Sofc¶
SOFC Power Plant Example¶
This notebook runs the SOFC power plant model over a range of net power outputs from 650 MW to 200 MW. The SOFC model is based on case ANGFC3B in the NETL report "Techno-Economic Analysis of Natural Gas Fuel Cell Plant Configurations" April 2022 https://www.netl.doe.gov/projects/files/TechnoEconomicAnalysisofNaturalGasFuelCellPlantConfigurations_043022.pdf
Module Imports¶
In [1]:
import os
import numpy as np
import pandas as pd
import pytest
from IPython.core.display import SVG
import pyomo.environ as pyo
from pyomo.environ import units as pyunits
from pyomo.util.infeasible import log_infeasible_constraints
import idaes
from idaes.core.solvers import use_idaes_solver_configuration_defaults
import idaes.core.util as iutil
from sofc import (
get_model,
initialize,
add_tags,
write_pfd,
make_stream_table
)
from sofc_costing import (
get_capital_cost,
get_fixed_costs,
get_variable_costs
)
Make Output Directories¶
This notebook can produce a large number of output files. To make it easier to manage, some subdirectories are used to organize output. This ensures that the directories exist.
In [2]:
# Make a directory if it doesn't exist
def make_directory(path):
if not os.path.exists(path):
os.mkdir(path)
make_directory("data")
make_directory("data_pfds")
make_directory("data_tabulated")
Global Solver Settings¶
Use the IDAES configuration system for solver settings. These will apply to all Ipopt instances created, including the ones created in initialization methods.
In [3]:
use_idaes_solver_configuration_defaults()
idaes.cfg.ipopt.options.nlp_scaling_method = "user-scaling"
idaes.cfg.ipopt.options.linear_solver = "ma57"
idaes.cfg.ipopt.options.OF_ma57_automatic_scaling = "yes"
idaes.cfg.ipopt.options.ma57_pivtol = 1e-5
idaes.cfg.ipopt.options.ma57_pivtolmax = 0.1
idaes.cfg.ipopt.options.bound_push = 1e-20
solver = pyo.SolverFactory("ipopt")
Create the SOFC model¶
Create the SOFC model and initialize it or read the saved initialization if available. The base SOFC model is configured to match the NGFC report.
In [4]:
def get_base_sofc_model():
m = get_model()
save_name = "sofc_init.json.gz"
if os.path.exists(save_name):
iutil.from_json(m, fname=save_name, wts=iutil.StoreSpec(suffix=False))
print("Loading initialized model from json")
else:
initialize(m)
iutil.to_json(m, fname=save_name)
print("Solving initialized model")
res = solver.solve(m, tee=True)
return m
Design Optimization¶
Optimize the heat exchanger sizes at the nameplate capacity of 650 MW.
In [5]:
m = get_base_sofc_model()
# add costs
get_capital_cost(m)
get_fixed_costs(m)
get_variable_costs(m)
# setup design optimization problem
m.fs.obj = pyo.Objective(
expr=m.fs.costing.annualized_tasc + m.fs.costing.total_fixed_OM_cost + m.fs.costing.total_variable_OM_cost[0]
)
# unfix decision vars
m.fs.anode_hx.area.unfix()
m.fs.cathode_hx.area.unfix()
m.fs.air_blower.inlet.flow_mol.unfix()
m.fs.cathode_recycle.split_fraction[0, 'recycle_outlet'].unfix()
m.fs.sofc.OTC.unfix()
m.fs.sofc.OTC.setlb(2.099)
m.fs.sofc.OTC.setub(2.2)
# add sofc operational constraints
@m.fs.Constraint()
def maximum_cell_temperature(fs):
return m.fs.sofc.max_cell_temperature <= 750
@m.fs.Constraint()
def maximum_cell_temperature_change(fs):
return m.fs.sofc.deltaT_cell <= 100
# enforce net power = 650 MW
m.fs.net_power_MW = pyo.Var(
m.fs.time,
initialize=650,
bounds=(100, 900),
units=pyunits.MW)
@m.fs.Constraint(m.fs.time)
def net_power_constraint(fs, t):
return fs.net_power_MW[t] == pyunits.convert(fs.net_power[t], pyunits.MW)
m.fs.anode_mix.feed_inlet.flow_mol.unfix()
m.fs.net_power_MW.fix(650)
save_name = "sofc_design_opt.json.gz"
if os.path.exists(save_name):
iutil.from_json(m, fname=save_name, wts=iutil.StoreSpec(suffix=False))
print("Loading optimized design from json")
else:
res = solver.solve(m, tee=True)
iutil.to_json(m, fname=save_name)
Loading initialized model from json
Solving initialized model
WARNING: model contains export suffix
'fs.flash.control_volume.properties_out[0.0].scaling_factor' that contains
12 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flash.control_volume.properties_in[0.0].scaling_factor' that contains
10 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flue_gas_translator.properties_out[0.0].scaling_factor' that contains
6 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flue_gas_translator.properties_in[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.properties_out[0.0].scaling_factor' that
contains 13 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.mixed_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.oxygen_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.anode_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.oxycombustor_translator.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor_translator.properties_in[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.ASU_O2_outlet.control_volume.properties_out[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.ASU_O2_outlet.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.asu.O2_outlet_state[0.0].scaling_factor' that contains 7 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.asu.N2_outlet_state[0.0].scaling_factor' that contains 5 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.asu.mixed_state[0.0].scaling_factor'
that contains 5 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.scaling_factor' that contains 1
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.control_volume.properties_out[0.0].scaling_factor'
that contains 8 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.control_volume.properties_in[0.0].scaling_factor'
that contains 9 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.scaling_factor' that contains 1
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.control_volume.properties_out[0.0].scaling_factor'
that contains 8 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.control_volume.properties_in[0.0].scaling_factor'
that contains 16 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.properties_out[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.recycle_outlet_state[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.exhaust_outlet_state[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.mixed_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_heat.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_heat.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_translator.properties_out[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_translator.properties_in[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.ion_outlet_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.air_outlet_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.mixed_state[0.0].scaling_factor' that contains 5 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.mixed_state[0.0].scaling_factor' that contains 7 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.recycle_inlet_state[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.air_inlet_state[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.cold_side.properties_out[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.cold_side.properties_in[0.0].scaling_factor' that contains
7 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.hot_side.properties_out[0.0].scaling_factor' that contains
7 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.hot_side.properties_in[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.cathode_hx.hot_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.cathode_hx.scaling_factor' that
contains 3 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_blower.properties_isentropic[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 17 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.recycle_translator.properties_out[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.recycle_translator.properties_in[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_blower.properties_isentropic[0.0].scaling_factor' that contains
12 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 12 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.recycle_outlet_state[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.exhaust_outlet_state[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.mixed_state[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode.control_volume.properties_out[0.0].scaling_factor' that contains
11 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode.control_volume.properties_in[0.0].scaling_factor' that contains
10 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode.control_volume.scaling_factor'
that contains 10 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.anode.scaling_factor' that contains
4 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.mixed_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.ion_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.fuel_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_translator.properties_out[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_translator.properties_in[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.properties_in[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.scaling_factor' that contains 9 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.prereformer.scaling_factor' that
contains 2 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_hx.cold_side.properties_out[0.0].scaling_factor' that contains
11 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.cold_side.properties_in[0.0].scaling_factor' that contains 11
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.cold_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.hot_side.properties_out[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.hot_side.properties_in[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.hot_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.scaling_factor' that
contains 3 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_mix.mixed_state[0.0].scaling_factor' that contains 11 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_mix.recycle_inlet_state[0.0].scaling_factor' that contains 11
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_mix.feed_inlet_state[0.0].scaling_factor' that contains 24
component keys that are not exported as part of the NL file. Skipping.
Ipopt 3.13.2: nlp_scaling_method=user-scaling
tol=1e-06
max_iter=200
linear_solver=ma57
ma57_pivtol=1e-05
ma57_pivtolmax=0.1
bound_push=1e-20
option_file_name=/tmp/tmp6jtm20qk_ipopt.opt
Using option file "/tmp/tmp6jtm20qk_ipopt.opt".
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
This version of Ipopt was compiled from source code available at
https://github.com/IDAES/Ipopt as part of the Institute for the Design of
Advanced Energy Systems Process Systems Engineering Framework (IDAES PSE
Framework) Copyright (c) 2018-2019. See https://github.com/IDAES/idaes-pse.
This version of Ipopt was compiled using HSL, a collection of Fortran codes
for large-scale scientific computation. All technical papers, sales and
publicity material resulting from use of the HSL codes within IPOPT must
contain the following acknowledgement:
HSL, a collection of Fortran codes for large-scale scientific
computation. See http://www.hsl.rl.ac.uk.
******************************************************************************
This is Ipopt version 3.13.2, running with linear solver ma57.
Number of nonzeros in equality constraint Jacobian...: 116906
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 4832
Total number of variables............................: 3173
variables with only lower bounds: 109
variables with lower and upper bounds: 1426
variables with only upper bounds: 5
Total number of equality constraints.................: 3173
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 0.0000000e+00 3.51e+01 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
Reallocating memory for MA57: lfact (5856712)
1 0.0000000e+00 2.27e+01 7.25e+06 -1.0 2.10e+01 - 2.84e-01 1.00e+00H 1
2 0.0000000e+00 8.82e-02 3.36e+05 -1.0 1.00e+00 - 9.53e-01 1.00e+00h 1
3 0.0000000e+00 1.75e-07 2.37e+03 -1.0 1.00e+00 - 9.93e-01 1.00e+00h 1
Number of Iterations....: 3
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 1.7455749912187457e-07 1.7455749912187457e-07
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 1.7455749912187457e-07 1.7455749912187457e-07
Number of objective function evaluations = 5
Number of objective gradient evaluations = 4
Number of equality constraint evaluations = 5
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 4
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 3
Total CPU secs in IPOPT (w/o function evaluations) = 2.421
Total CPU secs in NLP function evaluations = 0.059
EXIT: Optimal Solution Found.
WARNING: model contains export suffix
'fs.flash.control_volume.properties_out[0.0].scaling_factor' that contains
12 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flash.control_volume.properties_in[0.0].scaling_factor' that contains
10 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.condenser.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flue_gas_translator.properties_out[0.0].scaling_factor' that contains
6 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.flue_gas_translator.properties_in[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_HRSG.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.properties_out[0.0].scaling_factor' that
contains 13 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.properties_in[0.0].scaling_factor' that
contains 10 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.mixed_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.oxygen_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.combustor_mix.anode_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.oxycombustor_translator.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.oxycombustor_translator.properties_in[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.ASU_O2_outlet.control_volume.properties_out[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.ASU_O2_outlet.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.asu.O2_outlet_state[0.0].scaling_factor' that contains 7 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.asu.N2_outlet_state[0.0].scaling_factor' that contains 5 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.asu.mixed_state[0.0].scaling_factor'
that contains 5 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s2.control_volume.scaling_factor' that contains 1
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.control_volume.properties_out[0.0].scaling_factor'
that contains 8 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s2.control_volume.properties_in[0.0].scaling_factor'
that contains 9 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.intercooler_s1.control_volume.scaling_factor' that contains 1
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.control_volume.properties_out[0.0].scaling_factor'
that contains 8 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.air_compressor_s1.control_volume.properties_in[0.0].scaling_factor'
that contains 16 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.properties_out[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_hrsg.control_volume.scaling_factor' that contains 1 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.properties_isentropic[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 9 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.recycle_outlet_state[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.exhaust_outlet_state[0.0].scaling_factor' that
contains 5 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_recycle.mixed_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_heat.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_heat.control_volume.properties_in[0.0].scaling_factor' that
contains 7 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.cathode_translator.properties_out[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_translator.properties_in[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.ion_outlet_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.air_outlet_state[0.0].scaling_factor' that contains 5
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode.mixed_state[0.0].scaling_factor' that contains 5 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.mixed_state[0.0].scaling_factor' that contains 7 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.recycle_inlet_state[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_mix.air_inlet_state[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.cold_side.properties_out[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.cold_side.properties_in[0.0].scaling_factor' that contains
7 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.hot_side.properties_out[0.0].scaling_factor' that contains
7 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.cathode_hx.hot_side.properties_in[0.0].scaling_factor' that contains 7
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.cathode_hx.hot_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.cathode_hx.scaling_factor' that
contains 2 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_blower.properties_isentropic[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.air_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 8 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.air_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 16 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.recycle_translator.properties_out[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.recycle_translator.properties_in[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_blower.properties_isentropic[0.0].scaling_factor' that contains
12 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_blower.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_blower.control_volume.properties_in[0.0].scaling_factor' that
contains 12 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.recycle_outlet_state[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.exhaust_outlet_state[0.0].scaling_factor' that contains
8 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_recycle.mixed_state[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode.control_volume.properties_out[0.0].scaling_factor' that contains
11 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode.control_volume.properties_in[0.0].scaling_factor' that contains
10 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode.control_volume.scaling_factor'
that contains 10 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.anode.scaling_factor' that contains
4 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.mixed_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.ion_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.fuel_cell_mix.fuel_inlet_state[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_translator.properties_out[0.0].scaling_factor' that contains 8
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_translator.properties_in[0.0].scaling_factor' that contains 9
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.properties_out[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.properties_in[0.0].scaling_factor' that
contains 11 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.prereformer.control_volume.scaling_factor' that contains 9 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.prereformer.scaling_factor' that
contains 2 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_hx.cold_side.properties_out[0.0].scaling_factor' that contains
11 component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.cold_side.properties_in[0.0].scaling_factor' that contains 11
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.cold_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.hot_side.properties_out[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_hx.hot_side.properties_in[0.0].scaling_factor' that contains 10
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.hot_side.scaling_factor'
that contains 1 component keys that are not exported as part of the NL
file. Skipping.
WARNING: model contains export suffix 'fs.anode_hx.scaling_factor' that
contains 2 component keys that are not exported as part of the NL file.
Skipping.
WARNING: model contains export suffix
'fs.anode_mix.mixed_state[0.0].scaling_factor' that contains 11 component
keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_mix.recycle_inlet_state[0.0].scaling_factor' that contains 11
component keys that are not exported as part of the NL file. Skipping.
WARNING: model contains export suffix
'fs.anode_mix.feed_inlet_state[0.0].scaling_factor' that contains 23
component keys that are not exported as part of the NL file. Skipping.
Ipopt 3.13.2: nlp_scaling_method=user-scaling
tol=1e-06
max_iter=200
linear_solver=ma57
ma57_pivtol=1e-05
ma57_pivtolmax=0.1
bound_push=1e-20
option_file_name=/tmp/tmpjd8er7ac_ipopt.opt
Using option file "/tmp/tmpjd8er7ac_ipopt.opt".
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
This version of Ipopt was compiled from source code available at
https://github.com/IDAES/Ipopt as part of the Institute for the Design of
Advanced Energy Systems Process Systems Engineering Framework (IDAES PSE
Framework) Copyright (c) 2018-2019. See https://github.com/IDAES/idaes-pse.
This version of Ipopt was compiled using HSL, a collection of Fortran codes
for large-scale scientific computation. All technical papers, sales and
publicity material resulting from use of the HSL codes within IPOPT must
contain the following acknowledgement:
HSL, a collection of Fortran codes for large-scale scientific
computation. See http://www.hsl.rl.ac.uk.
******************************************************************************
This is Ipopt version 3.13.2, running with linear solver ma57.
Number of nonzeros in equality constraint Jacobian...: 117767
Number of nonzeros in inequality constraint Jacobian.: 2
Number of nonzeros in Lagrangian Hessian.............: 5258
Reallocating memory for MA57: lfact (5856694)
Total number of variables............................: 3310
variables with only lower bounds: 111
variables with lower and upper bounds: 1553
variables with only upper bounds: 5
Total number of equality constraints.................: 3305
Total number of inequality constraints...............: 2
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 2
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 2.5930054e+02 1.64e+01 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 2.5696055e+02 4.83e-01 3.28e+06 -1.0 2.04e+01 - 6.72e-01 1.00e+00h 1
2 2.5702844e+02 3.67e+00 4.71e+05 -1.0 4.43e+00 - 8.56e-01 1.00e+00h 1
3 2.5777344e+02 3.68e+02 1.56e+05 -1.0 3.24e+01 - 6.68e-01 1.00e+00f 1
4 2.5896506e+02 5.52e+01 3.85e+05 -1.0 1.81e+01 - 9.90e-01 1.00e+00h 1
5 2.6073340e+02 1.66e+02 1.00e+06 -1.0 3.07e+01 - 1.00e+00 1.00e+00h 1
6 2.6093255e+02 4.46e-01 4.19e+05 -1.0 4.18e+00 - 1.00e+00 1.00e+00h 1
7 2.6090517e+02 3.35e-02 1.18e+05 -1.0 1.07e+00 - 1.00e+00 1.00e+00h 1
8 2.5624596e+02 6.01e+02 1.93e+06 -2.5 1.03e+02 - 6.38e-01 8.37e-01f 1
9 2.5599592e+02 5.55e+02 1.51e+06 -2.5 9.99e+01 - 4.38e-01 8.25e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.5533660e+02 5.35e+02 6.22e+05 -2.5 3.23e+01 - 1.00e+00 1.00e+00h 1
11 2.5536750e+02 4.49e+02 5.11e+05 -2.5 2.39e+01 - 7.12e-01 1.74e-01h 1
12 2.5567715e+02 8.68e+01 5.22e+05 -2.5 1.43e+01 - 7.35e-01 8.10e-01h 1
13 2.5578515e+02 9.29e-01 5.40e+05 -2.5 4.40e+00 - 1.00e+00 1.00e+00h 1
14 2.5578143e+02 1.42e-01 3.17e+05 -2.5 1.35e+00 - 1.00e+00 1.00e+00h 1
15 2.5578163e+02 3.06e-03 1.13e+05 -2.5 1.00e+00 - 1.00e+00 1.00e+00h 1
16 2.5577315e+02 2.10e-02 1.86e+05 -3.8 1.00e+00 - 1.00e+00 6.13e-01h 1
17 2.5577142e+02 3.06e-03 3.69e+05 -3.8 1.00e+00 - 1.00e+00 1.00e+00h 1
18 2.5577134e+02 6.78e-04 2.58e+04 -3.8 1.00e+00 - 1.00e+00 1.00e+00h 1
19 2.5577134e+02 5.41e-07 2.34e+03 -3.8 1.00e+00 - 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 2.5577090e+02 1.64e-04 9.58e+04 -5.7 9.99e-01 - 9.88e-01 9.82e-01h 1
21 2.5577089e+02 1.15e-05 7.86e+02 -5.7 9.98e-01 - 1.00e+00 1.00e+00h 1
22 2.5577089e+02 5.17e-10 7.93e+00 -5.7 9.95e-01 - 1.00e+00 1.00e+00h 1
23 2.5577089e+02 5.63e-08 1.46e+03 -7.0 9.86e-01 - 1.00e+00 1.00e+00h 1
24 2.5577089e+02 1.16e-10 2.38e-01 -7.0 9.63e-01 - 1.00e+00 1.00e+00h 1
25 2.5577089e+02 1.16e-10 8.64e-02 -7.0 9.04e-01 - 1.00e+00 1.00e+00h 1
26 2.5577089e+02 1.67e-10 3.19e-03 -7.0 7.63e-01 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 26
(scaled) (unscaled)
Objective...............: 2.5577088635098298e+02 2.5577088635098298e+02
Dual infeasibility......: 3.1924724990009057e-03 3.1924724990009057e-01
Constraint violation....: 1.6734702512621880e-10 1.6734702512621880e-10
Complementarity.........: 9.0909091118737816e-08 9.0909091118737816e-08
Overall NLP error.......: 9.0909091118737816e-08 3.1924724990009057e-01
Number of objective function evaluations = 27
Number of objective gradient evaluations = 27
Number of equality constraint evaluations = 27
Number of inequality constraint evaluations = 27
Number of equality constraint Jacobian evaluations = 27
Number of inequality constraint Jacobian evaluations = 27
Number of Lagrangian Hessian evaluations = 26
Total CPU secs in IPOPT (w/o function evaluations) = 9.784
Total CPU secs in NLP function evaluations = 0.492
EXIT: Optimal Solution Found.
Show PFDs with design optimization results¶
This displays PFDs in the notebook, and saves them to files.
In [6]:
display(SVG(write_pfd(m)))
write_pfd(m, fname="data_pfds/sofc_results.svg")
In [7]:
# record and display results
optimal_anode_hx_area = m.fs.anode_hx.area.value
optimal_cathode_hx_area = m.fs.cathode_hx.area.value
# assert that flowsheet values have not changed from prior runs
assert m.fs.anode_hx.area.value == pytest.approx(2683.16, rel=0.01)
assert m.fs.cathode_hx.area.value == pytest.approx(15135.97, rel=0.01)
assert m.fs.cathode_recycle.split_fraction[0, 'recycle_outlet'].value == pytest.approx(0.2828, rel=0.01)
assert m.fs.air_blower.inlet.flow_mol[0].value == pytest.approx(11.007, rel=0.01)
print("------------------------------------------")
print("Decision Variable Results")
print("------------------------------------------")
print(f"Anode hx area = {m.fs.anode_hx.area.value} ft^2")
print(f"Cathode hx area = {m.fs.cathode_hx.area.value} ft^2")
print(f"Cathode recirculation fraction = {m.fs.cathode_recycle.split_fraction[0, 'recycle_outlet'].value}")
print(f"Cathode air flowrate = {m.fs.air_blower.inlet.flow_mol[0].value} kmol/s")
print("\n")
print("------------------------------------------")
print("Capital Costs")
print("------------------------------------------")
print(f"SOFC modules = MM${m.fs.sofc_modules.costing.total_plant_cost.value}")
print(f"SOFC balance of plant = MM${pyo.value(m.fs.costing.sofc_bop_cost)}")
print(f"Oxycombustor = MM${m.fs.oxycombustor.costing.total_plant_cost.value}")
print(f"Air separation unit = MM${m.fs.asu.costing.total_plant_cost.value}")
print(f"Carbon purification unit = MM${m.fs.cpu_cost.costing.total_plant_cost.value}")
print(f"Feedwater and misc. BOP systems = MM${pyo.value(m.fs.costing.feedwater_bop_cost)}")
print(f"HRSG, ductwork, and stack = MM${pyo.value(m.fs.costing.hrsg_ductwork_and_stack_cost)}")
print(f"Steam turbine generator = MM${pyo.value(m.fs.costing.steam_turbine_cost)}")
print(f"Cooling water system = MM${pyo.value(m.fs.costing.cooling_water_system_cost)}")
print(f"Electric equipment = MM${pyo.value(m.fs.costing.accessory_electric_plant_cost)}")
print(f"Instrumentation and control = MM${pyo.value(m.fs.costing.instrumentation_and_control_cost)}")
print(f"Improvements to site = MM${pyo.value(m.fs.costing.improvements_to_site_cost)}")
print(f"Buildings and structures = MM${pyo.value(m.fs.costing.buildings_and_structures_cost)}")
print("\n")
print(f"Total Plant Cost = MM${m.fs.costing.total_TPC.value}")
print(f"Total Overnight Cost = MM${m.fs.costing.total_overnight_cost.value}")
print(f"Total As Spent Cost = MM${m.fs.costing.total_as_spent_cost.value}")
print(f"Annualized TASC = MM${m.fs.costing.annualized_tasc.value}/year")
print("\n")
print("------------------------------------------")
print("Fixed and Variable O&M Costs")
print("------------------------------------------")
print(f"Annual operating labor = MM${m.fs.costing.annual_operating_labor_cost.value}/year")
print(f"Maintenance labor = MM${m.fs.costing.maintenance_labor_cost.value}/year")
print(f"Admin & support labor = MM${m.fs.costing.admin_and_support_labor_cost.value}/year")
print(f"Property taxes & insurance = MM${m.fs.costing.property_taxes_and_insurance.value}/year")
print(f"Maintenance material cost = MM${m.fs.costing.maintenance_material_cost.value}/year")
print(f"Stack replacement cost = MM${m.fs.costing.stack_replacement_cost.value}/year")
print(f"Total Fixed O&M Cost = MM${m.fs.costing.total_fixed_OM_cost.value}/year")
print(f"Total Variable O&M Cost = MM${m.fs.costing.total_variable_OM_cost[0].value}/year")
------------------------------------------ Decision Variable Results ------------------------------------------ Anode hx area = 2683.1608147162365 ft^2 Cathode hx area = 15135.972121851768 ft^2 Cathode recirculation fraction = 0.28286078699179706 Cathode air flowrate = 11.007126050466491 kmol/s ------------------------------------------ Capital Costs ------------------------------------------ SOFC modules = MM$216.351206607107 SOFC balance of plant = MM$22.168198605873528 Oxycombustor = MM$17.25766113649775 Air separation unit = MM$75.16656941296873 Carbon purification unit = MM$80.17568164876174 Feedwater and misc. BOP systems = MM$78.41974917660707 HRSG, ductwork, and stack = MM$44.92390515296145 Steam turbine generator = MM$50.98302022038936 Cooling water system = MM$32.59760880545278 Electric equipment = MM$67.15738319049805 Instrumentation and control = MM$20.48747362755321 Improvements to site = MM$28.837921346638318 Buildings and structures = MM$12.805970619738078 Total Plant Cost = MM$747.3323495510471 Total Overnight Cost = MM$904.272142956767 Total As Spent Cost = MM$988.3694522517463 Annualized TASC = MM$69.87772027419845/year ------------------------------------------ Fixed and Variable O&M Costs ------------------------------------------ Annual operating labor = MM$2.6306279999999997/year Maintenance labor = MM$5.679725856587957/year Admin & support labor = MM$2.0775884641469893/year Property taxes & insurance = MM$14.946646991020941/year Maintenance material cost = MM$8.519588784881934/year Stack replacement cost = MM$15.27286975208992/year Total Fixed O&M Cost = MM$49.12704784872775/year Total Variable O&M Cost = MM$136.76611822805677/year
Run SOFC Partial Load¶
This runs the SOFC model at partial load from 650 MW to 200 MW at 5 MW intervals. Results are tabulated for tags in the tags_output tag group in a Pandas data frame.
To run the series, change run_series to True. Running the turndown series takes a while, unless previous saved results are available.
In [8]:
run_series = False
if run_series:
idaes.cfg.ipopt.options.tol = 1e-6
idaes.cfg.ipopt.options.mu_init = 1e-3
solver = pyo.SolverFactory("ipopt")
# reload the model since capital costs are not important here
m = get_base_sofc_model()
get_variable_costs(m)
add_tags(m)
# setup operation optimization problem
m.fs.obj = pyo.Objective(
expr=m.fs.costing.total_variable_OM_cost[0]
)
# fix hx areas to their optimal values
m.fs.anode_hx.area.fix(optimal_anode_hx_area)
m.fs.cathode_hx.area.fix(optimal_cathode_hx_area)
# unfix operating decision vars
m.fs.air_blower.inlet.flow_mol.unfix()
m.fs.cathode_recycle.split_fraction[0, 'recycle_outlet'].unfix()
# add sofc operational constraints
@m.fs.Constraint()
def maximum_cell_temperature(fs):
return m.fs.sofc.max_cell_temperature <= 750
@m.fs.Constraint()
def maximum_cell_temperature_change(fs):
return m.fs.sofc.deltaT_cell <= 100
m.fs.sofc.current_density.setlb(1000)
# create var to enforce net power
m.fs.net_power_MW = pyo.Var(
m.fs.time,
initialize=650,
bounds=(100, 900),
units=pyunits.MW)
@m.fs.Constraint(m.fs.time)
def net_power_constraint(fs, t):
return fs.net_power_MW[t] == pyunits.convert(fs.net_power[t], pyunits.MW)
m.fs.anode_mix.feed_inlet.flow_mol.unfix()
df = pd.DataFrame(columns=m._tags_output.table_heading())
for p in range(650, 199, -20):
print(f"Solving for {p} MW net power")
m.fs.net_power_MW.fix(p)
turndown_ratio = p/650
m.fs.sofc.current_density.fix(turndown_ratio*4000)
fname = f"data/sofc_{int(p)}.json.gz"
if os.path.exists(fname):
iutil.from_json(m, fname=fname, wts=iutil.StoreSpec(suffix=False))
else:
res = solver.solve(m, tee=True, symbolic_solver_labels=True)
iutil.to_json(m, fname=fname)
df.loc[m._tags_output["net_power"].value] = m._tags_output.table_row(numeric=True)
df.to_csv("data_tabulated/sofc.csv")
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