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LinearConverter

A LinearConverter transforms inputs into outputs with fixed ratios.

Basic: Conversion Equation

\[ \sum_{in} a_f \cdot p_f(t) = \sum_{out} b_f \cdot p_f(t) \]

\(0.9 \cdot p_{gas}(t) = p_{heat}(t)\)

boiler = fx.LinearConverter(
    label='boiler',
    inputs=[fx.Flow(label='gas', bus=gas_bus, size=111)],
    outputs=[fx.Flow(label='heat', bus=heat_bus, size=100)],
    conversion_factors=[{'gas': 0.9, 'heat': 1}],
)

\(3.5 \cdot p_{el}(t) = p_{heat}(t)\)

hp = fx.LinearConverter(
    label='hp',
    inputs=[fx.Flow(label='el', bus=elec_bus, size=100)],
    outputs=[fx.Flow(label='heat', bus=heat_bus, size=350)],
    conversion_factors=[{'el': 3.5, 'heat': 1}],
)

Two constraints linking fuel to outputs:

chp = fx.LinearConverter(
    label='chp',
    inputs=[fx.Flow(label='fuel', bus=gas_bus, size=100)],
    outputs=[
        fx.Flow(label='el', bus=elec_bus, size=35),
        fx.Flow(label='heat', bus=heat_bus, size=50),
    ],
    conversion_factors=[
        {'fuel': 0.35, 'el': 1},
        {'fuel': 0.50, 'heat': 1},
    ],
)

Time-Varying Efficiency

Pass a list for time-dependent conversion:

cop = np.array([3.0, 3.2, 3.5, 4.0, 3.8, ...])  # Varies with ambient temperature

hp = fx.LinearConverter(
    ...,
    conversion_factors=[{'el': cop, 'heat': 1}],
)

Convenience Classes

# Boiler
boiler = fx.linear_converters.Boiler(
    label='boiler', eta=0.9,
    Q_th=fx.Flow(label='heat', bus=heat_bus, size=100),
    Q_fu=fx.Flow(label='fuel', bus=gas_bus),
)

# Heat Pump
hp = fx.linear_converters.HeatPump(
    label='hp', COP=3.5,
    P_el=fx.Flow(label='el', bus=elec_bus, size=100),
    Q_th=fx.Flow(label='heat', bus=heat_bus),
)

# CHP
chp = fx.linear_converters.CHP(
    label='chp', eta_el=0.35, eta_th=0.50,
    P_el=fx.Flow(...), Q_th=fx.Flow(...), Q_fu=fx.Flow(...),
)

Adding Features

A component is active when any of its flows is non-zero. Add startup costs, minimum run times:

gen = fx.LinearConverter(
    ...,
    status_parameters=fx.StatusParameters(
        effects_per_startup={'costs': 1000},
        min_uptime=4,
    ),
)

See StatusParameters.

For variable efficiency — all flows change together based on operating point:

chp = fx.LinearConverter(
    label='CHP',
    inputs=[fx.Flow('fuel', bus=gas_bus)],
    outputs=[
        fx.Flow('el', bus=elec_bus, size=60),
        fx.Flow('heat', bus=heat_bus),
    ],
    piecewise_conversion=fx.PiecewiseConversion({
        'el':   fx.Piecewise([fx.Piece(5, 30), fx.Piece(40, 60)]),
        'heat': fx.Piecewise([fx.Piece(6, 35), fx.Piece(45, 100)]),
        'fuel': fx.Piecewise([fx.Piece(12, 70), fx.Piece(90, 200)]),
    }),
)

See Piecewise.

Reference

The converter creates constraints linking flows, not new variables.

Symbol Type Description
\(p_f(t)\) \(\mathbb{R}_{\geq 0}\) Flow rate of flow \(f\) at timestep \(t\)
\(a_f\) \(\mathbb{R}\) Conversion factor for input flow \(f\)
\(b_f\) \(\mathbb{R}\) Conversion factor for output flow \(f\)

Classes: LinearConverter, LinearConverterModel