Skip to content

Time-varying flow limit#

An extension of Calliope in fragments. Calliope's example max_time_varying.yaml: outflow at most a share of the flow capacity that varies in time.

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

parameters:
  flow_cap_max_relative_per_ts:
    description: "`flow_cap_max_relative_per_ts` — the share of its flow capacity a technology may put out in a time step; given only where set"
    dims: [nodes, techs, timesteps]

given:
  parameters:
    flow_out_parasitic_eff: { dims: [nodes, techs, carriers, timesteps] }
  variables:
    flow_out: { dims: [nodes, techs, carriers, timesteps] }
    flow_cap: { dims: [nodes, techs, carriers] }

constraints:
  max_time_varying_flow_cap:
    description: "`max_time_varying_flow_cap` — outflow is at most a share of the flow capacity that varies in time"
    dims: [nodes, techs, carriers, timesteps]
    where: flow_out AND flow_cap_max_relative_per_ts
    expression: flow_out <= flow_cap_max_relative_per_ts * flow_cap * flow_out_parasitic_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

Parameters#

Symbol Meaning
\(\mathrm{flow\_cap\_max\_relative\_per\_ts}\) flow_cap_max_relative_per_ts over \(\mathcal{N} \times \mathcal{I} \times \mathcal{T}\) — flow_cap_max_relative_per_ts — the share of its flow capacity a technology may put out in a time step; given only where set

Given#

Symbol Meaning
\(\mathrm{flow\_out\_parasitic\_eff}\) flow_out_parasitic_eff over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C} \times \mathcal{T}\), data another file declares
\(\mathit{flow\_out}\) flow_out over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C} \times \mathcal{T}\)
\(\mathit{flow\_cap}\) flow_cap over \(\mathcal{N} \times \mathcal{I} \times \mathcal{C}\)

Subject to#

max_time_varying_flow_cap

\[ \mathit{flow\_out}_{n,i,c,t} \le \mathrm{flow\_cap\_max\_relative\_per\_ts}_{n,i,t} \cdot \mathit{flow\_cap}_{n,i,c} \cdot \mathrm{flow\_out\_parasitic\_eff}_{n,i,c,t} \qquad \forall\, n \in \mathcal{N},\ i \in \mathcal{I},\ c \in \mathcal{C},\ t \in \mathcal{T} \,:\, \mathit{flow\_out}_{n,i,c,t} \text{ exists} \wedge \mathrm{flow\_cap\_max\_relative\_per\_ts}_{n,i,t} \text{ is defined} \]