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.core.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.models_extra.power_generation.properties.flue_gas_ideal import FlueGasParameterBlock
from idaes.models.properties import iapws95
from idaes.models_extra.power_generation.unit_models.boiler_heat_exchanger import (
    BoilerHeatExchanger, 
    TubeArrangement, 
    HeatExchangerFlowPattern
)
import pyomo.environ as pyo

In [5]:

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

m.fs.econ = BoilerHeatExchanger(
    cold_side={"property_package": m.fs.prop_water,
               "has_pressure_change": True},
    hot_side={"property_package": m.fs.prop_fluegas,
              "has_pressure_change": True},
    has_holdup=False,
    flow_pattern=HeatExchangerFlowPattern.countercurrent,
    tube_arrangement=TubeArrangement.inLine,
    cold_side_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.cold_side_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.econ.cold_side_inlet.enth_mol[0].fix(h) #J/mol         
m.fs.econ.cold_side_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.hot_side.properties_in[0].flow_mol_comp[c].fix(fg_rate*fg_comp[c])    
m.fs.econ.hot_side_inlet.temperature[0].fix(682.335)  # K
m.fs.econ.hot_side_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.cold_side_inlet.flow_mol[0].value,
        "pressure": m.fs.econ.cold_side_inlet.pressure[0].value,
        "enth_mol": m.fs.econ.cold_side_inlet.enth_mol[0].value,
    },
    state_args_2={
        "flow_component":{
            "H2O": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "H2O"].value,
            "CO2": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "CO2"].value,
            "N2": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "N2"].value,
            "O2": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "O2"].value,
            "NO": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "NO"].value,
            "SO2": m.fs.econ.hot_side_inlet.flow_mol_comp[0, "SO2"].value,
        },
        "temperature": m.fs.econ.hot_side_inlet.temperature[0].value,
        "pressure": m.fs.econ.hot_side_inlet.pressure[0].value,
    }
)

2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.cold_side: Initialization Complete
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.hot_side.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.hot_side.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.hot_side.properties_out: fs.econ.hot_side.properties_out State Released.
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.hot_side: Initialization Complete
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2023-03-04 01:31:56 [INFO] idaes.init.fs.econ.hot_side.properties_in: fs.econ.hot_side.properties_in State Released.
2023-03-04 01:31:56 [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()

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.cold_side.properties_out[:].flow_mol"
df_meta["ECON_OUT_T"]["reference_string"] = "m.fs.econ.cold_side.properties_out[:].temperature"
df_meta["ECON_OUT_P"]["reference_string"] = "m.fs.econ.cold_side.properties_out[:].pressure"
df_meta["BFW_F"]["reference_string"] = "m.fs.econ.cold_side.properties_in[:].flow_mol"
df_meta["BFW_T"]["reference_string"] = "m.fs.econ.cold_side.properties_in[:].temperature"
df_meta["BFW_P"]["reference_string"] = "m.fs.econ.cold_side.properties_in[:].pressure"
df_meta["FG_2_ECON_Fm"]["reference_string"] = "m.fs.econ.hot_side.properties_in[:].flow_mass"
df_meta["FG_2_ECON_T"]["reference_string"] = "m.fs.econ.hot_side.properties_in[:].temperature"
df_meta["FG_2_ECON_P"]["reference_string"] = "m.fs.econ.hot_side.properties_in[:].pressure"
df_meta["FG_2_AIRPH_Fm"]["reference_string"] = "m.fs.econ.hot_side.properties_out[:].flow_mass"
df_meta["FG_2_AIRPH_T"]["reference_string"] = "m.fs.econ.hot_side.properties_out[:].temperature"
df_meta["FG_2_AIRPH_P"]["reference_string"] = "m.fs.econ.hot_side.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
from idaes.core.util.tags import ModelTagGroup

# 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.cold_side_inlet,
        "ECON_OUT": m.fs.econ.cold_side_outlet,
        "FG_2_ECON": m.fs.econ.hot_side_inlet,
        "FG_2_AIRPH": m.fs.econ.hot_side_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 = ModelTagGroup()

prop_dict = {
    "flow_mass": "_Fm",
    "flow_mol": "_F",
    "enth_mol": "_h",
    "temperature": "_T",
    "pressure": "_P",
}
comp_list = ["O2", "NO", "N2", "SO2", "CO2", "H2O"]

for state, block in state_dict.items():
    for prop, suffix in prop_dict.items():
        comp = getattr(block, prop)
        recon_tags.add(expr=comp, name=state+suffix, format_string="{:.3f}")
    # Add tags for molar flow rates of each component
    for j in comp_list:
        # Not all components appear in all streams
        try:
            comp = block.flow_mol_comp[j]
            recon_tags.add(expr=comp, name=f"{state}_F[{j}]", format_string="{:.3f}")
        except KeyError:
            pass

# Any addtional tags can be added.  This is required for tags that cannot be systematically generated 
# from the model streams.
recon_tags.add(expr=m.fs.econ.heat_duty[0], name="ECON_Q", format_string="{:.3f}")

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.tags import svg_tag  # utility to place numbers/text in an SVG

with open("econ.svg", "r") as f:
    s = svg_tag(svg=f, tag_group=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.hot_side.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.cold_side_inlet.unfix()
m.fs.econ.hot_side_inlet.unfix()
m.fs.econ.cold_side_outlet.unfix()
m.fs.econ.hot_side_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].expression)
    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: 3.1622331890495903
1 -- optimal, objective: 0.8197864499890314
2 -- optimal, objective: 1.4705020498257433
3 -- optimal, objective: 1.1898579077047484
4 -- optimal, objective: 6.266862831652643
5 -- optimal, objective: 2.353837799416942
6 -- optimal, objective: 0.5232270065114984
7 -- optimal, objective: 1.0234628569514321
8 -- optimal, objective: 1.692397720851685
9 -- optimal, objective: 5.200192745852479
10 -- optimal, objective: 2.025697843022476
11 -- optimal, objective: 1.3755022829202932
12 -- optimal, objective: 1.8040084546445863
13 -- optimal, objective: 1.0820697968578374
14 -- optimal, objective: 2.872565777305556
15 -- optimal, objective: 4.67937799614271
16 -- optimal, objective: 2.528568205492165
17 -- optimal, objective: 3.419105635591174
18 -- optimal, objective: 0.6733502043659465
19 -- optimal, objective: 1.3191453351997167
20 -- optimal, objective: 2.5910789518941666
21 -- optimal, objective: 0.7284892511624388
22 -- optimal, objective: 3.0961354376473573
23 -- optimal, objective: 8.046924273772184
24 -- optimal, objective: 9.434482098827047
25 -- optimal, objective: 2.9087156182745018
26 -- optimal, objective: 5.764858402612364
27 -- optimal, objective: 1.586994733305022
28 -- optimal, objective: 0.9849858467550563
29 -- optimal, objective: 5.420724866466431
30 -- optimal, objective: 0.15987314723602114
31 -- optimal, objective: 1.966274545593537
32 -- optimal, objective: 4.631981600955086
33 -- optimal, objective: 0.7898383615771404
34 -- optimal, objective: 4.9353180306590225
35 -- optimal, objective: 2.782272921404692
36 -- optimal, objective: 3.7935361234633205
37 -- optimal, objective: 7.39974416375716
38 -- optimal, objective: 1.8234832495958384
39 -- optimal, objective: 8.12319775531671
40 -- optimal, objective: 2.466967374172533
41 -- optimal, objective: 2.058995669731764
42 -- optimal, objective: 4.824845773329273
43 -- optimal, objective: 2.905354510994933
44 -- optimal, objective: 1.2573498031484729
45 -- optimal, objective: 2.762659514639501
46 -- optimal, objective: 3.9105414166260903
47 -- optimal, objective: 0.3638539213532054
48 -- optimal, objective: 6.48204512467072
49 -- optimal, objective: 0.8862853314576087
50 -- optimal, objective: 0.3533301795603448
51 -- optimal, objective: 0.6741716772662831
52 -- optimal, objective: 1.4465656566076062
53 -- optimal, objective: 2.365722448400615
54 -- optimal, objective: 1.4293144956083175
55 -- optimal, objective: 11.60889957738345
56 -- optimal, objective: 2.5845585147163397
57 -- optimal, objective: 2.228041896062202
58 -- optimal, objective: 2.4953667573534735
59 -- optimal, objective: 1.647314373365076
60 -- optimal, objective: 8.024762155447666
61 -- optimal, objective: 5.943580608761248
62 -- optimal, objective: 2.3358112651341743
63 -- optimal, objective: 4.38513490110046
64 -- optimal, objective: 0.5607991758545512
65 -- optimal, objective: 2.176886090478235
66 -- optimal, objective: 2.8233305625187795
67 -- optimal, objective: 4.396916342718716
68 -- optimal, objective: 3.391821500174123
69 -- optimal, objective: 0.614861768709231
70 -- optimal, objective: 0.3708295031059437
71 -- optimal, objective: 0.876241026808678
72 -- optimal, objective: 3.008619356231868
73 -- optimal, objective: 6.178310252873772
74 -- optimal, objective: 2.451573865746587
75 -- optimal, objective: 8.974808392536618
76 -- optimal, objective: 1.770701321328788
77 -- optimal, objective: 3.1265504086289444
78 -- optimal, objective: 5.203564818159552
79 -- optimal, objective: 4.769633196273789
80 -- optimal, objective: 4.816640912308049
81 -- optimal, objective: 0.653270596556715
82 -- optimal, objective: 2.4965339056024445
83 -- optimal, objective: 0.8032403793218241
84 -- optimal, objective: 0.3628436163258187
85 -- optimal, objective: 1.5238517213119334
86 -- optimal, objective: 3.865748917190463
87 -- optimal, objective: 1.7222638616761394
88 -- optimal, objective: 3.953870122426233
89 -- optimal, objective: 1.6523633158686517
90 -- optimal, objective: 3.3511178021618955
91 -- optimal, objective: 1.2094064053344298
92 -- optimal, objective: 1.578703926570243
93 -- optimal, objective: 3.4104161322803077
94 -- optimal, objective: 1.2638744445651577
95 -- optimal, objective: 3.295026970052376
96 -- optimal, objective: 1.5307297912770716
97 -- optimal, objective: 2.057619546085194
98 -- optimal, objective: 1.733201919869821
99 -- optimal, objective: 4.588294007037179
100 -- optimal, objective: 0.9292950798611487
101 -- optimal, objective: 1.1035420871623796
102 -- optimal, objective: 0.0054034303983518895
103 -- optimal, objective: 4.03037968399287
104 -- optimal, objective: 2.5977953040667674
105 -- optimal, objective: 3.718627904476693
106 -- optimal, objective: 2.220011645610575
107 -- optimal, objective: 1.7361501009358982
108 -- optimal, objective: 1.7827888202876916
109 -- optimal, objective: 0.80122559579786
110 -- optimal, objective: 0.4890883099159153
111 -- optimal, objective: 4.625468290421027
112 -- optimal, objective: 4.073067561398391
113 -- optimal, objective: 4.984142249931269
114 -- optimal, objective: 4.500896627466857
115 -- optimal, objective: 0.8012366493659453
116 -- optimal, objective: 2.687559753925411
117 -- optimal, objective: 6.864914207638007
118 -- optimal, objective: 3.0375383483442926
119 -- optimal, objective: 2.4940926825731284
120 -- optimal, objective: 0.4608312841132002
121 -- optimal, objective: 0.044472703115553146
122 -- optimal, objective: 1.9092249228761018
123 -- optimal, objective: 4.153943649844279
124 -- optimal, objective: 5.635795985484567
125 -- optimal, objective: 4.722375449559023
126 -- optimal, objective: 4.837800008333984
127 -- optimal, objective: 2.8954190363534136
128 -- optimal, objective: 0.1700741811184426
129 -- optimal, objective: 0.9837965852424274
130 -- optimal, objective: 8.052261850607346
131 -- optimal, objective: 6.260300019995981
132 -- optimal, objective: 2.572578545638929
133 -- optimal, objective: 3.7331869855918605
134 -- optimal, objective: 0.3400612362222525
135 -- optimal, objective: 3.6033342258730423
136 -- optimal, objective: 2.5015732182201575
137 -- optimal, objective: 0.39639975765004987
138 -- optimal, objective: 0.14140324820957903
139 -- optimal, objective: 8.317346638087258
140 -- optimal, objective: 5.424422727514848
141 -- optimal, objective: 2.8357278805421795
142 -- optimal, objective: 1.5376133193671455
143 -- optimal, objective: 3.62420847455168
144 -- optimal, objective: 4.95468987699023
145 -- optimal, objective: 0.5851604096299909
146 -- optimal, objective: 4.899590933174681
147 -- optimal, objective: 3.682270094664581
148 -- optimal, objective: 2.121080967168293
149 -- optimal, objective: 1.7199975728803218
150 -- optimal, objective: 3.3189081004099528
151 -- optimal, objective: 0.36850247207838444
152 -- optimal, objective: 1.948843909757939
153 -- optimal, objective: 2.6747587962823256
154 -- optimal, objective: 7.5857184235589985
155 -- optimal, objective: 3.3957385323820666
156 -- optimal, objective: 4.149647701070497
157 -- optimal, objective: 1.0001442053929916
158 -- optimal, objective: 3.064493879763522
159 -- optimal, objective: 5.014035878816116
160 -- optimal, objective: 3.8397987755888137
161 -- optimal, objective: 1.6576931969835833
162 -- optimal, objective: 0.4117628605308926
163 -- optimal, objective: 2.0406760523470697
164 -- optimal, objective: 2.00299564496912
165 -- optimal, objective: 2.5115163652865116
166 -- optimal, objective: 0.4825712086517368
167 -- optimal, objective: 3.888910896308239
168 -- optimal, objective: 1.0769836582038614
169 -- optimal, objective: 2.4991945390851953
170 -- optimal, objective: 1.845216182624875
171 -- optimal, objective: 4.5162931330312786
172 -- optimal, objective: 3.7260015810683855
173 -- optimal, objective: 1.9205761596254298
174 -- optimal, objective: 1.6040412254147172
175 -- optimal, objective: 0.329705327804772
176 -- optimal, objective: 3.1773422885568405
177 -- optimal, objective: 4.892213973195785
178 -- optimal, objective: 1.7344107256429018
179 -- optimal, objective: 2.0929976586354795
180 -- optimal, objective: 1.982201826026842
181 -- optimal, objective: 3.0950888485043486
182 -- optimal, objective: 2.5625036101031307
183 -- optimal, objective: 6.469916654594622
184 -- optimal, objective: 2.067453311742428
185 -- optimal, objective: 2.3845301568016093
186 -- optimal, objective: 1.5120049498654422
187 -- optimal, objective: 3.625438657158909
188 -- optimal, objective: 0.9836691585294073
189 -- optimal, objective: 1.9174264005471389
190 -- optimal, objective: 1.0199757612465605
191 -- optimal, objective: 1.8111213854884887
192 -- optimal, objective: 10.40708854331168
193 -- optimal, objective: 5.725259035852611
194 -- optimal, objective: 6.585221622378499
195 -- optimal, objective: 1.140414780445981
196 -- optimal, objective: 4.636480679503139
197 -- optimal, objective: 3.9218197675248376
198 -- optimal, objective: 1.0045560725784408
199 -- optimal, objective: 2.4181848045168044
200 -- optimal, objective: 2.9243929060255587
201 -- optimal, objective: 2.969005091737908
202 -- optimal, objective: 2.615291414013147
203 -- optimal, objective: 2.4914226639464307
204 -- optimal, objective: 1.7943475807253635
205 -- optimal, objective: 5.708343478588351
206 -- optimal, objective: 2.4056070209689806
207 -- optimal, objective: 0.9383083089043902
208 -- optimal, objective: 4.796697378270856
209 -- optimal, objective: 0.5067761258605348
210 -- optimal, objective: 2.189061857466013
211 -- optimal, objective: 3.2162690886396597
212 -- optimal, objective: 0.07970527067968351
213 -- optimal, objective: 0.3907213231728188
214 -- optimal, objective: 4.023957133776389
215 -- optimal, objective: 3.5942319390503137
216 -- optimal, objective: 1.6777705156089673
217 -- optimal, objective: 4.848036844041122
218 -- optimal, objective: 0.4885522475247492
219 -- optimal, objective: 12.37451227722671
220 -- optimal, objective: 1.4283806999185058
221 -- optimal, objective: 1.8180497328202705
222 -- optimal, objective: 0.4850228697954107
223 -- optimal, objective: 2.506763240151633
224 -- optimal, objective: 1.3976840129134172
225 -- optimal, objective: 0.9031881755465401
226 -- optimal, objective: 0.7285671677648223
227 -- optimal, objective: 2.470435148231497
228 -- optimal, objective: 2.675081338576942
229 -- optimal, objective: 3.3257208414747335
230 -- optimal, objective: 2.599060260920109
231 -- optimal, objective: 4.83762577330625
232 -- optimal, objective: 1.1329442637595963
233 -- optimal, objective: 1.639875911401635
234 -- optimal, objective: 3.008934968366903
235 -- optimal, objective: 1.4124067533104043
236 -- optimal, objective: 5.7719491959694
237 -- optimal, objective: 0.1493783831652131
238 -- optimal, objective: 1.2057382957613423
239 -- optimal, objective: 1.7168431018295964
240 -- optimal, objective: 4.60219948744476
241 -- optimal, objective: 2.123639453209505
242 -- optimal, objective: 2.531625086777071
243 -- optimal, objective: 1.7031702437789407
244 -- optimal, objective: 2.217786898491411
245 -- optimal, objective: 0.6465620718112349
246 -- optimal, objective: 1.291638547305462
247 -- optimal, objective: 7.789842761895717
248 -- optimal, objective: 1.0605811788975477
249 -- optimal, objective: 1.151459058786545

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 [ ]: