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,
    }
)

2021-09-02 15:58:15 [INFO] idaes.init.fs.econ.side_1: Initialization Complete
2021-09-02 15:58:15 [INFO] idaes.init.fs.econ.side_2.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2021-09-02 15:58:16 [INFO] idaes.init.fs.econ.side_2.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2021-09-02 15:58:16 [INFO] idaes.init.fs.econ.side_2.properties_out: fs.econ.side_2.properties_out State Released.
2021-09-02 15:58:16 [INFO] idaes.init.fs.econ.side_2: Initialization Complete
2021-09-02 15:58:16 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2021-09-02 15:58:16 [INFO] idaes.init.fs.econ.side_2.properties_in: fs.econ.side_2.properties_in State Released.
2021-09-02 15:58:16 [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")

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: 0.8197881540804665
2 -- optimal, objective: 1.4704961756860009
3 -- optimal, objective: 1.1898683973939073
4 -- optimal, objective: 6.266875727768015
5 -- optimal, objective: 2.353825037717043
6 -- optimal, objective: 0.5232293871180911
7 -- optimal, objective: 1.0234536307431457
8 -- optimal, objective: 1.6923868337124404
9 -- optimal, objective: 5.2001791228894945
10 -- optimal, objective: 2.0256916107501506
11 -- optimal, objective: 1.3755108208586757
12 -- optimal, objective: 1.8040192166107314
13 -- optimal, objective: 1.0820617353510786
14 -- optimal, objective: 2.872560865484746
15 -- optimal, objective: 4.679395550949352
16 -- optimal, objective: 2.5285609881579645
17 -- optimal, objective: 3.419089519402572
18 -- optimal, objective: 0.673341855201661
19 -- optimal, objective: 1.3191361601576406
20 -- optimal, objective: 2.591094538468207
21 -- optimal, objective: 0.7284917916188187
22 -- optimal, objective: 3.0961198470749545
23 -- optimal, objective: 8.046910612157626
24 -- optimal, objective: 9.43446787232482
25 -- optimal, objective: 2.90869932819942
26 -- optimal, objective: 5.764857210566872
27 -- optimal, objective: 1.5869915338535017
28 -- optimal, objective: 0.9849808635599643
29 -- optimal, objective: 5.420715582434442
30 -- optimal, objective: 0.15987321041189692
31 -- optimal, objective: 1.9662708564310052
32 -- optimal, objective: 4.631964135793527
33 -- optimal, objective: 0.7898364826192953
34 -- optimal, objective: 4.935317631382527
35 -- optimal, objective: 2.782254721512846
36 -- optimal, objective: 3.793558504591789
37 -- optimal, objective: 7.399727809415612
38 -- optimal, objective: 1.8234865166600738
39 -- optimal, objective: 8.123224199178962
40 -- optimal, objective: 2.4669745912045187
41 -- optimal, objective: 2.0590147462740016
42 -- optimal, objective: 4.824860326020595
43 -- optimal, objective: 2.9053571960692355
44 -- optimal, objective: 1.2573333384737084
45 -- optimal, objective: 2.7626548687168437
46 -- optimal, objective: 3.9105621874505987
47 -- optimal, objective: 0.36385114388096135
48 -- optimal, objective: 6.48207075131405
49 -- optimal, objective: 0.8862863572807927
50 -- optimal, objective: 0.35333271386302767
51 -- optimal, objective: 0.6741788395561905
52 -- optimal, objective: 1.4465659660224153
53 -- optimal, objective: 2.365712477678529
54 -- optimal, objective: 1.4293043476046117
55 -- optimal, objective: 11.608878616087802
56 -- optimal, objective: 2.58455852181556
57 -- optimal, objective: 2.228038588968435
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: 4.385136256674179
64 -- optimal, objective: 0.5607930691618417
65 -- optimal, objective: 2.1768732856567903
66 -- optimal, objective: 2.8233151497317923
67 -- optimal, objective: 4.396913088762424
68 -- optimal, objective: 3.391832817508344
69 -- optimal, objective: 0.6148676050767218
70 -- optimal, objective: 0.3708290390409646
71 -- optimal, objective: 0.8762486395429888
72 -- optimal, objective: 3.0086242664115774
73 -- optimal, objective: 6.178298889668418
74 -- optimal, objective: 2.4515810478692264
75 -- optimal, objective: 8.97478473639633
76 -- optimal, objective: 1.7706895755220056
77 -- optimal, objective: 3.1265400749414534
78 -- optimal, objective: 5.203571840723421
79 -- optimal, objective: 4.769621582501686
80 -- optimal, objective: 4.816642172570757
81 -- optimal, objective: 0.653274109417307
82 -- optimal, objective: 2.4965287219119565
83 -- optimal, objective: 0.8032383968120483
84 -- optimal, objective: 0.3628374751580809
85 -- optimal, objective: 1.523842549686509
86 -- optimal, objective: 3.8657617083927285
87 -- optimal, objective: 1.7222675119802968
88 -- optimal, objective: 3.9538723729634717
89 -- optimal, objective: 1.65236263434971
90 -- optimal, objective: 3.351100064860052
91 -- optimal, objective: 1.2094028270637767
92 -- optimal, objective: 1.5787041255816414
93 -- optimal, objective: 3.4104171739555014
94 -- optimal, objective: 1.2638821516691674
95 -- optimal, objective: 3.295021190107275
96 -- optimal, objective: 1.5307192842207231
97 -- optimal, objective: 2.0576184713664
98 -- optimal, objective: 1.7332046587097982
99 -- optimal, objective: 4.58827941036682
100 -- optimal, objective: 0.9293015277967474
101 -- optimal, objective: 1.1035467025831935
102 -- optimal, objective: 0.005403092725190185
103 -- optimal, objective: 4.030370198029041
104 -- optimal, objective: 2.5977866074240206
105 -- optimal, objective: 3.7186375390924087
106 -- optimal, objective: 2.2200082219901534
107 -- optimal, objective: 1.736160641358132
108 -- optimal, objective: 1.7827907915253507
109 -- optimal, objective: 0.8012179144633598
110 -- optimal, objective: 0.48908220135812036
111 -- optimal, objective: 4.625444642903938
112 -- optimal, objective: 4.07306180330844
113 -- optimal, objective: 4.984149658953242
114 -- optimal, objective: 4.500903765842288
115 -- optimal, objective: 0.8012381845209076
116 -- optimal, objective: 2.687554378776392
117 -- optimal, objective: 6.864920838087276
118 -- optimal, objective: 3.0375522321897814
119 -- optimal, objective: 2.4940980097073884
120 -- optimal, objective: 0.46083201829370657
121 -- optimal, objective: 0.04447225222365364
122 -- optimal, objective: 1.9092110321559406
123 -- optimal, objective: 4.153938460441821
124 -- optimal, objective: 5.635804261323757
125 -- optimal, objective: 4.722399489601871
126 -- optimal, objective: 4.837813299841362
127 -- optimal, objective: 2.8953995802785957
128 -- optimal, objective: 0.17007289875026932
129 -- optimal, objective: 0.983791567030946
130 -- optimal, objective: 8.052254099295862
131 -- optimal, objective: 6.2603162943051345
132 -- optimal, objective: 2.572598330268635
133 -- optimal, objective: 3.733201338067713
134 -- optimal, objective: 0.3400624609820915
135 -- optimal, objective: 3.6033161609589324
136 -- optimal, objective: 2.5015730968089547
137 -- optimal, objective: 0.39640424029665267
138 -- optimal, objective: 0.141403509224298
139 -- optimal, objective: 8.31731177795957
140 -- optimal, objective: 5.4244312679188464
141 -- optimal, objective: 2.835742168672142
142 -- optimal, objective: 1.5376013961506825
143 -- optimal, objective: 3.624196357700532
144 -- optimal, objective: 4.954703626295084
145 -- optimal, objective: 0.585159563006968
146 -- optimal, objective: 4.8995725253608935
147 -- optimal, objective: 3.6822688057449238
148 -- optimal, objective: 2.1210898431019127
149 -- optimal, objective: 1.7199795815279169
150 -- optimal, objective: 3.318912504228596
151 -- optimal, objective: 0.36850785731333546
152 -- optimal, objective: 1.9488329531202324
153 -- optimal, objective: 2.674768080965982
154 -- optimal, objective: 7.5856981034922
155 -- optimal, objective: 3.395738594834346
156 -- optimal, objective: 4.149632062900452
157 -- optimal, objective: 1.000138751954185
158 -- optimal, objective: 3.064483211734531
159 -- optimal, objective: 5.0140215566768225
160 -- optimal, objective: 3.83981890612392
161 -- optimal, objective: 1.657689349909335
162 -- optimal, objective: 0.41176973979173737
163 -- optimal, objective: 2.040678862856759
164 -- optimal, objective: 2.0029963443118484
165 -- optimal, objective: 2.511504386519103
166 -- optimal, objective: 0.4825771048999518
167 -- optimal, objective: 3.8889325125121696
168 -- optimal, objective: 1.0769714540447235
169 -- optimal, objective: 2.499194099134276
170 -- optimal, objective: 1.8452022889718802
171 -- optimal, objective: 4.5162757443335515
172 -- optimal, objective: 3.725984577303651
173 -- optimal, objective: 1.9205831842368086
174 -- optimal, objective: 1.6040433482387828
175 -- optimal, objective: 0.3297059921164121
176 -- optimal, objective: 3.17732925593057
177 -- optimal, objective: 4.892212873755828
178 -- optimal, objective: 1.7344211222125767
179 -- optimal, objective: 2.0930113767062535
180 -- optimal, objective: 1.982194408703398
181 -- optimal, objective: 3.095063944360138
182 -- optimal, objective: 2.5625165342165928
183 -- optimal, objective: 6.469891429283564
184 -- optimal, objective: 2.0674606386801786
185 -- optimal, objective: 2.3845354622360593
186 -- optimal, objective: 1.511992388747981
187 -- optimal, objective: 3.625418156825077
188 -- optimal, objective: 0.9836625190091582
189 -- optimal, objective: 1.9174184223605604
190 -- optimal, objective: 1.0199853616407286
191 -- optimal, objective: 1.8111192038560244
192 -- optimal, objective: 10.407061899274446
193 -- optimal, objective: 5.725243783932939
194 -- optimal, objective: 6.5851885546307
195 -- optimal, objective: 1.1404034774868907
196 -- optimal, objective: 4.63648573951036
197 -- optimal, objective: 3.921803798658364
198 -- optimal, objective: 1.004560737902494
199 -- optimal, objective: 2.418194887917387
200 -- optimal, objective: 2.924381439171225
201 -- optimal, objective: 2.968995475733458
202 -- optimal, objective: 2.615289296528611
203 -- optimal, objective: 2.4914182112444974
204 -- optimal, objective: 1.7943475851127992
205 -- optimal, objective: 5.7083246265968395
206 -- optimal, objective: 2.4056055297694683
207 -- optimal, objective: 0.9383160093488742
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: 4.02397171505382
215 -- optimal, objective: 3.594247720308196
216 -- optimal, objective: 1.6777755011210225
217 -- optimal, objective: 4.848035154404865
218 -- optimal, objective: 0.48854638442723286
219 -- optimal, objective: 12.374531482863176
220 -- optimal, objective: 1.428390679628554
221 -- optimal, objective: 1.8180474372486606
222 -- optimal, objective: 0.4850181471500386
223 -- optimal, objective: 2.506770452120046
224 -- optimal, objective: 1.3976831205728917
225 -- optimal, objective: 0.9031827797634286
226 -- optimal, objective: 0.7285597986984917
227 -- optimal, objective: 2.4704207267075544
228 -- optimal, objective: 2.6750989066858013
229 -- optimal, objective: 3.3257056456053364
230 -- optimal, objective: 2.599052712780132
231 -- optimal, objective: 4.837619200685974
232 -- optimal, objective: 1.1329374346636611
233 -- optimal, objective: 1.6398640882824427
234 -- optimal, objective: 3.0089508719252076
235 -- optimal, objective: 1.4124059496646608
236 -- optimal, objective: 5.7719654075989295
237 -- optimal, objective: 0.14938189272240587
238 -- optimal, objective: 1.2057413172016875
239 -- optimal, objective: 1.7168330910787664
240 -- optimal, objective: 4.602205543920224
241 -- optimal, objective: 2.123631117523288
242 -- optimal, objective: 2.531613551475251
243 -- optimal, objective: 1.7031605794317395
244 -- optimal, objective: 2.2177892333102562
245 -- optimal, objective: 0.6465633467363429
246 -- optimal, objective: 1.291637880047304
247 -- optimal, objective: 7.789851988626017
248 -- optimal, objective: 1.0605735856125036
249 -- optimal, objective: 1.151469126514051

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 [ ]: