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Cost

costs

Cost calculation utilities for PyPSA.

Referenced by:

Functions:

  • annuity –

    Calculate the annuity factor for given discount rate and lifetime.

  • periodized_cost –

    Calculate fixed costs for the modeled horizon from capital or overnight cost.

pypsa.costs.annuity 

annuity(discount_rate: float | Series, lifetime: float | Series) -> float | Series

Calculate the annuity factor for given discount rate and lifetime.

v1.1.0

Converts overnight investment cost to an annualized cost using the formula:

\[\frac{r}{1 - (1 + r)^{-n}}\]

Special cases:

  • Zero discount rate: returns 1/lifetime (simple depreciation)
  • Infinite lifetime with r > 0: returns the discount rate
  • Infinite lifetime with r <= 0: returns 0
  • Negative discount rates are allowed (penalizes the present)

Parameters:

  • discount_rate (float | Series) –

    Discount rate as decimal (e.g., 0.07 for 7%).

  • lifetime (float | Series) –

    Asset lifetime in years. Must be positive.

Returns:

  • float | Series –

    Annual annuity factor to multiply overnight cost by.

Examples:

>>> import pypsa
>>> pypsa.costs.annuity(0.07, 25)
0.0858...
>>> pypsa.costs.annuity(0.0, 20)  # 0% discount rate = simple depreciation
0.05
>>> pypsa.costs.annuity(-0.02, 20)
0.040...
Referenced by:

pypsa.costs.periodized_cost 

periodized_cost(capital_cost: float | Series, overnight_cost: float | Series, discount_rate: float | Series, lifetime: float | Series, fom_cost: float | Series | None = None, nyears: float | Series = 1.0) -> float | Series

Calculate fixed costs for the modeled horizon from capital or overnight cost.

v1.1.0

This function calculates the total fixed cost for the modeled horizon n.nyears by:

  1. If overnight_cost is provided (not NaN): annuitize it using discount_rate and lifetime, then scale by nyears and add fom_cost.
  2. If overnight_cost is NaN: use capital_cost directly (already scaled to the model horizon) and add fom_cost.

Parameters:

  • capital_cost (float | Series) –

    Investment cost per unit of capacity for the modeled horizon.

  • overnight_cost (float | Series) –

    Overnight (upfront) investment cost. If NaN, capital_cost is used.

  • discount_rate (float | Series) –

    Discount rate as decimal. Used only when overnight_cost is provided.

  • lifetime (float | Series) –

    Asset lifetime in years.

  • fom_cost (float | Series, default: None ) –

    Fixed operation and maintenance cost per unit of capacity for the modeled horizon. Default None.

  • nyears (float | Series, default: 1.0 ) –

    Modeled time horizon in years. Used only to scale annuitized overnight costs. If provided as a Series indexed by investment period, all values must be identical when overnight_cost is used. Default 1.0.

Returns:

  • float | Series –

    Fixed cost per unit of capacity for the modeled horizon.

Examples:

Using overnight cost with annuitization:

>>> periodized_cost(
...     capital_cost=0,
...     overnight_cost=1000,
...     discount_rate=0.07,
...     lifetime=25,
...     nyears=1.0,
... )
85.81...

Falling back to capital_cost when overnight_cost is NaN:

>>> periodized_cost(
...     capital_cost=100,
...     overnight_cost=np.nan,
...     discount_rate=0.07,
...     lifetime=25,
... )
100
Referenced by: