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Loads#

This fragment states Load from an open-source power system framework (PyPSA). The file declares the relation Load_port, the parameter Load_p_set and the constraint Load_withdrawal. The minus sign in front of Load_p_set is the only place where the file uses the sign convention of the surface.

description: PyPSA's `Load`, wired to a port rather than straight to a bus. What a load takes is data, so the file declares no variable.
given:
  variables:
    Port_p:
      dims: [snapshot, port]
      description: declared by the surface, and fixed at each load's port by `Load_withdrawal`
dimensions:
  snapshot: { dtype: datetime, description: dispatch periods }
  port: { dtype: str, description: "the connections components make, one label per connection" }
  load: { dtype: str, description: "demands, each on one port" }
relations:
  Load_port: { key: load, values: port }
parameters:
  Load_p_set: { dims: [snapshot, load], description: "`Load-p_set` — what a load takes in a snapshot" }
constraints:
  Load_withdrawal:
    description: >-
      What a load takes is what its port withdraws. PyPSA has no row for this
      constraint, because PyPSA writes the load into the balance.
    dims: [snapshot, load]
    expression: at(Port_p, by=Load_port[port]) == -Load_p_set

PyPSA's Load, wired to a port rather than straight to a bus. What a load takes is data, so the file declares no variable.

Given#

Symbol Meaning
\(f\) Port_p over \(\mathcal{J} \times \mathcal{T}\) — declared by the surface, and fixed at each load's port by Load_withdrawal

Sets#

Symbol Meaning
\(\mathcal{D}\) index \(d\) — load with \(\mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — demands, each on one port
\(\mathcal{J}\) index \(j\) — port with \(\mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — the connections components make, one label per connection
\(\mathcal{T}\) index \(t\) — snapshot — dispatch periods

Parameters#

Symbol Meaning
\(\mathrm{load}\) Load_p_set over \(\mathcal{D} \times \mathcal{T}\) — Load-p_set — what a load takes in a snapshot

Subject to#

Load_withdrawal

\[ f_{\mathrm{Load\_port}(d),t} = -\mathrm{load}_{d,t} \qquad \forall\, d \in \mathcal{D},\ t \in \mathcal{T} \]

See also