Rung 6: KVL — passive lines under Kirchhoff's voltage law¶

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'}
  line: {description: 'passive branches, each between two buses, their flow set by impedance'}
  cycle: {description: 'independent cycles of the passive network graph — the cycle basis, data prep'}
  global_constraint: {description: 'PyPSA''s `GlobalConstraint` rows, one label per declared limit'}
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}
  Line_bus0: {description: the bus a line's flow is measured at, key: line, values: bus}
  Line_bus1: {description: the bus at a line's other end, key: line, 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]
  Line_s_nom:
    description: nominal apparent power
    dims: [line]
  Line_s_nom_extendable:
    description: whether the nominal apparent power is a decision
    dims: [line]
    dtype: bool
  Line_s_max_pu:
    description: most flow either way, per unit of nominal apparent power
    dims: [snapshot, line]
  Line_s_nom_min:
    description: least nominal apparent power an extendable line may be built at
    dims: [line]
  Line_s_nom_max:
    description: most nominal apparent power an extendable line may be built at
    dims: [line]
  Line_capital_cost:
    description: cost of one unit of nominal apparent power — PyPSA's `capital_cost`, periodized as an
      annuity in data prep
    dims: [line]
  Line_s_nom_set:
    description: a given nominal apparent power for an extendable line; one without a value has no row
      here
    dims: [line]
  Line_s_set:
    description: a given flow schedule; a line without one has no row here
    dims: [snapshot, line]
  Line_cycle_weight:
    description: the line's series impedance, signed by its orientation in the cycle — the cycle basis,
      data prep; a line in no cycle has no row
    dims: [line, cycle]
  GlobalConstraint_type:
    description: which formula the row takes — `primary_energy`, `operational_limit`, `transmission_volume_expansion_limit`,
      `transmission_expansion_cost_limit` or `tech_capacity_expansion_limit`
    dims: [global_constraint]
    dtype: str
  GlobalConstraint_sense:
    description: which way the row binds — `<=`, `>=` or `==`
    dims: [global_constraint]
    dtype: str
  GlobalConstraint_constant:
    description: the constant the total is held against; what a variable cannot carry — an initial charge,
      a non-extendable build — is folded in here by data prep
    dims: [global_constraint]
  Line_volume_weight:
    description: the line's length where its carrier is in the row's set — data prep; a line outside it
      has no row
    dims: [global_constraint, line]
  Line_expansion_cost_weight:
    description: the line's capital cost where its carrier is in the row's set — data prep; a line outside
      it has no row
    dims: [global_constraint, line]
  Line_tech_capacity_weight:
    description: one where the line is in the row's carrier-and-bus set — data prep; one outside it has
      no row
    dims: [global_constraint, line]
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]
  Line_s:
    description: '`Line-s` — PyPSA''s `p0`, the flow measured at the `Line_bus0` end: a positive value
      withdraws there and injects at `Line_bus1`, lossless'
    dims: [snapshot, line]
  Line_s_nom_ext:
    description: '`Line-s_nom` — nominal apparent power where it is a decision; the parameter of the same
      PyPSA name carries the fixed regime'
    dims: [line]
    where: Line_s_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
  Line_fix_s_lower:
    description: '`Line-fix-s-lower` — a fixed line carries at least the negative of its rating'
    dims: [snapshot, line]
    where: not Line_s_nom_extendable
    expression: Line_s >= -Line_s_max_pu * Line_s_nom
  Line_fix_s_upper:
    description: '`Line-fix-s-upper` — a fixed line carries at most its rating'
    dims: [snapshot, line]
    where: not Line_s_nom_extendable
    expression: Line_s <= Line_s_max_pu * Line_s_nom
  Line_ext_s_lower:
    description: '`Line-ext-s-lower` — an extendable line carries at least the negative of its rating
      of the chosen build'
    dims: [snapshot, line]
    where: Line_s_nom_extendable
    expression: Line_s >= -Line_s_max_pu * Line_s_nom_ext
  Line_ext_s_upper:
    description: '`Line-ext-s-upper` — an extendable line carries at most its rating of the chosen build'
    dims: [snapshot, line]
    where: Line_s_nom_extendable
    expression: Line_s <= Line_s_max_pu * Line_s_nom_ext
  Line_ext_s_nom_lower:
    description: '`Line-ext-s_nom-lower` — the chosen build is at least its floor'
    dims: [line]
    where: Line_s_nom_extendable
    expression: Line_s_nom_ext >= Line_s_nom_min
  Line_ext_s_nom_upper:
    description: '`Line-ext-s_nom-upper` — the chosen build is at most its cap; a cap of infinity is no
      row'
    dims: [line]
    where: Line_s_nom_extendable AND Line_s_nom_max
    expression: Line_s_nom_ext <= Line_s_nom_max
  Line_s_nom_set:
    description: '`Line-s_nom_set` — the chosen build pinned, wherever a value is given'
    dims: [line]
    where: Line_s_nom_extendable AND Line_s_nom_set
    expression: Line_s_nom_ext == Line_s_nom_set
  Line_s_set:
    description: '`Line-s_set` — flow pinned to the given schedule, wherever one is given'
    dims: [snapshot, line]
    where: Line_s_set
    expression: Line_s == Line_s_set
  Kirchhoff_Voltage_Law:
    description: '`Kirchhoff-Voltage-Law` — around every independent cycle the impedance-weighted flows
      sum to nothing, which is what makes the linear power flow physical rather than transport'
    dims: [snapshot, cycle]
    expression: sum(Line_s * Line_cycle_weight, over=line) == 0
  GlobalConstraint_transmission_volume_expansion_limit_lb:
    description: '`transmission_volume_expansion_limit` — its total, at least its constant'
    dims: [global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense ==
      '>='
    expression: transmission_volume_expansion >= GlobalConstraint_constant
  GlobalConstraint_transmission_volume_expansion_limit_eq:
    description: '`transmission_volume_expansion_limit` — its total, at its constant'
    dims: [global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense ==
      '=='
    expression: transmission_volume_expansion == GlobalConstraint_constant
  GlobalConstraint_transmission_expansion_cost_limit_ub:
    description: '`transmission_expansion_cost_limit` — its total, at most its constant'
    dims: [global_constraint]
    where: GlobalConstraint_type == 'transmission_expansion_cost_limit' AND GlobalConstraint_sense ==
      '<='
    expression: transmission_expansion_cost <= GlobalConstraint_constant
  GlobalConstraint_transmission_expansion_cost_limit_lb:
    description: '`transmission_expansion_cost_limit` — its total, at least its constant'
    dims: [global_constraint]
    where: GlobalConstraint_type == 'transmission_expansion_cost_limit' AND GlobalConstraint_sense ==
      '>='
    expression: transmission_expansion_cost >= GlobalConstraint_constant
  GlobalConstraint_tech_capacity_expansion_limit_ub:
    description: '`tech_capacity_expansion_limit` — its total, at most its constant'
    dims: [global_constraint]
    where: GlobalConstraint_type == 'tech_capacity_expansion_limit' AND GlobalConstraint_sense == '<='
    expression: tech_capacity_expansion <= GlobalConstraint_constant
  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(Line_s, by=Line_bus0, over=line, into=bus) + sum(Line_s, by=Line_bus1, over=line, into=bus)
      == sum(Load_p_set, by=Load_bus, over=load, into=bus)
expressions:
  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)
  transmission_volume_expansion: {description: what a `transmission_volume_expansion_limit` row totals
      — length times the chosen build of the row's branches, expression: 'sum(Line_s_nom_ext * Line_volume_weight,
      over=line)'}
  transmission_expansion_cost: {description: what a `transmission_expansion_cost_limit` row totals — capital
      cost times the chosen build of the row's branches, expression: 'sum(Line_s_nom_ext * Line_expansion_cost_weight,
      over=line)'}
  tech_capacity_expansion: {description: what a `tech_capacity_expansion_limit` row totals — the chosen
      build of the row's carrier-and-bus set, expression: 'sum(Line_s_nom_ext * Line_tech_capacity_weight,
      over=line)'}
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(Line_s_nom_ext * Line_capital_cost)}

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


def _carrier_list(gc: pd.Series) -> list[str]:
    return [c.strip().strip('[]()') for c in str(gc['carrier_attribute']).split(',')]


def _cycle_weights(n: pypsa.Network) -> pd.DataFrame:
    """The KVL rows PyPSA itself writes — ``n.cycle_matrix(apply_weights=True)``, reactance on AC and resistance on DC, times the 1e5 PyPSA scales every cycle row by for conditioning."""
    n.determine_network_topology()
    n.calculate_dependent_values()
    cycles = n.cycle_matrix(apply_weights=True) * 1e5
    rows = [
        {'line': str(name), 'cycle': str(cycle), 'value': float(weight)}
        for (kind, name), weights in cycles.iterrows()
        for cycle, weight in weights.items()
        if kind == 'Line' and weight
    ]
    return pd.DataFrame(rows, columns=['line', 'cycle', 'value']).astype({'value': float})


def _emissions(n: pypsa.Network, gc: pd.Series) -> pd.Series:
    """The nonzero values of the carrier attribute a `primary_energy` row weighs."""
    values = n.carriers[gc['carrier_attribute']]
    return values[values != 0]


def _gc_constants(n: pypsa.Network) -> pd.DataFrame:
    """Each row's constant, net of the initial charge PyPSA folds into its side of the row.

    A `primary_energy` or `operational_limit` row counts what its non-cyclic
    storage draws down, so PyPSA adds the initial charge as a constant on the
    variable side; the file keeps the variables and moves it here.
    """
    rows = []
    for label, gc in n.global_constraints.iterrows():
        constant = float(gc['constant'])
        if gc['type'] == 'primary_energy':
            emissions = _emissions(n, gc)
            sus = n.storage_units
            member = sus['carrier'].isin(emissions.index) & ~sus['cyclic_state_of_charge']
            constant -= float(
                (sus.loc[member, 'carrier'].map(emissions) * sus.loc[member, 'state_of_charge_initial']).sum()
            )
            stores = n.stores
            member = stores['carrier'].isin(emissions.index) & ~stores['e_cyclic']
            constant -= float((stores.loc[member, 'carrier'].map(emissions) * stores.loc[member, 'e_initial']).sum())
        if gc['type'] == 'operational_limit':
            sus = n.storage_units
            member = (sus['carrier'] == gc['carrier_attribute']) & ~sus['cyclic_state_of_charge']
            constant -= float(sus.loc[member, 'state_of_charge_initial'].sum())
            stores = n.stores
            member = (stores['carrier'] == gc['carrier_attribute']) & ~stores['e_cyclic']
            constant -= float(stores.loc[member, 'e_initial'].sum())
        rows.append({'global_constraint': str(label), 'value': constant})
    return pd.DataFrame(rows, columns=['global_constraint', 'value']).astype({'value': float})


def _in_tech_set(gc: pd.Series, component: pd.Series, nominal: str, bus: str) -> bool:
    """PyPSA's membership for a `tech_capacity_expansion_limit` row: extendable, the carrier, and the bus if named."""
    at_bus = not gc.get('bus') or str(component[bus]) == str(gc['bus'])
    return bool(component[f'{nominal}_extendable'] and component['carrier'] == gc['carrier_attribute'] and at_bus)


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 _weights(gcs: pd.DataFrame, components: pd.DataFrame, dim: str, value) -> pd.DataFrame:
    """One row per (global constraint, member): *value* returns the weight, or 0/None outside the row's set."""
    rows = [
        {'global_constraint': str(label), dim: str(name), 'value': float(v)}
        for label, gc in gcs.iterrows()
        for name, component in components.iterrows()
        if (v := value(gc, component))
    ]
    return pd.DataFrame(rows, columns=['global_constraint', dim, 'value']).astype({'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),
    'line': pl.Series('line', list(names(lines.index).astype(str)), dtype=pl.String),
    'cycle': pl.Series('cycle', list(pd.unique(tables['Line_cycle_weight']['cycle'])), dtype=pl.String),
    'global_constraint': pl.Series(
            'global_constraint', list(names(n.global_constraints.index).astype(str)), dtype=pl.String
        ),
        **scenarios(n),
        **periods(n),
        **carriers(n),
    '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'),
    'Line_bus0': relation(n, 'Line', 'bus0'),
    'Line_bus1': relation(n, 'Line', 'bus1'),
    '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'),
    'Line_s_nom': static(n, 'Line', 's_nom'),
    'Line_s_nom_extendable': static(n, 'Line', 's_nom_extendable'),
    'Line_s_max_pu': varying(n, 'Line', 's_max_pu'),
    'Line_s_nom_min': static(n, 'Line', 's_nom_min'),
    'Line_s_nom_max': static(n, 'Line', 's_nom_max'),
    'Line_capital_cost': static(n, 'Line', 'capital_cost'),
    'Line_s_nom_set': static(n, 'Line', 's_nom_set').dropna(),
    'Line_s_set': varying(n, 'Line', 's_set').dropna(),
    'Line_cycle_weight': _cycle_weights(n),
    'GlobalConstraint_type': static(n, 'GlobalConstraint', 'type').astype({'value': str}),
    'GlobalConstraint_sense': static(n, 'GlobalConstraint', 'sense').astype({'value': str}),
    'GlobalConstraint_constant': _gc_constants(n),
    'Line_volume_weight': _weights(
            volume,
            lines,
            'line',
            lambda gc, c: c['length'] if c['s_nom_extendable'] and c['carrier'] in _carrier_list(gc) else 0.0,
        ),
    'Line_expansion_cost_weight': _weights(
            expansion_cost,
            lines,
            'line',
            lambda gc, c: c['capital_cost'] if c['s_nom_extendable'] and c['carrier'] in _carrier_list(gc) else 0.0,
        ),
    'Line_tech_capacity_weight': _weights(
            tech, lines, 'line', lambda gc, c: float(_in_tech_set(gc, c, 's_nom', 'bus0'))
        ),
}

with sps.solve('differential/pypsa/rungs/rung_06_kvl.yaml', sources) as solution:
    solution.objective  # 23962.0

"""Rung 6: KVL — passive lines under Kirchhoff's voltage law."""

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.add('Bus', 'a')
    n.add('Bus', 'b')
    n.add('Bus', 'c')
    n.add('Generator', 'hydro', bus='a', p_nom=80, marginal_cost=10)
    n.add('Generator', 'diesel6', bus='b', p_nom=80, marginal_cost=50)
    n.add('Load', 'town', bus='c', p_set=45)
    n.add('Line', 'ab', bus0='a', bus1='b', carrier='AC', length=30, x=0.1, r=0.01, s_nom=60)
    n.add('Line', 'bc', bus0='b', bus1='c', carrier='AC', length=40, x=0.2, r=0.01, s_nom=60, s_set=[16, nan, nan, nan])
    n.add('Line', 'ca', bus0='c', bus1='a', carrier='AC', length=35, x=0.1, r=0.01, s_nom=60)
    n.add(
        'Line',
        'ca2',
        bus0='c',
        bus1='a',
        carrier='AC',
        length=50,
        x=0.15,
        r=0.01,
        s_nom_extendable=True,
        capital_cost=10,
        s_nom_max=40,
        s_nom_set=30,
    )
    n.add(
        'Line',
        'ca3',
        bus0='c',
        bus1='a',
        carrier='AC',
        length=80,
        x=0.12,
        r=0.01,
        s_nom_extendable=True,
        capital_cost=8,
        s_nom_max=40,
    )
    n.add(
        'GlobalConstraint',
        'vol_ac',
        type='transmission_volume_expansion_limit',
        carrier_attribute='AC',
        sense='==',
        constant=2300,
    )
    n.add(
        'GlobalConstraint',
        'vol_ac_floor',
        type='transmission_volume_expansion_limit',
        carrier_attribute='AC',
        sense='>=',
        constant=1000,
    )
    n.add(
        'GlobalConstraint',
        'cost_ac',
        type='transmission_expansion_cost_limit',
        carrier_attribute='AC',
        sense='<=',
        constant=500,
    )
    n.add(
        'GlobalConstraint',
        'cost_ac_floor',
        type='transmission_expansion_cost_limit',
        carrier_attribute='AC',
        sense='>=',
        constant=100,
    )
    n.add(
        'GlobalConstraint',
        'tech_ac',
        type='tech_capacity_expansion_limit',
        carrier_attribute='AC',
        sense='<=',
        constant=60,
    )
    return n

n = build()
n.optimize(solver_name='highs')
n.objective  # 23962.0