Rung 34: maintenance of committable units — a fixed, an extendable and a modular committable generator, link and process, each taken off for one event¶

description: A plain `n.optimize()`, and its multi-period and stochastic classes, in one file. Every second-stage
  quantity spans a `scenario` (a future dispatch is chosen in) and every asset stands in the investment
  `period`s its build year and lifetime span. A parameter spans `scenario` exactly when PyPSA reads it
  per scenario. Capacity is chosen once, before the future is known, and paid once per active period at
  its cost in expectation over the scenarios; operation is the expectation over the scenarios' weights,
  with a share priced at the tail through the CVaR rows, which stand only where that share is positive.
  A plain run feeds one scenario, one period, all-active masks and unit weights, and the model collapses
  to the standard one. A security-constrained run copies each branch flow limit once per outage in an
  `outage` set that a plain run leaves empty. Which snapshots an asset is active in, a scenario's weight,
  and the outage factors are data prep.
dimensions:
  scenario: {description: 'the futures dispatch is chosen in, each with a weight'}
  snapshot: {description: dispatch periods, dtype: datetime}
  bus: {description: network nodes}
  generator: {description: 'generating units, each on one bus'}
  link: {description: 'controllable connections, each from one bus to the buses it delivers to'}
  link_output: {description: 'a link''s output ports, one label per port a link declares — PyPSA''s `bus1`,
      `bus2`, … columns read long, so a link of any number of output ports is one term in the balance,
      data prep'}
  process: {description: 'generalized multi-port converters, each with an internal power that every port
      draws or delivers at its own rate'}
  process_output: {description: 'a process''s ports, one label per port a process declares — PyPSA''s
      `bus0`, `bus1`, … each carry a signed `rate`, so a process of any number of ports is one term in
      the balance, data prep'}
  load: {description: 'demands, each on one bus'}
  period: {description: investment periods — PyPSA's `investment_periods`, dtype: int}
relations:
  snapshot_period: {description: the investment period a snapshot falls in, key: snapshot, values: period}
  Generator_bus: {description: the bus a generator sits on, key: generator, values: bus}
  Link_bus0: {description: the bus a link leaves, key: link, values: bus}
  Link_output_link: {description: the link an output port belongs to, key: link_output, values: link}
  Link_output_bus: {description: 'the bus an output port delivers to — PyPSA''s `bus1`, `bus2`, … columns.
      A link of three output ports is three labels here rather than a third relation, so the file states
      any number of them', key: link_output, values: bus}
  Process_output_process: {description: the process a port belongs to, key: process_output, values: process}
  Process_output_bus: {description: 'the bus a port draws from or delivers to — PyPSA''s `bus0`, `bus1`,
      … columns. A process of three ports is three labels here rather than a third relation, so the file
      states any number of them', key: process_output, values: bus}
  Load_bus: {description: the bus a load sits on, key: load, values: bus}
  Generator_maintenance_cover:
    description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
      the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
      data prep; no rows for a generator that is not maintainable
    key:
      scenario: scenario
      generator: generator
      start: snapshot
      covered: snapshot
  Link_maintenance_cover:
    description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
      the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
      data prep; no rows for a link that is not maintainable
    key:
      scenario: scenario
      link: link
      start: snapshot
      covered: snapshot
  Process_maintenance_cover:
    description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
      the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
      data prep; no rows for a process that is not maintainable
    key:
      scenario: scenario
      process: process
      start: snapshot
      covered: snapshot
parameters:
  snapshot_weightings_objective:
    description: PyPSA's `snapshot_weightings.objective` — hours a snapshot stands for in the cost
    dims: [snapshot]
  Generator_p_nom:
    description: nominal power
    dims: [scenario, generator]
  Generator_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [generator]
    dtype: bool
  Generator_p_min_pu:
    description: least output, per unit of nominal power
    dims: [scenario, snapshot, generator]
  Generator_p_max_pu:
    description: most output, per unit of nominal power — an availability profile
    dims: [scenario, snapshot, generator]
  Generator_marginal_cost:
    description: cost of one unit of output
    dims: [scenario, snapshot, generator]
  Generator_marginal_cost_quadratic:
    description: cost of the square of one unit of output
    dims: [scenario, snapshot, generator]
  Generator_sign:
    description: the sign output enters its bus's balance with — PyPSA's `sign`, `1` unless given, `-1`
      for a unit that draws power. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
    dims: [generator]
  Generator_committable:
    description: whether output is gated by an on/off status decision
    dims: [generator]
    dtype: bool
  Generator_status_initial:
    description: one where the unit was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, generator]
    dtype: int
  Generator_start_up_cost:
    description: cost of one start
    dims: [scenario, generator]
  Generator_shut_down_cost:
    description: cost of one stop
    dims: [scenario, generator]
  Generator_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, generator]
  Generator_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [generator]
  Generator_modules_installed:
    description: 'how many whole modules a committable build has in place: `Generator_p_nom / Generator_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, generator]
  Generator_big_m:
    description: a bound safely above any feasible output — the build cap at full availability, data prep
    dims: [scenario, generator]
  Generator_p_min_pu_nonneg:
    description: true where none of the generator's own minimums-per-unit is negative — PyPSA's per-unit
      `(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
    dims: [generator]
    dtype: bool
  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:1016-1019`)
    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 the horizon holds
    dims: [scenario, generator]
    dtype: int
  Generator_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the generator does not stand in — PyPSA's `active & ~valid`,
      from `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, generator]
    dtype: bool
  Link_p_nom:
    description: nominal power
    dims: [scenario, link]
  Link_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [link]
    dtype: bool
  Link_p_min_pu:
    description: least flow, per unit of nominal power — negative for a link that carries both ways
    dims: [scenario, snapshot, link]
  Link_p_max_pu:
    description: most flow, per unit of nominal power
    dims: [scenario, snapshot, link]
  Link_efficiency:
    description: share of the flow that arrives at an output port, PyPSA's `efficiency`, `efficiency2`,
      … read long — negative where that port consumes rather than delivers. Read at the snapshot the flow
      arrives, so a delayed port delivers at its arrival snapshot's efficiency (`constraints.py:1522`)
    dims: [scenario, snapshot, link_output]
  Link_output_delay:
    description: snapshots a port's delivery lags its link's flow — PyPSA's `delay`, `delay2`, … read
      long, in `snapshot_weightings.generators` units, which the file states as whole snapshots; zero
      for a port that delivers at once. Each scenario takes its own. PyPSA `1.3.0` groups the ports by
      delay over all scenarios and shifts each group in every one, so a delay that differs by scenario
      delivers the flow twice (`constraints.py:1269-1276`, PyPSA/PyPSA#1941)
    dims: [scenario, link_output]
    dtype: int
  Link_output_cyclic_delay:
    description: whether a delayed port's flow wraps from the end of its investment period — PyPSA's `cyclic_delay`,
      `cyclic_delay2`, …; where it does not, the flow still in transit at each period's first snapshots
      is lost. Each scenario takes its own, as the delay
    dims: [scenario, link_output]
    dtype: bool
  Link_marginal_cost:
    description: cost of one unit of flow
    dims: [scenario, snapshot, link]
  Link_marginal_cost_quadratic:
    description: cost of the square of one unit of flow
    dims: [scenario, snapshot, link]
  Link_committable:
    description: whether flow is gated by an on/off status decision
    dims: [link]
    dtype: bool
  Link_status_initial:
    description: one where the link was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, link]
    dtype: int
  Link_start_up_cost:
    description: cost of one start
    dims: [scenario, link]
  Link_shut_down_cost:
    description: cost of one stop
    dims: [scenario, link]
  Link_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, link]
  Link_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [link]
  Link_modules_installed:
    description: 'how many whole modules a committable build has in place: `Link_p_nom / Link_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, link]
  Link_big_m:
    description: a bound safely above any feasible flow — the build cap at full availability, data prep
    dims: [scenario, link]
  Link_p_min_pu_nonneg:
    description: true where none of the link's own minimums-per-unit is negative — PyPSA's per-unit `(p_min_pu
      >= 0).all()` over every snapshot and scenario, data prep
    dims: [link]
    dtype: bool
  Link_maintainable:
    description: whether a link must be taken off for maintenance within the horizon — in any scenario,
      as PyPSA takes the union over them (`components.py:1016-1019`)
    dims: [link]
    dtype: bool
  Link_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, link]
  Link_maintenance_events:
    description: how many maintenance events the horizon holds
    dims: [scenario, link]
    dtype: int
  Link_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the link does not stand in — PyPSA's `active & ~valid`, from
      `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, link]
    dtype: bool
  Process_p_nom:
    description: nominal internal power
    dims: [scenario, process]
  Process_p_nom_extendable:
    description: whether the nominal internal power is a decision
    dims: [process]
    dtype: bool
  Process_p_min_pu:
    description: least internal power, per unit of nominal power — negative for a process that runs both
      ways
    dims: [scenario, snapshot, process]
  Process_p_max_pu:
    description: most internal power, per unit of nominal power
    dims: [scenario, snapshot, process]
  Process_rate:
    description: the energy a port draws or delivers per unit of internal power, PyPSA's `rate0`, `rate1`,
      … read long — negative where the port withdraws, positive where it injects; a link is a process
      whose `bus0` rate is minus one and whose output rates are its efficiencies. Read at the snapshot
      the transfer arrives, so a delayed port transfers at its arrival snapshot's rate (`constraints.py:1522`)
    dims: [scenario, snapshot, process_output]
  Process_output_delay:
    description: snapshots a port's transfer lags its process's internal power — PyPSA's `delay0`, `delay1`,
      … read long, in `snapshot_weightings.generators` units, which the file states as whole snapshots;
      zero for a port that transfers at once. Each scenario takes its own, as a link's
    dims: [scenario, process_output]
    dtype: int
  Process_output_cyclic_delay:
    description: whether a delayed port's transfer wraps from the end of its investment period — PyPSA's
      `cyclic_delay0`, `cyclic_delay1`, …; where it does not, the energy still in transit at each period's
      first snapshots is lost. Each scenario takes its own, as the delay
    dims: [scenario, process_output]
    dtype: bool
  Process_marginal_cost:
    description: cost of one unit of internal power
    dims: [scenario, snapshot, process]
  Process_marginal_cost_quadratic:
    description: cost of the square of one unit of internal power
    dims: [scenario, snapshot, process]
  Process_p_nom_min:
    description: least nominal power an extendable process may be built at
    dims: [scenario, process]
  Process_p_nom_max:
    description: most nominal power an extendable process may be built at
    dims: [scenario, process]
  Process_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, process]
  Process_committable:
    description: whether internal power is gated by an on/off status decision
    dims: [process]
    dtype: bool
  Process_status_initial:
    description: one where the process was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, process]
    dtype: int
  Process_start_up_cost:
    description: cost of one start
    dims: [scenario, process]
  Process_shut_down_cost:
    description: cost of one stop
    dims: [scenario, process]
  Process_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, process]
  Process_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [process]
  Process_modules_installed:
    description: 'how many whole modules a committable build has in place: `Process_p_nom / Process_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, process]
  Process_big_m:
    description: a bound safely above any feasible internal power — the build cap at full availability,
      data prep
    dims: [scenario, process]
  Process_p_min_pu_nonneg:
    description: true where none of the process's own minimums-per-unit is negative — PyPSA's per-unit
      `(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
    dims: [process]
    dtype: bool
  Process_maintainable:
    description: whether a process must be taken off for maintenance within the horizon — in any scenario,
      as PyPSA takes the union over them (`components.py:1016-1019`)
    dims: [process]
    dtype: bool
  Process_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, process]
  Process_maintenance_events:
    description: how many maintenance events the horizon holds
    dims: [scenario, process]
    dtype: int
  Process_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the process does not stand in — PyPSA's `active & ~valid`, from
      `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, process]
    dtype: bool
  Load_p_set:
    description: demand
    dims: [scenario, snapshot, load]
  Load_sign:
    description: the sign a load's demand enters its bus's balance with — PyPSA's `sign`, `-1` unless
      given, `1` for a load that feeds its bus. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
    dims: [load]
  Load_active:
    description: whether a load stands in the model — PyPSA's `active`. A load has no build year and no
      lifetime, so the flag holds in every snapshot. PyPSA refuses one that differs by scenario (`consistency.py:1195`)
    dims: [load]
    dtype: bool
  scenario_weight:
    description: PyPSA's `scenario_weightings.weight` — the probability of a future
    dims: [scenario]
  CVaR_omega:
    description: PyPSA's `risk_preference['omega']` — the share of operating cost priced at the tail rather
      than in expectation; zero recovers the risk-neutral model
    dims: []
  period_weight_objective:
    description: PyPSA's `investment_period_weightings.objective` — what a period's cost weighs
    dims: [period]
  Generator_active:
    description: whether a generator stands in a snapshot's period — PyPSA's `active`, from build year
      and lifetime, data prep
    dims: [snapshot, generator]
    dtype: bool
  Link_active:
    description: whether a link stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, link]
    dtype: bool
  Process_active:
    description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, process]
    dtype: bool
  Generator_capital_weight:
    description: the sum of period weights a generator stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [generator]
  Link_capital_weight:
    description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [link]
  Process_capital_weight:
    description: the sum of period weights a process stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [process]
  Generator_p_nom_min:
    description: least nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_p_nom_max:
    description: most nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, generator]
  Link_p_nom_min:
    description: least nominal power an extendable link may be built at
    dims: [scenario, link]
  Link_p_nom_max:
    description: most nominal power an extendable link may be built at
    dims: [scenario, link]
  Link_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, link]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_active
  Link_p:
    description: '`Link-p` — PyPSA''s `p0`, the flow measured at the `Link_bus0` end: a positive value
      withdraws there and injects at every bus the link''s output ports deliver to'
    dims: [scenario, snapshot, link]
    where: Link_active
  Process_p:
    description: '`Process-p` — PyPSA''s internal power `p`: a positive value drives every port at its
      own rate, withdrawing where the rate is negative and injecting where it is positive'
    dims: [scenario, snapshot, process]
    where: Process_active
  Generator_n_mod:
    description: '`Generator-n_mod` — how many modules of an extendable modular build'
    dims: [generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0
    domain: integer
    bounds: {lower: 0}
  Generator_status:
    description: '`Generator-status` — how much of a committable unit is on: an integer the rows below
      cap at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_active
    domain: integer
    bounds: {lower: 0}
  Generator_start_up:
    description: '`Generator-start_up` — how much of a committable unit turns on this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_active
    domain: integer
    bounds: {lower: 0}
  Generator_shut_down:
    description: '`Generator-shut_down` — how much of a committable unit turns off this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_active
    domain: integer
    bounds: {lower: 0}
  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
    absence: zero
    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
    absence: zero
    domain: binary
  Generator_maintenance_capacity:
    description: '`Generator-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
      > 0) AND Generator_active
    absence: zero
    bounds: {lower: 0}
  Generator_maintenance_status:
    description: '`Generator-maintenance_status` — the status while in maintenance, zero otherwise: the
      product the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committable AND NOT (Generator_p_nom_extendable AND NOT
      (Generator_p_nom_mod > 0)) AND Generator_active
    absence: zero
    bounds: {lower: 0}
  Link_n_mod:
    description: '`Link-n_mod` — how many modules of an extendable modular build'
    dims: [link]
    where: Link_p_nom_extendable AND Link_p_nom_mod > 0
    domain: integer
    bounds: {lower: 0}
  Link_status:
    description: '`Link-status` — how much of a committable link is on: an integer the rows below cap
      at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_active
    domain: integer
    bounds: {lower: 0}
  Link_start_up:
    description: '`Link-start_up` — how much of a committable link turns on this snapshot, capped as the
      status is'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_active
    domain: integer
    bounds: {lower: 0}
  Link_shut_down:
    description: '`Link-shut_down` — how much of a committable link turns off this snapshot, capped as
      the status is'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_active
    domain: integer
    bounds: {lower: 0}
  Link_maintenance:
    description: '`Link-maintenance` — whether a maintainable link is in maintenance: continuous, and
      one exactly where an event covers the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active
    absence: zero
    bounds: {lower: 0, upper: 1}
  Link_maintenance_start:
    description: '`Link-maintenance_start` — whether a maintenance event starts in this snapshot'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active
    absence: zero
    domain: binary
  Link_maintenance_capacity:
    description: '`Link-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
      0) AND Link_active
    absence: zero
    bounds: {lower: 0}
  Link_maintenance_status:
    description: '`Link-maintenance_status` — the status while in maintenance, zero otherwise: the product
      the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND NOT (Link_p_nom_extendable AND NOT (Link_p_nom_mod
      > 0)) AND Link_active
    absence: zero
    bounds: {lower: 0}
  Process_n_mod:
    description: '`Process-n_mod` — how many modules of an extendable modular build'
    dims: [process]
    where: Process_p_nom_extendable AND Process_p_nom_mod > 0
    domain: integer
    bounds: {lower: 0}
  Process_status:
    description: '`Process-status` — how much of a committable process is on: an integer the rows below
      cap at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    domain: integer
    bounds: {lower: 0}
  Process_start_up:
    description: '`Process-start_up` — how much of a committable process turns on this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    domain: integer
    bounds: {lower: 0}
  Process_shut_down:
    description: '`Process-shut_down` — how much of a committable process turns off this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    domain: integer
    bounds: {lower: 0}
  Process_maintenance:
    description: '`Process-maintenance` — whether a maintainable process is in maintenance: continuous,
      and one exactly where an event covers the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active
    absence: zero
    bounds: {lower: 0, upper: 1}
  Process_maintenance_start:
    description: '`Process-maintenance_start` — whether a maintenance event starts in this snapshot'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active
    absence: zero
    domain: binary
  Process_maintenance_capacity:
    description: '`Process-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active
    absence: zero
    bounds: {lower: 0}
  Process_maintenance_status:
    description: '`Process-maintenance_status` — the status while in maintenance, zero otherwise: the
      product the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND NOT (Process_p_nom_extendable AND NOT (Process_p_nom_mod
      > 0)) AND Process_active
    absence: zero
    bounds: {lower: 0}
  Generator_p_nom_ext:
    description: '`Generator-p_nom` — nominal power where it is a decision; the parameter of the same
      PyPSA name carries the fixed regime'
    dims: [generator]
    where: Generator_p_nom_extendable
  Link_p_nom_ext:
    description: '`Link-p_nom` — nominal power where it is a decision; the parameter of the same PyPSA
      name carries the fixed regime'
    dims: [link]
    where: Link_p_nom_extendable
  Process_p_nom_ext:
    description: '`Process-p_nom` — nominal internal power where it is a decision; the parameter of the
      same PyPSA name carries the fixed regime'
    dims: [process]
    where: Process_p_nom_extendable
  CVaR_a:
    description: '`CVaR-a` — how far a scenario''s operating cost exceeds the tail''s start; nothing where
      it does not'
    dims: [scenario]
    bounds: {lower: 0}
  CVaR_theta:
    description: '`CVaR-theta` — where the tail starts, the value at risk'
    dims: []
  CVaR:
    description: '`CVaR` — the tail''s average cost, what the objective prices at `omega`'
    dims: []
constraints:
  Generator_fix_p_lower:
    description: '`Generator-fix-p-lower` — a fixed generator outputs at least its minimum'
    dims: [scenario, snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * (1 - Generator_maintenance_pu *
      Generator_maintenance)
  Generator_fix_p_upper:
    description: '`Generator-fix-p-upper` — a fixed generator outputs at most what is available'
    dims: [scenario, snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom * (1 - Generator_maintenance_pu *
      Generator_maintenance)
  Link_fix_p_lower:
    description: '`Link-fix-p-lower` — a fixed link carries at least its minimum, negative for the other
      way'
    dims: [scenario, snapshot, link]
    where: not Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p >= Link_p_min_pu * Link_p_nom * (1 - Link_maintenance_pu * Link_maintenance)
  Link_fix_p_upper:
    description: '`Link-fix-p-upper` — a fixed link carries at most its nominal power'
    dims: [scenario, snapshot, link]
    where: not Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p <= Link_p_max_pu * Link_p_nom * (1 - Link_maintenance_pu * Link_maintenance)
  Generator_ext_p_nom_lower:
    description: '`Generator-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable
    expression: Generator_p_nom_ext >= Generator_p_nom_min
  Generator_ext_p_nom_upper:
    description: '`Generator-ext-p_nom-upper` — the chosen build is at most its cap in every scenario;
      a cap of infinity is no row'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_max
    expression: Generator_p_nom_ext <= Generator_p_nom_max
  Link_ext_p_nom_lower:
    description: '`Link-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, link]
    where: Link_p_nom_extendable
    expression: Link_p_nom_ext >= Link_p_nom_min
  Link_ext_p_nom_upper:
    description: '`Link-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a cap
      of infinity is no row'
    dims: [scenario, link]
    where: Link_p_nom_extendable AND Link_p_nom_max
    expression: Link_p_nom_ext <= Link_p_nom_max
  Process_ext_p_nom_lower:
    description: '`Process-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, process]
    where: Process_p_nom_extendable
    expression: Process_p_nom_ext >= Process_p_nom_min
  Process_ext_p_nom_upper:
    description: '`Process-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a
      cap of infinity is no row'
    dims: [scenario, process]
    where: Process_p_nom_extendable AND Process_p_nom_max
    expression: Process_p_nom_ext <= Process_p_nom_max
  Generator_com_p_lower:
    description: '`Generator-com-p-lower` — a committed unit outputs at least its minimum; off, at least
      nothing'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND not Generator_p_nom_extendable AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_p_upper:
    description: '`Generator-com-p-upper` — a committed unit outputs at most what is available; off, at
      most nothing'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND not Generator_p_nom_extendable AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_transition_start_up:
    description: '`Generator-com-transition-start-up` — turning on is a start, counted against the state
      the unit carried into the snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_active
    expression: Generator_start_up >= Generator_status - Generator_previous_status
  Generator_com_transition_shut_down:
    description: '`Generator-com-transition-shut-down` — turning off is a stop, counted against the state
      the unit carried into the snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_active
    expression: Generator_shut_down >= Generator_previous_status - Generator_status
  Generator_p_nom_modularity:
    description: '`Generator-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0
    expression: Generator_p_nom_ext == Generator_p_nom_mod * Generator_n_mod
  Generator_com_ext_p_upper_cap:
    description: '`Generator-com-ext-p-upper-cap` — a committed extendable unit outputs at most what is
      available of the chosen build, whatever its status'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_p <= Generator_p_max_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
      Generator_maintenance_capacity)
  Generator_com_ext_p_upper_big_m:
    description: '`Generator-com-ext-p-upper-bigM` — off, a unit outputs nothing; on, the big M is no
      bound'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_p <= Generator_big_m * Generator_status
  Generator_com_ext_p_lower:
    description: '`Generator-com-ext-p-lower` — a committed extendable unit outputs at least its minimum
      of the chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_p >= Generator_p_min_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
      Generator_maintenance_capacity) + Generator_big_m * Generator_status - Generator_big_m
  Generator_com_ext_p_lower_nonneg:
    description: '`Generator-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, output is
      also plainly non-negative, a row the big-M lower cannot assert while the unit is off'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_min_pu_nonneg AND NOT
      (Generator_p_nom_mod > 0) AND Generator_active
    expression: Generator_p >= 0
  Generator_com_mod_p_lower:
    description: '`Generator-com-mod-p-lower` — a committed modular unit outputs at least its minimum
      of one module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_mod_p_upper:
    description: '`Generator-com-mod-p-upper` — a committed modular unit outputs at most one module''s
      share, whether the build is fixed or a decision'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_status_p_fixed_upper:
    description: '`Generator-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_status <= Generator_modules_installed
  Generator_start_up_p_fixed_upper:
    description: '`Generator-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_start_up <= Generator_modules_installed
  Generator_shut_down_p_fixed_upper:
    description: '`Generator-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
      Generator_active
    expression: Generator_shut_down <= Generator_modules_installed
  Generator_status_p_nom_variable_upper:
    description: '`Generator-status-p_nom-variable-upper` — a modular unit is on only where a module is
      built'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_status <= Generator_n_mod
  Generator_start_up_p_nom_variable_upper:
    description: '`Generator-start_up-p_nom-variable-upper` — a modular unit starts only where a module
      is built'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_start_up <= Generator_n_mod
  Generator_shut_down_p_nom_variable_upper:
    description: '`Generator-shut_down-p_nom-variable-upper` — a modular unit stops only where a module
      is built'
    dims: [scenario, snapshot, generator]
    where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_shut_down <= Generator_n_mod
  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, by=Generator_maintenance_cover,
      over=start, into=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_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
      > 0) AND Generator_active
    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_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
      > 0) AND Generator_active
    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_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
      > 0) AND Generator_active
    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_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
      > 0) AND Generator_active 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_committable AND NOT Generator_p_nom_extendable AND Generator_active
    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_committable AND NOT Generator_p_nom_extendable AND Generator_active
    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_committable AND NOT Generator_p_nom_extendable AND Generator_active
    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_committable AND Generator_p_nom_mod > 0 AND Generator_active
    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 the modules the build cap holds'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_maintenance_status <= Generator_p_nom_max / Generator_p_nom_mod * 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_committable AND Generator_p_nom_mod > 0 AND Generator_active
    expression: Generator_maintenance_status >= Generator_status - Generator_p_nom_max / Generator_p_nom_mod
      * (1 - Generator_maintenance)
  Link_com_p_lower:
    description: '`Link-com-p-lower` — a committed link flows at least its minimum; off, at least nothing'
    dims: [scenario, snapshot, link]
    where: Link_committable AND not Link_p_nom_extendable AND Link_active
    expression: Link_p >= Link_p_min_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_p_upper:
    description: '`Link-com-p-upper` — a committed link flows at most what is available; off, at most
      nothing'
    dims: [scenario, snapshot, link]
    where: Link_committable AND not Link_p_nom_extendable AND Link_active
    expression: Link_p <= Link_p_max_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_transition_start_up:
    description: '`Link-com-transition-start-up` — turning on is a start, counted against the state the
      link carried into the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_active
    expression: Link_start_up >= Link_status - Link_previous_status
  Link_com_transition_shut_down:
    description: '`Link-com-transition-shut-down` — turning off is a stop, counted against the state the
      link carried into the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_active
    expression: Link_shut_down >= Link_previous_status - Link_status
  Link_p_nom_modularity:
    description: '`Link-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [link]
    where: Link_p_nom_extendable AND Link_p_nom_mod > 0
    expression: Link_p_nom_ext == Link_p_nom_mod * Link_n_mod
  Link_com_ext_p_upper_cap:
    description: '`Link-com-ext-p-upper-cap` — a committed extendable link flows at most what is available
      of the chosen build, whatever its status'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
    expression: Link_p <= Link_p_max_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
  Link_com_ext_p_upper_big_m:
    description: '`Link-com-ext-p-upper-bigM` — off, a link flows nothing; on, the big M is no bound'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
    expression: Link_p <= Link_big_m * Link_status
  Link_com_ext_p_lower:
    description: '`Link-com-ext-p-lower` — a committed extendable link flows at least its minimum of the
      chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
    expression: Link_p >= Link_p_min_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
      + Link_big_m * Link_status - Link_big_m
  Link_com_ext_p_lower_nonneg:
    description: '`Link-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, flow is also
      plainly non-negative, a row the big-M lower cannot assert while the link is off'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND Link_p_min_pu_nonneg AND NOT (Link_p_nom_mod
      > 0) AND Link_active
    expression: Link_p >= 0
  Link_com_mod_p_lower:
    description: '`Link-com-mod-p-lower` — a committed modular link flows at least its minimum of one
      module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_p >= Link_p_min_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_mod_p_upper:
    description: '`Link-com-mod-p-upper` — a committed modular link flows at most one module''s share,
      whether the build is fixed or a decision'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_p <= Link_p_max_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_status_p_fixed_upper:
    description: '`Link-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
    expression: Link_status <= Link_modules_installed
  Link_start_up_p_fixed_upper:
    description: '`Link-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
    expression: Link_start_up <= Link_modules_installed
  Link_shut_down_p_fixed_upper:
    description: '`Link-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
    expression: Link_shut_down <= Link_modules_installed
  Link_status_p_nom_variable_upper:
    description: '`Link-status-p_nom-variable-upper` — a modular link is on only where a module is built'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_status <= Link_n_mod
  Link_start_up_p_nom_variable_upper:
    description: '`Link-start_up-p_nom-variable-upper` — a modular link starts only where a module is
      built'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_start_up <= Link_n_mod
  Link_shut_down_p_nom_variable_upper:
    description: '`Link-shut_down-p_nom-variable-upper` — a modular link stops only where a module is
      built'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_shut_down <= Link_n_mod
  Link_maint_event_count:
    description: '`Link-maint-event-count` — a maintainable link holds its number of maintenance events
      over the horizon'
    dims: [scenario, link]
    where: Link_maintainable
    expression: sum(Link_maintenance_start, over=snapshot) == Link_maintenance_events
  Link_maint_window:
    description: '`Link-maint-window` — a link 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, link]
    where: Link_maintainable AND Link_active
    expression: Link_maintenance == sum(Link_maintenance_start, by=Link_maintenance_cover, over=start,
      into=covered)
  Link_maint_start_horizon:
    description: '`Link-maint-start-horizon` — no event starts where it could not run its whole duration'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active AND Link_maintenance_start_blocked
    expression: Link_maintenance_start == 0
  Link_maintcap_upper:
    description: '`Link-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, link]
    where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
      0) AND Link_active
    expression: Link_maintenance_capacity <= Link_p_nom_ext - Link_p_nom_min * (1 - Link_maintenance)
  Link_maintcap_upper_nommax:
    description: '`Link-maintcap_upper_nommax` — out of maintenance, no build is taken off'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
      0) AND Link_active
    expression: Link_maintenance_capacity <= Link_p_nom_max * Link_maintenance
  Link_maintcap_lower_nommax:
    description: '`Link-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
      0) AND Link_active
    expression: Link_maintenance_capacity >= Link_p_nom_ext - Link_p_nom_max * (1 - Link_maintenance)
  Link_maintcap_lower_nommin:
    description: '`Link-maintcap_lower_nommin` — in maintenance, at least the floor of the build is taken
      off'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
      0) AND Link_active AND Link_p_nom_min > 0
    expression: Link_maintenance_capacity >= Link_p_nom_min * Link_maintenance
  Link_maint_status_le_status:
    description: '`Link-maint-status-le-status` — the status in maintenance is at most the status'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
    expression: Link_maintenance_status <= Link_status
  Link_maint_status_le_maint:
    description: '`Link-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
    expression: Link_maintenance_status <= Link_maintenance
  Link_maint_status_lb:
    description: '`Link-maint-status-lb` — on and in maintenance, the status in maintenance is one'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
    expression: Link_maintenance_status >= Link_status + Link_maintenance - 1
  Link_maint_modstatus_le_status:
    description: '`Link-maint-modstatus-le-status` — the modules on in maintenance are at most the modules
      on'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_maintenance_status <= Link_status
  Link_maint_modstatus_le_maint:
    description: '`Link-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
      in it, at most the modules the build cap holds'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_maintenance_status <= Link_p_nom_max / Link_p_nom_mod * Link_maintenance
  Link_maint_modstatus_lb:
    description: '`Link-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
    expression: Link_maintenance_status >= Link_status - Link_p_nom_max / Link_p_nom_mod * (1 - Link_maintenance)
  Process_com_p_lower:
    description: '`Process-com-p-lower` — a committed process runs at least its minimum; off, at least
      nothing'
    dims: [scenario, snapshot, process]
    where: Process_committable AND not Process_p_nom_extendable AND Process_active
    expression: Process_p >= Process_p_min_pu * Process_p_nom * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_p_upper:
    description: '`Process-com-p-upper` — a committed process runs at most what is available; off, at
      most nothing'
    dims: [scenario, snapshot, process]
    where: Process_committable AND not Process_p_nom_extendable AND Process_active
    expression: Process_p <= Process_p_max_pu * Process_p_nom * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_transition_start_up:
    description: '`Process-com-transition-start-up` — turning on is a start, counted against the state
      the process carried into the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    expression: Process_start_up >= Process_status - Process_previous_status
  Process_com_transition_shut_down:
    description: '`Process-com-transition-shut-down` — turning off is a stop, counted against the state
      the process carried into the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    expression: Process_shut_down >= Process_previous_status - Process_status
  Process_p_nom_modularity:
    description: '`Process-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [process]
    where: Process_p_nom_extendable AND Process_p_nom_mod > 0
    expression: Process_p_nom_ext == Process_p_nom_mod * Process_n_mod
  Process_com_ext_p_upper_cap:
    description: '`Process-com-ext-p-upper-cap` — a committed extendable process runs at most what is
      available of the chosen build, whatever its status'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
    expression: Process_p <= Process_p_max_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
  Process_com_ext_p_upper_big_m:
    description: '`Process-com-ext-p-upper-bigM` — off, a process does not run; on, the big M is no bound'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
    expression: Process_p <= Process_big_m * Process_status
  Process_com_ext_p_lower:
    description: '`Process-com-ext-p-lower` — a committed extendable process runs at least its minimum
      of the chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
    expression: Process_p >= Process_p_min_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
      + Process_big_m * Process_status - Process_big_m
  Process_com_ext_p_lower_nonneg:
    description: '`Process-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, internal power
      is also plainly non-negative, a row the big-M lower cannot assert while the process is off'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND Process_p_min_pu_nonneg AND NOT (Process_p_nom_mod
      > 0) AND Process_active
    expression: Process_p >= 0
  Process_com_mod_p_lower:
    description: '`Process-com-mod-p-lower` — a committed modular process runs at least its minimum of
      one module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_p >= Process_p_min_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_mod_p_upper:
    description: '`Process-com-mod-p-upper` — a committed modular process runs at most one module''s share,
      whether the build is fixed or a decision'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_p <= Process_p_max_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_status_p_fixed_upper:
    description: '`Process-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
    expression: Process_status <= Process_modules_installed
  Process_start_up_p_fixed_upper:
    description: '`Process-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
    expression: Process_start_up <= Process_modules_installed
  Process_shut_down_p_fixed_upper:
    description: '`Process-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
    expression: Process_shut_down <= Process_modules_installed
  Process_status_p_nom_variable_upper:
    description: '`Process-status-p_nom-variable-upper` — a modular process is on only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_status <= Process_n_mod
  Process_start_up_p_nom_variable_upper:
    description: '`Process-start_up-p_nom-variable-upper` — a modular process starts only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_start_up <= Process_n_mod
  Process_shut_down_p_nom_variable_upper:
    description: '`Process-shut_down-p_nom-variable-upper` — a modular process stops only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_shut_down <= Process_n_mod
  Process_maint_event_count:
    description: '`Process-maint-event-count` — a maintainable process holds its number of maintenance
      events over the horizon'
    dims: [scenario, process]
    where: Process_maintainable
    expression: sum(Process_maintenance_start, over=snapshot) == Process_maintenance_events
  Process_maint_window:
    description: '`Process-maint-window` — a process 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, process]
    where: Process_maintainable AND Process_active
    expression: Process_maintenance == sum(Process_maintenance_start, by=Process_maintenance_cover, over=start,
      into=covered)
  Process_maint_start_horizon:
    description: '`Process-maint-start-horizon` — no event starts where it could not run its whole duration'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active AND Process_maintenance_start_blocked
    expression: Process_maintenance_start == 0
  Process_maintcap_upper:
    description: '`Process-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, process]
    where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active
    expression: Process_maintenance_capacity <= Process_p_nom_ext - Process_p_nom_min * (1 - Process_maintenance)
  Process_maintcap_upper_nommax:
    description: '`Process-maintcap_upper_nommax` — out of maintenance, no build is taken off'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active
    expression: Process_maintenance_capacity <= Process_p_nom_max * Process_maintenance
  Process_maintcap_lower_nommax:
    description: '`Process-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active
    expression: Process_maintenance_capacity >= Process_p_nom_ext - Process_p_nom_max * (1 - Process_maintenance)
  Process_maintcap_lower_nommin:
    description: '`Process-maintcap_lower_nommin` — in maintenance, at least the floor of the build is
      taken off'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active AND Process_p_nom_min > 0
    expression: Process_maintenance_capacity >= Process_p_nom_min * Process_maintenance
  Process_maint_status_le_status:
    description: '`Process-maint-status-le-status` — the status in maintenance is at most the status'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
    expression: Process_maintenance_status <= Process_status
  Process_maint_status_le_maint:
    description: '`Process-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
    expression: Process_maintenance_status <= Process_maintenance
  Process_maint_status_lb:
    description: '`Process-maint-status-lb` — on and in maintenance, the status in maintenance is one'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
    expression: Process_maintenance_status >= Process_status + Process_maintenance - 1
  Process_maint_modstatus_le_status:
    description: '`Process-maint-modstatus-le-status` — the modules on in maintenance are at most the
      modules on'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_maintenance_status <= Process_status
  Process_maint_modstatus_le_maint:
    description: '`Process-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
      in it, at most the modules the build cap holds'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_maintenance_status <= Process_p_nom_max / Process_p_nom_mod * Process_maintenance
  Process_maint_modstatus_lb:
    description: '`Process-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
    expression: Process_maintenance_status >= Process_status - Process_p_nom_max / Process_p_nom_mod *
      (1 - Process_maintenance)
  Bus_nodal_balance:
    description: '`Bus-nodal_balance` — what is generated at a bus, storage dispatch and stores included,
      less what the links take away, plus what arrives over them after losses and any delay at every port
      they deliver to, each process port drawing or delivering at its own rate and each passive branch
      carrying its flow, meets the load there, less half of every incident line''s and transformer''s
      loss — PyPSA dissipates a branch''s loss half at either end. Each generator, storage unit, store
      and load term enters with its component''s `sign` (`constraints.py:1428-1429`, `:1538`), and an
      inactive load not at all. A bus nothing is attached to has no row; PyPSA refuses one that carries
      load, and this file does not yet.'
    dims: [scenario, snapshot, bus]
    expression: Bus_injection == 0
expressions:
  Generator_previous_status:
    description: the commitment state a generator carries into a snapshot — the state it brought into
      the horizon at the first, the previous snapshot's after that
    dims: [scenario, snapshot, generator]
    cases:
      opening: {when: position(snapshot) == 0, expression: Generator_status_initial}
    otherwise: shift(Generator_status, along=snapshot, offset=1)
  Link_previous_status:
    description: the commitment state a link carries into a snapshot — the state it brought into the horizon
      at the first, the previous snapshot's after that
    dims: [scenario, snapshot, link]
    cases:
      opening: {when: position(snapshot) == 0, expression: Link_status_initial}
    otherwise: shift(Link_status, along=snapshot, offset=1)
  Process_previous_status:
    description: the commitment state a process carries into a snapshot — the state it brought into the
      horizon at the first, the previous snapshot's after that
    dims: [scenario, snapshot, process]
    cases:
      opening: {when: position(snapshot) == 0, expression: Process_status_initial}
    otherwise: shift(Process_status, along=snapshot, offset=1)
  total_cost:
    dims: []
    expression: ((Generator_capex + Link_capex) + Process_capex) + risk_weighted_opex
    description: what the system costs — capacity once per active period at its expected cost over the
      scenarios, operation in expectation over the scenarios, and a share of it at the tail
  Bus_injection:
    dims: [scenario, snapshot, bus]
    expression: ((Generator_injection + Link_injection) + Load_injection) + Process_injection
    description: what every component puts into a bus, less what it takes out of it; PyPSA writes each
      term into the balance, and a load on its right-hand side
  Generator_capex: {expression: sum(scenario_weight * Generator_p_nom_ext * Generator_capital_cost * Generator_capital_weight)}
  Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_capital_weight)}
  Process_capex: {expression: sum(scenario_weight * Process_p_nom_ext * Process_capital_cost * Process_capital_weight)}
  risk_weighted_opex: {expression: '(1 - CVaR_omega) * sum(scenario_weight * scenario_opex, over=scenario)
      + CVaR_omega * CVaR'}
  Generator_injection: {expression: 'sum(Generator_sign * Generator_p, by=Generator_bus, over=generator,
      into=bus)'}
  Link_injection: {expression: '-sum(Link_p, by=Link_bus0, over=link, into=bus) + sum(Link_output_arrival,
      by=Link_output_bus, over=link_output, into=bus)'}
  Load_injection: {expression: 'sum(Load_demand, by=Load_bus, over=load, into=bus)'}
  Process_injection: {expression: 'sum(Process_output_arrival, by=Process_output_bus, over=process_output,
      into=bus)'}
  Link_output_arrival:
    description: what a link delivers to an output port at a snapshot — its flow delayed by the port's
      `delay` within its investment period, times the port's efficiency at the snapshot the flow arrives;
      where the port is `cyclic_delay` the delayed flow wraps from the period's end, and where it is not
      the flow still in transit at the period's first snapshots is lost. A port that does not delay (`delay`
      zero) delivers its flow unshifted, cyclic or not
    dims: [scenario, snapshot, link_output]
    cases:
      wrapping: {when: Link_output_cyclic_delay, expression: 'shift(at(Link_p, by=Link_output_link, over=link,
          into=link_output), along=snapshot, offset=Link_output_delay, edge=''wrap'', by=snapshot_period,
          within=period) * Link_efficiency'}
    otherwise: shift(at(Link_p, by=Link_output_link, over=link, into=link_output), along=snapshot, offset=Link_output_delay,
      edge=0, by=snapshot_period, within=period) * Link_efficiency
  Process_output_arrival:
    description: what a process transfers at a port at a snapshot — its internal power delayed by the
      port's `delay` within its investment period, times the port's rate at the snapshot the transfer
      arrives; where the port is `cyclic_delay` the delayed transfer wraps from the period's end, and
      where it is not the energy still in transit at the period's first snapshots is lost. A port that
      does not delay (`delay` zero) transfers at once, cyclic or not
    dims: [scenario, snapshot, process_output]
    cases:
      wrapping: {when: Process_output_cyclic_delay, expression: 'shift(at(Process_p, by=Process_output_process,
          over=process, into=process_output), along=snapshot, offset=Process_output_delay, edge=''wrap'',
          by=snapshot_period, within=period) * Process_rate'}
    otherwise: shift(at(Process_p, by=Process_output_process, over=process, into=process_output), along=snapshot,
      offset=Process_output_delay, edge=0, by=snapshot_period, within=period) * Process_rate
  scenario_opex:
    dims: [scenario]
    expression: ((((Generator_opex + Generator_commitment_opex) + Link_opex) + Link_commitment_opex) +
      Process_opex) + Process_commitment_opex
    description: what a future costs to run — every operating term, weighted by the snapshot's hours and
      its period, before the scenario's own weight; a start and a stop cost what they cost, unweighted,
      as PyPSA adds them (`optimize.py:414-429`)
  Load_demand:
    description: what a load draws from its bus's balance — its demand times its sign where it is active,
      nothing where it is not, since PyPSA drops an inactive load from the balance (`constraints.py:1537-1538`)
    dims: [scenario, snapshot, load]
    cases:
      active: {when: Load_active, expression: Load_sign * Load_p_set}
    otherwise: 0
  Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
      over=snapshot) + sum(sum((((Generator_p * Generator_p) * Generator_marginal_cost_quadratic) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
      over=snapshot)'}
  Generator_commitment_opex: {expression: 'sum(sum(((Generator_status * Generator_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
      over=snapshot) + sum(sum(Generator_start_up * Generator_start_up_cost, over=generator), over=snapshot)
      + sum(sum(Generator_shut_down * Generator_shut_down_cost, over=generator), over=snapshot)'}
  Link_opex: {expression: 'sum(sum(((Link_p * Link_marginal_cost) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot) + sum(sum((((Link_p
      * Link_p) * Link_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot)'}
  Link_commitment_opex: {expression: 'sum(sum(((Link_status * Link_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot)
      + sum(sum(Link_start_up * Link_start_up_cost, over=link), over=snapshot) + sum(sum(Link_shut_down
      * Link_shut_down_cost, over=link), over=snapshot)'}
  Process_opex: {expression: 'sum(sum(((Process_p * Process_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)
      + sum(sum((((Process_p * Process_p) * Process_marginal_cost_quadratic) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)'}
  Process_commitment_opex: {expression: 'sum(sum(((Process_status * Process_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)
      + sum(sum(Process_start_up * Process_start_up_cost, over=process), over=snapshot) + sum(sum(Process_shut_down
      * Process_shut_down_cost, over=process), over=snapshot)'}
objective: {sense: minimize, expression: total_cost}