Scenarios¶

Multi-year planning with uncertain demand scenarios.

This notebook introduces:

Periods: Multiple planning years with different conditions
Scenarios: Uncertain futures (mild vs. harsh winter)
Scenario weights: Probability-weighted optimization
Multi-dimensional data: Parameters that vary by time, period, and scenario

Setup¶

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import pandas as pd
import xarray as xr

import flixopt as fx

fx.CONFIG.notebook()
import pandas as pd import xarray as xr import flixopt as fx fx.CONFIG.notebook()

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flixopt.config.CONFIG

The Planning Problem¶

We're designing a heating system with:

3 periods (years): 2024, 2025, 2026 - gas prices expected to rise
2 scenarios: "Mild Winter" (60% probability) and "Harsh Winter" (40% probability)
Investment decision: Size of CHP unit (made once, works across all futures)

The optimizer finds the investment that minimizes expected cost across all scenarios.

Define Dimensions¶

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from data.tutorial_data import get_scenarios_data

data = get_scenarios_data()
timesteps = data['timesteps']
periods = data['periods']
scenarios = data['scenarios']
scenario_weights = data['scenario_weights']
heat_demand = data['heat_demand']
gas_prices = data['gas_prices']
elec_prices = data['elec_prices']
from data.tutorial_data import get_scenarios_data data = get_scenarios_data() timesteps = data['timesteps'] periods = data['periods'] scenarios = data['scenarios'] scenario_weights = data['scenario_weights'] heat_demand = data['heat_demand'] gas_prices = data['gas_prices'] elec_prices = data['elec_prices']

Scenario-Dependent Demand Profiles¶

Heat demand differs significantly between mild and harsh winters:

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# Visualize demand scenarios with plotly
demand_ds = xr.Dataset(
    {
        scenario: xr.DataArray(
            heat_demand[scenario].values,
            dims=['time'],
            coords={'time': timesteps},
        )
        for scenario in scenarios
    }
)
demand_ds.plotly.line(x='time', title='Heat Demand by Scenario')
# Visualize demand scenarios with plotly demand_ds = xr.Dataset( { scenario: xr.DataArray( heat_demand[scenario].values, dims=['time'], coords={'time': timesteps}, ) for scenario in scenarios } ) demand_ds.plotly.line(x='time', title='Heat Demand by Scenario')

Build the Flow System¶

Initialize with all dimensions:

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flow_system = fx.FlowSystem(
    timesteps=timesteps,
    periods=periods,
    scenarios=scenarios,
    scenario_weights=scenario_weights,
    name='Both Scenarios',
)
flow_system.add_carriers(
    fx.Carrier('gas', '#3498db', 'kW'),
    fx.Carrier('electricity', '#f1c40f', 'kW'),
    fx.Carrier('heat', '#e74c3c', 'kW'),
)

flow_system
flow_system = fx.FlowSystem( timesteps=timesteps, periods=periods, scenarios=scenarios, scenario_weights=scenario_weights, name='Both Scenarios', ) flow_system.add_carriers( fx.Carrier('gas', '#3498db', 'kW'), fx.Carrier('electricity', '#f1c40f', 'kW'), fx.Carrier('heat', '#e74c3c', 'kW'), ) flow_system

Out[4]:

FlowSystem
==========
Timesteps: 168 (Hour) [2024-01-15 to 2024-01-21]
Periods: 3 (2024, 2025, 2026)
Scenarios: 2 (Mild Winter, Harsh Winter)
Status: ⚠

Add Components¶

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flow_system.add_elements(
    # === Buses ===
    fx.Bus('Electricity', carrier='electricity'),
    fx.Bus('Heat', carrier='heat'),
    fx.Bus('Gas', carrier='gas'),
    # === Effects ===
    fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),
    # === Gas Supply (price varies by period) ===
    fx.Source(
        'GasGrid',
        outputs=[
            fx.Flow(
                'Gas',
                bus='Gas',
                size=1000,
                effects_per_flow_hour=gas_prices,  # Array = varies by period
            )
        ],
    ),
    # === CHP Unit (investment decision) ===
    fx.linear_converters.CHP(
        'CHP',
        electrical_efficiency=0.35,
        thermal_efficiency=0.50,
        electrical_flow=fx.Flow(
            'P_el',
            bus='Electricity',
            # Investment optimization: find optimal CHP size
            size=fx.InvestParameters(
                minimum_size=0,
                maximum_size=100,
                effects_of_investment_per_size={'costs': 15},  # 15 €/kW/week annualized
            ),
        ),
        thermal_flow=fx.Flow('Q_th', bus='Heat'),
        fuel_flow=fx.Flow('Q_fuel', bus='Gas'),
    ),
    # === Gas Boiler (existing backup) ===
    fx.linear_converters.Boiler(
        'Boiler',
        thermal_efficiency=0.90,
        thermal_flow=fx.Flow('Q_th', bus='Heat', size=500),
        fuel_flow=fx.Flow('Q_fuel', bus='Gas'),
    ),
    # === Electricity Sales (revenue varies by period) ===
    fx.Sink(
        'ElecSales',
        inputs=[
            fx.Flow(
                'P_el',
                bus='Electricity',
                size=100,
                effects_per_flow_hour=-elec_prices,  # Negative = revenue
            )
        ],
    ),
    # === Heat Demand (varies by scenario) ===
    fx.Sink(
        'HeatDemand',
        inputs=[
            fx.Flow(
                'Q_th',
                bus='Heat',
                size=1,
                fixed_relative_profile=heat_demand,  # DataFrame with scenario columns
            )
        ],
    ),
)
flow_system.add_elements( # === Buses === fx.Bus('Electricity', carrier='electricity'), fx.Bus('Heat', carrier='heat'), fx.Bus('Gas', carrier='gas'), # === Effects === fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True), # === Gas Supply (price varies by period) === fx.Source( 'GasGrid', outputs=[ fx.Flow( 'Gas', bus='Gas', size=1000, effects_per_flow_hour=gas_prices, # Array = varies by period ) ], ), # === CHP Unit (investment decision) === fx.linear_converters.CHP( 'CHP', electrical_efficiency=0.35, thermal_efficiency=0.50, electrical_flow=fx.Flow( 'P_el', bus='Electricity', # Investment optimization: find optimal CHP size size=fx.InvestParameters( minimum_size=0, maximum_size=100, effects_of_investment_per_size={'costs': 15}, # 15 €/kW/week annualized ), ), thermal_flow=fx.Flow('Q_th', bus='Heat'), fuel_flow=fx.Flow('Q_fuel', bus='Gas'), ), # === Gas Boiler (existing backup) === fx.linear_converters.Boiler( 'Boiler', thermal_efficiency=0.90, thermal_flow=fx.Flow('Q_th', bus='Heat', size=500), fuel_flow=fx.Flow('Q_fuel', bus='Gas'), ), # === Electricity Sales (revenue varies by period) === fx.Sink( 'ElecSales', inputs=[ fx.Flow( 'P_el', bus='Electricity', size=100, effects_per_flow_hour=-elec_prices, # Negative = revenue ) ], ), # === Heat Demand (varies by scenario) === fx.Sink( 'HeatDemand', inputs=[ fx.Flow( 'Q_th', bus='Heat', size=1, fixed_relative_profile=heat_demand, # DataFrame with scenario columns ) ], ), )

Run Optimization¶

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flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));
flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));

Analyze Results¶

Optimal Investment Decision¶

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chp_size = flow_system.stats.sizes['CHP(P_el)']

pd.DataFrame(
    {
        'CHP Electrical [kW]': float(chp_size.max()),
        'CHP Thermal [kW]': float(chp_size.max()) * 0.50 / 0.35,
        'Expected Cost [EUR]': float(flow_system.solution['costs'].sum()),
    },
    index=['Optimal'],
).T
chp_size = flow_system.stats.sizes['CHP(P_el)'] pd.DataFrame( { 'CHP Electrical [kW]': float(chp_size.max()), 'CHP Thermal [kW]': float(chp_size.max()) * 0.50 / 0.35, 'Expected Cost [EUR]': float(flow_system.solution['costs'].sum()), }, index=['Optimal'], ).T

Out[7]:

	Optimal
CHP Electrical [kW]	99.671000
CHP Thermal [kW]	142.387143
Expected Cost [EUR]	77.793625

Heat Balance by Scenario¶

See how the system operates differently in each scenario:

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flow_system.stats.plot.balance('Heat')
flow_system.stats.plot.balance('Heat')

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CHP Operation Patterns¶

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flow_system.stats.plot.heatmap('CHP(Q_th)')
flow_system.stats.plot.heatmap('CHP(Q_th)')

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Multi-Dimensional Data Access¶

Results include all dimensions (time, period, scenario):

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flow_rates = flow_system.stats.flow_rates

# Plot flow rates
flow_system.stats.plot.flows()
flow_rates = flow_system.stats.flow_rates # Plot flow rates flow_system.stats.plot.flows()

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# CHP operation summary by scenario
chp_heat = flow_rates['CHP(Q_th)']

pd.DataFrame(
    {
        scenario: {
            'Avg [kW]': float(chp_heat.sel(scenario=scenario).mean()),
            'Max [kW]': float(chp_heat.sel(scenario=scenario).max()),
        }
        for scenario in scenarios
    }
)
# CHP operation summary by scenario chp_heat = flow_rates['CHP(Q_th)'] pd.DataFrame( { scenario: { 'Avg [kW]': float(chp_heat.sel(scenario=scenario).mean()), 'Max [kW]': float(chp_heat.sel(scenario=scenario).max()), } for scenario in scenarios } )

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	Mild Winter	Harsh Winter
Avg [kW]	101.749508	133.619672
Max [kW]	142.387143	142.387143

Sensitivity: What if Only Mild Winter?¶

Compare optimal CHP size if we only planned for mild winters:

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# Select only the mild winter scenario
fs_mild = flow_system.transform.sel(scenario='Mild Winter')
fs_mild.optimize(fx.solvers.HighsSolver(mip_gap=0.01))

chp_size_mild = float(fs_mild.stats.sizes['CHP(P_el)'].max())
chp_size_both = float(chp_size.max())

pd.DataFrame(
    {
        'Mild Only': {'CHP Size [kW]': chp_size_mild},
        'Both Scenarios': {'CHP Size [kW]': chp_size_both},
        'Uncertainty Buffer': {'CHP Size [kW]': chp_size_both - chp_size_mild},
    }
)
# Select only the mild winter scenario fs_mild = flow_system.transform.sel(scenario='Mild Winter') fs_mild.optimize(fx.solvers.HighsSolver(mip_gap=0.01)) chp_size_mild = float(fs_mild.stats.sizes['CHP(P_el)'].max()) chp_size_both = float(chp_size.max()) pd.DataFrame( { 'Mild Only': {'CHP Size [kW]': chp_size_mild}, 'Both Scenarios': {'CHP Size [kW]': chp_size_both}, 'Uncertainty Buffer': {'CHP Size [kW]': chp_size_both - chp_size_mild}, } )

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	Mild Only	Both Scenarios	Uncertainty Buffer
CHP Size [kW]	84.561091	99.671	15.109909

Energy Flow Sankey¶

A Sankey diagram visualizes the total energy flows through the system:

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flow_system.stats.plot.sankey.flows()
flow_system.stats.plot.sankey.flows()

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Key Concepts¶

Multi-Dimensional FlowSystem¶

flow_system = fx.FlowSystem(
    timesteps=timesteps,      # Time dimension
    periods=periods,          # Planning periods (years)
    scenarios=scenarios,      # Uncertain futures
    scenario_weights=weights, # Probabilities
)

Dimension-Varying Parameters¶

Data Shape	Meaning
Scalar	Same for all time/period/scenario
Array (n_periods,)	Varies by period
Array (n_scenarios,)	Varies by scenario
DataFrame with columns	Columns match scenario names
Full array (time, period, scenario)	Full specification

Scenario Optimization¶

The optimizer minimizes expected cost: $$\min \sum_s w_s \cdot \text{Cost}_s$$

where $w_s$ is the scenario weight (probability).

Selection Methods¶

# Select specific scenario
fs_mild = flow_system.transform.sel(scenario='Mild Winter')

# Select specific period
fs_2025 = flow_system.transform.sel(period=2025)

# Select time range
fs_day1 = flow_system.transform.sel(time=slice('2024-01-15', '2024-01-16'))

Summary¶

You learned how to:

Define multiple periods for multi-year planning
Create scenarios for uncertain futures
Use scenario weights for probability-weighted optimization
Pass dimension-varying parameters (arrays and DataFrames)
Select specific scenarios or periods for analysis

Next Steps¶

08a-Aggregation: Speed up large problems with resampling and clustering
08b-Rolling Horizon: Decompose large problems into sequential time segments