Rung 25: committable links — a link held on by the up time it brought in, one held off by its down time, one kept on by its own up time, and committable builds that are extendable, modular or both¶

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'}
  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}
  Load_bus: {description: the bus a load sits on, key: load, values: bus}
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
  Link_ramp_limit_up:
    description: most a link may raise its flow between snapshots, per unit of nominal power; no value
      means no limit — read at the later of the two snapshots, so the limit may change over time
    dims: [scenario, snapshot, link]
  Link_ramp_limit_down:
    description: most a link may lower its flow between snapshots, per unit of nominal power; no value
      means no limit — read at the later of the two snapshots, so the limit may change over time
    dims: [scenario, snapshot, link]
  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_ramp_limit_start_up:
    description: most flow in the snapshot a link starts, per unit of nominal power
    dims: [scenario, link]
  Link_ramp_limit_shut_down:
    description: most flow in the snapshot before a link stops, per unit of nominal power
    dims: [scenario, link]
  Link_min_up_time:
    description: least snapshots a link stays on once started
    dims: [scenario, link]
    dtype: int
  Link_min_down_time:
    description: least snapshots a link stays off once stopped
    dims: [scenario, link]
    dtype: int
  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_p_init:
    description: the flow a link brought into the horizon — PyPSA's `p_init`, read only where the link
      came in running; no value means it is unknown, so the link carries no ramp row at the first snapshot
    dims: [scenario, link]
  Link_must_stay_up:
    description: true while the up time a link brought into the horizon still binds — data prep, since
      `position()` compares against a literal rather than a parameter
    dims: [scenario, snapshot, link]
    dtype: bool
  Link_must_stay_down:
    description: true while the down time a link brought into the horizon still binds — PyPSA's `min_down_time
      - down_time_before` snapshots, where `down_time_before > 0`, data prep for the same reason
    dims: [scenario, snapshot, link]
    dtype: bool
  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
  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
  Link_capital_weight:
    description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [link]
  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
  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_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
  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
  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
  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
  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
  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
  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_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_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_com_up_time:
    description: '`Link-com-up-time` — a link started within its own minimum up time is still on. The
      first snapshot''s share of the window is the brought-in up time''s, which the must-stay-up mask
      carries'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_min_up_time > 0 AND position(snapshot) > 0 AND Link_active
    expression: sum_back(Link_start_up, along=snapshot, window=Link_min_up_time) <= Link_status
  Link_com_down_time:
    description: '`Link-com-down-time` — a link stopped within its own minimum down time is still off.
      The first snapshot''s share of the window is the brought-in down time''s, which the must-stay-down
      mask carries'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_min_down_time > 0 AND position(snapshot) > 0 AND Link_active
    expression: sum_back(Link_shut_down, along=snapshot, window=Link_min_down_time) <= 1 - Link_status
  Link_com_status_must_stay_up:
    description: '`Link-com-status-min_up_time_must_stay_up` — a link still serving the up time it brought
      in stays on'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_must_stay_up AND Link_active
    expression: Link_status == 1
  Link_com_status_must_stay_down:
    description: '`Link-com-status-min_down_time_must_stay_up` — a link still serving the down time it
      brought in stays off; PyPSA names the row `_must_stay_up`'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_must_stay_down AND Link_active
    expression: Link_status == 0
  Link_p_ramp_limit_up_run_big_m:
    description: '`Link-p-ramp_limit_up-run-bigM` — a committed extendable link raises flow no faster
      than its limit of the chosen build; the big M releases the row in the snapshot it turns on'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND (Link_ramp_limit_up
      OR Link_ramp_limit_start_up) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR (position(snapshot)
      == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_p - Link_previous_p <= Link_ramp_up_rate * Link_p_nom_ext + Link_big_m - Link_big_m
      * Link_previous_status
  Link_p_ramp_limit_up_start_big_m:
    description: '`Link-p-ramp_limit_up-start-bigM` — in the snapshot it turns on, a committed extendable
      link ramps no further than its start-up ramp of the chosen build; the big M releases the row everywhere
      else'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND (Link_ramp_limit_up
      OR Link_ramp_limit_start_up) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR (position(snapshot)
      == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_p - Link_previous_p <= Link_start_up_rate * Link_p_nom_ext + Link_big_m - Link_big_m
      * Link_start_up
  Link_p_ramp_limit_down_run_big_m:
    description: '`Link-p-ramp_limit_down-run-bigM` — a committed extendable link lowers flow no faster
      than its limit of the chosen build; the big M releases the row in the snapshot it turns off'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND (Link_ramp_limit_down
      OR Link_ramp_limit_shut_down) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR
      (position(snapshot) == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_previous_p - Link_p <= Link_ramp_down_rate * Link_p_nom_ext + Link_big_m - Link_big_m
      * Link_status
  Link_p_ramp_limit_down_shut_big_m:
    description: '`Link-p-ramp_limit_down-shut-bigM` — in the snapshot it turns off, a committed extendable
      link ramps no further than its shut-down ramp of the chosen build; the big M releases the row everywhere
      else'
    dims: [scenario, snapshot, link]
    where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND (Link_ramp_limit_down
      OR Link_ramp_limit_shut_down) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR
      (position(snapshot) == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_previous_p - Link_p <= Link_shut_down_rate * Link_p_nom_ext + Link_big_m - Link_big_m
      * Link_shut_down
  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_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_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_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_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_p_ramp_limit_up:
    description: '`Link-p-ramp_limit_up` — a link raises flow no faster than its ramp limit of the build,
      and a committed one no further than its start-up ramp in the snapshot it turns on. A link that came
      into the horizon running carries a row at the first snapshot only where its `p_init` gives the flow
      it brought in, and no link carries one at the start of a later investment period — nor does any
      link a big M releases instead'
    dims: [scenario, snapshot, link]
    where: (Link_ramp_limit_up OR Link_ramp_limit_start_up) AND NOT (Link_committable AND Link_p_nom_extendable
      AND NOT (Link_p_nom_mod > 0)) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR
      (position(snapshot) == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_p - Link_previous_p <= Link_ramp_up_allowance
  Link_p_ramp_limit_down:
    description: '`Link-p-ramp_limit_down` — a link lowers flow no faster than its ramp limit of the build,
      and a committed one no further than its shut-down ramp in the snapshot it turns off. A link that
      came into the horizon running carries a row at the first snapshot only where its `p_init` gives
      the flow it brought in, and no link carries one at the start of a later investment period — nor
      does any link a big M releases instead'
    dims: [scenario, snapshot, link]
    where: (Link_ramp_limit_down OR Link_ramp_limit_shut_down) AND NOT (Link_committable AND Link_p_nom_extendable
      AND NOT (Link_p_nom_mod > 0)) AND (position(snapshot, by=snapshot_period, within=period) > 0 OR
      (position(snapshot) == 0 AND (Link_status_initial == 0 OR Link_p_init))) AND Link_active
    expression: Link_previous_p - Link_p <= Link_ramp_down_allowance
  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:
  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)
  Link_previous_p:
    description: the flow a link carries into a snapshot — at the first, the `p_init` it brought in where
      it came in running and nothing where it came in off; the previous snapshot's after that
    dims: [scenario, snapshot, link]
    cases:
      opening: {when: position(snapshot) == 0, expression: Link_status_initial * Link_p_init}
    otherwise: shift(Link_p, along=snapshot, offset=1)
  Link_ramp_up_rate:
    description: the ramp limit a link's up row reads — PyPSA's `ramp_limit_up`, or the full build where
      it has none, since a start-up ramp alone builds the row
    dims: [scenario, snapshot, link]
    cases:
      given: {when: Link_ramp_limit_up, expression: Link_ramp_limit_up}
    otherwise: 1
  Link_ramp_down_rate:
    description: the ramp limit a link's down row reads — PyPSA's `ramp_limit_down`, or the full build
      where it has none, since a shut-down ramp alone builds the row
    dims: [scenario, snapshot, link]
    cases:
      given: {when: Link_ramp_limit_down, expression: Link_ramp_limit_down}
    otherwise: 1
  Link_start_up_rate:
    description: the start-up ramp a link's up row reads — PyPSA's `ramp_limit_start_up`, or the full
      build where it has none
    dims: [scenario, link]
    cases:
      given: {when: Link_ramp_limit_start_up, expression: Link_ramp_limit_start_up}
    otherwise: 1
  Link_shut_down_rate:
    description: the shut-down ramp a link's down row reads — PyPSA's `ramp_limit_shut_down`, or the full
      build where it has none
    dims: [scenario, link]
    cases:
      given: {when: Link_ramp_limit_shut_down, expression: Link_ramp_limit_shut_down}
    otherwise: 1
  Link_ramp_up_allowance:
    description: how far a link may raise flow between two snapshots — its ramp limit of the build while
      it stays on, plus its start-up ramp in the snapshot it turns on
    dims: [scenario, snapshot, link]
    cases:
      committed: {when: Link_committable, expression: Link_ramp_up_rate * Link_p_nom_committed * Link_previous_status
          + Link_start_up_rate * Link_p_nom_committed * (Link_status - Link_previous_status)}
    otherwise: Link_ramp_up_rate * Link_p_nom_effective
  Link_ramp_down_allowance:
    description: how far a link may lower flow between two snapshots — its ramp limit of the build while
      it stays on, plus its shut-down ramp in the snapshot it turns off
    dims: [scenario, snapshot, link]
    cases:
      committed: {when: Link_committable, expression: Link_ramp_down_rate * Link_p_nom_committed * Link_status
          + Link_shut_down_rate * Link_p_nom_committed * (Link_previous_status - Link_status)}
    otherwise: Link_ramp_down_rate * Link_p_nom_effective
  total_cost:
    dims: []
    expression: Link_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
    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
  Link_p_nom_effective:
    description: the build a link's limits are taken against — the chosen one where it is extendable,
      the given one otherwise
    dims: [scenario, link]
    cases:
      extendable: {when: Link_p_nom_extendable, expression: Link_p_nom_ext}
    otherwise: Link_p_nom
  Link_p_nom_committed:
    description: the build a committed link's ramp rows are taken against — one module where the build
      is extendable and modular, the given build otherwise
    dims: [scenario, link]
    cases:
      modular_build: {when: Link_p_nom_extendable AND Link_p_nom_mod > 0, expression: Link_p_nom_mod}
    otherwise: Link_p_nom
  Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_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)'}
  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
  scenario_opex:
    dims: [scenario]
    expression: (Generator_opex + Link_opex) + Link_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)'}
  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)'}
objective: {sense: minimize, expression: total_cost}

from differential.pypsa.prep import relation, static, varying, weighting


n = build()  # the network from the PyPSA tab

sources = {
    'snapshot': pl.Series('snapshot', list(timesteps(n)), dtype=pl.Datetime('us')),
    'bus': pl.Series('bus', list(names(n.buses.index).astype(str)), dtype=pl.String),
        **{
            dim: pl.Series(dim, list(names(n.static(component).index).astype(str)), dtype=pl.String)
            for component, dim in DIM.items()
        },
        **scenarios(n),
        **periods(n),
        **carriers(n, multi),
    'Generator_bus': relation(n, 'Generator', 'bus'),
    'Link_bus0': relation(n, 'Link', 'bus0'),
    'Load_bus': relation(n, 'Load', 'bus'),
    'snapshot_weightings_objective': weighting(n, 'objective'),
    'Generator_sign': per_component('Generator', first_scenario(n.generators['sign'])),
    'Load_p_set': varying(n, 'Load', 'p_set'),
    'Load_sign': per_component('Load', first_scenario(loads['sign'])),
    'Load_active': per_component('Load', first_scenario(loads['active']), bool),
}

with sps.solve('differential/pypsa/rungs/rung_25_committable_link.yaml', sources) as solution:
    solution.objective  # 14013.0