Sizing¶

Size a solar heating system - let the optimizer decide equipment sizes.

This notebook introduces:

InvestParameters: Define investment decisions with size bounds and costs
Investment costs: Fixed costs and size-dependent costs
Optimal sizing: Let the optimizer find the best equipment sizes
Trade-off analysis: Balance investment vs. operating costs

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

System Description¶

The swimming pool heating system:

Solar collectors: Convert solar radiation to heat (size to be optimized)
Gas boiler: Backup heating when solar is insufficient (existing, 200 kW)
Buffer tank: Store excess solar heat (size to be optimized)
Pool: Constant heat demand of 150 kW during operating hours

   ☀️ Solar ──► [Heat] ◄── Boiler ◄── [Gas]
                  │
                  ▼
              Buffer Tank
                  │
                  ▼
                Pool 🏊

Define Time Horizon and Profiles¶

We model one representative summer week:

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from data.tutorial_data import get_investment_data

data = get_investment_data()
timesteps = data['timesteps']
solar_profile = data['solar_profile']
pool_demand = data['pool_demand']
GAS_PRICE = data['gas_price']
SOLAR_COST_WEEKLY = data['solar_cost_per_kw_week']
TANK_COST_WEEKLY = data['tank_cost_per_kwh_week']
from data.tutorial_data import get_investment_data data = get_investment_data() timesteps = data['timesteps'] solar_profile = data['solar_profile'] pool_demand = data['pool_demand'] GAS_PRICE = data['gas_price'] SOLAR_COST_WEEKLY = data['solar_cost_per_kw_week'] TANK_COST_WEEKLY = data['tank_cost_per_kwh_week']

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# Visualize profiles with plotly
profiles = xr.Dataset(
    {
        'Solar Profile [kW/kW]': xr.DataArray(solar_profile, dims=['time'], coords={'time': timesteps}),
        'Pool Demand [kW]': xr.DataArray(pool_demand, dims=['time'], coords={'time': timesteps}),
    }
)
profiles.plotly.line(x='time', title='Solar and Pool Profiles', height=300)
# Visualize profiles with plotly profiles = xr.Dataset( { 'Solar Profile [kW/kW]': xr.DataArray(solar_profile, dims=['time'], coords={'time': timesteps}), 'Pool Demand [kW]': xr.DataArray(pool_demand, dims=['time'], coords={'time': timesteps}), } ) profiles.plotly.line(x='time', title='Solar and Pool Profiles', height=300)

Build the System with Investment Options¶

Use InvestParameters to define which sizes should be optimized:

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flow_system = fx.FlowSystem(timesteps)
flow_system.add_carriers(
    fx.Carrier('gas', '#3498db', 'kW'),
    fx.Carrier('heat', '#e74c3c', 'kW'),
)
flow_system.add_elements(
    # === Buses ===
    fx.Bus('Heat', carrier='heat'),
    fx.Bus('Gas', carrier='gas'),
    # === Effects ===
    fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),
    # === Gas Supply ===
    fx.Source(
        'GasGrid',
        outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=GAS_PRICE)],
    ),
    # === Gas Boiler (existing, fixed size) ===
    fx.linear_converters.Boiler(
        'GasBoiler',
        thermal_efficiency=0.92,
        thermal_flow=fx.Flow('Heat', bus='Heat', size=200),  # 200 kW existing
        fuel_flow=fx.Flow('Gas', bus='Gas'),
    ),
    # === Solar Collectors (size to be optimized) ===
    fx.Source(
        'SolarCollectors',
        outputs=[
            fx.Flow(
                'Heat',
                bus='Heat',
                # Investment optimization: find optimal size between 0-500 kW
                size=fx.InvestParameters(
                    minimum_size=0,
                    maximum_size=500,
                    effects_of_investment_per_size={'costs': SOLAR_COST_WEEKLY},
                ),
                # Solar output depends on radiation profile
                fixed_relative_profile=solar_profile,
            )
        ],
    ),
    # === Buffer Tank (size to be optimized) ===
    fx.Storage(
        'BufferTank',
        # Investment optimization: find optimal capacity between 0-2000 kWh
        capacity_in_flow_hours=fx.InvestParameters(
            minimum_size=0,
            maximum_size=2000,
            effects_of_investment_per_size={'costs': TANK_COST_WEEKLY},
        ),
        initial_charge_state=0,
        eta_charge=0.95,
        eta_discharge=0.95,
        relative_loss_per_hour=0.01,  # 1% loss per hour
        charging=fx.Flow('Charge', bus='Heat', size=200),
        discharging=fx.Flow('Discharge', bus='Heat', size=200),
    ),
    # === Pool Heat Demand ===
    fx.Sink(
        'Pool',
        inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=pool_demand)],
    ),
)
flow_system = fx.FlowSystem(timesteps) flow_system.add_carriers( fx.Carrier('gas', '#3498db', 'kW'), fx.Carrier('heat', '#e74c3c', 'kW'), ) flow_system.add_elements( # === Buses === fx.Bus('Heat', carrier='heat'), fx.Bus('Gas', carrier='gas'), # === Effects === fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True), # === Gas Supply === fx.Source( 'GasGrid', outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=GAS_PRICE)], ), # === Gas Boiler (existing, fixed size) === fx.linear_converters.Boiler( 'GasBoiler', thermal_efficiency=0.92, thermal_flow=fx.Flow('Heat', bus='Heat', size=200), # 200 kW existing fuel_flow=fx.Flow('Gas', bus='Gas'), ), # === Solar Collectors (size to be optimized) === fx.Source( 'SolarCollectors', outputs=[ fx.Flow( 'Heat', bus='Heat', # Investment optimization: find optimal size between 0-500 kW size=fx.InvestParameters( minimum_size=0, maximum_size=500, effects_of_investment_per_size={'costs': SOLAR_COST_WEEKLY}, ), # Solar output depends on radiation profile fixed_relative_profile=solar_profile, ) ], ), # === Buffer Tank (size to be optimized) === fx.Storage( 'BufferTank', # Investment optimization: find optimal capacity between 0-2000 kWh capacity_in_flow_hours=fx.InvestParameters( minimum_size=0, maximum_size=2000, effects_of_investment_per_size={'costs': TANK_COST_WEEKLY}, ), initial_charge_state=0, eta_charge=0.95, eta_discharge=0.95, relative_loss_per_hour=0.01, # 1% loss per hour charging=fx.Flow('Charge', bus='Heat', size=200), discharging=fx.Flow('Discharge', bus='Heat', size=200), ), # === Pool Heat Demand === fx.Sink( 'Pool', inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=pool_demand)], ), )

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 Investment Decisions¶

Optimal Sizes¶

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solar_size = flow_system.stats.sizes['SolarCollectors(Heat)'].item()
tank_size = flow_system.stats.sizes['BufferTank'].item()

pd.DataFrame(
    {
        'Solar [kW]': solar_size,
        'Tank [kWh]': tank_size,
        'Ratio [kWh/kW]': tank_size / solar_size if solar_size > 0 else float('nan'),
    },
    index=['Optimal Size'],
).T
solar_size = flow_system.stats.sizes['SolarCollectors(Heat)'].item() tank_size = flow_system.stats.sizes['BufferTank'].item() pd.DataFrame( { 'Solar [kW]': solar_size, 'Tank [kWh]': tank_size, 'Ratio [kWh/kW]': tank_size / solar_size if solar_size > 0 else float('nan'), }, index=['Optimal Size'], ).T

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	Optimal Size
Solar [kW]	458.451276
Tank [kWh]	747.696332
Ratio [kWh/kW]	1.630918

Visualize Sizes¶

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flow_system.stats.plot.sizes()
flow_system.stats.plot.sizes()

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Cost Breakdown¶

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total_costs = flow_system.solution['costs'].item()

# Calculate cost components
solar_invest = solar_size * SOLAR_COST_WEEKLY
tank_invest = tank_size * TANK_COST_WEEKLY
gas_costs = total_costs - solar_invest - tank_invest

pd.DataFrame(
    {
        'Solar Investment': {'EUR': solar_invest, '%': solar_invest / total_costs * 100},
        'Tank Investment': {'EUR': tank_invest, '%': tank_invest / total_costs * 100},
        'Gas Costs': {'EUR': gas_costs, '%': gas_costs / total_costs * 100},
        'Total': {'EUR': total_costs, '%': 100.0},
    }
)
total_costs = flow_system.solution['costs'].item() # Calculate cost components solar_invest = solar_size * SOLAR_COST_WEEKLY tank_invest = tank_size * TANK_COST_WEEKLY gas_costs = total_costs - solar_invest - tank_invest pd.DataFrame( { 'Solar Investment': {'EUR': solar_invest, '%': solar_invest / total_costs * 100}, 'Tank Investment': {'EUR': tank_invest, '%': tank_invest / total_costs * 100}, 'Gas Costs': {'EUR': gas_costs, '%': gas_costs / total_costs * 100}, 'Total': {'EUR': total_costs, '%': 100.0}, } )

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	Solar Investment	Tank Investment	Gas Costs	Total
EUR	176.327414	21.568163	585.088163	782.98374
%	22.519933	2.754612	74.725455	100.00000

System Operation¶

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

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flow_system.stats.plot.heatmap('SolarCollectors(Heat)')
flow_system.stats.plot.heatmap('SolarCollectors(Heat)')

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

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Compare: What if No Solar?¶

Let's see how much the solar system saves:

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# Gas-only scenario for comparison
total_demand = pool_demand.sum()
gas_only_cost = total_demand / 0.92 * GAS_PRICE  # All heat from gas boiler
savings = gas_only_cost - total_costs

pd.DataFrame(
    {
        'Gas-only [EUR/week]': gas_only_cost,
        'With Solar [EUR/week]': total_costs,
        'Savings [EUR/week]': savings,
        'Savings [%]': savings / gas_only_cost * 100,
        'Savings [EUR/year]': savings * 52,
    },
    index=['Value'],
).T
# Gas-only scenario for comparison total_demand = pool_demand.sum() gas_only_cost = total_demand / 0.92 * GAS_PRICE # All heat from gas boiler savings = gas_only_cost - total_costs pd.DataFrame( { 'Gas-only [EUR/week]': gas_only_cost, 'With Solar [EUR/week]': total_costs, 'Savings [EUR/week]': savings, 'Savings [%]': savings / gas_only_cost * 100, 'Savings [EUR/year]': savings * 52, }, index=['Value'], ).T

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	Value
Gas-only [EUR/week]	2465.217391
With Solar [EUR/week]	782.983740
Savings [EUR/week]	1682.233651
Savings [%]	68.238755
Savings [EUR/year]	87476.149872

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¶

InvestParameters Options¶

fx.InvestParameters(
    minimum_size=0,           # Lower bound (can be 0 for optional)
    maximum_size=500,         # Upper bound
    fixed_size=100,           # Or: fixed size (binary decision)
    mandatory=True,           # Force investment to happen
    effects_of_investment={'costs': 1000},      # Fixed cost if invested
    effects_of_investment_per_size={'costs': 25},  # Cost per unit size
)

Where to Use InvestParameters¶

Flow.size: Optimize converter/source/sink capacity
Storage.capacity_in_flow_hours: Optimize storage capacity

Summary¶

You learned how to:

Define investment decisions with InvestParameters
Set size bounds (minimum/maximum)
Add investment costs (per-size and fixed)
Access optimal sizes via statistics.sizes
Visualize sizes with statistics.plot.sizes()

Next Steps¶

04-operational-constraints: Add startup costs and minimum run times
05-multi-carrier-system: Model combined heat and power