walkthrough

The dispatch model plus a macro and a named expression — the one used to print every pipeline stage.

The model

The same model, as math

The dispatch model of README.md, plus one macro and one named expression — small enough to print in full, complete enough that every pipeline stage in examples/walkthrough.py has something to show.

Sets

Symbol	Meaning
\(\mathcal{S}\)	index \(s\) --- snapshot --- dispatch periods
\(\mathcal{G}\)	index \(g\) --- generator --- generating units, including oil, which is retired and gets no columns at all

Parameters

Symbol	Meaning
\(\bar p\)	p_max over \(\mathcal{G}\) --- installed capacity, zero for a retired unit
\(\ell\)	load over \(\mathcal{S}\) --- demand to be met
\(c\)	cost over \(\mathcal{G}\) --- marginal cost

Variables

Symbol	Meaning
\(p\)	p over \(\mathcal{S} \times \mathcal{G}\) --- output of a generator in a snapshot — the where drops the retired unit entirely, so the built model is smaller than the coordinate product

Objective

\[\min \sum_{s \in \mathcal{S}} \sum_{g \in \mathcal{G}} p_{s,g} \cdot c_{g}\]

Subject to

power_balance

\[\sum_{g \in \mathcal{G}} p_{s,g} = \ell_{s} \qquad \forall\thinspace s \in \mathcal{S}\]

Variable domains

p

\[0 \le p_{s,g} \le \bar p_{g} \qquad \forall\thinspace s \in \mathcal{S},\enspace g \in \mathcal{G} \thinspace:\thinspace \bar p_{g} > 0\]

description: >-
  The dispatch model of README.md, plus one macro and one named expression —
  small enough to print in full, complete enough that every pipeline stage in
  examples/walkthrough.py has something to show.

dimensions:
  snapshot:
    description: dispatch periods
    dtype: int
  generator:
    description: >-
      generating units, including oil, which is retired and gets no columns at
      all
    values: [wind, solar, gas, oil]

parameters:
  p_max: {dims: [generator], description: "installed capacity, zero for a retired unit"}
  load: {dims: [snapshot], description: "demand to be met"}
  cost: {dims: [generator], description: "marginal cost"}

expressions:
  total_supply:
    expression: sum(p, over=generator)
    description: what the whole fleet produces in a snapshot

macros:
  weighted_sum:
    description: an array priced by a second one and summed over a dimension
    args: [array, weights]
    kwargs: [over]
    template: sum(array * weights, over=over)

variables:
  p:
    description: >-
      output of a generator in a snapshot — the `where` drops the retired unit
      entirely, so the built model is smaller than the coordinate product
    foreach: [snapshot, generator]
    where: "p_max > 0"
    bounds:
      lower: 0
      upper: p_max

constraints:
  power_balance:
    description: the fleet meets the load exactly in every snapshot
    foreach: [snapshot]
    expression: total_supply == load

objective:
  sense: minimize
  description: total cost of generation over the horizon
  expression: weighted_sum(p, cost, over=generator)

What it exercises

This is the model behind python examples/walkthrough.py, which runs it through every stage — YAML → schema → core AST → logical plan → model frames → LP text → solution — printing what each stage produces, then two models the language refuses and why. The committed output is examples/walkthrough.out if you would rather read than run.

It is the only model here that uses tier 2: a macro and a named expression. The macro does not survive past expansion — nothing downstream of expansion.py knows it existed, which is what makes it free. The named expression is substituted the same way wherever a constraint uses it, but its name survives on the model: stage 6 reads total_supply back at the solution with expression(), lowered on that read rather than at build, so declaring it still costs the build nothing.

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examples/walkthrough.yaml · back to all models