP stages	Turbine stages in the intermediate-pressure section (`TurbineStage <technical_specs/model_libraries/power_generation/unit_models/turbine_stage:Turbine (Stage)>`)
`lp_stages`	LP stages	Turbine stages in the low-pressure section (`TurbineStage <technical_specs/model_libraries/power_generation/unit_models/turbine_stage:Turbine (Stage)>`)
`hp_splits`	subset of HP stages	Extraction splitters in the high-pressure section (`Separator <technical_specs/model_libraries/generic/unit_models/separator:Separator>`)
`ip_splits`	subset of IP stages	Extraction splitters in the high-pressure section (`Separator <technical_specs/model_libraries/generic/unit_models/separator:Separator>`)
`lp_splits`	subset of LP stages	Extraction splitters in the high-pressure section (`Separator <technical_specs/model_libraries/generic/unit_models/separator:Separator>`)
`outlet_stage`	None	The final stage in the turbine, which calculates exhaust losses (`TurbineOutlet <technical_specs/model_libraries/power_generation/unit_models/turbine_outlet:Turbine (Outlet Stage)>`)

Initialization

The initialization approach is to sequentially initialize each sub-unit using the outlet of the previous model. Before initializing the model, the inlet of the turbine, and any stage that is disconnected should be given a reasonable guess. The efficiency and pressure ration of the stages in the HP, IP and LP sections should be specified. For the inlet and outlet stages the flow coefficient should be specified. Valve coefficients should also be specified. A reasonable guess for split fractions should also be given for any extraction splitters present. The most likely cause of initialization failure is flow coefficients in inlet stage, outlet stage, or valves that do not pair well with the specified flow rates.