Econ Recon

Jupyter Notebook source file

Data Reconciliation for a Single Unit - Economizer¶

This notebook demonstrates data reconciliation with a single unit model, an economizer. Data for this example was generated by adding noise to supercritical power plant simulations.

Why reconcile data?¶

Data reconciliation uses mass and energy balances along with redundant measurements to improve data quality by:

1. reducing measurement error,
2. ensuring measurements satisfy mass and energy balances, and
3. filling in unmeasured quantities.

Data reconciliation is used to refine process data before parameter estimation.

1. Read Plant Data¶

The first step is to read in process data. In this case, data was simulated by adding measurement error to supercritical steam cycle simulation results. IDAES includes functions to read process data, convert units to match a model, and map data to a model.

In [1]:

# IDAES module with functions to read, analyze and visualize plant data
import idaes.dmf.model_data as da
# Suppress some warnings
from idaes.logger import getLogger
import logging
getLogger('idaes.core').setLevel(logging.ERROR)

Process data is contained in two CSV files, a data file and a metadata file. The first column in the data file is row indexes and the first row is process measurement tags. The index column has an entry for each data row, and is often a time-stamp. The data file format is illustrated by the table below.

	tag1	tag2	tag3	...
index1	data(1,1)	data(1,2)	data(1, 3)	...
index2	data(2,1)	data(2,2)	data(2, 3)	...
...	...	...	...	...

The metadata file contains information about the tags including units of measurement, description, and model mapping information. The meta data format is show below, any of the columns my be empty.

tag1	model reference 1	description 1	unit of measure 1	Additional comments, additional columns are ignored
tag2	model reference 2	description 2	unit of measure 2	...
tag3	model reference 3	description 3	unit of measure 3	...
...	...	...	...	...

Once the process data is read in, the data is assigned to bins based on the value in a given column, in this case gross power. Dividing the data into bins allows rough estimation of measurement uncertainty.

In [2]:

# Read data and column metadata
df, df_meta = da.read_data("plant_data.csv", "plant_data_meta.csv")

# Add bin information where the data is sorted into 5 MW bins based on the "GROSS_POWER" column
# A bin number column is added along with a column for nominal gross power in the bin. 
bin_count = da.bin_data(df, bin_by="POWER_GROSS", bin_no="bin_no", bin_nom="bin_power", bin_size=5e6)

# Calculate the standard deviation by bin for each column.  The resulting standard devations can be 
# accessed like so: bin_stdev[bin number][column name]
bin_stdev = da.bin_stdev(df, bin_no="bin_no")

It can be useful to visualize the measurement data and estimated uncertainty. The following creates box and whisker plots for each tag based on the data bins. A large number of plots may be created, so to manage them more easily, they are saved as PDFs and merged into a single multi-page PDF document. The deafault file name for the resulting PDF is "data_plot_book.pdf."

In [3]:

# Create a pdf book of plots that shows box and whisker plots for each column by bin
import os
if not os.path.isfile("data_plot_book.pdf"):
    da.data_plot_book(df, bin_nom="bin_power", xlabel="gross power (W)", metadata=df_meta, file="data_plot_book.pdf")
# There should now be a data_plot_book.pdf file in this directory

2. Create Unit model¶

Now that we have the plant data, we need to create a unit model that we can use for data reconciliation. Although we need a model that has just mass and energy balances and feasibility constraints for the data reconciliation problem, we start with the full economizer model here. Using the same model for data reconciliation, parameter estimation, validation, and simulation reduces the work required to move between steps in the workflow.

Once the full model is created, constraints that are not needed for data reconciliation can be deactivated.

In [4]:

# Import models
from idaes.core import FlowsheetBlock
from idaes.power_generation.properties.flue_gas_ideal import FlueGasParameterBlock
from idaes.generic_models.properties import iapws95
from idaes.power_generation.unit_models.boiler_heat_exchanger import (
    BoilerHeatExchanger, 
    TubeArrangement, 
    DeltaTMethod
)
import pyomo.environ as pyo

In [5]:

# Create flowsheet with economizer
m = pyo.ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.prop_water = iapws95.Iapws95ParameterBlock()
m.fs.prop_fluegas = FlueGasParameterBlock()

m.fs.econ = BoilerHeatExchanger(default={
        "side_1_property_package": m.fs.prop_water,
        "side_2_property_package": m.fs.prop_fluegas,
        "has_pressure_change": True,
        "has_holdup": False,
        "delta_T_method": DeltaTMethod.counterCurrent,
        "tube_arrangement": TubeArrangement.inLine,
        "side_1_water_phase": "Liq",
        "has_radiation": False
    }
)

In [6]:

# Set up and initialize the model

# The steam properties use enthalpy as a state variable, so use the known 
# temperature and pressure to calculate the feedwater inlet enthalpy
h = pyo.value(iapws95.htpx(563.706*pyo.units.K, 2.5449e7*pyo.units.Pa))

m.fs.econ.side_1_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.econ.side_1_inlet.enth_mol[0].fix(h) #J/mol         
m.fs.econ.side_1_inlet.pressure[0].fix(2.5449e7) # Pa

# Set the flue gas flow and composition
fg_rate = 28.3876e3  # mol/s equivalent of ~1930.08 klb/hr
fg_comp = { # mol fraction of flue gas components
    "H2O":8.69/100,
    "CO2":14.49/100,
    "O2":2.47/100,
    "NO":0.0006,
    "SO2":0.002,
}
# The rest is N2
fg_comp["N2"] = 1 - sum(fg_comp[i] for i in fg_comp)

# Set economizer inlets
for c in fg_comp:
    m.fs.econ.side_2.properties_in[0].flow_mol_comp[c].fix(fg_rate*fg_comp[c])    
m.fs.econ.side_2_inlet.temperature[0].fix(682.335)  # K
m.fs.econ.side_2_inlet.pressure[0].fix(100145)  # Pa

# Set economizer design variables and parameters
ITM = 0.0254  # inch to meter conversion
# Based on NETL Baseline Report Rev4
m.fs.econ.tube_thickness.fix(0.188*ITM)  # tube thickness
m.fs.econ.tube_di.fix((2.0 - 2.0 * 0.188)*ITM) # calc inner diameter
m.fs.econ.pitch_x.fix(3.5*ITM)
m.fs.econ.pitch_y.fix(5.03*ITM)
m.fs.econ.tube_length.fix(53.41*12*ITM)  # use tube length (53.41 ft)
m.fs.econ.tube_nrow.fix(36*2.5) # use to match baseline performance
m.fs.econ.tube_ncol.fix(130) # 130 from thermoflow
m.fs.econ.nrow_inlet.fix(2)
m.fs.econ.delta_elevation.fix(50)
m.fs.econ.tube_r_fouling = 0.000176
m.fs.econ.shell_r_fouling = 0.00088
m.fs.econ.fcorrection_htc.fix(1.5)
m.fs.econ.fcorrection_dp_tube.fix(1.0)
m.fs.econ.fcorrection_dp_shell.fix(1.0)

In [7]:

# Initialize economizer
m.fs.econ.initialize(
    state_args_1={
        "flow_mol": m.fs.econ.side_1_inlet.flow_mol[0].value,
        "pressure": m.fs.econ.side_1_inlet.pressure[0].value,
        "enth_mol": m.fs.econ.side_1_inlet.enth_mol[0].value,
    },
    state_args_2={
        "flow_component":{
            "H2O": m.fs.econ.side_2_inlet.flow_mol_comp[0, "H2O"].value,
            "CO2": m.fs.econ.side_2_inlet.flow_mol_comp[0, "CO2"].value,
            "N2": m.fs.econ.side_2_inlet.flow_mol_comp[0, "N2"].value,
            "O2": m.fs.econ.side_2_inlet.flow_mol_comp[0, "O2"].value,
            "NO": m.fs.econ.side_2_inlet.flow_mol_comp[0, "NO"].value,
            "SO2": m.fs.econ.side_2_inlet.flow_mol_comp[0, "SO2"].value,
        },
        "temperature": m.fs.econ.side_2_inlet.temperature[0].value,
        "pressure": m.fs.econ.side_2_inlet.pressure[0].value,
    }
)

2021-11-30 19:27:10 [INFO] idaes.init.fs.econ.side_1: Initialization Complete
2021-11-30 19:27:10 [INFO] idaes.init.fs.econ.side_2.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2021-11-30 19:27:10 [INFO] idaes.init.fs.econ.side_2.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2021-11-30 19:27:10 [INFO] idaes.init.fs.econ.side_2.properties_out: fs.econ.side_2.properties_out State Released.
2021-11-30 19:27:10 [INFO] idaes.init.fs.econ.side_2: Initialization Complete
2021-11-30 19:27:10 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2021-11-30 19:27:11 [INFO] idaes.init.fs.econ.side_2.properties_in: fs.econ.side_2.properties_in State Released.
2021-11-30 19:27:11 [INFO] idaes.init.fs.econ: fs.econ Initialisation Complete.

3. Simplify to Mass and Energy Balances¶

For data reconciliation, the model should be reduced to mass and energy balances and potentially limited performance constraints to keep the results feasible.

In [8]:

# Deactivate constraints for heat transfer
m.fs.econ.overall_heat_transfer_coefficient_eqn.deactivate()
m.fs.econ.rcond_wall_eqn.deactivate()
m.fs.econ.hconv_shell_total_eqn.deactivate()
m.fs.econ.hconv_shell_conv_eqn.deactivate()
m.fs.econ.N_Nu_shell_eqn.deactivate()
m.fs.econ.N_Pr_shell_eqn.deactivate()
m.fs.econ.deltaP_shell_eqn.deactivate()
m.fs.econ.friction_factor_shell_eqn.deactivate()
m.fs.econ.N_Re_shell_eqn.deactivate()
m.fs.econ.v_shell_eqn.deactivate()
m.fs.econ.hconv_tube_eqn.deactivate()
m.fs.econ.N_Nu_tube_eqn.deactivate()
m.fs.econ.N_Pr_tube_eqn.deactivate()
m.fs.econ.deltaP_tube_eqn.deactivate()
m.fs.econ.deltaP_tube_uturn_eqn.deactivate()
m.fs.econ.deltaP_tube_friction_eqn.deactivate()
m.fs.econ.friction_factor_tube_eqn.deactivate()
m.fs.econ.N_Re_tube_eqn.deactivate()
m.fs.econ.v_tube_eqn.deactivate()

4. Map Data to the Model¶

Although the model mapping can be included in the tag metadata file, here we just add the mapping information to the tag metadata after reading the data. Sometime a data set may be used with more than one model or you may want to examine data before creating a model, in which case it is convenient to defer mapping the data to the model as we have done here.

In [9]:

df_meta["ECON_OUT_F"]["reference_string"] = "m.fs.econ.side_1.properties_out[:].flow_mol"
df_meta["ECON_OUT_T"]["reference_string"] = "m.fs.econ.side_1.properties_out[:].temperature"
df_meta["ECON_OUT_P"]["reference_string"] = "m.fs.econ.side_1.properties_out[:].pressure"
df_meta["BFW_F"]["reference_string"] = "m.fs.econ.side_1.properties_in[:].flow_mol"
df_meta["BFW_T"]["reference_string"] = "m.fs.econ.side_1.properties_in[:].temperature"
df_meta["BFW_P"]["reference_string"] = "m.fs.econ.side_1.properties_in[:].pressure"
df_meta["FG_2_ECON_Fm"]["reference_string"] = "m.fs.econ.side_2.properties_in[:].flow_mass"
df_meta["FG_2_ECON_T"]["reference_string"] = "m.fs.econ.side_2.properties_in[:].temperature"
df_meta["FG_2_ECON_P"]["reference_string"] = "m.fs.econ.side_2.properties_in[:].pressure"
df_meta["FG_2_AIRPH_Fm"]["reference_string"] = "m.fs.econ.side_2.properties_out[:].flow_mass"
df_meta["FG_2_AIRPH_T"]["reference_string"] = "m.fs.econ.side_2.properties_out[:].temperature"
df_meta["FG_2_AIRPH_P"]["reference_string"] = "m.fs.econ.side_2.properties_out[:].pressure"

In [10]:

# Add the model references to the tag metadata based on the strings above.
da.upadate_metadata_model_references(m, df_meta)

In [11]:

# Create a dictionary of data tags that we want to use for the data reconciliation problem.  
# The key is the tag and the value is a reference to a quantity in the model.
data_tags = {k:v["reference"][0] for k, v in df_meta.items() if v["reference"] is not None}

In [12]:

# Now for result output, the data reconciliation usually can give full stream information for a flowsheet
# including quantities that are unmeasured.  To more easily use the results, it is good practice to map most of
# the data reconciliation results to flowsheet stream names.  
import idaes.core.util.tables as ta

# This function creates a dictionary of streams based of streams based on model arcs.  The function
# also takes an addtional set of stream-like objects for add to the stream dictionary.  In this case,
# this is a single unit and the flowsheet doesn't contain any arcs, so we add the economized inlet and
# outlet ports to the stream dictionary.
stream_dict = ta.arcs_to_stream_dict(
    m, 
    additional={
        "BFW": m.fs.econ.side_1_inlet,
        "ECON_OUT": m.fs.econ.side_1_outlet,
        "FG_2_ECON": m.fs.econ.side_2_inlet,
        "FG_2_AIRPH": m.fs.econ.side_2_outlet,
    },
    sort=True,
)

# The next function converts the stream dictionary into a dictionary of state block representing the
# streams at a given time point.  In this case, we have a steady state model, so we only have one 
# time point (0).
state_dict = ta.stream_states_dict(stream_dict, time_point=0)

# The 'tag_state_quantities()' function below iterates through the state block dictionary and 
# creates tags for the listed attributes by combining the state block label with the attribute label 
# in the labels argument.  For example, pressure in the S001 state block would get the tag 'S001_P'.
recon_tags = ta.tag_state_quantities(
    blocks=state_dict, 
    attributes=(
        "flow_mass", 
        "flow_mol", 
        "enth_mol", 
        "temperature", 
        "pressure", 
        ("flow_mol_comp", "O2"),
        ("flow_mol_comp", "NO"),
        ("flow_mol_comp", "N2"),
        ("flow_mol_comp", "SO2"),
        ("flow_mol_comp", "CO2"),
        ("flow_mol_comp", "H2O"),
    ), 
    labels=("_Fm", "_F", "_h", "_T", "_P", "_F[O2]", "_F[NO]", "_F[N2]", "_F[SO2]", "_F[CO2]", "_F[H2O]"),
)

# Any addtional tags can be added.  This is required for tags that cannot be systematically generated 
# from the model streams.
recon_tags["ECON_Q"] = m.fs.econ.heat_duty[0]

5. View model flowsheet¶

Model results or other quantities can be added to a process flow diagram. The PFD was drawn beforehand and the model results are added to tagged locations on the PFD.

In [13]:

from idaes.core.util.misc import svg_tag  # utility to place numbers/text in an SVG

with open("econ.svg", "r") as f:
    s = svg_tag(svg=f, tags={"subtitle":"Initialized Model"})
    s = svg_tag(svg=s, tags=recon_tags, outfile="econ_init.svg")

WARNING: DEPRECATED: idaes.core.util.misc.svg_tag has moved to
    idaes.core.util.tags.svg_tag  (deprecated in 1.12) (called from
    /home/lbianchi/opt/conda/envs/build-idaes-
    examples-1.12.0rc0/lib/python3.8/site-
    packages/IPython/core/interactiveshell.py:3457)
WARNING: DEPRECATED: DEPRECATED: svg_tag, the tags, tag_format and
    tag_format_default arguments are deprecated use tag_group instead.
    (deprecated in 1.12) (called from /home/lbianchi/opt/conda/envs/build-
    idaes-examples-1.12.0rc0/lib/python3.8/site-
    packages/idaes/core/util/misc.py:146)

In [14]:

from IPython.display import SVG, display

display(SVG(s))

6. Write Objective¶

Next we write the objective function and additional constraints for the data reconciliation problem. The objective is

$$\min \sum_i \left(\frac{x_{\text{data}, i} - x_{\text{model}, i}}{\sigma_i} \right)^2$$

Where $i \in \{\text{Measured Quantities}\}$ and $\sigma_i$ is the standard deviation of measurement i. In this case, for lack of better information, the standard deviation was estimated by binning the data and calculating the standard deviation of each measured variable in each bin.

In [15]:

# Add model parameters to contain measured data.  These are mutable so we can set a specific data point later.
m.data = pyo.Param(data_tags, mutable=True, doc="Process data for a specific point in time.")
m.data_stdev = pyo.Param(data_tags, mutable=True, doc="Process data standard deviation.")

In [16]:

# The 'set_data' function below takes data from the process data DataFrame and updates the
# data parameters in the model.
def set_data(m, df, data_tags, index=None, indexindex=None):
    if index is None:
        index = df.index[indexindex]
    m.bin_no = df.iloc[index]["bin_no"]
    for t in data_tags:
        m.data[t] = df.iloc[index][t]
        m.data_stdev[t] = bin_stdev[m.bin_no][t]

In [17]:

# So we have something reasonable to start, set the data attached to the model to the first 
# data point.
set_data(m, df, data_tags, indexindex=0)

Add an expression for error divided by the standard deviation, and use it to write the data reconciliation objective function.

In [18]:

@m.Expression(data_tags)
def err(m, i):
    return (m.data[i] - data_tags[i])/m.data_stdev[i]

m.objective = pyo.Objective(expr=sum(m.err[t]**2 for t in m.err))

Add constraints that ensure reasonable temperature and keep the flue gas composition correct.

In [19]:

# Limit temperature approach
m.c1 = pyo.Constraint(expr=m.fs.econ.deltaT_1[0] >= 1.0)
m.c2 = pyo.Constraint(expr=m.fs.econ.deltaT_2[0] >= 1.0)

# Constrain flue gas composition
m.flow_fg = pyo.Var(initialize=fg_rate)
@m.Constraint(fg_comp)
def eq_fg_comp(b, c):
    return m.fs.econ.side_2.properties_in[0].flow_mol_comp[c] == fg_comp[c]*m.flow_fg

7. Solve Optimization¶

Now we need to solve the data reconciliation problem for every data point. The important results are stored in two DataFrames df_result, which contains results tagged based on model stream names to be used in the parameter estimation step and df_result_cmp which contains reconciled data based on the original measurement tags and can be used to compare the original measurements to the reconciled results.

In [20]:

# Make sure the inlet and outlet ports are unfixed.  We want to leave these free 
# to best match the data.
m.fs.econ.side_1_inlet.unfix()
m.fs.econ.side_2_inlet.unfix()
m.fs.econ.side_1_outlet.unfix()
m.fs.econ.side_2_outlet.unfix()

In [21]:

# Create a Pyomo solver object
solver = pyo.SolverFactory('ipopt')

In [22]:

import pandas as pd
# Add bin information to reconciliation results so it can be used in parameter estimation
df_result = pd.DataFrame(columns=list(recon_tags.keys())+["termination", "bin_no", "bin_power"], index=df.index)
df_result_cmp = pd.DataFrame(columns=list(data_tags.keys())+["termination"], index=df.index)

# Loop through each data point and solve the data reconciliation problem. 
for i in df.index:
    set_data(m, df, data_tags, index=i)
    res = solver.solve(m)
    tc = str(res.solver.termination_condition)
    df_result.iloc[i]["termination"] = tc
    df_result.iloc[i]["bin_no"] = df.iloc[i]["bin_no"]
    df_result.iloc[i]["bin_power"] = df.iloc[i]["bin_power"]
    df_result_cmp.iloc[i]["termination"] = tc
    for t in recon_tags:
        df_result.iloc[i][t] = pyo.value(recon_tags[t])
    for t in data_tags:
        df_result_cmp.iloc[i][t] = pyo.value(data_tags[t])
    # Show something so you can tell progress is happening
    print(f"{i} -- {tc}, objective: {pyo.value(m.objective)}")

0 -- optimal, objective: 3.1622227267477236
1 -- optimal, objective: 0.8197881540804663
2 -- optimal, objective: 1.4704961756860007
3 -- optimal, objective: 1.1898683973939073
4 -- optimal, objective: 6.2668757277680145
5 -- optimal, objective: 2.353825037717043
6 -- optimal, objective: 0.5232293871180912
7 -- optimal, objective: 1.0234536307431457
8 -- optimal, objective: 1.6923868337124404
9 -- optimal, objective: 5.200179122889494
10 -- optimal, objective: 2.02569161075015
11 -- optimal, objective: 1.375510820858676
12 -- optimal, objective: 1.8040192166107316
13 -- optimal, objective: 1.0820617353510786
14 -- optimal, objective: 2.872560865484746
15 -- optimal, objective: 4.679395550949352
16 -- optimal, objective: 2.528560988157964
17 -- optimal, objective: 3.4190895194025726
18 -- optimal, objective: 0.6733418552016611
19 -- optimal, objective: 1.3191361601576406
20 -- optimal, objective: 2.591094538468206
21 -- optimal, objective: 0.7284917916188187
22 -- optimal, objective: 3.096119847074954
23 -- optimal, objective: 8.046910612157625
24 -- optimal, objective: 9.43446787232482
25 -- optimal, objective: 2.908699328199419
26 -- optimal, objective: 5.76485721056687
27 -- optimal, objective: 1.5869915338535021
28 -- optimal, objective: 0.9849808635599643
29 -- optimal, objective: 5.420715582434443
30 -- optimal, objective: 0.1598732104118969
31 -- optimal, objective: 1.9662708564310054
32 -- optimal, objective: 4.6319641357935275
33 -- optimal, objective: 0.7898364826192952
34 -- optimal, objective: 4.935317631382528
35 -- optimal, objective: 2.782254721512846
36 -- optimal, objective: 3.7935585045917892
37 -- optimal, objective: 7.3997278094156105
38 -- optimal, objective: 1.823486516660074
39 -- optimal, objective: 8.123224199178962
40 -- optimal, objective: 2.4669745912045182
41 -- optimal, objective: 2.0590147462740016
42 -- optimal, objective: 4.824860326020594
43 -- optimal, objective: 2.905357196069236
44 -- optimal, objective: 1.2573333384737084
45 -- optimal, objective: 2.762654868716844
46 -- optimal, objective: 3.910562187450599
47 -- optimal, objective: 0.3638511438809614
48 -- optimal, objective: 6.48207075131405
49 -- optimal, objective: 0.8862863572807926
50 -- optimal, objective: 0.35333271386302767
51 -- optimal, objective: 0.6741788395561904
52 -- optimal, objective: 1.4465659660224155
53 -- optimal, objective: 2.3657124776785285
54 -- optimal, objective: 1.4293043476046114
55 -- optimal, objective: 11.608878616087804
56 -- optimal, objective: 2.58455852181556
57 -- optimal, objective: 2.2280385889684355
58 -- optimal, objective: 2.495375700856505
59 -- optimal, objective: 1.6473059536498185
60 -- optimal, objective: 8.024782999051263
61 -- optimal, objective: 5.943571679649429
62 -- optimal, objective: 2.3358029808076184
63 -- optimal, objective: 4.38513625667418
64 -- optimal, objective: 0.5607930691618418
65 -- optimal, objective: 2.1768732856567903
66 -- optimal, objective: 2.8233151497317914
67 -- optimal, objective: 4.396913088762425
68 -- optimal, objective: 3.3918328175083436
69 -- optimal, objective: 0.6148676050767217
70 -- optimal, objective: 0.3708290390409646
71 -- optimal, objective: 0.8762486395429888
72 -- optimal, objective: 3.0086242664115765
73 -- optimal, objective: 6.178298889668417
74 -- optimal, objective: 2.451581047869226
75 -- optimal, objective: 8.974784736396328
76 -- optimal, objective: 1.7706895755220056
77 -- optimal, objective: 3.1265400749414534
78 -- optimal, objective: 5.203571840723419
79 -- optimal, objective: 4.769621582501687
80 -- optimal, objective: 4.816642172570757
81 -- optimal, objective: 0.6532741094173069
82 -- optimal, objective: 2.496528721911957
83 -- optimal, objective: 0.8032383968120484
84 -- optimal, objective: 0.36283747515808096
85 -- optimal, objective: 1.5238425496865087
86 -- optimal, objective: 3.8657617083927285
87 -- optimal, objective: 1.7222675119802966
88 -- optimal, objective: 3.953872372963472
89 -- optimal, objective: 1.6523626343497102
90 -- optimal, objective: 3.3511000648600526
91 -- optimal, objective: 1.2094028270637769
92 -- optimal, objective: 1.5787041255816416
93 -- optimal, objective: 3.410417173955502
94 -- optimal, objective: 1.2638821516691674
95 -- optimal, objective: 3.295021190107275
96 -- optimal, objective: 1.5307192842207231
97 -- optimal, objective: 2.0576184713664
98 -- optimal, objective: 1.733204658709798
99 -- optimal, objective: 4.5882794103668205
100 -- optimal, objective: 0.9293015277967475
101 -- optimal, objective: 1.1035467025831933
102 -- optimal, objective: 0.005403092725190184
103 -- optimal, objective: 4.030370198029042
104 -- optimal, objective: 2.5977866074240206
105 -- optimal, objective: 3.718637539092409
106 -- optimal, objective: 2.2200082219901534
107 -- optimal, objective: 1.7361606413581323
108 -- optimal, objective: 1.7827907915253505
109 -- optimal, objective: 0.8012179144633598
110 -- optimal, objective: 0.4890822013581204
111 -- optimal, objective: 4.625444642903938
112 -- optimal, objective: 4.07306180330844
113 -- optimal, objective: 4.984149658953241
114 -- optimal, objective: 4.500903765842289
115 -- optimal, objective: 0.8012381845209076
116 -- optimal, objective: 2.687554378776392
117 -- optimal, objective: 6.864920838087274
118 -- optimal, objective: 3.0375522321897814
119 -- optimal, objective: 2.494098009707389
120 -- optimal, objective: 0.46083201829370657
121 -- optimal, objective: 0.04447225222365364
122 -- optimal, objective: 1.9092110321559408
123 -- optimal, objective: 4.153938460441822
124 -- optimal, objective: 5.635804261323758
125 -- optimal, objective: 4.72239948960187
126 -- optimal, objective: 4.837813299841361
127 -- optimal, objective: 2.8953995802785957
128 -- optimal, objective: 0.1700728987502693
129 -- optimal, objective: 0.983791567030946
130 -- optimal, objective: 8.05225409929586
131 -- optimal, objective: 6.260316294305136
132 -- optimal, objective: 2.572598330268635
133 -- optimal, objective: 3.7332013380677833
134 -- optimal, objective: 0.34006246098208825
135 -- optimal, objective: 3.6033161609590403
136 -- optimal, objective: 2.501573096808958
137 -- optimal, objective: 0.39640424029669713
138 -- optimal, objective: 0.1414035092242955
139 -- optimal, objective: 8.317311777959498
140 -- optimal, objective: 5.424431267918817
141 -- optimal, objective: 2.8357421686721
142 -- optimal, objective: 1.5376013961507509
143 -- optimal, objective: 3.6241963577005194
144 -- optimal, objective: 4.954703626295027
145 -- optimal, objective: 0.585159563006957
146 -- optimal, objective: 4.89957252536089
147 -- optimal, objective: 3.6822688057449264
148 -- optimal, objective: 2.12108984310195
149 -- optimal, objective: 1.7199795815279166
150 -- optimal, objective: 3.318912504228596
151 -- optimal, objective: 0.36850785731333546
152 -- optimal, objective: 1.9488329531202326
153 -- optimal, objective: 2.6747680809659813
154 -- optimal, objective: 7.5856981034921125
155 -- optimal, objective: 3.395738594834344
156 -- optimal, objective: 4.149632062900599
157 -- optimal, objective: 1.0001387519541236
158 -- optimal, objective: 3.0644832117345655
159 -- optimal, objective: 5.014021556676823
160 -- optimal, objective: 3.8398189061238397
161 -- optimal, objective: 1.6576893499093268
162 -- optimal, objective: 0.41176973979161824
163 -- optimal, objective: 2.040678862856759
164 -- optimal, objective: 2.0029963443118506
165 -- optimal, objective: 2.511504386519033
166 -- optimal, objective: 0.4825771048999583
167 -- optimal, objective: 3.888932512512223
168 -- optimal, objective: 1.0769714540448008
169 -- optimal, objective: 2.499194099134282
170 -- optimal, objective: 1.845202288971921
171 -- optimal, objective: 4.5162757443336305
172 -- optimal, objective: 3.7259845773036906
173 -- optimal, objective: 1.9205831842368681
174 -- optimal, objective: 1.6040433482387517
175 -- optimal, objective: 0.3297059921164168
176 -- optimal, objective: 3.1773292559303705
177 -- optimal, objective: 4.89221287375584
178 -- optimal, objective: 1.7344211222125672
179 -- optimal, objective: 2.0930113767061584
180 -- optimal, objective: 1.9821944087033123
181 -- optimal, objective: 3.095063944360138
182 -- optimal, objective: 2.5625165342165928
183 -- optimal, objective: 6.469891429283569
184 -- optimal, objective: 2.067460638680301
185 -- optimal, objective: 2.3845354622360526
186 -- optimal, objective: 1.5119923887480426
187 -- optimal, objective: 3.625418156825069
188 -- optimal, objective: 0.9836625190091582
189 -- optimal, objective: 1.9174184223605604
190 -- optimal, objective: 1.0199853616407286
191 -- optimal, objective: 1.8111192038560038
192 -- optimal, objective: 10.40706189927436
193 -- optimal, objective: 5.725243783933129
194 -- optimal, objective: 6.585188554630437
195 -- optimal, objective: 1.1404034774868888
196 -- optimal, objective: 4.6364857395103485
197 -- optimal, objective: 3.9218037986581695
198 -- optimal, objective: 1.0045607379024488
199 -- optimal, objective: 2.418194887917511
200 -- optimal, objective: 2.924381439171248
201 -- optimal, objective: 2.9689954757333767
202 -- optimal, objective: 2.615289296528611
203 -- optimal, objective: 2.491418211244421
204 -- optimal, objective: 1.7943475851127997
205 -- optimal, objective: 5.708324626597137
206 -- optimal, objective: 2.4056055297694727
207 -- optimal, objective: 0.9383160093489363
208 -- optimal, objective: 4.796686075011124
209 -- optimal, objective: 0.5067752382992995
210 -- optimal, objective: 2.189070601163973
211 -- optimal, objective: 3.2162721207000833
212 -- optimal, objective: 0.0797030982595503
213 -- optimal, objective: 0.39071980305706655
214 -- optimal, objective: 4.023971715053819
215 -- optimal, objective: 3.5942477203081955
216 -- optimal, objective: 1.6777755011210227
217 -- optimal, objective: 4.848035154404865
218 -- optimal, objective: 0.48854638442723286
219 -- optimal, objective: 12.374531482863178
220 -- optimal, objective: 1.4283906796285541
221 -- optimal, objective: 1.8180474372486608
222 -- optimal, objective: 0.4850181471500386
223 -- optimal, objective: 2.506770452120046
224 -- optimal, objective: 1.3976831205728915
225 -- optimal, objective: 0.9031827797634284
226 -- optimal, objective: 0.7285597986984916
227 -- optimal, objective: 2.470420726707554
228 -- optimal, objective: 2.6750989066858013
229 -- optimal, objective: 3.325705645605336
230 -- optimal, objective: 2.5990527127801317
231 -- optimal, objective: 4.837619200685973
232 -- optimal, objective: 1.1329374346636611
233 -- optimal, objective: 1.6398640882824427
234 -- optimal, objective: 3.008950871925208
235 -- optimal, objective: 1.4124059496646608
236 -- optimal, objective: 5.7719654075989295
237 -- optimal, objective: 0.14938189272240585
238 -- optimal, objective: 1.205741317201688
239 -- optimal, objective: 1.7168330910788303
240 -- optimal, objective: 4.602205543920219
241 -- optimal, objective: 2.123631117523279
242 -- optimal, objective: 2.5316135514751825
243 -- optimal, objective: 1.7031605794317117
244 -- optimal, objective: 2.2177892333102482
245 -- optimal, objective: 0.64656334673633
246 -- optimal, objective: 1.291637880047304
247 -- optimal, objective: 7.7898519886260615
248 -- optimal, objective: 1.0605735856126097
249 -- optimal, objective: 1.151469126514001

In [23]:

# Save the reconciled data to be used for parameter estimation
df_result.to_csv("econ_recon.csv")

In [24]:

try:
    # Create a new plot book to compare the original data to the reconciled data.
    da.data_rec_plot_book(
        df_data=df, 
        df_rec=df_result_cmp,
        file="econ_data_rec_plot_book.pdf",
        bin_nom="bin_power", 
        xlabel="gross power (W)", 
        metadata=df_meta
    )
except:
    print("Plotting failed")

Plotting data requires the 'seaborn' and 'PyPDF2' packages. Install the required packages before using the data_book() function. Plot terminated.

In [ ]: