Carriers#

This file states the growth limits of each carrier. It is one of the 25 whole specs of one topic each (fragments) that merge composes into the spec of examples/pypsa.yaml. Its limits contain the sum Carrier_additions, which it lists under given. Carrier_growth_limit compares the additions of each period with those of the period before through shift. Its edge=0 leaves the first period its bare allowance.

given:
  expressions:
    Carrier_additions: { dims: [carrier, period] }

dimensions:
  period:
    description: investment periods. It is PyPSA's `investment_periods`
    dtype: int
    ordered: true
  carrier:
    description: energy carriers, what a growth limit is set per

parameters:
  Carrier_max_growth:
    description: >-
      most capacity of a carrier that may be added in a period. No value means
      no limit. It is the least over the scenarios, as PyPSA takes it
      (`global_constraints.py:239-243`), data prep. PyPSA reads it only under
      `multi_investment_periods` (`global_constraints.py:232-233`). Otherwise
      you feed no value in data prep
    dims: [carrier]
    missing: absent
  Carrier_max_relative_growth:
    description: >-
      share of the previous period's additions that may be added on top: the
      least over the scenarios, as PyPSA takes it, data prep
    dims: [carrier]

expressions:
  Carrier_relative_growth:
    description: >-
      the share of the previous period's additions in a carrier's growth
      limit, PyPSA's `max_relative_growth` clipped at zero. A negative share
      thus adds nothing and never tightens the limit
    dims: [carrier]
    cases:
      positive: { when: Carrier_max_relative_growth > 0, expression: Carrier_max_relative_growth }
    otherwise: 0

constraints:
  Carrier_growth_limit:
    description: >-
      `Carrier-growth_limit` — what a carrier adds in a period is at most its
      allowance plus a share of what it added the period before. It counts
      what its extendable components add, each build in the first period it
      is active in. The first period has no predecessor, so `edge=0` leaves it
      the bare allowance
    dims: [carrier, period]
    where: Carrier_max_growth
    expression: >-
      Carrier_additions
      - shift(Carrier_additions, along=period, offset=1, edge=0) * Carrier_relative_growth
      <= Carrier_max_growth

Given#

Symbol	Meaning
\(\mathit{Carrier\_additions}\)	`Carrier_additions` over \(\mathcal{I} \times \mathcal{Y}\), an expression another file defines

Sets#

Symbol	Meaning
\(\mathcal{I}\)	index \(i\) — `carrier` — energy carriers, what a growth limit is set per
\(\mathcal{Y}\)	index \(y\) — `period` — investment periods. It is PyPSA's `investment_periods`

Parameters#

Symbol	Meaning
\(\overline{\Delta}\)	`Carrier_max_growth` over \(\mathcal{I}\), `absent` where the data has no row — most capacity of a carrier that may be added in a period. No value means no limit. It is the least over the scenarios, as PyPSA takes it (`global_constraints.py:239-243`), data prep. PyPSA reads it only under `multi_investment_periods` (`global_constraints.py:232-233`). Otherwise you feed no value in data prep
\(\mathrm{r}\)	`Carrier_max_relative_growth` over \(\mathcal{I}\) — share of the previous period's additions that may be added on top: the least over the scenarios, as PyPSA takes it, data prep

Definitions#

Symbol	Meaning
\(\mathrm{r}^{+}\)	`Carrier_relative_growth` over \(\mathcal{I}\) — the share of the previous period's additions in a carrier's growth limit, PyPSA's `max_relative_growth` clipped at zero. A negative share thus adds nothing and never tightens the limit

Notation#

Symbol	Meaning
\(t \boxminus_{v} k\)	`edge=v` — \(t-k\), and \(v\) past the edge

Definitions#

Carrier_relative_growth

\[ \mathrm{r}^{+}_{i} = \begin{cases} \mathrm{r}_{i} & \text{if } \mathrm{r}_{i} > 0 \\ 0 & \text{otherwise} \end{cases} \qquad \forall\, i \in \mathcal{I} \]

Subject to#

Carrier_growth_limit

\[ \mathit{Carrier\_additions}_{i,y} - \mathit{Carrier\_additions}_{i,y \boxminus_{0} 1} \cdot \mathrm{r}^{+}_{i} \le \overline{\Delta}_{i} \qquad \forall\, i \in \mathcal{I},\ y \in \mathcal{Y} \,:\, \overline{\Delta}_{i} \text{ is defined} \]