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,
    }
)

2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_1: Initialization Complete
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_2.properties_in: Initialisation Complete, optimal - Optimal Solution Found.
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_2.properties_out: Initialisation Complete, optimal - Optimal Solution Found.
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_2.properties_out: fs.econ.side_2.properties_out State Released.
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_2: Initialization Complete
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ: fs.econ Initialisation Step 1 Complete.
2021-08-25 20:10:18 [INFO] idaes.init.fs.econ.side_2.properties_in: fs.econ.side_2.properties_in State Released.
2021-08-25 20:10:18 [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: 3.162222726747723
1 -- optimal, objective: 0.8197881540804663
2 -- optimal, objective: 1.4704961756860007
3 -- optimal, objective: 1.189868397393907
4 -- optimal, objective: 6.2668757277680145
5 -- optimal, objective: 2.353825037717043
6 -- optimal, objective: 0.5232293871180911
7 -- optimal, objective: 1.0234536307431459
8 -- optimal, objective: 1.6923868337124404
9 -- optimal, objective: 5.2001791228894945
10 -- optimal, objective: 2.02569161075015
11 -- optimal, objective: 1.3755108208586757
12 -- optimal, objective: 1.8040192166107316
13 -- optimal, objective: 1.0820617353510784
14 -- optimal, objective: 2.8725608654847457
15 -- optimal, objective: 4.679395550949352
16 -- optimal, objective: 2.528560988157964
17 -- optimal, objective: 3.419089519402572
18 -- optimal, objective: 0.6733418552016611
19 -- optimal, objective: 1.3191361601576406
20 -- optimal, objective: 2.5910945384682056
21 -- optimal, objective: 0.7284917916188188
22 -- optimal, objective: 3.096119847074955
23 -- optimal, objective: 8.046910612157625
24 -- optimal, objective: 9.43446787232482
25 -- optimal, objective: 2.9086993281994196
26 -- optimal, objective: 5.764857210566871
27 -- optimal, objective: 1.5869915338535017
28 -- optimal, objective: 0.9849808635599643
29 -- optimal, objective: 5.420715582434443
30 -- optimal, objective: 0.1598732104118969
31 -- optimal, objective: 1.9662708564310052
32 -- optimal, objective: 4.631964135793527
33 -- optimal, objective: 0.7898364826192952
34 -- optimal, objective: 4.935317631382528
35 -- optimal, objective: 2.782254721512846
36 -- optimal, objective: 3.7935585045917892
37 -- optimal, objective: 7.3997278094156105
38 -- optimal, objective: 1.8234865166600738
39 -- optimal, objective: 8.12322419917896
40 -- optimal, objective: 2.4669745912045187
41 -- optimal, objective: 2.059014746274002
42 -- optimal, objective: 4.824860326020595
43 -- optimal, objective: 2.905357196069236
44 -- optimal, objective: 1.2573333384737082
45 -- optimal, objective: 2.762654868716844
46 -- optimal, objective: 3.9105621874505982
47 -- optimal, objective: 0.3638511438809614
48 -- optimal, objective: 6.482070751314051
49 -- optimal, objective: 0.8862863572807927
50 -- optimal, objective: 0.3533327138630277
51 -- optimal, objective: 0.6741788395561906
52 -- optimal, objective: 1.4465659660224157
53 -- optimal, objective: 2.3657124776785285
54 -- optimal, objective: 1.4293043476046114
55 -- optimal, objective: 11.608878616087802
56 -- optimal, objective: 2.5845585218155596
57 -- optimal, objective: 2.228038588968436
58 -- optimal, objective: 2.4953757008565054
59 -- optimal, objective: 1.6473059536498185
60 -- optimal, objective: 8.024782999051263
61 -- optimal, objective: 5.943571679649429
62 -- optimal, objective: 2.335802980807619
63 -- optimal, objective: 4.385136256674179
64 -- optimal, objective: 0.5607930691618417
65 -- optimal, objective: 2.1768732856567903
66 -- optimal, objective: 2.823315149731792
67 -- optimal, objective: 4.396913088762425
68 -- optimal, objective: 3.391832817508344
69 -- optimal, objective: 0.6148676050767216
70 -- optimal, objective: 0.37082903904096465
71 -- optimal, objective: 0.8762486395429889
72 -- optimal, objective: 3.0086242664115765
73 -- optimal, objective: 6.178298889668418
74 -- optimal, objective: 2.4515810478692264
75 -- optimal, objective: 8.97478473639633
76 -- optimal, objective: 1.7706895755220058
77 -- optimal, objective: 3.1265400749414534
78 -- optimal, objective: 5.203571840723419
79 -- optimal, objective: 4.769621582501686
80 -- optimal, objective: 4.816642172570757
81 -- optimal, objective: 0.6532741094173069
82 -- optimal, objective: 2.4965287219119565
83 -- optimal, objective: 0.8032383968120484
84 -- optimal, objective: 0.36283747515808096
85 -- optimal, objective: 1.5238425496865087
86 -- optimal, objective: 3.8657617083927276
87 -- optimal, objective: 1.7222675119802966
88 -- optimal, objective: 3.9538723729634717
89 -- optimal, objective: 1.6523626343497104
90 -- optimal, objective: 3.351100064860053
91 -- optimal, objective: 1.2094028270637767
92 -- optimal, objective: 1.5787041255816414
93 -- optimal, objective: 3.410417173955501
94 -- optimal, objective: 1.2638821516691674
95 -- optimal, objective: 3.2950211901072746
96 -- optimal, objective: 1.5307192842207231
97 -- optimal, objective: 2.057618471366399
98 -- optimal, objective: 1.733204658709798
99 -- optimal, objective: 4.58827941036682
100 -- optimal, objective: 0.9293015277967475
101 -- optimal, objective: 1.1035467025831933
102 -- optimal, objective: 0.005403092725190185
103 -- optimal, objective: 4.030370198029042
104 -- optimal, objective: 2.5977866074240206
105 -- optimal, objective: 3.718637539092409
106 -- optimal, objective: 2.2200082219901534
107 -- optimal, objective: 1.7361606413581323
108 -- optimal, objective: 1.7827907915253505
109 -- optimal, objective: 0.8012179144633597
110 -- optimal, objective: 0.48908220135812036
111 -- optimal, objective: 4.625444642903937
112 -- optimal, objective: 4.073061803308441
113 -- optimal, objective: 4.984149658953241
114 -- optimal, objective: 4.500903765842289
115 -- optimal, objective: 0.8012381845209074
116 -- optimal, objective: 2.687554378776392
117 -- optimal, objective: 6.864920838087275
118 -- optimal, objective: 3.037552232189781
119 -- optimal, objective: 2.494098009707388
120 -- optimal, objective: 0.4608320182937066
121 -- optimal, objective: 0.04447225222365364
122 -- optimal, objective: 1.9092110321559406
123 -- optimal, objective: 4.153938460441821
124 -- optimal, objective: 5.635804261323758
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: 8.05225409929586
131 -- optimal, objective: 6.260316294305136
132 -- optimal, objective: 2.5725983302686344
133 -- optimal, objective: 3.733201338067713
134 -- optimal, objective: 0.3400624609820915
135 -- optimal, objective: 3.603316160958933
136 -- optimal, objective: 2.501573096808955
137 -- optimal, objective: 0.3964042402966527
138 -- optimal, objective: 0.14140350922429804
139 -- optimal, objective: 8.317311777959569
140 -- optimal, objective: 5.424431267918848
141 -- optimal, objective: 2.835742168672142
142 -- optimal, objective: 1.5376013961506827
143 -- optimal, objective: 3.6241963577005314
144 -- optimal, objective: 4.954703626295083
145 -- optimal, objective: 0.5851595630069681
146 -- optimal, objective: 4.899572525360894
147 -- optimal, objective: 3.6822688057449238
148 -- optimal, objective: 2.1210898431019127
149 -- optimal, objective: 1.7199795815279166
150 -- optimal, objective: 3.3189125042285954
151 -- optimal, objective: 0.36850785731333535
152 -- optimal, objective: 1.9488329531202326
153 -- optimal, objective: 2.674768080965982
154 -- optimal, objective: 7.585698103492201
155 -- optimal, objective: 3.395738594834345
156 -- optimal, objective: 4.149632062900453
157 -- optimal, objective: 1.000138751954185
158 -- optimal, objective: 3.0644832117345313
159 -- optimal, objective: 5.014021556676822
160 -- optimal, objective: 3.8398189061239196
161 -- optimal, objective: 1.6576893499093353
162 -- optimal, objective: 0.41176973979173737
163 -- optimal, objective: 2.040678862856759
164 -- optimal, objective: 2.0029963443118484
165 -- optimal, objective: 2.5115043865191033
166 -- optimal, objective: 0.4825771048999518
167 -- optimal, objective: 3.888932512512169
168 -- optimal, objective: 1.0769714540447233
169 -- optimal, objective: 2.4991940991342765
170 -- optimal, objective: 1.8452022889718802
171 -- optimal, objective: 4.5162757443335515
172 -- optimal, objective: 3.7259845773036506
173 -- optimal, objective: 1.920583184236809
174 -- optimal, objective: 1.604043348238783
175 -- optimal, objective: 0.3297059921164121
176 -- optimal, objective: 3.1773292559305704
177 -- optimal, objective: 4.892212873755829
178 -- optimal, objective: 1.734421122212577
179 -- optimal, objective: 2.0930113767062535
180 -- optimal, objective: 1.982194408703398
181 -- optimal, objective: 3.095063944360138
182 -- optimal, objective: 2.5625165342165928
183 -- optimal, objective: 6.469891429283565
184 -- optimal, objective: 2.0674606386801786
185 -- optimal, objective: 2.3845354622360593
186 -- optimal, objective: 1.5119923887479807
187 -- optimal, objective: 3.6254181568250767
188 -- optimal, objective: 0.9836625190091582
189 -- optimal, objective: 1.9174184223605606
190 -- optimal, objective: 1.0199853616407288
191 -- optimal, objective: 1.8111192038560247
192 -- optimal, objective: 10.407061899274446
193 -- optimal, objective: 5.725243783932939
194 -- optimal, objective: 6.585188554630699
195 -- optimal, objective: 1.140403477486891
196 -- optimal, objective: 4.63648573951036
197 -- optimal, objective: 3.921803798658364
198 -- optimal, objective: 1.004560737902494
199 -- optimal, objective: 2.4181948879173865
200 -- optimal, objective: 2.924381439171226
201 -- optimal, objective: 2.968995475733458
202 -- optimal, objective: 2.6152892965286108
203 -- optimal, objective: 2.491418211244498
204 -- optimal, objective: 1.7943475851127995
205 -- optimal, objective: 5.708324626596838
206 -- optimal, objective: 2.4056055297694687
207 -- optimal, objective: 0.9383160093488742
208 -- optimal, objective: 4.796686075011125
209 -- optimal, objective: 0.5067752382992995
210 -- optimal, objective: 2.189070601163973
211 -- optimal, objective: 3.2162721207000837
212 -- optimal, objective: 0.0797030982595503
213 -- optimal, objective: 0.39071980305706655
214 -- optimal, objective: 4.02397171505382
215 -- optimal, objective: 3.5942477203081955
216 -- optimal, objective: 1.6777755011210227
217 -- optimal, objective: 4.848035154404866
218 -- optimal, objective: 0.4885463844272328
219 -- optimal, objective: 12.374531482863175
220 -- optimal, objective: 1.428390679628554
221 -- optimal, objective: 1.8180474372486606
222 -- optimal, objective: 0.4850181471500386
223 -- optimal, objective: 2.5067704521200462
224 -- optimal, objective: 1.3976831205728917
225 -- optimal, objective: 0.9031827797634285
226 -- optimal, objective: 0.7285597986984916
227 -- optimal, objective: 2.4704207267075544
228 -- optimal, objective: 2.6750989066858017
229 -- optimal, objective: 3.3257056456053355
230 -- optimal, objective: 2.599052712780132
231 -- optimal, objective: 4.837619200685972
232 -- optimal, objective: 1.132937434663661
233 -- optimal, objective: 1.6398640882824427
234 -- optimal, objective: 3.008950871925208
235 -- optimal, objective: 1.412405949664661
236 -- optimal, objective: 5.771965407598931
237 -- optimal, objective: 0.14938189272240587
238 -- optimal, objective: 1.205741317201688
239 -- optimal, objective: 1.7168330910787666
240 -- optimal, objective: 4.602205543920224
241 -- optimal, objective: 2.1236311175232885
242 -- optimal, objective: 2.5316135514752514
243 -- optimal, objective: 1.7031605794317393
244 -- optimal, objective: 2.2177892333102567
245 -- optimal, objective: 0.6465633467363427
246 -- optimal, objective: 1.2916378800473038
247 -- optimal, objective: 7.789851988626017
248 -- optimal, objective: 1.0605735856125036
249 -- optimal, objective: 1.1514691265140509

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 [ ]: