Rung 2: storage — a cyclic battery, an inflow reservoir with a set state of charge, and a store¶

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'}
  storage_unit: {description: 'storage units, dispatch and store behind one bus connection'}
  store: {description: 'pure energy stores, 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}
  StorageUnit_bus: {description: the bus a storage unit sits on, key: storage_unit, values: bus}
  Store_bus: {description: the bus a store sits on, key: store, 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
  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]
  snapshot_weightings_stores:
    description: PyPSA's `snapshot_weightings.stores` — hours a snapshot stands for in a storage balance
    dims: [snapshot]
  StorageUnit_p_nom:
    description: nominal power
    dims: [storage_unit]
  StorageUnit_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [storage_unit]
    dtype: bool
  StorageUnit_p_min_pu:
    description: most storing, per unit of nominal power and negated
    dims: [snapshot, storage_unit]
  StorageUnit_p_max_pu:
    description: most dispatch, per unit of nominal power
    dims: [snapshot, storage_unit]
  StorageUnit_max_hours:
    description: energy capacity, as hours of dispatch at nominal power
    dims: [storage_unit]
  StorageUnit_efficiency_store:
    description: share of the power drawn from the bus that becomes charge
    dims: [storage_unit]
  StorageUnit_efficiency_dispatch:
    description: share of the charge drawn down that reaches the bus
    dims: [storage_unit]
  StorageUnit_retention:
    description: share of charge kept over a snapshot — PyPSA's `(1 - standing_loss) ** elapsed hours`,
      data prep
    dims: [snapshot, storage_unit]
  StorageUnit_inflow:
    description: energy arriving per hour, a river into a reservoir
    dims: [snapshot, storage_unit]
  StorageUnit_state_of_charge_initial:
    description: charge held before the first snapshot
    dims: [storage_unit]
  StorageUnit_cyclic_state_of_charge:
    description: whether the horizon closes on itself instead of opening on the initial charge
    dims: [storage_unit]
    dtype: bool
  StorageUnit_marginal_cost:
    description: cost of one unit of dispatch
    dims: [snapshot, storage_unit]
  StorageUnit_marginal_cost_storage:
    description: cost of one unit of charge held over one snapshot
    dims: [snapshot, storage_unit]
  StorageUnit_spill_cost:
    description: cost of one unit of inflow passed on unused
    dims: [snapshot, storage_unit]
  StorageUnit_p_set:
    description: a given net dispatch schedule; a unit without one has no row here
    dims: [snapshot, storage_unit]
  StorageUnit_state_of_charge_set:
    description: a given charge schedule; a unit without one has no row here
    dims: [snapshot, storage_unit]
  Store_e_nom:
    description: nominal energy capacity
    dims: [store]
  Store_e_nom_extendable:
    description: whether the nominal energy capacity is a decision
    dims: [store]
    dtype: bool
  Store_e_min_pu:
    description: least energy held, per unit of nominal capacity — negative for a store that may go short
    dims: [snapshot, store]
  Store_e_max_pu:
    description: most energy held, per unit of nominal capacity
    dims: [snapshot, store]
  Store_retention:
    description: share of energy kept over a snapshot — PyPSA's `(1 - standing_loss) ** elapsed hours`,
      data prep
    dims: [snapshot, store]
  Store_e_initial:
    description: energy held before the first snapshot
    dims: [store]
  Store_e_cyclic:
    description: whether the horizon closes on itself instead of opening on the initial energy
    dims: [store]
    dtype: bool
  Store_marginal_cost:
    description: cost of one unit of power delivered
    dims: [snapshot, store]
  Store_marginal_cost_storage:
    description: cost of one unit of energy held over one snapshot
    dims: [snapshot, store]
  Store_e_set:
    description: a given energy schedule; a store without one has no row here
    dims: [snapshot, store]
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]
  StorageUnit_p_dispatch:
    description: '`StorageUnit-p_dispatch` — power delivered to the bus'
    dims: [snapshot, storage_unit]
  StorageUnit_p_store:
    description: '`StorageUnit-p_store` — power drawn from the bus into charge'
    dims: [snapshot, storage_unit]
  StorageUnit_state_of_charge:
    description: '`StorageUnit-state_of_charge` — energy held at the end of a snapshot'
    dims: [snapshot, storage_unit]
  StorageUnit_spill:
    description: '`StorageUnit-spill` — inflow passed on unused. Zero where there is no inflow, so the
      balance keeps its row there; the bounds are PyPSA''s, on the variable rather than as rows'
    dims: [snapshot, storage_unit]
    where: StorageUnit_inflow > 0
    absence: zero
    bounds: {lower: 0, upper: StorageUnit_inflow}
  Store_e:
    description: '`Store-e` — energy held at the end of a snapshot'
    dims: [snapshot, store]
  Store_p:
    description: '`Store-p` — power delivered to the bus; charging is negative'
    dims: [snapshot, store]
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
  StorageUnit_fix_p_dispatch_lower:
    description: '`StorageUnit-fix-p_dispatch-lower` — dispatch is non-negative'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_p_dispatch >= 0
  StorageUnit_fix_p_dispatch_upper:
    description: '`StorageUnit-fix-p_dispatch-upper` — a fixed unit dispatches at most its nominal power'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_p_dispatch <= StorageUnit_p_max_pu * StorageUnit_p_nom
  StorageUnit_fix_p_store_lower:
    description: '`StorageUnit-fix-p_store-lower` — storing is non-negative'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_p_store >= 0
  StorageUnit_fix_p_store_upper:
    description: '`StorageUnit-fix-p_store-upper` — a fixed unit stores at most its nominal power, the
      minimum-per-unit column carrying that cap negated'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_p_store <= -StorageUnit_p_min_pu * StorageUnit_p_nom
  StorageUnit_fix_state_of_charge_lower:
    description: '`StorageUnit-fix-state_of_charge-lower` — charge is non-negative'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_state_of_charge >= 0
  StorageUnit_fix_state_of_charge_upper:
    description: '`StorageUnit-fix-state_of_charge-upper` — a fixed unit holds at most its hours at nominal
      power'
    dims: [snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable
    expression: StorageUnit_state_of_charge <= StorageUnit_max_hours * StorageUnit_p_nom
  StorageUnit_energy_balance:
    description: '`StorageUnit-energy_balance` — the charge carried in, plus what is stored after its
      efficiency, less what dispatch draws down before its own, plus inflow not spilled'
    dims: [snapshot, storage_unit]
    expression: StorageUnit_state_of_charge == StorageUnit_charge_carried_in + StorageUnit_efficiency_store
      * StorageUnit_p_store * snapshot_weightings_stores - StorageUnit_p_dispatch * snapshot_weightings_stores
      / StorageUnit_efficiency_dispatch + (StorageUnit_inflow - StorageUnit_spill) * snapshot_weightings_stores
  Store_fix_e_lower:
    description: '`Store-fix-e-lower` — a fixed store holds at least its floor'
    dims: [snapshot, store]
    where: not Store_e_nom_extendable
    expression: Store_e >= Store_e_min_pu * Store_e_nom
  Store_fix_e_upper:
    description: '`Store-fix-e-upper` — a fixed store holds at most its nominal capacity'
    dims: [snapshot, store]
    where: not Store_e_nom_extendable
    expression: Store_e <= Store_e_max_pu * Store_e_nom
  Store_energy_balance:
    description: '`Store-energy_balance` — the energy carried in, less what is delivered to the bus'
    dims: [snapshot, store]
    expression: Store_e == Store_energy_carried_in - Store_p * snapshot_weightings_stores
  StorageUnit_p_set:
    description: '`StorageUnit-p_set` — net dispatch pinned to the given schedule, wherever one is given'
    dims: [snapshot, storage_unit]
    where: StorageUnit_p_set
    expression: StorageUnit_p_dispatch - StorageUnit_p_store == StorageUnit_p_set
  StorageUnit_state_of_charge_set:
    description: '`StorageUnit-state_of_charge_set` — charge pinned to the given schedule, wherever one
      is given'
    dims: [snapshot, storage_unit]
    where: StorageUnit_state_of_charge_set
    expression: StorageUnit_state_of_charge == StorageUnit_state_of_charge_set
  Store_e_set:
    description: '`Store-e_set` — energy pinned to the given schedule, wherever one is given'
    dims: [snapshot, store]
    where: Store_e_set
    expression: Store_e == Store_e_set
  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(StorageUnit_p_dispatch
      - StorageUnit_p_store, by=StorageUnit_bus, over=storage_unit, into=bus) + sum(Store_p, by=Store_bus,
      over=store, 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:
  StorageUnit_charge_carried_in:
    description: the charge a unit opens a snapshot with — its last snapshot's less standing loss where
      it is cyclic, the given initial charge at the start of the horizon, which no standing loss has touched
      yet, and the previous snapshot's less standing loss otherwise
    dims: [snapshot, storage_unit]
    cases:
      cyclic: {when: StorageUnit_cyclic_state_of_charge, expression: 'StorageUnit_retention * shift(StorageUnit_state_of_charge,
          along=snapshot, offset=1, edge=''wrap'')'}
      opening: {when: not StorageUnit_cyclic_state_of_charge AND position(snapshot) == 0, expression: StorageUnit_state_of_charge_initial}
    otherwise: StorageUnit_retention * shift(StorageUnit_state_of_charge, along=snapshot, offset=1)
  Store_energy_carried_in:
    description: the energy a store opens a snapshot with — its last snapshot's less standing loss where
      it is cyclic, the given initial energy at the start of the horizon, which no standing loss has touched
      yet, and the previous snapshot's less standing loss otherwise
    dims: [snapshot, store]
    cases:
      cyclic: {when: Store_e_cyclic, expression: 'Store_retention * shift(Store_e, along=snapshot, offset=1,
          edge=''wrap'')'}
      opening: {when: not Store_e_cyclic AND position(snapshot) == 0, expression: Store_e_initial}
    otherwise: Store_retention * shift(Store_e, along=snapshot, offset=1)
  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)
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) + sum(StorageUnit_p_dispatch * StorageUnit_marginal_cost
    * snapshot_weightings_objective) + sum(StorageUnit_state_of_charge * StorageUnit_marginal_cost_storage
    * snapshot_weightings_objective) + sum(StorageUnit_spill * StorageUnit_spill_cost * snapshot_weightings_objective)
    + sum(Store_p * Store_marginal_cost * snapshot_weightings_objective) + sum(Store_e * Store_marginal_cost_storage
    * 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})


def _retention(n: pypsa.Network, component: str, dim: str) -> pd.DataFrame:
    losses = n.static(component)['standing_loss']
    hours = n.snapshot_weightings['stores'].to_numpy()
    dense = pd.DataFrame({name: (1.0 - loss) ** hours for name, loss in losses.items()}, index=timesteps(n))
    table = dense.melt(ignore_index=False, var_name=dim).reset_index(names='snapshot')
    return table.astype({dim: str, 'value': float})


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),
    'storage_unit': pl.Series('storage_unit', list(names(storage_units.index).astype(str)), dtype=pl.String),
    'store': pl.Series('store', list(names(stores.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'),
    'StorageUnit_bus': relation(n, 'StorageUnit', 'bus'),
    'Store_bus': relation(n, 'Store', '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'),
    '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'),
    'snapshot_weightings_stores': weighting(n, 'stores'),
    'StorageUnit_p_nom': static(n, 'StorageUnit', 'p_nom'),
    'StorageUnit_p_nom_extendable': static(n, 'StorageUnit', 'p_nom_extendable'),
    'StorageUnit_p_min_pu': varying(n, 'StorageUnit', 'p_min_pu'),
    'StorageUnit_p_max_pu': varying(n, 'StorageUnit', 'p_max_pu'),
    'StorageUnit_max_hours': static(n, 'StorageUnit', 'max_hours'),
    'StorageUnit_efficiency_store': static(n, 'StorageUnit', 'efficiency_store'),
    'StorageUnit_efficiency_dispatch': static(n, 'StorageUnit', 'efficiency_dispatch'),
    'StorageUnit_retention': _retention(n, 'StorageUnit', 'storage_unit'),
    'StorageUnit_inflow': varying(n, 'StorageUnit', 'inflow'),
    'StorageUnit_state_of_charge_initial': static(n, 'StorageUnit', 'state_of_charge_initial'),
    'StorageUnit_cyclic_state_of_charge': static(n, 'StorageUnit', 'cyclic_state_of_charge'),
    'StorageUnit_marginal_cost': varying(n, 'StorageUnit', 'marginal_cost'),
    'StorageUnit_marginal_cost_storage': varying(n, 'StorageUnit', 'marginal_cost_storage'),
    'StorageUnit_spill_cost': varying(n, 'StorageUnit', 'spill_cost'),
    'StorageUnit_p_set': varying(n, 'StorageUnit', 'p_set').dropna(),
    'StorageUnit_state_of_charge_set': varying(n, 'StorageUnit', 'state_of_charge_set').dropna(),
    'Store_e_nom': static(n, 'Store', 'e_nom'),
    'Store_e_nom_extendable': static(n, 'Store', 'e_nom_extendable'),
    'Store_e_min_pu': varying(n, 'Store', 'e_min_pu'),
    'Store_e_max_pu': varying(n, 'Store', 'e_max_pu'),
    'Store_retention': _retention(n, 'Store', 'store'),
    'Store_e_initial': static(n, 'Store', 'e_initial'),
    'Store_e_cyclic': static(n, 'Store', 'e_cyclic'),
    'Store_marginal_cost': varying(n, 'Store', 'marginal_cost'),
    'Store_marginal_cost_storage': varying(n, 'Store', 'marginal_cost_storage'),
    'Store_e_set': varying(n, 'Store', 'e_set').dropna(),
}

with sps.solve('differential/pypsa/rungs/rung_02_storage.yaml', sources) as solution:
    solution.objective  # 4456.659315422355

"""Rung 2: storage — a cyclic battery, an inflow reservoir with a set state of charge, and a store."""

from __future__ import annotations

from math import nan

import spine


def build():
    """The spine plus this rung's additions, as a ``pypsa.Network``."""
    n = spine.build()
    n.generators_t.marginal_cost['gas'] = [15, 15, 60, 60]
    n.add(
        'StorageUnit',
        'battery',
        bus='south',
        p_nom=20,
        max_hours=4,
        efficiency_store=0.95,
        efficiency_dispatch=0.9,
        standing_loss=0.01,
        cyclic_state_of_charge=True,
        marginal_cost=0.5,
        p_set=[0, nan, nan, nan],
    )
    n.add(
        'StorageUnit',
        'reservoir',
        bus='south',
        p_nom=10,
        max_hours=2,
        spill_cost=2,
        state_of_charge_initial=5,
        marginal_cost_storage=0.1,
        inflow=[12, 12, 12, 12],
        state_of_charge_set=[nan, nan, nan, 10],
    )
    n.add(
        'Store',
        'cavern',
        bus='south',
        e_nom=40,
        e_initial=25,
        standing_loss=0.005,
        marginal_cost=0.2,
        e_set=[nan, nan, nan, 20],
    )
    return n

n = build()
n.optimize(solver_name='highs')
n.objective  # 4456.659315422355