Generators#

This fragment states Generator from an open-source power system framework (PyPSA). The file declares its three dimensions, the relation Generator_port, two parameters and the variable Generator_p. The file lists Port_p and total_cost under given, and the surface declares them. Generator_cost is a named expression that adds to total_cost (a term). Generator_injection equates Generator_p with the flow at the port through at, so the balance of the surface contains no generator variable.

description: >-
  PyPSA's `Generator`, wired to a port rather than straight to a bus, and cut
  to what a dispatch spec needs: a fixed capacity, no availability profile, no
  ramp limits.
given:
  variables:
    Port_p:
      dims: [snapshot, port]
      description: declared by the surface, and fixed at each generator's port by `Generator_injection`
  expressions:
    total_cost: { dims: [] }
dimensions:
  snapshot: { dtype: datetime, description: dispatch periods }
  port: { dtype: str, description: "the connections components make, one label per connection" }
  generator: { dtype: str, description: "generating units, each on one port" }
maps:
  generator: { port: port }
parameters:
  Generator_p_nom: { dims: [generator], description: nominal power }
  Generator_marginal_cost: { dims: [generator], description: cost of one unit of output }
variables:
  Generator_p:
    dims: [snapshot, generator]
    bounds: { lower: 0, upper: Generator_p_nom }
    description: "`Generator-p` — what a generator produces in a snapshot"
constraints:
  Generator_injection:
    description: >-
      What a generator produces is what its port injects. PyPSA has no row for
      this constraint, because PyPSA writes the generator into the balance.
    dims: [snapshot, generator]
    expression: at(Port_p, by=generator[port]) == Generator_p
expressions:
  Generator_cost:
    expression: sum(Generator_p * Generator_marginal_cost)
    adds_to: total_cost

PyPSA's Generator, wired to a port rather than straight to a bus, and cut to what a dispatch spec needs: a fixed capacity, no availability profile, no ramp limits.

Given#

Symbol	Meaning
\(f\)	`Port_p` over \(\mathcal{J} \times \mathcal{T}\) — declared by the surface, and fixed at each generator's port by `Generator_injection`
\(\mathit{total\_cost}\)	`total_cost` (scalar), an expression this file adds `Generator_cost` to

Sets#

Symbol	Meaning
\(\mathcal{G}\)	index \(g\) — `generator` with \(\mathrm{port}: \mathcal{G} \to \mathcal{J}\) — generating units, each on one port
\(\mathcal{J}\)	index \(j\) — `port` with \(\mathrm{port}: \mathcal{G} \to \mathcal{J}\) — the connections components make, one label per connection
\(\mathcal{T}\)	index \(t\) — `snapshot` — dispatch periods

Parameters#

Symbol	Meaning
\(\mathrm{c}\)	`Generator_marginal_cost` over \(\mathcal{G}\) — cost of one unit of output
\(\mathrm{p}^{\mathrm{nom}}\)	`Generator_p_nom` over \(\mathcal{G}\) — nominal power

Variables#

Symbol	Meaning
\(p\)	`Generator_p` over \(\mathcal{G} \times \mathcal{T}\) — `Generator-p` — what a generator produces in a snapshot

Definitions#

Symbol	Meaning
\(\mathit{Generator\_cost}\)	`Generator_cost` (scalar)

Variable domains#

Generator_p

\[ 0 \le p_{g,t} \le \mathrm{p}^{\mathrm{nom}}_{g} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]

Definitions#

Generator_cost

\[ \mathit{Generator\_cost} = \sum_{g \in \mathcal{G},\ t \in \mathcal{T}} p_{g,t} \cdot \mathrm{c}_{g} \]

Subject to#

Generator_injection

\[ f_{\mathrm{port}(g),t} = p_{g,t} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]