SizingParameters.md

SizingParameters

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

!!! note "Naming Change" SizingParameters replaces the deprecated InvestParameters. For investment timing with fixed lifetime (when to invest), see InvestmentParameters.

Basic: Size as Variable

$$ P^{min} \leq P \leq P^{max} $$

battery = fx.Storage(
    ...,
    capacity_in_flow_hours=fx.SizingParameters(
        minimum_size=10,
        maximum_size=1000,
        effects_per_size={'costs': 600},  # €600/kWh
    ),
)

---

Sizing Modes

By default, sizing is optional — the optimizer can choose $P = 0$ (don't build).

=== "Continuous"

Choose size within range (or zero):

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

=== "Binary"

Fixed size or nothing:

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

=== "Mandatory"

Force sizing with `mandatory=True` — zero not allowed:

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

---

Sizing Effects

=== "Per-Size Cost"

Cost proportional to capacity (€/kW):

$E = P \cdot c_{spec}$

```python
fx.SizingParameters(
    effects_per_size={'costs': 1200},  # €1200/kW
)
```

=== "Fixed Cost"

One-time cost if sizing:

$E = s_{sized} \cdot c_{fix}$

```python
fx.SizingParameters(
    effects_of_size={'costs': 25000},  # €25k
)
```

=== "Retirement Cost"

Cost if NOT sizing (demolition, opportunity cost):

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

```python
fx.SizingParameters(
    effects_of_retirement={'costs': 8000},  # Demolition
)
```

=== "Piecewise Cost"

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

$E = f_{piecewise}(P)$

```python
fx.SizingParameters(
    piecewise_effects_per_size=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](Piecewise.md) for details on the formulation.

---

Reference

Symbol	Type	Description
$P$	$\mathbb{R}_{\geq 0}$	Size (capacity)
$s_{sized}$	${0, 1}$	Binary sizing 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_per_size)
$c_{fix}$	$\mathbb{R}$	Fixed effect (effects_of_size)
$c_{ret}$	$\mathbb{R}$	Retirement effect (effects_of_retirement)

Classes: [SizingParameters][flixopt.interface.SizingParameters], [SizingModel][flixopt.features.SizingModel]