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,
    }
)

2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_1: Initialization Complete
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_2.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_2.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_2.properties_out: fs.econ.side_2.properties_out State Released.
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_2: Initialization Complete
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2021-03-03 18:47:00 [INFO] idaes.init.fs.econ.side_2.properties_in: fs.econ.side_2.properties_in State Released.
2021-03-03 18:47:00 [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: 3.162222726747968
1 -- optimal, objective: 0.8197881545980185
2 -- optimal, objective: 1.470496175685844
3 -- optimal, objective: 1.1898689454668425
4 -- optimal, objective: 6.266875727768326
5 -- optimal, objective: 2.3538250377171823
6 -- optimal, objective: 0.5232313790289039
7 -- optimal, objective: 1.0234536307430704
8 -- optimal, objective: 1.6923868337123018
9 -- optimal, objective: 5.200209442856769
10 -- optimal, objective: 2.0256916107502394
11 -- optimal, objective: 1.375510820858698
12 -- optimal, objective: 1.804019216610838
13 -- optimal, objective: 1.08206173535119
14 -- optimal, objective: 2.8725608654848287
15 -- optimal, objective: 4.679395550949055
16 -- optimal, objective: 2.5285609881579614
17 -- optimal, objective: 3.4190895194024344
18 -- optimal, objective: 0.6733418552017972
19 -- optimal, objective: 1.3191361601576488
20 -- optimal, objective: 2.5910945384684085
21 -- optimal, objective: 0.728491791618817
22 -- optimal, objective: 3.096119847075016
23 -- optimal, objective: 8.046910612157816
24 -- optimal, objective: 9.43446787232504
25 -- optimal, objective: 2.9086993281997673
26 -- optimal, objective: 5.764857210566854
27 -- optimal, objective: 1.58699153385346
28 -- optimal, objective: 0.9849808635599673
29 -- optimal, objective: 5.4207155824345215
30 -- optimal, objective: 0.1606656770535343
31 -- optimal, objective: 1.9662708564310243
32 -- optimal, objective: 4.631964135793516
33 -- optimal, objective: 0.7898364826193093
34 -- optimal, objective: 4.935317631382524
35 -- optimal, objective: 2.78225472151281
36 -- optimal, objective: 3.793558504591668
37 -- optimal, objective: 7.39972780941562
38 -- optimal, objective: 1.8234865166601
39 -- optimal, objective: 8.123224199179202
40 -- optimal, objective: 2.46697459120451
41 -- optimal, objective: 2.0590147535300045
42 -- optimal, objective: 4.824860326020504
43 -- optimal, objective: 2.905357196069195
44 -- optimal, objective: 1.257333338473369
45 -- optimal, objective: 2.76265486871704
46 -- optimal, objective: 3.9105621874505854
47 -- optimal, objective: 0.3638511438811604
48 -- optimal, objective: 6.482070751314464
49 -- optimal, objective: 0.8862863572808333
50 -- optimal, objective: 0.3533327138629876
51 -- optimal, objective: 0.6741788395561827
52 -- optimal, objective: 1.446565966022411
53 -- optimal, objective: 2.365712477678524
54 -- optimal, objective: 1.4293043476045446
55 -- optimal, objective: 11.608878616087884
56 -- optimal, objective: 2.584558521815561
57 -- optimal, objective: 2.228038588968418
58 -- optimal, objective: 2.495375700856382
59 -- optimal, objective: 1.6473059536498238
60 -- optimal, objective: 8.024782999051054
61 -- optimal, objective: 5.943571679649568
62 -- optimal, objective: 2.335802980807593
63 -- optimal, objective: 4.385136256674274
64 -- optimal, objective: 0.5607930691618319
65 -- optimal, objective: 2.1768732856568835
66 -- optimal, objective: 2.823315149731952
67 -- optimal, objective: 4.396913088762367
68 -- optimal, objective: 3.3918328175085604
69 -- optimal, objective: 0.6148676050770127
70 -- optimal, objective: 0.3708290390409603
71 -- optimal, objective: 0.8762486395431996
72 -- optimal, objective: 3.008624266411604
73 -- optimal, objective: 6.178298889668614
74 -- optimal, objective: 2.4515810478691464
75 -- optimal, objective: 8.974784736396623
76 -- optimal, objective: 1.770689575521973
77 -- optimal, objective: 3.126540074941558
78 -- optimal, objective: 5.205287002120055
79 -- optimal, objective: 4.769621582501587
80 -- optimal, objective: 4.816642172570766
81 -- optimal, objective: 0.6532741094173582
82 -- optimal, objective: 2.4965287219127754
83 -- optimal, objective: 0.8032383968120292
84 -- optimal, objective: 0.3628374751580951
85 -- optimal, objective: 1.5238425496864934
86 -- optimal, objective: 3.8657617083925864
87 -- optimal, objective: 1.7222675119803528
88 -- optimal, objective: 3.953872372963456
89 -- optimal, objective: 1.6523626343497047
90 -- optimal, objective: 3.3511000648603217
91 -- optimal, objective: 1.2094028270637631
92 -- optimal, objective: 1.5787041255816434
93 -- optimal, objective: 3.4104171739555547
94 -- optimal, objective: 1.2638821516690988
95 -- optimal, objective: 3.295021190107257
96 -- optimal, objective: 1.5307192842206216
97 -- optimal, objective: 2.0576184713663865
98 -- optimal, objective: 1.7332046587097525
99 -- optimal, objective: 4.588279548069923
100 -- optimal, objective: 0.9295043769734126
101 -- optimal, objective: 1.1035467025832209
102 -- optimal, objective: 0.005403092725190978
103 -- optimal, objective: 4.030370198029115
104 -- optimal, objective: 2.5977866074242697
105 -- optimal, objective: 3.7186375390922226
106 -- optimal, objective: 2.220008221990124
107 -- optimal, objective: 1.7361606413580666
108 -- optimal, objective: 1.7827907915253882
109 -- optimal, objective: 0.8012179144633669
110 -- optimal, objective: 0.48908220135822317
111 -- optimal, objective: 4.625444642904321
112 -- optimal, objective: 4.073061803308539
113 -- optimal, objective: 4.984149658953359
114 -- optimal, objective: 4.500903765842314
115 -- optimal, objective: 0.8012381845209081
116 -- optimal, objective: 2.6875543787764764
117 -- optimal, objective: 6.864920838087304
118 -- optimal, objective: 3.037552232197139
119 -- optimal, objective: 2.4940980097073764
120 -- optimal, objective: 0.46083201829371145
121 -- optimal, objective: 0.04447225222365011
122 -- optimal, objective: 1.909211032156085
123 -- optimal, objective: 4.153938460441966
124 -- optimal, objective: 5.635804261323822
125 -- optimal, objective: 4.7223994896017265
126 -- optimal, objective: 4.838394177659147
127 -- optimal, objective: 2.8953995802787063
128 -- optimal, objective: 0.1700728987512572
129 -- optimal, objective: 0.9837915670309542
130 -- optimal, objective: 8.052258242765056
131 -- optimal, objective: 6.2603162943050155
132 -- optimal, objective: 2.572598330268942
133 -- optimal, objective: 3.7332013380678513
134 -- optimal, objective: 0.3400624609820808
135 -- optimal, objective: 3.603316160959041
136 -- optimal, objective: 2.501573096808961
137 -- optimal, objective: 0.39640424029669047
138 -- optimal, objective: 0.141403509224551
139 -- optimal, objective: 8.317311777960114
140 -- optimal, objective: 5.4244312679188464
141 -- optimal, objective: 2.83574216867205
142 -- optimal, objective: 1.5376013961506176
143 -- optimal, objective: 3.624196357700736
144 -- optimal, objective: 4.9547036262952275
145 -- optimal, objective: 0.5851595630069605
146 -- optimal, objective: 4.899572525361231
147 -- optimal, objective: 3.6822688057452084
148 -- optimal, objective: 2.1210898431019656
149 -- optimal, objective: 1.7199795815280758
150 -- optimal, objective: 3.3189125042286505
151 -- optimal, objective: 0.3685078573134288
152 -- optimal, objective: 1.9488329531202053
153 -- optimal, objective: 2.6747680809658476
154 -- optimal, objective: 7.585698103492058
155 -- optimal, objective: 3.3957385948343433
156 -- optimal, objective: 4.149632062900599
157 -- optimal, objective: 1.000138751954143
158 -- optimal, objective: 3.064483211734674
159 -- optimal, objective: 5.014021556677024
160 -- optimal, objective: 3.839818906127815
161 -- optimal, objective: 1.6576893499093415
162 -- optimal, objective: 0.41176973979165993
163 -- optimal, objective: 2.040678862860498
164 -- optimal, objective: 2.0029963443118493
165 -- optimal, objective: 2.5115043865189794
166 -- optimal, objective: 0.48257710490008476
167 -- optimal, objective: 3.8889325125122527
168 -- optimal, objective: 1.0769714540478792
169 -- optimal, objective: 2.4991940991342885
170 -- optimal, objective: 1.845218524340827
171 -- optimal, objective: 4.516275744333873
172 -- optimal, objective: 3.7259845773037887
173 -- optimal, objective: 1.9205831842368353
174 -- optimal, objective: 1.6040433482387257
175 -- optimal, objective: 0.329705992116415
176 -- optimal, objective: 3.177329255930121
177 -- optimal, objective: 4.892212873755818
178 -- optimal, objective: 1.7344211785701278
179 -- optimal, objective: 2.0930113767061425
180 -- optimal, objective: 1.9821944087033758
181 -- optimal, objective: 3.095063944359873
182 -- optimal, objective: 2.562516534216427
183 -- optimal, objective: 6.46989153194382
184 -- optimal, objective: 2.067460638680131
185 -- optimal, objective: 2.3845354622360735
186 -- optimal, objective: 1.5119923998654472
187 -- optimal, objective: 3.6254181568253823
188 -- optimal, objective: 0.9836625253930571
189 -- optimal, objective: 1.9174184223605648
190 -- optimal, objective: 1.0199853616407706
191 -- optimal, objective: 1.8111192038560597
192 -- optimal, objective: 10.407061899281672
193 -- optimal, objective: 5.7252437839675965
194 -- optimal, objective: 6.585188554630548
195 -- optimal, objective: 1.1404034774870133
196 -- optimal, objective: 4.636485739510397
197 -- optimal, objective: 3.921803798658291
198 -- optimal, objective: 1.0045607379024837
199 -- optimal, objective: 2.418194887917503
200 -- optimal, objective: 2.924381439171275
201 -- optimal, objective: 2.968995475733562
202 -- optimal, objective: 2.61528929652863
203 -- optimal, objective: 2.4914182112444854
204 -- optimal, objective: 1.7943475851127995
205 -- optimal, objective: 5.708324626596885
206 -- optimal, objective: 2.405605529769485
207 -- optimal, objective: 0.9383166249962259
208 -- optimal, objective: 4.796686075011132
209 -- optimal, objective: 0.5067752382993186
210 -- optimal, objective: 2.1890706012206813
211 -- optimal, objective: 3.2162721207001193
212 -- optimal, objective: 0.07970309825956173
213 -- optimal, objective: 0.39071980305707377
214 -- optimal, objective: 4.02397171505367
215 -- optimal, objective: 3.5942477203080117
216 -- optimal, objective: 1.6777755212887788
217 -- optimal, objective: 4.848035154404844
218 -- optimal, objective: 0.48854638442716647
219 -- optimal, objective: 12.374531482863102
220 -- optimal, objective: 1.4283906796283696
221 -- optimal, objective: 1.8180474372486768
222 -- optimal, objective: 0.48501814714993935
223 -- optimal, objective: 2.5067704521200924
224 -- optimal, objective: 1.3976831205728764
225 -- optimal, objective: 0.9031827797633734
226 -- optimal, objective: 0.72855979869843
227 -- optimal, objective: 2.470420726707512
228 -- optimal, objective: 2.6750989066859323
229 -- optimal, objective: 3.3257056456052108
230 -- optimal, objective: 2.599052712779955
231 -- optimal, objective: 4.837619200685889
232 -- optimal, objective: 1.132937434663585
233 -- optimal, objective: 1.6398640882825928
234 -- optimal, objective: 3.0089508719252733
235 -- optimal, objective: 1.4124059496646542
236 -- optimal, objective: 5.7719654075990094
237 -- optimal, objective: 0.1493818927224376
238 -- optimal, objective: 1.2057413172019444
239 -- optimal, objective: 1.7168330910787672
240 -- optimal, objective: 4.602205543920195
241 -- optimal, objective: 2.123645709357305
242 -- optimal, objective: 2.5316135514752443
243 -- optimal, objective: 1.7031605794315978
244 -- optimal, objective: 2.2177892333102287
245 -- optimal, objective: 0.6465633467363466
246 -- optimal, objective: 1.2916378800472939
247 -- optimal, objective: 7.790239583323649
248 -- optimal, objective: 1.0605735856125913
249 -- optimal, objective: 1.1514839068115028

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 [ ]: