Rung 4: ramps — ramp limits on fixed and extendable generators and links¶

description: The spec of the model a plain `n.optimize()` builds, in one file. Every declaration is named
  `Component_attribute` after the PyPSA statement it stands for, and each constraint's description opens
  with the linopy name PyPSA gives that row, so the two can be read side by side. PyPSA's regimes — extendable,
  committable — are data columns and become `where:` masks. Bounds are the explicit rows PyPSA writes,
  so their duals are row duals. Parameters no PyPSA table carries verbatim are computed in data prep and
  say so in their description.
dimensions:
  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'}
relations:
  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: [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: [snapshot, generator]
  Generator_p_max_pu:
    description: most output, per unit of nominal power — an availability profile
    dims: [snapshot, generator]
  Generator_marginal_cost:
    description: cost of one unit of output
    dims: [snapshot, generator]
  Generator_committable:
    description: whether output is gated by an on/off status decision
    dims: [generator]
    dtype: bool
  Generator_ramp_limit_up:
    description: most a generator may raise its output between snapshots, per unit of nominal power; no
      value means no limit
    dims: [generator]
  Generator_ramp_limit_down:
    description: most a generator may lower its output between snapshots, per unit of nominal power; no
      value means no limit
    dims: [generator]
  Generator_ramp_limit_start_up:
    description: most output in the snapshot a unit starts, per unit of nominal power
    dims: [generator]
  Generator_ramp_limit_shut_down:
    description: most output in the snapshot before a unit stops, per unit of nominal power
    dims: [generator]
  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: [generator]
    dtype: int
  Link_ramp_limit_up:
    description: most a link may raise its flow between snapshots, per unit of nominal power; no value
      means no limit
    dims: [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
    dims: [link]
  Link_p_nom:
    description: nominal power
    dims: [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: [snapshot, link]
  Link_p_max_pu:
    description: most flow, per unit of nominal power
    dims: [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
    dims: [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
    dims: [link_output]
    dtype: int
  Link_output_cyclic_delay:
    description: whether a delayed port's flow wraps from the horizon's end — PyPSA's `cyclic_delay`,
      `cyclic_delay2`, …; where it does not, the flow still in transit at the first snapshots is lost
    dims: [link_output]
    dtype: bool
  Link_marginal_cost:
    description: cost of one unit of flow
    dims: [snapshot, link]
  Load_p_set:
    description: demand
    dims: [snapshot, load]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [snapshot, generator]
  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: [snapshot, link]
  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: [snapshot, generator]
    where: Generator_committable
    domain: integer
    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
constraints:
  Generator_fix_p_lower:
    description: '`Generator-fix-p-lower` — a fixed generator outputs at least its minimum'
    dims: [snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable
    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: [snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable
    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: [snapshot, link]
    where: not Link_p_nom_extendable
    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: [snapshot, link]
    where: not Link_p_nom_extendable
    expression: Link_p <= Link_p_max_pu * Link_p_nom
  Generator_p_ramp_limit_up:
    description: '`Generator-p-ramp_limit_up` — a generator raises output 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 unit that came into the horizon running brought an unknown output, so it carries no row at the
      first snapshot — nor does any unit a big M releases instead'
    dims: [snapshot, generator]
    where: Generator_ramp_limit_up AND NOT (Generator_committable AND Generator_p_nom_extendable) AND
      (position(snapshot) > 0 OR (Generator_committable AND Generator_status_initial == 0))
    expression: Generator_p - Generator_previous_p <= Generator_ramp_up_allowance
  Generator_p_ramp_limit_down:
    description: '`Generator-p-ramp_limit_down` — a generator lowers output 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 unit that came into the horizon running brought an unknown output, so it carries no row at the
      first snapshot — nor does any unit a big M releases instead'
    dims: [snapshot, generator]
    where: Generator_ramp_limit_down AND NOT (Generator_committable AND Generator_p_nom_extendable) AND
      (position(snapshot) > 0 OR (Generator_committable AND Generator_status_initial == 0))
    expression: Generator_previous_p - Generator_p <= Generator_ramp_down_allowance
  Link_p_ramp_limit_up:
    description: '`Link-p-ramp_limit_up` — a link raises flow no faster than its limit of the build. The
      translated term vacates the first snapshot, where a plain optimize builds no row either'
    dims: [snapshot, link]
    where: Link_ramp_limit_up
    expression: Link_p - shift(Link_p, along=snapshot, offset=1) <= Link_ramp_limit_up * Link_p_nom_effective
  Link_p_ramp_limit_down:
    description: '`Link-p-ramp_limit_down` — a link lowers flow no faster than its limit of the build'
    dims: [snapshot, link]
    where: Link_ramp_limit_down
    expression: shift(Link_p, along=snapshot, offset=1) - Link_p <= Link_ramp_limit_down * Link_p_nom_effective
  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, meets the load there. A bus nothing is attached to has no row; PyPSA refuses one
      that carries load, and this file does not yet.'
    dims: [snapshot, bus]
    expression: sum(Generator_p, by=Generator_bus, over=generator, into=bus) - sum(Link_p, by=Link_bus0,
      over=link, into=bus) + sum(Link_output_arrival, by=Link_output_bus, over=link_output, into=bus)
      == sum(Load_p_set, by=Load_bus, over=load, into=bus)
expressions:
  Generator_previous_p:
    description: the output a generator carries into a snapshot — nothing at the start of the horizon,
      which is why a unit that came in running carries no ramp row there
    dims: [snapshot, generator]
    cases:
      opening: {when: position(snapshot) == 0, expression: 0}
    otherwise: shift(Generator_p, along=snapshot, offset=1)
  Generator_ramp_up_allowance:
    description: how far a generator may raise output 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: [snapshot, generator]
    cases:
      committed: {when: Generator_committable, expression: Generator_ramp_limit_up * Generator_p_nom *
          Generator_previous_status + Generator_ramp_limit_start_up * Generator_p_nom * (Generator_status
          - Generator_previous_status)}
    otherwise: Generator_ramp_limit_up * Generator_p_nom_effective
  Generator_ramp_down_allowance:
    description: how far a generator may lower output 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: [snapshot, generator]
    cases:
      committed: {when: Generator_committable, expression: Generator_ramp_limit_down * Generator_p_nom
          * Generator_status + Generator_ramp_limit_shut_down * Generator_p_nom * (Generator_previous_status
          - Generator_status)}
    otherwise: Generator_ramp_limit_down * Generator_p_nom_effective
  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: [link]
    cases:
      extendable: {when: Link_p_nom_extendable, expression: Link_p_nom_ext}
    otherwise: Link_p_nom
  Link_output_arrival:
    description: what a link delivers to an output port at a snapshot — its flow after the port's efficiency,
      delayed by the port's `delay`; where the port is `cyclic_delay` the delayed flow wraps from the
      horizon's end, and where it is not the flow still in transit at the first snapshots is lost. A port
      that does not delay (`delay` zero) delivers its flow unshifted, cyclic or not
    dims: [snapshot, link_output]
    cases:
      wrapping: {when: Link_output_cyclic_delay, expression: 'shift(at(Link_p, by=Link_output_link, over=link,
          into=link_output) * Link_efficiency, along=snapshot, offset=Link_output_delay, edge=''wrap'')'}
    otherwise: shift(at(Link_p, by=Link_output_link, over=link, into=link_output) * Link_efficiency, along=snapshot,
      offset=Link_output_delay, edge=0)
  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: [snapshot, generator]
    cases:
      opening: {when: position(snapshot) == 0, expression: Generator_status_initial}
    otherwise: shift(Generator_status, along=snapshot, offset=1)
  Generator_p_nom_effective:
    description: the build a generator's limits are taken against — the chosen one where it is extendable,
      the given one otherwise
    dims: [generator]
    cases:
      extendable: {when: Generator_p_nom_extendable, expression: Generator_p_nom_ext}
    otherwise: Generator_p_nom
objective: {sense: minimize, description: 'operating cost, each snapshot weighted by the hours it stands
    for', expression: sum(Generator_p * Generator_marginal_cost * snapshot_weightings_objective) + sum(Link_p
    * Link_marginal_cost * snapshot_weightings_objective)}

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


def _link_ports(n: pypsa.Network) -> pd.DataFrame:
    """A link's output ports read long — one row per port a link declares, carrying the link, the bus it delivers to and its efficiency.

    PyPSA spells the ports across columns — ``bus1``/``efficiency``, ``bus2``/``efficiency2``, … — and a
    link declares a port by naming a bus in one, so a link of any port count is as many rows here and
    one term in the balance. The label is the link and the column the port came from.
    """
    links = n.static('Link')
    blank = pd.Series('', index=links.index, dtype=str)
    frames = []
    for port in ['1', *n.components.links.additional_ports]:
        suffix = '' if port == '1' else port
        buses = links.get(f'bus{port}', blank).astype(str)
        # `efficiency`, `delay` and `cyclic_delay` are PyPSA's unsuffixed attributes: port 1
        # spells them bare and every port after it takes the number
        efficiencies = links.get(f'efficiency{suffix}', pd.Series(1.0, index=links.index)).astype(float)
        delays = links.get(f'delay{suffix}', pd.Series(0, index=links.index)).fillna(0).astype(int)
        cyclic = links.get(f'cyclic_delay{suffix}', pd.Series(False, index=links.index)).fillna(False).astype(bool)
        frame = pd.DataFrame(
            keyed(links.index, 'link')
            | {
                'bus': buses.to_numpy(),
                'value': efficiencies.to_numpy(),
                'delay': delays.to_numpy(),
                'cyclic_delay': cyclic.to_numpy(),
                'port': int(port),
            }
        )
        frames.append(frame[buses.to_numpy() != ''])
    ports = pd.concat(frames, ignore_index=True).sort_values(['link', 'port'], kind='stable')
    ports['link_output'] = ports['link'] + '_bus' + ports['port'].astype(str)
    return ports.drop(columns='port').reset_index(drop=True)


def _per_port(n: pypsa.Network, column: str, as_name: str | None = None) -> pd.DataFrame:
    """One column of the long port table keyed by ``link_output`` — what a port names, or what it carries.

    *as_name* is what the file calls it: a relation keeps its target dimension's
    own name, and every parameter over the ports lands under ``value``.
    """
    ports = _link_ports(n)
    keys = [key for key in ('scenario', 'link_output') if key in ports.columns]
    return ports[[*keys, column]].rename(columns={column: as_name or column})


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),
    'generator': pl.Series('generator', list(names(generators.index).astype(str)), dtype=pl.String),
    'link': pl.Series('link', list(names(links.index).astype(str)), dtype=pl.String),
    'link_output': pl.Series('link_output', list(pd.unique(_link_ports(n)['link_output'])), dtype=pl.String),
    'load': pl.Series('load', list(names(loads.index).astype(str)), dtype=pl.String),
    'Generator_bus': relation(n, 'Generator', 'bus'),
    'Link_bus0': relation(n, 'Link', 'bus0'),
    'Link_output_link': _per_port(n, 'link'),
    'Link_output_bus': _per_port(n, 'bus'),
    'Load_bus': relation(n, 'Load', 'bus'),
    'snapshot_weightings_objective': weighting(n, 'objective'),
    'Generator_p_nom': static(n, 'Generator', 'p_nom'),
    'Generator_p_nom_extendable': static(n, 'Generator', 'p_nom_extendable'),
    'Generator_p_min_pu': varying(n, 'Generator', 'p_min_pu'),
    'Generator_p_max_pu': varying(n, 'Generator', 'p_max_pu'),
    'Generator_marginal_cost': varying(n, 'Generator', 'marginal_cost'),
    'Generator_committable': static(n, 'Generator', 'committable'),
    'Generator_ramp_limit_up': static(n, 'Generator', 'ramp_limit_up').dropna(),
    'Generator_ramp_limit_down': static(n, 'Generator', 'ramp_limit_down').dropna(),
    'Generator_ramp_limit_start_up': static(n, 'Generator', 'ramp_limit_start_up').fillna({'value': 1.0}),
    'Generator_ramp_limit_shut_down': static(n, 'Generator', 'ramp_limit_shut_down').fillna({'value': 1.0}),
    'Generator_status_initial': pd.DataFrame(
            keyed(generators.index, 'generator')
            | {
                'value': (generators['up_time_before'] > 0).astype(int).to_numpy(),
            }
        ),
    'Link_ramp_limit_up': static(n, 'Link', 'ramp_limit_up').dropna(),
    'Link_ramp_limit_down': static(n, 'Link', 'ramp_limit_down').dropna(),
    'Link_p_nom': static(n, 'Link', 'p_nom'),
    'Link_p_nom_extendable': static(n, 'Link', 'p_nom_extendable'),
    'Link_p_min_pu': varying(n, 'Link', 'p_min_pu'),
    'Link_p_max_pu': varying(n, 'Link', 'p_max_pu'),
    'Link_efficiency': _per_port(n, 'value'),
    'Link_output_delay': _per_port(n, 'delay', 'value'),
    'Link_output_cyclic_delay': _per_port(n, 'cyclic_delay', 'value'),
    'Link_marginal_cost': varying(n, 'Link', 'marginal_cost'),
    'Load_p_set': varying(n, 'Load', 'p_set'),
}

with sps.solve('differential/pypsa/rungs/rung_04_ramps.yaml', sources) as solution:
    solution.objective  # 8785.0

"""Rung 4: ramps — ramp limits on fixed and extendable generators and links."""

from __future__ import annotations

import spine


def build():
    """The spine plus this rung's additions, as a ``pypsa.Network``."""
    n = spine.build()
    n.add('Bus', 'east')
    n.add('Generator', 'coal_slow', bus='north', p_nom=80, marginal_cost=8, ramp_limit_up=0.2, ramp_limit_down=0.2)
    n.add('Link', 'tie', bus0='north', bus1='east', p_nom=50, efficiency=1, ramp_limit_up=0.4, ramp_limit_down=0.4)
    n.add('Load', 'east_load', bus='east', p_set=[5, 20, 25, 10])
    n.add('Load', 'swing', bus='north', p_set=[0, 25, 45, 0])
    return n

n = build()
n.optimize(solver_name='highs')
n.objective  # 8785.0