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InvestParameters

InvestParameters make capacity a decision variable — should we build this? How big?

Basic: Size as Variable

\[ P^{min} \leq P \leq P^{max} \]
battery = fx.Storage(
    ...,
    capacity_in_flow_hours=fx.InvestParameters(
        minimum_size=10,
        maximum_size=1000,
        specific_effects={'costs': 600},  # €600/kWh
    ),
)

Investment Modes

By default, investment is optional — the optimizer can choose \(P = 0\) (don't invest).

Choose size within range (or zero):

fx.InvestParameters(
    minimum_size=10,
    maximum_size=1000,
)
# → P = 0  OR  10 ≤ P ≤ 1000

Fixed size or nothing:

fx.InvestParameters(
    fixed_size=100,  # 100 kW or 0
)
# → P ∈ {0, 100}

Force investment with mandatory=True — zero not allowed:

fx.InvestParameters(
    minimum_size=50,
    maximum_size=200,
    mandatory=True,
)
# → 50 ≤ P ≤ 200 (no zero option)

Investment Effects

Cost proportional to capacity (€/kW):

\(E = P \cdot c_{spec}\)

fx.InvestParameters(
    specific_effects={'costs': 1200},  # €1200/kW
)

One-time cost if investing:

\(E = s_{inv} \cdot c_{fix}\)

fx.InvestParameters(
    effects_of_investment={'costs': 25000},  # €25k
)

Cost if NOT investing:

\(E = (1 - s_{inv}) \cdot c_{ret}\)

fx.InvestParameters(
    effects_of_retirement={'costs': 8000},  # Demolition
)

Non-linear cost curves (e.g., economies of scale):

\(E = f_{piecewise}(P)\)

fx.InvestParameters(
    piecewise_effects_of_investment=fx.PiecewiseEffects(
        piecewise_origin=fx.Piecewise([
            fx.Piece(0, 100),
            fx.Piece(100, 500),
        ]),
        piecewise_shares={
            'costs': fx.Piecewise([
                fx.Piece(0, 80_000),      # €800/kW for 0-100
                fx.Piece(80_000, 280_000), # €500/kW for 100-500
            ])
        },
    ),
)

See Piecewise for details on the formulation.

Reference

Symbol Type Description
\(P\) \(\mathbb{R}_{\geq 0}\) Investment size (capacity)
\(s_{inv}\) \(\{0, 1\}\) Binary investment decision (0=no, 1=yes)
\(P^{min}\) \(\mathbb{R}_{\geq 0}\) Minimum size (minimum_size)
\(P^{max}\) \(\mathbb{R}_{\geq 0}\) Maximum size (maximum_size)
\(c_{spec}\) \(\mathbb{R}\) Per-size effect (effects_of_investment_per_size)
\(c_{fix}\) \(\mathbb{R}\) Fixed effect (effects_of_investment)
\(c_{ret}\) \(\mathbb{R}\) Retirement effect (effects_of_retirement)

Classes: InvestParameters, InvestmentModel