Supply with storage#

One of the base fragments of Calliope in fragments. Calliope's balance_supply_with_storage, the one row that couples a supply technology to a store. It is a file of its own so that supply and storage each compose without the other.

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:
    base_tech: { dims: [techs], dtype: str }
    carrier_out: { dims: [nodes, techs, carriers], dtype: bool }
    source_eff: { dims: [nodes, techs, timesteps] }
  variables:
    storage: { dims: [nodes, techs, timesteps] }
    source_use: { dims: [nodes, techs, timesteps] }
  expressions:
    storage_previous_step: { dims: [nodes, techs, timesteps] }
    flow_out_inc_eff: { dims: [nodes, techs, carriers, timesteps] }

constraints:
  balance_supply_with_storage:
    description: >-
      `balance_supply_with_storage` — a supply technology with a store puts
      in what it takes from its source and draws out what it puts out
    dims: [nodes, techs, carriers, timesteps]
    where: carrier_out AND storage AND base_tech == 'supply'
    expression: storage == storage_previous_step + source_use * source_eff - flow_out_inc_eff

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
\(\mathrm{base\_tech}\)	`base_tech` over \(\mathcal{I}\), data another file declares
\(\mathrm{carrier\_out}\)	`carrier_out` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C}\), data another file declares
\(\mathrm{source\_eff}\)	`source_eff` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{T}\), data another file declares
\(\mathit{storage}\)	`storage` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{T}\)
\(\mathit{source\_use}\)	`source_use` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{T}\)
\(\mathit{storage}^{\mathrm{previous,step}}\)	`storage_previous_step` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{T}\), an expression another file defines
\(\mathit{flow\_out\_inc\_eff}\)	`flow_out_inc_eff` over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C} \times \mathcal{T}\), an expression another file defines

Subject to#

balance_supply_with_storage

\[ \mathit{storage}_{n,i,t} = \mathit{storage}^{\mathrm{previous,step}}_{n,i,t} + \mathit{source\_use}_{n,i,t} \cdot \mathrm{source\_eff}_{n,i,t} - \mathit{flow\_out\_inc\_eff}_{n,i,c,t} \qquad \forall\, n \in \mathcal{N},\ i \in \mathcal{I},\ c \in \mathcal{C},\ t \in \mathcal{T} \,:\, \mathrm{carrier\_out}_{n,i,c} \wedge \mathit{storage}_{n,i,t} \text{ exists} \wedge \mathrm{base\_tech}_{i} = \text{'}\mathrm{supply}\text{'} \]