Defining piecewise linear constraints¶

In this tutorial, we use the national scale example model to implement a piecewise linear constraint. This constraint will represent a non-linear relationship between capacity and cost per unit capacity of Concentrating Solar Power (CSP).

In [1]:

import numpy as np
import plotly.express as px

import calliope
from calliope.io import read_rich_yaml

calliope.set_log_verbosity("INFO", include_solver_output=False)

import numpy as np import plotly.express as px import calliope from calliope.io import read_rich_yaml calliope.set_log_verbosity("INFO", include_solver_output=False)

Model setup¶

Defining our piecewise curve¶

In the base national scale model, the CSP has a maximum rated capacity of 10,000 kW and a cost to invest in that capacity of 1000 USD / kW.

In our updated model, the cost to invest in capacity will vary from 5000 USD / kW to 500 USD / kW as the CSP capacity increases:

In [2]:

capacity_steps = [0, 2500, 5000, 7500, 10000]
cost_steps = [0, 3.75e6, 6e6, 7.5e6, 8e6]

cost_per_cap = np.nan_to_num(np.divide(cost_steps, capacity_steps)).astype(int)

fig = px.line(
    x=capacity_steps,
    y=cost_steps,
    labels={"x": "Capacity (kW)", "y": "Investment cost (USD)"},
    markers="o",
    range_y=[0, 10e6],
    text=[f"{i} USD/kW" for i in cost_per_cap],
)
fig.update_traces(textposition="top center")
fig.show()

capacity_steps = [0, 2500, 5000, 7500, 10000] cost_steps = [0, 3.75e6, 6e6, 7.5e6, 8e6] cost_per_cap = np.nan_to_num(np.divide(cost_steps, capacity_steps)).astype(int) fig = px.line( x=capacity_steps, y=cost_steps, labels={"x": "Capacity (kW)", "y": "Investment cost (USD)"}, markers="o", range_y=[0, 10e6], text=[f"{i} USD/kW" for i in cost_per_cap], ) fig.update_traces(textposition="top center") fig.show()

[2025-03-14 18:56:48] WARNING  /tmp/ipykernel_3151/173276940.py:4: RuntimeWarning: invalid value encountered in divide
  cost_per_cap = np.nan_to_num(np.divide(cost_steps, capacity_steps)).astype(int)