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,
    }
)

2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_1: Initialization Complete
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_2.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_2.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_2.properties_out: fs.econ.side_2.properties_out State Released.
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_2: Initialization Complete
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2021-01-13 17:30:56 [INFO] idaes.init.fs.econ.side_2.properties_in: fs.econ.side_2.properties_in State Released.
2021-01-13 17:30:56 [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()
m.fs.econ.LMTD.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")

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: 3.1622013606267907
1 -- optimal, objective: 0.8197916348655789
2 -- optimal, objective: 1.4704841795757935
3 -- optimal, objective: 1.1898903678088835
4 -- optimal, objective: 6.2669020645852225
5 -- optimal, objective: 2.353798975733269
6 -- optimal, objective: 0.5232362409291367
7 -- optimal, objective: 1.02343478899574
8 -- optimal, objective: 1.6923646000433064
9 -- optimal, objective: 5.200181621760986
10 -- optimal, objective: 2.0256788832442947
11 -- optimal, objective: 1.3755282573107501
12 -- optimal, objective: 1.804041195022807
13 -- optimal, objective: 1.0820452721992382
14 -- optimal, objective: 2.87255083467852
15 -- optimal, objective: 4.679431401768802
16 -- optimal, objective: 2.5285462489988135
17 -- optimal, objective: 3.419056606899124
18 -- optimal, objective: 0.6733248046041784
19 -- optimal, objective: 1.3191174229584868
20 -- optimal, objective: 2.591126369762725
21 -- optimal, objective: 0.7284969800023029
22 -- optimal, objective: 3.0960880080286306
23 -- optimal, objective: 8.046882712386477
24 -- optimal, objective: 9.434438819029037
25 -- optimal, objective: 2.9086660605523385
26 -- optimal, objective: 5.7648547763232205
27 -- optimal, objective: 1.586985000119729
28 -- optimal, objective: 0.984970687035872
29 -- optimal, objective: 5.420696622705247
30 -- optimal, objective: 0.16066578746342522
31 -- optimal, objective: 1.9662633227547253
32 -- optimal, objective: 4.631928468438899
33 -- optimal, objective: 0.789832645766975
34 -- optimal, objective: 4.935316816207539
35 -- optimal, objective: 2.7822175536743163
36 -- optimal, objective: 3.7936042118830064
37 -- optimal, objective: 7.399694410586135
38 -- optimal, objective: 1.8234931889047263
39 -- optimal, objective: 8.123278203552482
40 -- optimal, objective: 2.4669893302566903
41 -- optimal, objective: 2.0590537122733528
42 -- optimal, objective: 4.82489004591247
43 -- optimal, objective: 2.9053626799280337
44 -- optimal, objective: 1.2572997144472058
45 -- optimal, objective: 2.7626453809391625
46 -- optimal, objective: 3.9106046062439104
47 -- optimal, objective: 0.36384547188945693
48 -- optimal, objective: 6.4821230867244175
49 -- optimal, objective: 0.8862884524238979
50 -- optimal, objective: 0.35333788962392987
51 -- optimal, objective: 0.674193466689683
52 -- optimal, objective: 1.4465665980891902
53 -- optimal, objective: 2.36569211553337
54 -- optimal, objective: 1.4292836233966975
55 -- optimal, objective: 11.608835808833591
56 -- optimal, objective: 2.584558536493548
57 -- optimal, objective: 2.2280318353693698
58 -- optimal, objective: 2.495393965552233
59 -- optimal, objective: 1.6472887590070486
60 -- optimal, objective: 8.024825566331032
61 -- optimal, objective: 5.943553444690339
62 -- optimal, objective: 2.3357860625599507
63 -- optimal, objective: 4.38513902517736
64 -- optimal, objective: 0.5607805981597604
65 -- optimal, objective: 2.176847135635383
66 -- optimal, objective: 2.8232836736980373
67 -- optimal, objective: 4.396906443658452
68 -- optimal, objective: 3.3918559300377327
69 -- optimal, objective: 0.614879524322046
70 -- optimal, objective: 0.3708280914479124
71 -- optimal, objective: 0.8762641865696106
72 -- optimal, objective: 3.0086342942362223
73 -- optimal, objective: 6.178275683704545
74 -- optimal, objective: 2.4515957154908636
75 -- optimal, objective: 8.97473642570067
76 -- optimal, objective: 1.770665588225432
77 -- optimal, objective: 3.126518971476404
78 -- optimal, objective: 5.205301238989112
79 -- optimal, objective: 4.76959786483013
80 -- optimal, objective: 4.816644746436761
81 -- optimal, objective: 0.6532812835414774
82 -- optimal, objective: 2.496518135836005
83 -- optimal, objective: 0.8032343482262432
84 -- optimal, objective: 0.36282493375250396
85 -- optimal, objective: 1.523823819480709
86 -- optimal, objective: 3.8657878309560236
87 -- optimal, objective: 1.7222749668715736
88 -- optimal, objective: 3.9538769691814224
89 -- optimal, objective: 1.652361242674854
90 -- optimal, objective: 3.3510638416837253
91 -- optimal, objective: 1.209395519639386
92 -- optimal, objective: 1.5787045321362916
93 -- optimal, objective: 3.4104193014724364
94 -- optimal, objective: 1.2638978913499865
95 -- optimal, objective: 3.2950093864133354
96 -- optimal, objective: 1.530697826703603
97 -- optimal, objective: 2.0576162766855446
98 -- optimal, objective: 1.733210252160942
99 -- optimal, objective: 4.588249738737896
100 -- optimal, objective: 0.92951754484715
101 -- optimal, objective: 1.1035561284195947
102 -- optimal, objective: 0.0054024032812002905
103 -- optimal, objective: 4.030350825817906
104 -- optimal, objective: 2.5977688471875235
105 -- optimal, objective: 3.718657215182353
106 -- optimal, objective: 2.220001230383609
107 -- optimal, objective: 1.7361821672875886
108 -- optimal, objective: 1.7827948173523487
109 -- optimal, objective: 0.8012022277039043
110 -- optimal, objective: 0.48906972652973535
111 -- optimal, objective: 4.625396349830533
112 -- optimal, objective: 4.073050044233131
113 -- optimal, objective: 4.984164789951488
114 -- optimal, objective: 4.500918344081629
115 -- optimal, objective: 0.801241319826576
116 -- optimal, objective: 2.687543401764695
117 -- optimal, objective: 6.864934379080611
118 -- optimal, objective: 3.0375805861815914
119 -- optimal, objective: 2.4941088890247958
120 -- optimal, objective: 0.46083351785483423
121 -- optimal, objective: 0.04447133159164325
122 -- optimal, objective: 1.9091826645137384
123 -- optimal, objective: 4.1539278628050935
124 -- optimal, objective: 5.635821162573107
125 -- optimal, objective: 4.722448584729228
126 -- optimal, objective: 4.838421311326324
127 -- optimal, objective: 2.895359847029753
128 -- optimal, objective: 0.1700702801133807
129 -- optimal, objective: 0.9837813189594008
130 -- optimal, objective: 8.052242413116605
131 -- optimal, objective: 6.260349530098593
132 -- optimal, objective: 2.5726387350162483
133 -- optimal, objective: 3.7332306491081377
134 -- optimal, objective: 0.3400649625011723
135 -- optimal, objective: 3.6032792688193607
136 -- optimal, objective: 2.501572849060018
137 -- optimal, objective: 0.3964133950014609
138 -- optimal, objective: 0.14140404247147736
139 -- optimal, objective: 8.31724058642861
140 -- optimal, objective: 5.424448709520636
141 -- optimal, objective: 2.8357713483631617
142 -- optimal, objective: 1.5375770466935483
143 -- optimal, objective: 3.62417161274446
144 -- optimal, objective: 4.954731705445229
145 -- optimal, objective: 0.5851578341559459
146 -- optimal, objective: 4.899534932815304
147 -- optimal, objective: 3.682266173635674
148 -- optimal, objective: 2.121107969962777
149 -- optimal, objective: 1.7199428396592482
150 -- optimal, objective: 3.3189214980332977
151 -- optimal, objective: 0.36851885526625244
152 -- optimal, objective: 1.948810577615916
153 -- optimal, objective: 2.67478704241622
154 -- optimal, objective: 7.585656605848088
155 -- optimal, objective: 3.3957387225186713
156 -- optimal, objective: 4.149600126698557
157 -- optimal, objective: 1.0001276150024228
158 -- optimal, objective: 3.0644614255860447
159 -- optimal, objective: 5.0139923079556645
160 -- optimal, objective: 3.8398600172207185
161 -- optimal, objective: 1.6576814935989073
162 -- optimal, objective: 0.4117837889199685
163 -- optimal, objective: 2.0406846027880032
164 -- optimal, objective: 2.002997772812926
165 -- optimal, objective: 2.511479923614843
166 -- optimal, objective: 0.48258914652156576
167 -- optimal, objective: 3.8889766576259204
168 -- optimal, objective: 1.0769465308249426
169 -- optimal, objective: 2.499193200876663
170 -- optimal, objective: 1.8451901507025137
171 -- optimal, objective: 4.516240233107525
172 -- optimal, objective: 3.7259498522239074
173 -- optimal, objective: 1.9205975302204013
174 -- optimal, objective: 1.604047683771153
175 -- optimal, objective: 0.3297073490067204
176 -- optimal, objective: 3.177302640760672
177 -- optimal, objective: 4.892210628679255
178 -- optimal, objective: 1.7344424108099796
179 -- optimal, objective: 2.0930393921890142
180 -- optimal, objective: 1.9821792611905547
181 -- optimal, objective: 3.0950130851163937
182 -- optimal, objective: 2.562542928308156
183 -- optimal, objective: 6.469840016661604
184 -- optimal, objective: 2.0674756021955227
185 -- optimal, objective: 2.3845462972645826
186 -- optimal, objective: 1.5119667476079248
187 -- optimal, objective: 3.6253762909982634
188 -- optimal, objective: 0.9836489663297104
189 -- optimal, objective: 1.9174021295225794
190 -- optimal, objective: 1.0200049678523286
191 -- optimal, objective: 1.811114748637613
192 -- optimal, objective: 10.40700748664943
193 -- optimal, objective: 5.725212636472607
194 -- optimal, objective: 6.585121023533178
195 -- optimal, objective: 1.1403803946150923
196 -- optimal, objective: 4.636496073472227
197 -- optimal, objective: 3.9217711869994343
198 -- optimal, objective: 1.00457026568275
199 -- optimal, objective: 2.418215480545875
200 -- optimal, objective: 2.924358021526806
201 -- optimal, objective: 2.9689758379686415
202 -- optimal, objective: 2.6152849723015565
203 -- optimal, objective: 2.4914091180308597
204 -- optimal, objective: 1.794347594257792
205 -- optimal, objective: 5.708286126988911
206 -- optimal, objective: 2.4056024845433326
207 -- optimal, objective: 0.9383323510763955
208 -- optimal, objective: 4.796662991506752
209 -- optimal, objective: 0.506773425862618
210 -- optimal, objective: 2.1890884578837966
211 -- optimal, objective: 3.216278312969685
212 -- optimal, objective: 0.07969866183081314
213 -- optimal, objective: 0.39071669881267745
214 -- optimal, objective: 4.024001493294549
215 -- optimal, objective: 3.594279949173519
216 -- optimal, objective: 1.6777857029028622
217 -- optimal, objective: 4.848031703923862
218 -- optimal, objective: 0.48853441088523125
219 -- optimal, objective: 12.374570705038183
220 -- optimal, objective: 1.4284110604965086
221 -- optimal, objective: 1.818042749358927
222 -- optimal, objective: 0.4850085026530443
223 -- optimal, objective: 2.5067851806563355
224 -- optimal, objective: 1.3976812984152867
225 -- optimal, objective: 0.9031717605986198
226 -- optimal, objective: 0.7285447496525985
227 -- optimal, objective: 2.4703912750522545
228 -- optimal, objective: 2.675134784707579
229 -- optimal, objective: 3.325674612581462
230 -- optimal, objective: 2.5990372980399847
231 -- optimal, objective: 4.8376057781493635
232 -- optimal, objective: 1.1329234883415469
233 -- optimal, objective: 1.6398399431286828
234 -- optimal, objective: 3.0089833505496166
235 -- optimal, objective: 1.4124043086038174
236 -- optimal, objective: 5.771998515376791
237 -- optimal, objective: 0.149389060156801
238 -- optimal, objective: 1.205747487805747
239 -- optimal, objective: 1.7168126471500196
240 -- optimal, objective: 4.602217912756729
241 -- optimal, objective: 2.1236286863590923
242 -- optimal, objective: 2.531589994116756
243 -- optimal, objective: 1.7031408430137989
244 -- optimal, objective: 2.2177940017210624
245 -- optimal, objective: 0.6465659506433649
246 -- optimal, objective: 1.2916365175647821
247 -- optimal, objective: 7.7902584211708366
248 -- optimal, objective: 1.0605580786757942
249 -- optimal, objective: 1.1515044674820794

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 [ ]: