Uncertainty Analysis¶

In this tutorial, we will perform an uncertainty analysis using the EnergyScope model. We will explore how varying certain parameters affects the energy system configuration and results. This is achieved by generating a sequence of parameter values using Sobol sequences, running multiple optimizations, and analyzing the outcomes.

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Import Necessary Libraries¶

First, we import all the required libraries and modules:

In [1]:

import pandas as pd
import numpy as np
import seaborn as sns
from energyscope.energyscope import Energyscope
from energyscope.models import infrastructure_ch_2050
from energyscope.result import postprocessing
from energyscope.datasets import gen_sobol_sequence

import pandas as pd import numpy as np import seaborn as sns from energyscope.energyscope import Energyscope from energyscope.models import infrastructure_ch_2050 from energyscope.result import postprocessing from energyscope.datasets import gen_sobol_sequence

• pandas: For data manipulation and analysis.
• numpy: For numerical operations.
• seaborn: For statistical data visualization.
• Energyscope: Main class for initializing and running the EnergyScope model.
• infrastructure_ch_2050: Predefined model for different configurations.
• postprocessing: Functions to process results after optimizations.
• gen_sobol_sequence: Function to generate Sobol sequences for parameter sampling.

---

Manual Parameter Definition¶

Define Parameters for Uncertainty Analysis¶

We manually define a list of parameters whose uncertainty we want to analyze. Each parameter includes a name, a lower bound, and an upper bound:

In [2]:

varying_parameter = 'c_inv'
parameters = [
    {'name': 'PV_LV', 'lower_bound': 0, 'upper_bound': 50},
    {'name': 'WIND', 'lower_bound': 0, 'upper_bound': 20},
    {'name': 'CCGT', 'lower_bound': 0, 'upper_bound': 10}
]

varying_parameter = 'c_inv' parameters = [ {'name': 'PV_LV', 'lower_bound': 0, 'upper_bound': 50}, {'name': 'WIND', 'lower_bound': 0, 'upper_bound': 20}, {'name': 'CCGT', 'lower_bound': 0, 'upper_bound': 10} ]

• PV_LV: Photovoltaic at Low Voltage level.
• WIND: Wind energy capacity.
• CCGT: Combined Cycle Gas Turbine capacity.
• The bounds represent the range within which the parameter values will vary during the analysis.

Generate Sobol Sequence for Parameter Sampling¶

We use the gen_sobol_sequence function to generate a Sobol sequence, which provides quasi-random samples of parameter values within the specified bounds:

In [3]:

seq, prob = gen_sobol_sequence(parameters=parameters, trajectories=4)

seq, prob = gen_sobol_sequence(parameters=parameters, trajectories=4)

• trajectories=4: Specifies the number of trajectories or samples to generate.
• seq: The generated sequence of parameter values.
• prob: Metadata about the parameters and their sampling.

Display Number of Generated Samples¶

We can display the number of generated samples to verify:

In [4]:

display(len(seq))

display(len(seq))

20

• This should output the total number of parameter sets generated.

Prepare Parameter DataFrame¶

We prepare a DataFrame to hold the generated parameter sequences in a format suitable for the EnergyScope model:

In [5]:

df = pd.DataFrame(seq, columns=prob['names']).T
df.columns = ['value' + str(x) for x in list(df.columns) if not str(x) == "nan"]
df = df.reset_index(names=['index0'])
df['param'] = varying_parameter

df['index1'] = np.nan
df['index2'] = np.nan
df['index3'] = np.nan
df

df = pd.DataFrame(seq, columns=prob['names']).T df.columns = ['value' + str(x) for x in list(df.columns) if not str(x) == "nan"] df = df.reset_index(names=['index0']) df['param'] = varying_parameter df['index1'] = np.nan df['index2'] = np.nan df['index3'] = np.nan df

Out[5]:

	index0	value0	value1	value2	value3	value4	value5	value6	value7	value8	...	value14	value15	value16	value17	value18	value19	param	index1	index2	index3
0	PV_LV	4.6875	32.8125	4.6875	4.6875	32.8125	29.6875	7.8125	29.6875	29.6875	...	45.3125	17.1875	20.3125	17.1875	17.1875	20.3125	c_inv	NaN	NaN	NaN
1	WIND	9.3750	9.3750	5.6250	9.3750	5.6250	19.3750	19.3750	15.6250	19.3750	...	10.6250	14.3750	14.3750	0.6250	14.3750	0.6250	c_inv	NaN	NaN	NaN
2	CCGT	4.6875	4.6875	4.6875	9.6875	9.6875	9.6875	9.6875	9.6875	4.6875	...	2.1875	7.1875	7.1875	7.1875	7.1875	7.1875	c_inv	NaN	NaN	NaN

3 rows × 25 columns

• Transpose the DataFrame: To match the expected format.
• Rename Columns: Prefix columns with 'value'.
• Reset Index: To ensure the parameters are properly indexed.
• Add Parameter Type: We specify that these values correspond to 'c_inv' (investment costs).
• Add Empty Indices: Additional indices are added for compatibility with the model's expectations.

---

Define Solver Options¶

We specify solver options to control the optimization process:

In [6]:

solver_options = {
    'solver': 'gurobi',
    'presolve_eps': 5e-9,
    'presolve_fixeps': 7e-10,
    'mipgap': 1e-10,
    'display_eps': 1e-10,
    'omit_zero_rows': 1,
    'omit_zero_cols': 1,
    'show_stats': 0,
    'solver_msg': 0,
    'cplex_options': 'integrality=5e-7',
}

solver_options = { 'solver': 'gurobi', 'presolve_eps': 5e-9, 'presolve_fixeps': 7e-10, 'mipgap': 1e-10, 'display_eps': 1e-10, 'omit_zero_rows': 1, 'omit_zero_cols': 1, 'show_stats': 0, 'solver_msg': 0, 'cplex_options': 'integrality=5e-7', }

• 'solver': 'gurobi': Specifies that the Gurobi solver should be used.
• Other options fine-tune the solver's precision and output behavior.

---

Initialize and Run the Model with Parameter Variations¶

Initialize the EnergyScope Model¶

We create an instance of the EnergyScope model using the infrastructure_ch_2050 dataset and the specified solver options:

In [7]:

es_infra_ch = Energyscope(model=infrastructure_ch_2050, solver_options=solver_options)

es_infra_ch = Energyscope(model=infrastructure_ch_2050, solver_options=solver_options)

Run Multiple Optimizations with Varying Parameters¶

We use the calc_sequence method to run the model multiple times, each time with a different set of parameters from the Sobol sequence:

In [8]:

results_ch_n = es_infra_ch.calc_sequence(df)

results_ch_n = es_infra_ch.calc_sequence(df)

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Post-Process and Analyze Results¶

Post-Process Results¶

In [9]:

# Postcompute KPIs
results_ch_n = postprocessing(results_ch_n, df_monthly=True)

# Postcompute KPIs results_ch_n = postprocessing(results_ch_n, df_monthly=True)

• df_monthly=True: Indicates that monthly data should be included in the post-processing.

Extract Annual Results¶

We extract the annual results DataFrame for further analysis:

In [10]:

df_annual = results_ch_n.postprocessing['df_annual']
df_annual = df_annual.loc[:, ['F_Mult']]
df_annual = df_annual.reset_index()

df_annual = results_ch_n.postprocessing['df_annual'] df_annual = df_annual.loc[:, ['F_Mult']] df_annual = df_annual.reset_index()

• F_Mult: Represents the flow multipliers or capacities of technologies.

Pivot the Results DataFrame¶

We pivot the DataFrame to have technologies as columns and runs as rows:

In [11]:

df_annual = pd.pivot_table(df_annual, values='F_Mult', index=['Run'], columns='level_0')
df_annual.sample(5)

df_annual = pd.pivot_table(df_annual, values='F_Mult', index=['Run'], columns='level_0') df_annual.sample(5)

Out[11]:

level_0	ACETIC_ACID	ACETONE	ALKALINE_ELECTROLYSIS	ALUMINUM	AL_MAKING	AL_MAKING_HR	AN_DIG	AN_DIG_SI	BATTERY	BENZENE	...	UNMINEABLE_COAL_SEAM	URANIUM	WASTE	WASTE_BIO	WASTE_FOS	WET_BIOMASS	WIND	WOOD	WOOD_METHANOL	XYLENE
Run
14	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
12	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
16	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
18	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
3	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0

5 rows × 289 columns

• This format is suitable for statistical analysis and visualization.

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Visualize Technology Distribution¶

Plot Pairwise Relationships¶

We use Seaborn's pairplot function to visualize pairwise relationships between the capacities of different technologies:

In [12]:

cols = ['CCGT_CC', 'DEC_COGEN_GAS', 'DEC_HP_ELEC', 'GASIFICATION_H2', 'IND_BOILER_WASTE', 'IND_COGEN_WASTE', 'PV_LV', 'WIND']
display(sns.pairplot(df_annual[cols].fillna(0), diag_kind="kde"))

cols = ['CCGT_CC', 'DEC_COGEN_GAS', 'DEC_HP_ELEC', 'GASIFICATION_H2', 'IND_BOILER_WASTE', 'IND_COGEN_WASTE', 'PV_LV', 'WIND'] display(sns.pairplot(df_annual[cols].fillna(0), diag_kind="kde"))

<seaborn.axisgrid.PairGrid at 0x7d64ba4da500>

• cols: List of technologies to include in the plot.
• fillna(0): Replaces NaN values with zero for plotting purposes.
• diag_kind="kde": Uses Kernel Density Estimation for the diagonal plots.

---

Semi-Automated Sequence Creation¶

In this section, we automate the generation of parameter sequences based on existing model parameters.

Initialize the Model¶

We initialize the EnergyScope model again:

In [13]:

es_infra_ch = Energyscope(model=infrastructure_ch_2050)

es_infra_ch = Energyscope(model=infrastructure_ch_2050)

Run the Base Model¶

We perform an initial calculation to obtain baseline parameter values:

In [14]:

# Solve the model
results_ch = es_infra_ch.calc()

# Solve the model results_ch = es_infra_ch.calc()

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Gurobi 12.0.3: optimal solution; objective 9229.740656
7346 simplex iterations
1 branching node

Extract and Adjust Investment Costs¶

We extract the investment costs (c_inv) from the model parameters and define new bounds for uncertainty analysis:

In [15]:

c_inv = results_ch.parameters['c_inv'].drop('Run', axis=1)
c_inv['lower_bound'] = 0.5 * c_inv['c_inv']
c_inv['upper_bound'] = 1.5 * c_inv['c_inv']
c_inv = c_inv.reset_index(names=['name']).drop('c_inv', axis=1)
c_inv = c_inv.loc[c_inv['lower_bound'] != 0, :]

c_inv = results_ch.parameters['c_inv'].drop('Run', axis=1) c_inv['lower_bound'] = 0.5 * c_inv['c_inv'] c_inv['upper_bound'] = 1.5 * c_inv['c_inv'] c_inv = c_inv.reset_index(names=['name']).drop('c_inv', axis=1) c_inv = c_inv.loc[c_inv['lower_bound'] != 0, :]

• Adjust Bounds: We set the lower and upper bounds to ±50% of the original investment costs.
• Filter Out Zero Costs: Remove parameters where the lower bound is zero.

Select Key Technologies¶

Due to computational limitations, we select a subset of technologies to include in the uncertainty analysis:

In [16]:

selected_technologies = ['PV_LV', 'PV_MV', 'PV_HV', 'PV_EHV', 'DEC_HP_ELEC', 'WIND', 'GASIFICATION_H2', 'GASIFICATION_SNG']
c_inv = c_inv.loc[c_inv['name'].isin(selected_technologies), :]

selected_technologies = ['PV_LV', 'PV_MV', 'PV_HV', 'PV_EHV', 'DEC_HP_ELEC', 'WIND', 'GASIFICATION_H2', 'GASIFICATION_SNG'] c_inv = c_inv.loc[c_inv['name'].isin(selected_technologies), :]

• selected_technologies: List of technologies chosen for analysis.

Convert Parameters to Dictionary Format¶

We convert the DataFrame of parameters to a list of dictionaries required by the gen_sobol_sequence function:

In [17]:

c_inv = c_inv.to_dict(orient='records')

c_inv = c_inv.to_dict(orient='records')

Generate Sobol Sequence for Selected Parameters¶

We generate a Sobol sequence for the selected parameters:

In [18]:

seq, prob = gen_sobol_sequence(parameters=c_inv, trajectories=8)

seq, prob = gen_sobol_sequence(parameters=c_inv, trajectories=8)

• trajectories=8: Generates more samples for a more detailed analysis.

Display Number of Generated Samples¶

In [19]:

display(len(seq))

display(len(seq))

80

Prepare Parameter DataFrame¶

We prepare the DataFrame for the new sequence:

In [20]:

df = pd.DataFrame(seq, columns=prob['names']).T
df.columns = ['value' + str(x) for x in list(df.columns) if not str(x) == "nan"]
df = df.reset_index(names=['index0'])
df['param'] = 'c_inv'

df['index1'] = np.nan
df['index2'] = np.nan
df['index3'] = np.nan
df

df = pd.DataFrame(seq, columns=prob['names']).T df.columns = ['value' + str(x) for x in list(df.columns) if not str(x) == "nan"] df = df.reset_index(names=['index0']) df['param'] = 'c_inv' df['index1'] = np.nan df['index2'] = np.nan df['index3'] = np.nan df

Out[20]:

	index0	value0	value1	value2	value3	value4	value5	value6	value7	value8	...	value74	value75	value76	value77	value78	value79	param	index1	index2	index3
0	DEC_HP_ELEC	311.985938	509.029688	311.985938	311.985938	311.985938	311.985938	311.985938	311.985938	311.985938	...	377.667188	377.667188	377.667188	377.667188	377.667188	706.073438	c_inv	NaN	NaN	NaN
1	GASIFICATION_H2	1383.181250	1383.181250	936.993750	1383.181250	1383.181250	1383.181250	1383.181250	1383.181250	1383.181250	...	1918.606250	1918.606250	1918.606250	1918.606250	1918.606250	1829.368750	c_inv	NaN	NaN	NaN
2	GASIFICATION_SNG	2838.544063	2838.544063	2838.544063	1739.752812	2838.544063	2838.544063	2838.544063	2838.544063	2838.544063	...	1739.752812	1739.752812	1739.752812	1739.752812	1739.752812	3571.071563	c_inv	NaN	NaN	NaN
3	PV_EHV	1503.125000	1503.125000	1503.125000	1503.125000	1178.125000	1503.125000	1503.125000	1503.125000	1503.125000	...	1015.625000	1340.625000	1340.625000	1340.625000	1340.625000	1015.625000	c_inv	NaN	NaN	NaN
4	PV_HV	367.187500	367.187500	367.187500	367.187500	367.187500	543.437500	367.187500	367.187500	367.187500	...	425.937500	249.687500	425.937500	425.937500	425.937500	249.687500	c_inv	NaN	NaN	NaN
5	PV_LV	954.687500	954.687500	954.687500	954.687500	954.687500	954.687500	751.562500	954.687500	954.687500	...	710.937500	710.937500	832.812500	710.937500	710.937500	832.812500	c_inv	NaN	NaN	NaN
6	PV_MV	629.062500	629.062500	629.062500	629.062500	629.062500	629.062500	629.062500	514.687500	629.062500	...	400.312500	400.312500	400.312500	590.937500	400.312500	590.937500	c_inv	NaN	NaN	NaN
7	WIND	1969.426875	1969.426875	1969.426875	1969.426875	1969.426875	1969.426875	1969.426875	1969.426875	778.610625	...	1419.819375	1419.819375	1419.819375	1419.819375	961.813125	961.813125	c_inv	NaN	NaN	NaN

8 rows × 85 columns

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Run Optimizations with New Parameter Sets¶

Define Solver Options¶

We define the solver options again (same as before):

In [21]:

solver_options = {
    'solver': 'gurobi',
    'presolve_eps': 5e-9,
    'presolve_fixeps': 7e-10,
    'mipgap': 1e-10,
    'display_eps': 1e-10,
    'omit_zero_rows': 1,
    'omit_zero_cols': 1,
    'show_stats': 0,
    'solver_msg': 0,
    'cplex_options': 'integrality=5e-7',
}

solver_options = { 'solver': 'gurobi', 'presolve_eps': 5e-9, 'presolve_fixeps': 7e-10, 'mipgap': 1e-10, 'display_eps': 1e-10, 'omit_zero_rows': 1, 'omit_zero_cols': 1, 'show_stats': 0, 'solver_msg': 0, 'cplex_options': 'integrality=5e-7', }

Initialize the Model with Solver Options¶

In [22]:

es_infra_ch = Energyscope(model=infrastructure_ch_2050, solver_options=solver_options)

es_infra_ch = Energyscope(model=infrastructure_ch_2050, solver_options=solver_options)

Run Multiple Optimizations¶

We run the model multiple times with the new parameter sets:

In [23]:

results_ch_n = es_infra_ch.calc_sequence(df)

results_ch_n = es_infra_ch.calc_sequence(df)

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Post-Process and Analyze Results¶

Post-Process Results¶

In [24]:

# Postcompute KPIs
results_ch_n = postprocessing(results_ch_n, df_monthly=False)

# Postcompute KPIs results_ch_n = postprocessing(results_ch_n, df_monthly=False)

• df_monthly=False: We are focusing on annual data in this case.

Extract and Prepare Annual Results¶

In [25]:

df_annual = results_ch_n.postprocessing['df_annual']
df_annual = df_annual.loc[:, ['F_Mult']]
df_annual = df_annual.reset_index()

df_annual = pd.pivot_table(df_annual, values='F_Mult', index=['Run'], columns='level_0')
df_annual.sample(5)

df_annual = results_ch_n.postprocessing['df_annual'] df_annual = df_annual.loc[:, ['F_Mult']] df_annual = df_annual.reset_index() df_annual = pd.pivot_table(df_annual, values='F_Mult', index=['Run'], columns='level_0') df_annual.sample(5)

Out[25]:

level_0	ACETIC_ACID	ACETONE	ALKALINE_ELECTROLYSIS	ALUMINUM	AL_MAKING	AL_MAKING_HR	AN_DIG	AN_DIG_SI	BATTERY	BENZENE	...	UNMINEABLE_COAL_SEAM	URANIUM	WASTE	WASTE_BIO	WASTE_FOS	WET_BIOMASS	WIND	WOOD	WOOD_METHANOL	XYLENE
Run
65	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
8	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
73	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
47	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0
18	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	20.0	0.0	0.0	0.0

5 rows × 289 columns

Visualize Technology Distribution¶

In [26]:

cols = ['CCGT_CC', 'DEC_COGEN_GAS', 'DEC_HP_ELEC', 'GASIFICATION_H2', 'IND_BOILER_WASTE', 'IND_COGEN_WASTE', 'PV_LV', 'WIND']
display(sns.pairplot(df_annual[cols].fillna(0), diag_kind="kde"))

cols = ['CCGT_CC', 'DEC_COGEN_GAS', 'DEC_HP_ELEC', 'GASIFICATION_H2', 'IND_BOILER_WASTE', 'IND_COGEN_WASTE', 'PV_LV', 'WIND'] display(sns.pairplot(df_annual[cols].fillna(0), diag_kind="kde"))

<seaborn.axisgrid.PairGrid at 0x7d64b98889a0>

• We plot the distributions to understand how the uncertainty in investment costs affects the capacities of different technologies.

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By following these steps, we perform an uncertainty analysis on the EnergyScope model by varying the investment costs of selected technologies. This approach allows us to understand the sensitivity of the energy system configuration to changes in key parameters.

Note: Ensure that all the necessary data files and dependencies are correctly set up in your environment. The computational time may vary depending on the number of optimizations and the complexity of the model.