dispatch

Least-cost generation against a load profile — the smallest model that is still a model.

The problem

Pick an output \(p_{s,g}\) for every generator in every snapshot, so that the fleet meets the load exactly and costs as little as possible:

\[\min \sum_{s,g} c_g \, p_{s,g} \quad\text{s.t.}\quad \sum_g p_{s,g} = \ell_s ,\quad 0 \le p_{s,g} \le \bar p_g\]

The model

dimensions:
  snapshot:
    dtype: int
  generator:
    values: [wind, solar, gas]

parameters:
  p_max:
    dims: [generator]
  load:
    dims: [snapshot]
  cost:
    dims: [generator]

variables:
  p:
    foreach: [snapshot, generator]
    where: "p_max > 0"
    bounds:
      lower: 0
      upper: p_max

constraints:
  power_balance:
    foreach: [snapshot]
    equations:
      - expression: sum(p, over=generator) == load

objectives:
  total_cost:
    sense: minimize
    equations:
      - expression: p * cost

What it exercises

where: "p_max > 0" is the one line worth pausing on. A generator with no capacity gets no columns at all — not a column pinned to zero — so a retired unit costs nothing to carry in the data. That is row absence, and it is how sparsity is spelled throughout: see where in the language reference.

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examples/dispatch.yaml · back to all models