The balance#

One of the base fragments of Calliope in fragments. Calliope's system_balance: at each node, in each time step, a carrier's production equals its consumption. The file declares the sum carrier_flow empty, and every file that moves a carrier adds its term.

dimensions:
  nodes:
    description: Calliope's `nodes` — the places technologies stand at
  techs:
    description: Calliope's `techs` — technologies
  carriers:
    description: Calliope's `carriers` — energy and commodity carriers
  timesteps:
    description: Calliope's `timesteps` — time steps, in order
    dtype: datetime

given:
  parameters:
    carrier_in:
      description: whether a technology consumes a carrier at a node
      dims: [nodes, techs, carriers]
      dtype: bool
    carrier_out:
      description: whether a technology produces a carrier at a node
      dims: [nodes, techs, carriers]
      dtype: bool

expressions:
  carrier_flow:
    description: >-
      what every technology and every other file puts into a node's carrier,
      less what it takes out
    dims: [nodes, carriers, timesteps]
    empty: true

constraints:
  system_balance:
    description: >-
      `system_balance` — at every node, in every time step, a carrier's
      production equals its consumption. Built where a technology at the
      node produces or consumes the carrier
    dims: [nodes, carriers, timesteps]
    where: count(carrier_in, over=techs) >= 1 OR count(carrier_out, over=techs) >= 1
    expression: carrier_flow == 0

Sets#

Symbol	Meaning
\(\mathcal{N}\)	index \(n\) — `nodes` — Calliope's `nodes` — the places technologies stand at
\(\mathcal{I}\)	index \(i\) — `techs` — Calliope's `techs` — technologies
\(\mathcal{C}\)	index \(c\) — `carriers` — Calliope's `carriers` — energy and commodity carriers
\(\mathcal{T}\)	index \(t\) — `timesteps` — Calliope's `timesteps` — time steps, in order

Given#

Symbol	Meaning
\(\mathrm{carrier\_in}\)	`carrier_in` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C}\), data another file declares — whether a technology consumes a carrier at a node
\(\mathrm{carrier\_out}\)	`carrier_out` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C}\), data another file declares — whether a technology produces a carrier at a node

Definitions#

Symbol	Meaning
\(\mathit{carrier\_flow}\)	`carrier_flow` over \(\mathcal{N} \times \mathcal{C} \times \mathcal{T}\) — what every technology and every other file puts into a node's carrier, less what it takes out

Subject to#

system_balance

\[ \mathit{carrier\_flow}_{n,c,t} = 0 \qquad \forall\, n \in \mathcal{N},\ c \in \mathcal{C},\ t \in \mathcal{T} \,:\, \lvert \{ i \in \mathcal{I} \,:\, \mathrm{carrier\_in}_{n,i,c} \} \rvert \ge 1 \vee \lvert \{ i \in \mathcal{I} \,:\, \mathrm{carrier\_out}_{n,i,c} \} \rvert \ge 1 \]

Definitions#

carrier_flow

\[ \mathit{carrier\_flow}_{n,c,t} = \cdots \qquad \forall\, n \in \mathcal{N},\ c \in \mathcal{C},\ t \in \mathcal{T} \]