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Generator maintenance#

This file states the maintenance rows of PyPSA's Generator. It is one of the 25 whole specs of one topic each (fragments) that merge composes into the spec of examples/pypsa.yaml. Generator_maint_window states that a unit is in maintenance exactly where an event it started covers the snapshot, through a sum by a relation.

given:
  parameters:
    Generator_p_nom_extendable: { dims: [generator], dtype: bool }
    Generator_committable: { dims: [generator], dtype: bool }
    Generator_p_nom_mod: { dims: [generator] }
    Generator_modules_installed: { dims: [scenario, generator] }
    Generator_active: { dims: [snapshot, generator], dtype: bool }
    snapshot_weightings_generators: { dims: [snapshot] }
    Generator_p_nom_min: { dims: [scenario, generator] }
    Generator_p_nom_max: { dims: [scenario, generator] }
  variables:
    Generator_status: { dims: [scenario, snapshot, generator], domain: integer }
    Generator_p_nom_ext: { dims: [generator] }
  conditions:
    Generator_committed: { dims: [generator, snapshot] }

dimensions:
  scenario:
    description: the futures dispatch is chosen in, each with a weight
  snapshot:
    description: dispatch periods
    dtype: datetime
    ordered: true
  generator:
    description: generating units, each on one bus

relations:
  Generator_maintenance_cover:
    description: >-
      the snapshots a maintenance event covers, by the snapshot it starts in,
      data prep. In a scenario, they are the start and the snapshots after it,
      until their generator weightings reach that scenario's
      `maintenance_duration`. A generator that is not maintainable has no rows
    dims: { scenario: scenario, generator: generator, start: snapshot, covered: snapshot }
    missing: absent

parameters:
  Generator_maintainable:
    description: >-
      whether a generator must be taken off for maintenance within the
      horizon: in any scenario, as PyPSA takes the union over them
      (`components.py:1000-1003`)
    dims: [generator]
    dtype: bool
  Generator_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, generator]
  Generator_maintenance_events:
    description: how many maintenance events occur within the horizon
    dims: [scenario, generator]
    dtype: int
  Generator_maintenance_duration:
    description: >-
      the hours of generator weightings one maintenance event covers, PyPSA's
      `maintenance_duration`. It has no value where the generator is not
      maintainable. No row contains it. In data prep you turn it into
      `Generator_maintenance_cover` and `Generator_maintenance_start_blocked`.
      The assumptions state that it fits the horizon
    dims: [scenario, generator]
    missing: absent
  Generator_maintenance_start_blocked:
    description: >-
      true where no maintenance event may start, data prep. The snapshots it
      would cover there run past the end of the horizon or into one the
      generator is not active in. It is PyPSA's `active & ~valid`, from
      `maintenance_duration` and the generator weightings
    dims: [scenario, snapshot, generator]
    dtype: bool

variables:
  Generator_maintenance:
    description: >-
      `Generator-maintenance` — whether a maintainable generator is in maintenance:
      continuous, and one exactly where an event covers the snapshot
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    missing: 0
    bounds:
      lower: 0
      upper: 1
  Generator_maintenance_start:
    description: "`Generator-maintenance_start` — whether a maintenance event starts in this snapshot"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    missing: 0
    domain: binary
  Generator_maintenance_capacity:
    description: >-
      `Generator-maintenance_capacity` — the chosen build while in
      maintenance, zero otherwise: the product the `maintcap` rows linearise
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    missing: 0
    bounds:
      lower: 0
  Generator_maintenance_status:
    description: >-
      `Generator-maintenance_status` — the status while in maintenance, zero
      otherwise: the product the `maint-status` rows linearise, so a unit in
      maintenance may also be off
    dims: [scenario, snapshot, generator]
    where: >-
      Generator_maintainable
      AND Generator_committed
      AND NOT (Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0))
    missing: 0
    bounds:
      lower: 0

expressions:
  Generator_maintenance_modules:
    description: >-
      how many modules of a modular committable generator can be on in
      maintenance: its build cap in modules where the build is extendable,
      and the modules installed where it is fixed (`constraints.py:588-594`)
    dims: [scenario, generator]
    cases:
      extendable: { when: Generator_p_nom_extendable, expression: Generator_p_nom_max / Generator_p_nom_mod }
    otherwise: Generator_modules_installed

conditions:
  Generator_maint_ext:
    description: >-
      a maintainable generator with an extendable build that is active in the
      snapshot's period, unless it is committable and modular. These are the
      maintenance rows against the chosen build
    condition: >-
      Generator_maintainable
      AND Generator_p_nom_extendable
      AND NOT (Generator_committable AND Generator_p_nom_mod > 0)
      AND Generator_active

constraints:
  Generator_maint_event_count:
    description: "`Generator-maint-event-count` — a maintainable generator holds its number of maintenance events over the horizon"
    dims: [scenario, generator]
    where: Generator_maintainable
    expression: sum(Generator_maintenance_start, over=snapshot) == Generator_maintenance_events
  Generator_maint_window:
    description: >-
      `Generator-maint-window` — a generator is in maintenance exactly where
      an event it started covers the snapshot. Two events do not overlap,
      since the maintenance status is at most one
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    expression: Generator_maintenance == sum(Generator_maintenance_start, over=start, by=Generator_maintenance_cover[covered])
  Generator_maint_start_horizon:
    description: "`Generator-maint-start-horizon` — no event starts where it could not run its whole duration"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active AND Generator_maintenance_start_blocked
    expression: Generator_maintenance_start == 0
  Generator_maintcap_upper:
    description: >-
      `Generator-maintcap_upper` — the build taken off is at most the chosen build in
      maintenance, and at most the build less its floor out of it
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity <= Generator_p_nom_ext - Generator_p_nom_min * (1 - Generator_maintenance)
  Generator_maintcap_upper_nommax:
    description: "`Generator-maintcap_upper_nommax` — out of maintenance, no build is taken off"
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity <= Generator_p_nom_max * Generator_maintenance
  Generator_maintcap_lower_nommax:
    description: "`Generator-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off"
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity >= Generator_p_nom_ext - Generator_p_nom_max * (1 - Generator_maintenance)
  Generator_maintcap_lower_nommin:
    description: "`Generator-maintcap_lower_nommin` — in maintenance, at least the floor of the build is taken off"
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext AND Generator_p_nom_min > 0
    expression: Generator_maintenance_capacity >= Generator_p_nom_min * Generator_maintenance
  Generator_maint_status_le_status:
    description: "`Generator-maint-status-le-status` — the status in maintenance is at most the status"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0)
    expression: Generator_maintenance_status <= Generator_status
  Generator_maint_status_le_maint:
    description: "`Generator-maint-status-le-maint` — out of maintenance, the status in maintenance is zero"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0)
    expression: Generator_maintenance_status <= Generator_maintenance
  Generator_maint_status_lb:
    description: "`Generator-maint-status-lb` — on and in maintenance, the status in maintenance is one"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0)
    expression: Generator_maintenance_status >= Generator_status + Generator_maintenance - 1
  Generator_maint_modstatus_le_status:
    description: "`Generator-maint-modstatus-le-status` — the modules on in maintenance are at most the modules on"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status <= Generator_status
  Generator_maint_modstatus_le_maint:
    description: >-
      `Generator-maint-modstatus-le-maint` — out of maintenance, no module is
      on in maintenance. In it, at most its modules in maintenance
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status <= Generator_maintenance_modules * Generator_maintenance
  Generator_maint_modstatus_lb:
    description: "`Generator-maint-modstatus-lb` — in maintenance, every module on is on in maintenance"
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status >= Generator_status - Generator_maintenance_modules * (1 - Generator_maintenance)

assumptions:
  Generator_maintenance_events_positive:
    holds: "Generator_maintenance_events > 0"
    where: "Generator_maintainable"
    description: >-
      a maintainable generator with no event schedules no maintenance. PyPSA
      refuses it (`consistency.py:1541`)
  Generator_maintenance_duration_positive:
    holds: "Generator_maintenance_duration > 0"
    where: "Generator_maintainable"
    description: >-
      an event that covers no hours is no maintenance window. PyPSA refuses it
      (`consistency.py:1531`)
  Generator_maintenance_duration_fits_the_horizon:
    holds: "Generator_maintenance_duration <= sum(snapshot_weightings_generators, over=snapshot)"
    where: "Generator_maintainable"
    description: >-
      one event longer than the horizon, in generator weightings, blocks every
      start and makes the event count infeasible. PyPSA refuses it
      (`consistency.py:1552`)
  Generator_maintenance_events_fit_the_horizon:
    holds: "Generator_maintenance_duration * Generator_maintenance_events <= sum(snapshot_weightings_generators, over=snapshot)"
    where: "Generator_maintainable"
    description: >-
      the events together longer than the horizon, in generator weightings,
      cannot all be scheduled. PyPSA refuses it (`consistency.py:1564`)
  Generator_maintenance_build_cap_is_finite:
    holds: "Generator_p_nom_max < inf"
    where: "Generator_maintainable AND Generator_p_nom_extendable"
    description: >-
      the `maintcap` rows bound the chosen build in maintenance by
      `p_nom_max`, so an infinite cap is an infinite coefficient. PyPSA
      refuses it (`consistency.py:1576`)

Given#

Symbol Meaning
\(\mathrm{on}\) Generator_active over \(\mathcal{G} \times \mathcal{T}\), data another file declares
\(\mathrm{com}\) Generator_committable over \(\mathcal{G}\), data another file declares
\(\mathrm{N}^{\mathrm{fix}}\) Generator_modules_installed over \(\mathcal{G} \times \Xi\), data another file declares
\(\mathrm{ext}\) Generator_p_nom_extendable over \(\mathcal{G}\), data another file declares
\(\overline{\mathrm{p}}^{\mathrm{nom}}\) Generator_p_nom_max over \(\mathcal{G} \times \Xi\), data another file declares
\(\underline{\mathrm{p}}^{\mathrm{nom}}\) Generator_p_nom_min over \(\mathcal{G} \times \Xi\), data another file declares
\(\mathrm{p}^{\mathrm{mod}}\) Generator_p_nom_mod over \(\mathcal{G}\), data another file declares
\(\mathrm{w}^{\mathrm{gen}}\) snapshot_weightings_generators over \(\mathcal{T}\), data another file declares
\(P\) Generator_p_nom_ext over \(\mathcal{G}\)
\(u\) Generator_status over \(\mathcal{G} \times \Xi \times \mathcal{T}\)
\(\mathrm{on}^{\mathrm{com}}\) Generator_committed over \(\mathcal{G} \times \mathcal{T}\), a condition another file defines

Sets#

Symbol Meaning
\(\mathcal{G}\) index \(g\) — generator with \(\mathrm{Generator\_maintenance\_cover} \subseteq \mathcal{T} \times \mathcal{G} \times \Xi \times \mathcal{T}\), Generator_maintenance_cover is absent where the data has no row — generating units, each on one bus
\(\Xi\) index \(\xi\) — scenario with \(\mathrm{Generator\_maintenance\_cover} \subseteq \mathcal{T} \times \mathcal{G} \times \Xi \times \mathcal{T}\), Generator_maintenance_cover is absent where the data has no row — the futures dispatch is chosen in, each with a weight
\(\mathcal{T}\) index \(t\) — snapshot with \(\mathrm{Generator\_maintenance\_cover} \subseteq \mathcal{T} \times \mathcal{G} \times \Xi \times \mathcal{T}\), Generator_maintenance_cover is absent where the data has no row — dispatch periods

Parameters#

Symbol Meaning
\(\mathrm{mnt}\) Generator_maintainable over \(\mathcal{G}\) — whether a generator must be taken off for maintenance within the horizon: in any scenario, as PyPSA takes the union over them (components.py:1000-1003)
\(\tau^{\mathrm{mnt}}\) Generator_maintenance_duration over \(\mathcal{G} \times \Xi\), absent where the data has no row — the hours of generator weightings one maintenance event covers, PyPSA's maintenance_duration. It has no value where the generator is not maintainable. No row contains it. In data prep you turn it into Generator_maintenance_cover and Generator_maintenance_start_blocked. The assumptions state that it fits the horizon
\(\mathrm{n}^{\mathrm{mnt}}\) Generator_maintenance_events over \(\mathcal{G} \times \Xi\) — how many maintenance events occur within the horizon
\(\gamma\) Generator_maintenance_pu over \(\mathcal{G} \times \Xi\) — the share of the build a maintenance event takes off
\(\mathrm{blk}\) Generator_maintenance_start_blocked over \(\mathcal{G} \times \Xi \times \mathcal{T}\) — true where no maintenance event may start, data prep. The snapshots it would cover there run past the end of the horizon or into one the generator is not active in. It is PyPSA's active & ~valid, from maintenance_duration and the generator weightings

Conditions#

Symbol Meaning
\(\mathrm{on}^{\mathrm{mnt,ext}}\) Generator_maint_ext over \(\mathcal{G} \times \mathcal{T}\) — a maintainable generator with an extendable build that is active in the snapshot's period, unless it is committable and modular. These are the maintenance rows against the chosen build

Variables#

Symbol Meaning
\(\mu\) Generator_maintenance over \(\mathcal{G} \times \Xi \times \mathcal{T}\), \(0\) where the mask leaves it out — Generator-maintenance — whether a maintainable generator is in maintenance: continuous, and one exactly where an event covers the snapshot
\(\mu^{\mathrm{nom}}\) Generator_maintenance_capacity over \(\mathcal{G} \times \Xi \times \mathcal{T}\), \(0\) where the mask leaves it out — Generator-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearise
\(\mu^{\mathrm{up}}\) Generator_maintenance_start over \(\mathcal{G} \times \Xi \times \mathcal{T}\), \(0\) where the mask leaves it out — Generator-maintenance_start — whether a maintenance event starts in this snapshot
\(\mu^{u}\) Generator_maintenance_status over \(\mathcal{G} \times \Xi \times \mathcal{T}\), \(0\) where the mask leaves it out — Generator-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearise, so a unit in maintenance may also be off

Definitions#

Symbol Meaning
\(\mathrm{Generator\_maintenance\_modules}\) Generator_maintenance_modules over \(\mathcal{G} \times \Xi\) — how many modules of a modular committable generator can be on in maintenance: its build cap in modules where the build is extendable, and the modules installed where it is fixed (constraints.py:588-594)

Conditions#

Generator_maint_ext

\[ \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \iff \mathrm{mnt}_{g} \wedge \mathrm{ext}_{g} \wedge \neg \left( \mathrm{com}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \wedge \mathrm{on}_{g,t} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]

Variable domains#

Generator_maintenance

\[ 0 \le \mu_{g,\xi,t} \le 1 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{g,t} \]

Generator_maintenance_capacity

\[ \mu^{\mathrm{nom}}_{g,\xi,t} \ge 0 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \]

Generator_maintenance_start

\[ \mu^{\mathrm{up}}_{g,\xi,t} \in \{0, 1\} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{g,t} \]

Generator_maintenance_status

\[ \mu^{u}_{g,\xi,t} \ge 0 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \neg \left( \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \right) \]

Definitions#

Generator_maintenance_modules

\[ \mathrm{Generator\_maintenance\_modules}_{g,\xi} = \begin{cases} \frac{\overline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi}}{\mathrm{p}^{\mathrm{mod}}_{g}} & \text{if } \mathrm{ext}_{g} \\ \mathrm{N}^{\mathrm{fix}}_{g,\xi} & \text{otherwise} \end{cases} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \]

Subject to#

Generator_maint_event_count

\[ \sum_{t \in \mathcal{T}} \mu^{\mathrm{up}}_{g,\xi,t} = \mathrm{n}^{\mathrm{mnt}}_{g,\xi} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \]

Generator_maint_modstatus_lb

\[ \mu^{u}_{g,\xi,t} \ge u_{g,\xi,t} - \mathrm{Generator\_maintenance\_modules}_{g,\xi} \cdot \left( 1 - \mu_{g,\xi,t} \right) \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_modstatus_le_maint

\[ \mu^{u}_{g,\xi,t} \le \mathrm{Generator\_maintenance\_modules}_{g,\xi} \cdot \mu_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_modstatus_le_status

\[ \mu^{u}_{g,\xi,t} \le u_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_start_horizon

\[ \mu^{\mathrm{up}}_{g,\xi,t} = 0 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{g,t} \wedge \mathrm{blk}_{g,\xi,t} \]

Generator_maint_status_lb

\[ \mu^{u}_{g,\xi,t} \ge u_{g,\xi,t} + \mu_{g,\xi,t} - 1 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_status_le_maint

\[ \mu^{u}_{g,\xi,t} \le \mu_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_status_le_status

\[ \mu^{u}_{g,\xi,t} \le u_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}^{\mathrm{com}}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_window

\[ \mu_{g,\xi,t} = \sum_{t' \in \mathcal{T} \,:\, \left( t,\ g,\ \xi,\ t' \right) \in \mathrm{Generator\_maintenance\_cover}} \mu^{\mathrm{up}}_{g,\xi,t'} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{g,t} \]

Generator_maintcap_lower_nommax

\[ \mu^{\mathrm{nom}}_{g,\xi,t} \ge P_{g} - \overline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} \cdot \left( 1 - \mu_{g,\xi,t} \right) \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \]

Generator_maintcap_lower_nommin

\[ \mu^{\mathrm{nom}}_{g,\xi,t} \ge \underline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} \cdot \mu_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \wedge \underline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} > 0 \]

Generator_maintcap_upper

\[ \mu^{\mathrm{nom}}_{g,\xi,t} \le P_{g} - \underline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} \cdot \left( 1 - \mu_{g,\xi,t} \right) \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \]

Generator_maintcap_upper_nommax

\[ \mu^{\mathrm{nom}}_{g,\xi,t} \le \overline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} \cdot \mu_{g,\xi,t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi,\ t \in \mathcal{T} \,:\, \mathrm{on}^{\mathrm{mnt,ext}}_{g,t} \]

Assumptions#

Generator_maintenance_build_cap_is_finite

\[ \overline{\mathrm{p}}^{\mathrm{nom}}_{g,\xi} < \infty \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \wedge \mathrm{ext}_{g} \]

Generator_maintenance_duration_fits_the_horizon

\[ \tau^{\mathrm{mnt}}_{g,\xi} \le \sum_{t \in \mathcal{T}} \mathrm{w}^{\mathrm{gen}}_{t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \]

Generator_maintenance_duration_positive

\[ \tau^{\mathrm{mnt}}_{g,\xi} > 0 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \]

Generator_maintenance_events_fit_the_horizon

\[ \tau^{\mathrm{mnt}}_{g,\xi} \cdot \mathrm{n}^{\mathrm{mnt}}_{g,\xi} \le \sum_{t \in \mathcal{T}} \mathrm{w}^{\mathrm{gen}}_{t} \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \]

Generator_maintenance_events_positive

\[ \mathrm{n}^{\mathrm{mnt}}_{g,\xi} > 0 \qquad \forall\, g \in \mathcal{G},\ \xi \in \Xi \,:\, \mathrm{mnt}_{g} \]

See also