Constraints¶

import numpy as np
import pandas as pd
import plotly.express as px
import xarray as xr

import flixopt as fx

fx.CONFIG.notebook()

# 3 days, hourly resolution
timesteps = pd.date_range('2024-03-11', periods=72, freq='h')
hours = np.arange(72)
hour_of_day = hours % 24

# Factory operates in shifts:
# - Day shift (6am-2pm): 400 kW
# - Evening shift (2pm-10pm): 350 kW
# - Night (10pm-6am): 80 kW (maintenance heating only)

steam_demand = np.select(
    [
        (hour_of_day >= 6) & (hour_of_day < 14),  # Day shift
        (hour_of_day >= 14) & (hour_of_day < 22),  # Evening shift
    ],
    [400, 350],
    default=80,  # Night
)

# Add some variation
np.random.seed(123)
steam_demand = steam_demand + np.random.normal(0, 20, len(steam_demand))
steam_demand = np.clip(steam_demand, 50, 450).astype(float)

print(f'Peak demand: {steam_demand.max():.0f} kW')
print(f'Min demand: {steam_demand.min():.0f} kW')

px.line(x=timesteps, y=steam_demand, title='Factory Steam Demand', labels={'x': 'Time', 'y': 'kW'})

flow_system.statistics.plot.balance('Steam')

flow_system.statistics.plot.heatmap('MainBoiler(Steam)')

# Merge solution DataArrays directly - xarray aligns coordinates automatically
status_ds = xr.Dataset(
    {
        'Status': flow_system.solution['MainBoiler|status'],
        'Steam Production [kW]': flow_system.solution['MainBoiler(Steam)|flow_rate'],
    }
)

df = status_ds.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')
fig = px.line(df, x='time', y='value', facet_col='variable', height=300, title='Main Boiler Operation')
fig.update_yaxes(matches=None, showticklabels=True)
fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))
fig

total_startups = int(flow_system.solution['MainBoiler|startup'].sum().item())
total_costs = flow_system.solution['costs'].item()
startup_costs = total_startups * 50
gas_costs = total_costs - startup_costs

print(
    f'{total_startups} startups × 50€ = {startup_costs:.0f}€ startup + {gas_costs:.0f}€ gas = {total_costs:.0f}€ total'
)

flow_system.statistics.plot.duration_curve('MainBoiler(Steam)')

flow_system.statistics.plot.duration_curve('BackupBoiler(Steam)')

# Build unconstrained system
fs_unconstrained = fx.FlowSystem(timesteps)
fs_unconstrained.add_carriers(
    fx.Carrier('gas', '#3498db', 'kW'),
    fx.Carrier('steam', '#87CEEB', 'kW_th', 'Process steam'),
)

fs_unconstrained.add_elements(
    fx.Bus('Gas', carrier='gas'),
    fx.Bus('Steam', carrier='steam'),
    fx.Effect('costs', '€', 'Operating Costs', is_standard=True, is_objective=True),
    fx.Source('GasGrid', outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour=0.06)]),
    # Main boiler WITHOUT status parameters
    fx.linear_converters.Boiler(
        'MainBoiler',
        thermal_efficiency=0.94,
        thermal_flow=fx.Flow('Steam', bus='Steam', size=500),
        fuel_flow=fx.Flow('Gas', bus='Gas'),
    ),
    fx.linear_converters.Boiler(
        'BackupBoiler',
        thermal_efficiency=0.85,
        thermal_flow=fx.Flow('Steam', bus='Steam', size=150),
        fuel_flow=fx.Flow('Gas', bus='Gas'),
    ),
    fx.Sink('Factory', inputs=[fx.Flow('Steam', bus='Steam', size=1, fixed_relative_profile=steam_demand)]),
)

fs_unconstrained.optimize(fx.solvers.HighsSolver())
unconstrained_costs = fs_unconstrained.solution['costs'].item()

constraint_overhead = (total_costs - unconstrained_costs) / unconstrained_costs * 100
print(f'Constraints add {constraint_overhead:.1f}% cost: {unconstrained_costs:.0f}€ → {total_costs:.0f}€')

flow_system.statistics.plot.sankey.flows()