Global constraints#

This file states the five system totals that PyPSA caps. Each total is a sum that the components add to. It is one of the 25 whole specs of one topic each (fragments) that merge composes into the spec of examples/pypsa.yaml. Each total has an upper-bound, a lower-bound and an equality row, such as GlobalConstraint_primary_energy_ub.

given:
  parameters:
    scenario_weight: { dims: [scenario] }
  expressions:
    primary_energy: { dims: [global_constraint, scenario] }
    operational_limit: { dims: [global_constraint, scenario] }
    transmission_volume_expansion: { dims: [global_constraint, scenario] }
    transmission_expansion_cost: { dims: [global_constraint, scenario] }
    tech_capacity_expansion: { dims: [global_constraint] }

dimensions:
  scenario:
    description: the futures dispatch is chosen in, each with a weight
  global_constraint:
    description: PyPSA's `GlobalConstraint` rows, one label per declared limit

parameters:
  GlobalConstraint_type:
    description: >-
      which formula the row takes: `primary_energy`, `operational_limit`,
      `transmission_volume_expansion_limit`,
      `transmission_expansion_cost_limit`, `tech_capacity_expansion_limit` or
      `flow_based`
    dims: [global_constraint]
    dtype: str
  GlobalConstraint_sense:
    description: >-
      the row's sense in each scenario: `<=`, `>=` or `==`. PyPSA reads a
      row's sense per scenario (`global_constraints.py:576`, `:779`, `:859-864`)
    dims: [scenario, global_constraint]
    dtype: str
  GlobalConstraint_constant:
    description: >-
      the constant the total is held against. What a variable cannot represent
      is folded in here in data prep. That is an initial charge, times its
      period's years for each counted period where the storage reopens per
      period, or a non-extendable build. PyPSA reads it per scenario
      (`global_constraints.py:577`, `:780`, `:859-864`)
    dims: [scenario, global_constraint]

constraints:
  GlobalConstraint_primary_energy_ub:
    description: "`primary_energy` — its total, at most its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'primary_energy' AND GlobalConstraint_sense == '<='
    expression: primary_energy <= GlobalConstraint_constant
  GlobalConstraint_primary_energy_lb:
    description: "`primary_energy` — its total, at least its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'primary_energy' AND GlobalConstraint_sense == '>='
    expression: primary_energy >= GlobalConstraint_constant
  GlobalConstraint_primary_energy_eq:
    description: "`primary_energy` — its total, at its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'primary_energy' AND GlobalConstraint_sense == '=='
    expression: primary_energy == GlobalConstraint_constant
  GlobalConstraint_operational_limit_ub:
    description: "`operational_limit` — its total, at most its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'operational_limit' AND GlobalConstraint_sense == '<='
    expression: operational_limit <= GlobalConstraint_constant
  GlobalConstraint_operational_limit_lb:
    description: "`operational_limit` — its total, at least its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'operational_limit' AND GlobalConstraint_sense == '>='
    expression: operational_limit >= GlobalConstraint_constant
  GlobalConstraint_operational_limit_eq:
    description: "`operational_limit` — its total, at its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'operational_limit' AND GlobalConstraint_sense == '=='
    expression: operational_limit == GlobalConstraint_constant
  GlobalConstraint_transmission_volume_expansion_limit_ub:
    description: "`transmission_volume_expansion_limit` — its total, at most its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense == '<='
    expression: transmission_volume_expansion <= GlobalConstraint_constant
  GlobalConstraint_transmission_volume_expansion_limit_lb:
    description: "`transmission_volume_expansion_limit` — its total, at least its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense == '>='
    expression: transmission_volume_expansion >= GlobalConstraint_constant
  GlobalConstraint_transmission_volume_expansion_limit_eq:
    description: "`transmission_volume_expansion_limit` — its total, at its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense == '=='
    expression: transmission_volume_expansion == GlobalConstraint_constant
  GlobalConstraint_transmission_expansion_cost_limit_ub:
    description: "`transmission_expansion_cost_limit` — its total, at most its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_expansion_cost_limit' AND GlobalConstraint_sense == '<='
    expression: transmission_expansion_cost <= GlobalConstraint_constant
  GlobalConstraint_transmission_expansion_cost_limit_lb:
    description: "`transmission_expansion_cost_limit` — its total, at least its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_expansion_cost_limit' AND GlobalConstraint_sense == '>='
    expression: transmission_expansion_cost >= GlobalConstraint_constant
  GlobalConstraint_transmission_expansion_cost_limit_eq:
    description: "`transmission_expansion_cost_limit` — its total, at its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_expansion_cost_limit' AND GlobalConstraint_sense == '=='
    expression: transmission_expansion_cost == GlobalConstraint_constant
  GlobalConstraint_tech_capacity_expansion_limit_ub:
    description: "`tech_capacity_expansion_limit` — its total, at most its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'tech_capacity_expansion_limit' AND GlobalConstraint_sense == '<='
    expression: tech_capacity_expansion <= GlobalConstraint_constant
  GlobalConstraint_tech_capacity_expansion_limit_lb:
    description: "`tech_capacity_expansion_limit` — its total, at least its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'tech_capacity_expansion_limit' AND GlobalConstraint_sense == '>='
    expression: tech_capacity_expansion >= GlobalConstraint_constant
  GlobalConstraint_tech_capacity_expansion_limit_eq:
    description: "`tech_capacity_expansion_limit` — its total, at its constant"
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'tech_capacity_expansion_limit' AND GlobalConstraint_sense == '=='
    expression: tech_capacity_expansion == GlobalConstraint_constant

assumptions:
  GlobalConstraint_tech_capacity_expansion_limit_without_scenarios:
    holds: "GlobalConstraint_type != 'tech_capacity_expansion_limit'"
    where: "count(scenario_weight, over=scenario) > 1"
    description: >-
      PyPSA does not build a `tech_capacity_expansion_limit` row on a network
      with scenarios and refuses it (`global_constraints.py:68-70`). The spec
      cannot tell a network with one scenario from one with none. A tool thus
      refuses the row only where there is more than one scenario

Given#

Symbol	Meaning
\(\pi\)	`scenario_weight` over \(\Xi\), data another file declares
\(\mathit{operational\_limit}\)	`operational_limit` over \(\mathcal{G} \times \Xi\), an expression another file defines
\(\mathit{primary\_energy}\)	`primary_energy` over \(\mathcal{G} \times \Xi\), an expression another file defines
\(\mathit{tech\_capacity\_expansion}\)	`tech_capacity_expansion` over \(\mathcal{G}\), an expression another file defines
\(\mathit{transmission\_expansion\_cost}\)	`transmission_expansion_cost` over \(\mathcal{G} \times \Xi\), an expression another file defines
\(\mathit{transmission\_volume\_expansion}\)	`transmission_volume_expansion` over \(\mathcal{G} \times \Xi\), an expression another file defines

Sets#

Symbol	Meaning
\(\mathcal{G}\)	index \(g\) — `global_constraint` — PyPSA's `GlobalConstraint` rows, one label per declared limit
\(\Xi\)	index \(\xi\) — `scenario` — the futures dispatch is chosen in, each with a weight

Parameters#

Symbol	Meaning
\(\mathrm{K}\)	`GlobalConstraint_constant` over \(\mathcal{G} \times \Xi\) — the constant the total is held against. What a variable cannot represent is folded in here in data prep. That is an initial charge, times its period's years for each counted period where the storage reopens per period, or a non-extendable build. PyPSA reads it per scenario (`global_constraints.py:577`, `:780`, `:859-864`)
\(\mathrm{sense}\)	`GlobalConstraint_sense` over \(\mathcal{G} \times \Xi\) — the row's sense in each scenario: `<=`, `>=` or `==`. PyPSA reads a row's sense per scenario (`global_constraints.py:576`, `:779`, `:859-864`)
\(\mathrm{type}\)	`GlobalConstraint_type` over \(\mathcal{G}\) — which formula the row takes: `primary_energy`, `operational_limit`, `transmission_volume_expansion_limit`, `transmission_expansion_cost_limit`, `tech_capacity_expansion_limit` or `flow_based`

Subject to#

GlobalConstraint_operational_limit_eq

\[ \mathit{operational\_limit}_{g,\xi} = \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{operational\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{==}\text{'} \]

GlobalConstraint_operational_limit_lb

\[ \mathit{operational\_limit}_{g,\xi} \ge \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{operational\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{>=}\text{'} \]

GlobalConstraint_operational_limit_ub

\[ \mathit{operational\_limit}_{g,\xi} \le \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{operational\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{<=}\text{'} \]

GlobalConstraint_primary_energy_eq

\[ \mathit{primary\_energy}_{g,\xi} = \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{primary\_energy}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{==}\text{'} \]

GlobalConstraint_primary_energy_lb

\[ \mathit{primary\_energy}_{g,\xi} \ge \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{primary\_energy}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{>=}\text{'} \]

GlobalConstraint_primary_energy_ub

\[ \mathit{primary\_energy}_{g,\xi} \le \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{primary\_energy}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{<=}\text{'} \]

GlobalConstraint_tech_capacity_expansion_limit_eq

\[ \mathit{tech\_capacity\_expansion}_{g} = \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{tech\_capacity\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{==}\text{'} \]

GlobalConstraint_tech_capacity_expansion_limit_lb

\[ \mathit{tech\_capacity\_expansion}_{g} \ge \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{tech\_capacity\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{>=}\text{'} \]

GlobalConstraint_tech_capacity_expansion_limit_ub

\[ \mathit{tech\_capacity\_expansion}_{g} \le \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{tech\_capacity\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{<=}\text{'} \]

GlobalConstraint_transmission_expansion_cost_limit_eq

\[ \mathit{transmission\_expansion\_cost}_{g,\xi} = \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_expansion\_cost\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{==}\text{'} \]

GlobalConstraint_transmission_expansion_cost_limit_lb

\[ \mathit{transmission\_expansion\_cost}_{g,\xi} \ge \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_expansion\_cost\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{>=}\text{'} \]

GlobalConstraint_transmission_expansion_cost_limit_ub

\[ \mathit{transmission\_expansion\_cost}_{g,\xi} \le \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_expansion\_cost\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{<=}\text{'} \]

GlobalConstraint_transmission_volume_expansion_limit_eq

\[ \mathit{transmission\_volume\_expansion}_{g,\xi} = \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_volume\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{==}\text{'} \]

GlobalConstraint_transmission_volume_expansion_limit_lb

\[ \mathit{transmission\_volume\_expansion}_{g,\xi} \ge \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_volume\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{>=}\text{'} \]

GlobalConstraint_transmission_volume_expansion_limit_ub

\[ \mathit{transmission\_volume\_expansion}_{g,\xi} \le \mathrm{K}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{type}_{g} = \text{'}\mathrm{transmission\_volume\_expansion\_limit}\text{'} \wedge \mathrm{sense}_{g,\xi} = \text{'}\mathrm{<=}\text{'} \]

Assumptions#

GlobalConstraint_tech_capacity_expansion_limit_without_scenarios

\[ \mathrm{type}_{g} \neq \text{'}\mathrm{tech\_capacity\_expansion\_limit}\text{'} \qquad \forall\, g \in \mathcal{G} \,:\, \lvert \{ \xi \in \Xi \,:\, \pi_{\xi} \text{ is defined} \} \rvert > 1 \]