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.unit_models.power_generation import (
TurbineMultistage, TurbineStage, TurbineInletStage, TurbineOutletStage)
from idaes.property_models 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 = TurbineMultistage(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) |
throttle_valve |
Admission Arcs | Throttle valves for each admission arc (SteamValve) |
inlet_stage |
Admission Arcs | Parallel inlet turbine stages that represent admission arcs (TurbineInlet) |
inlet_mix |
None | Mixer to combine the streams from each arc back to one stream (Mixer) |
hp_stages |
HP stages | Turbine stages in the high-pressure section (TurbineStage) |
ip_stages |
IP stages | Turbine stages in the intermediate-pressure section (TurbineStage) |
lp_stages |
LP stages | Turbine stages in the low-pressure section (TurbineStage) |
hp_splits |
subset of HP stages | Extraction splitters in the high-pressure section (Separator) |
ip_splits |
subset of IP stages | Extraction splitters in the high-pressure section (Separator) |
lp_splits |
subset of LP stages | Extraction splitters in the high-pressure section (Separator) |
outlet_stage |
None | The final stage in the turbine, which calculates exhaust losses (TurbineOutlet) |
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.
TurbineMultistage Class¶
-
class
idaes.unit_models.power_generation.turbine_multistage.TurbineMultistage(*args, **kwargs)¶ Multistage steam turbine with optional reheat and extraction
Parameters: - rule (function) – A rule function or None. Default rule calls build().
- concrete (bool) – If True, make this a toplevel model. Default - False.
- ctype (str) – Pyomo ctype of the block. Default - “Block”
- default (dict) –
Default ProcessBlockData config
- Keys
- dynamic
- Indicates whether the model is dynamic.
- has_holdup
- Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { True - construct holdup terms, False - do not construct holdup terms}
- has_phase_equilibrium
- Argument indicating whether phase equilibrium should be calculated for the resulting mixed stream, default - False. Valid values: { True - calculate phase equilibrium in mixed stream, False - do not calculate equilibrium in mixed stream.}
- material_balance_type
- Indicates what type of mass balance should be constructed, default - MaterialBalanceType.componentTotal`. Valid values: { MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}
- property_package
- Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PropertyParameterObject - a PropertyParameterBlock object.}
- property_package_args
- A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}
- num_parallel_inlet_stages
- Number of parallel inlet stages to simulate partial arc admission. Default=4
- num_hp
- Number of high pressure stages not including inlet stage
- num_ip
- Number of intermediate pressure stages
- num_lp
- Number of low pressure stages not including outlet stage
- hp_split_locations
- A list of index locations of splitters in the HP section. The indexes indicate after which stage to include splitters. 0 is between the inlet stage and the first regular HP stage.
- ip_split_locations
- A list of index locations of splitters in the IP section. The indexes indicate after which stage to include splitters.
- lp_split_locations
- A list of index locations of splitters in the LP section. The indexes indicate after which stage to include splitters.
- hp_disconnect
- HP Turbine stages to not connect to next with an arc. This is usually used to insert addtional units between stages on a flowsheet, such as a reheater
- ip_disconnect
- IP Turbine stages to not connect to next with an arc. This is usually used to insert addtional units between stages on a flowsheet, such as a reheater
- lp_disconnect
- LP Turbine stages to not connect to next with an arc. This is usually used to insert addtional units between stages on a flowsheet, such as a reheater
- hp_split_num_outlets
- Dict, hp split index: number of splitter outlets, if not 2
- ip_split_num_outlets
- Dict, ip split index: number of splitter outlets, if not 2
- lp_split_num_outlets
- Dict, lp split index: number of splitter outlets, if not 2
- initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
- idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to overide the default behavior of matching the BlockData index exactly to the index in initialize.
Returns: (TurbineMultistage) New instance
TurbineMultistageData Class¶
-
class
idaes.unit_models.power_generation.turbine_multistage.TurbineMultistageData(component)[source]¶ -
build()[source]¶ General build method for UnitModelBlockData. This method calls a number of sub-methods which automate the construction of expected attributes of unit models.
Inheriting models should call super().build.
Parameters: None – Returns: None
-
throttle_cv_fix(value)[source]¶ Fix the thottle valve coefficients. These are generally the same for each of the parallel stages so this provides a convenient way to set them.
Parameters: value – The value to fix the turbine inlet flow coefficients at
-