Rung 11: PyPSA's own ac_dc_meshed example, whole — meshed AC and DC, extendable lines, links and generators, carriers, a CO2 budget¶

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'}
  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'}
  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}
  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_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_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
  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]
  period_weight_years:
    description: PyPSA's `investment_period_weightings.years` — what a period's energy weighs in a `primary_energy`
      or `operational_limit` row; PyPSA reads it only under `multi_investment_periods`, so data prep feeds
      one otherwise
    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
  Line_active:
    description: whether a line stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, line]
    dtype: bool
  Generator_capital_weight:
    description: the sum of period weights a generator stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [generator]
  Link_capital_weight:
    description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [link]
  Line_capital_weight:
    description: the sum of period weights a line stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [line]
  snapshot_weightings_generators:
    description: PyPSA's `snapshot_weightings.generators` — hours a snapshot stands for in an energy total
    dims: [snapshot]
  Generator_p_nom_min:
    description: least nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, generator]
  Link_p_nom_min:
    description: least nominal power an extendable link may be built at
    dims: [scenario, link]
  Link_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, link]
  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: [scenario, snapshot, line]
  Line_s_nom_min:
    description: least nominal apparent power an extendable line may be built at
    dims: [scenario, 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: [scenario, 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. PyPSA builds the cycle basis from the first scenario only
      (`networks.py:1354-1361`)
    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 in each scenario — `<=`, `>=` or `==`; PyPSA reads a row's sense
      per scenario (`global_constraints.py:556`, `:748`, `:860`)
    dims: [scenario, global_constraint]
    dtype: str
  GlobalConstraint_constant:
    description: the constant the total is held against; what a variable cannot carry — an initial charge,
      times its period's years for each counted period where the storage reopens per period, or a non-extendable
      build — is folded in here by data prep. PyPSA reads it per scenario (`global_constraints.py:557`,
      `:749`, `:861`)
    dims: [scenario, global_constraint]
  GlobalConstraint_counts_snapshot:
    description: 'whether a row counts a snapshot in a scenario — PyPSA''s `investment_period`: every
      snapshot where the row names none, and only that period''s where it names one, data prep. A row
      that names a period the run does not model has no label here, as PyPSA skips it (`global_constraints.py:377`);
      PyPSA reads the column only under `multi_investment_periods`, and fails on a row that names a period
      without it (`global_constraints.py:375`)'
    dims: [scenario, global_constraint, snapshot]
    dtype: bool
  Generator_primary_energy_weight:
    description: the constrained attribute per unit of energy at the bus — the carrier's `co2_emissions`
      over the generator's efficiency at the snapshot, data prep; a generator of an unweighted carrier
      has no row
    dims: [scenario, global_constraint, snapshot, generator]
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
  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: [scenario, snapshot, line]
    where: Line_active
  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
  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
  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_ext_p_lower:
    description: '`Generator-ext-p-lower` — an extendable generator outputs at least its minimum of the
      chosen build'
    dims: [scenario, snapshot, generator]
    where: Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom_ext
  Generator_ext_p_upper:
    description: '`Generator-ext-p-upper` — an extendable generator outputs at most what is available
      of the chosen build'
    dims: [scenario, snapshot, generator]
    where: Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom_ext
  Generator_ext_p_nom_lower:
    description: '`Generator-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable
    expression: Generator_p_nom_ext >= Generator_p_nom_min
  Link_ext_p_lower:
    description: '`Link-ext-p-lower` — an extendable link carries at least its minimum of the chosen build,
      negative for the other way'
    dims: [scenario, snapshot, link]
    where: Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p >= Link_p_min_pu * Link_p_nom_ext
  Link_ext_p_upper:
    description: '`Link-ext-p-upper` — an extendable link carries at most the chosen build'
    dims: [scenario, snapshot, link]
    where: Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p <= Link_p_max_pu * Link_p_nom_ext
  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
  Line_ext_s_lower:
    description: '`Line-ext-s-lower` — an extendable line carries at least the negative of its rating
      of the chosen build, the loss counted against it'
    dims: [scenario, snapshot, line]
    where: Line_s_nom_extendable AND Line_active
    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,
      the loss included'
    dims: [scenario, snapshot, line]
    where: Line_s_nom_extendable AND Line_active
    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 in every scenario'
    dims: [scenario, line]
    where: Line_s_nom_extendable
    expression: Line_s_nom_ext >= Line_s_nom_min
  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. A transformer''s
      flow weighs its effective reactance, and its phase shift enters the cycle sum too: a constant where
      the shift is fixed, or the shift decision times its cycle weight where the shift is a phase-shifting
      transformer''s to choose'
    dims: [scenario, snapshot, cycle]
    expression: Cycle_angle_sum == 0
  GlobalConstraint_primary_energy_ub:
    description: '`primary_energy` — its total, at most its constant'
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'primary_energy' AND GlobalConstraint_sense == '<='
    expression: primary_energy <= 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, 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:
  primary_energy:
    dims: [scenario, global_constraint]
    expression: Generator_primary_energy
    description: what a `primary_energy` row totals — weighted generator energy over the snapshots it
      counts, less the charge left in weighted storage at the close; the initial charge it is compared
      against is folded into the row's constant
  total_cost:
    dims: []
    expression: ((Generator_capex + Link_capex) + Line_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 + Line_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
  Cycle_angle_sum:
    dims: [scenario, snapshot, cycle]
    expression: Line_angle_sum
    description: 'the voltage angle differences around a cycle: every branch flow times its cycle weight,
      and every transformer phase shift'
  Generator_primary_energy: {expression: 'sum(sum((Generator_p * GlobalConstraint_energy_weight) * Generator_primary_energy_weight,
      over=snapshot), over=generator)'}
  Generator_capex: {expression: sum(scenario_weight * Generator_p_nom_ext * Generator_capital_cost * Generator_capital_weight)}
  Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_capital_weight)}
  Line_capex: {expression: sum(scenario_weight * Line_s_nom_ext * Line_capital_cost * Line_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)'}
  Line_injection: {expression: '(-sum(Line_s, by=Line_bus0, over=line, into=bus)) + sum(Line_s, by=Line_bus1,
      over=line, 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)'}
  Line_angle_sum: {expression: 'sum(Line_s * Line_cycle_weight, over=line)'}
  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
  GlobalConstraint_energy_weight:
    description: what one unit of power at a snapshot counts for in a row — the generator weighting times
      the years of the snapshot's period, where the row counts the snapshot, and nothing where it does
      not
    dims: [scenario, global_constraint, snapshot]
    cases:
      counted: {when: GlobalConstraint_counts_snapshot, expression: 'snapshot_weightings_generators *
          at(period_weight_years, by=snapshot_period, over=period, into=snapshot)'}
    otherwise: 0
  scenario_opex:
    dims: [scenario]
    expression: Generator_opex + Link_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)'}
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),
    'snapshot_weightings_generators': weighting(n, 'generators'),
}

with sps.solve('differential/pypsa/rungs/rung_11_ac_dc_meshed.yaml', sources) as solution:
    solution.objective  # 18441021.477729

# SPDX-FileCopyrightText: mathspec Contributors
#
# SPDX-License-Identifier: MIT

"""Rung 11: PyPSA's own `ac_dc_meshed` example, whole — meshed AC and DC, extendable lines, links and generators, carriers, a CO2 budget."""

from __future__ import annotations

from datetime import datetime

#: Ten hourly stamps, the example's own. Every weighting column there is 1.0, which is
#: also the default, so no row below sets one.
SNAPSHOTS = [datetime(2015, 1, 1, hour) for hour in range(10)]

#: Wind availability per snapshot, for the three generators that carry a profile.
P_MAX_PU = {
    'Manchester Wind': [0.930019875, 0.4857475804, 0.2336917351, 0.2576042221, 0.6269055694, 0.6035984088, 0.6789075462, 0.3613026112, 0.6216040549, 0.5215183715],
    'Norway Wind': [0.9745832033, 0.4812903778, 0.4072258018, 0.5999649628, 0.524468219, 0.0096927054, 0.2204533621, 0.8239185004, 0.5562297265, 0.4394160378],
    'Frankfurt Wind': [0.5590784039, 0.7529103711, 0.1234650887, 0.9666766524, 0.8590078044, 0.5261537924, 0.077893008, 0.0590234716, 0.2485544952, 0.1080601728],
}  # fmt: skip

#: Demand per snapshot, for each of the six loads.
P_SET = {
    'London': [35.7962441027, 976.8245614698, 250.5873120464, 130.7531445827, 151.1001686, 931.857051942, 289.8482871447, 864.3433217147, 689.5772637703, 627.8789859434],
    'Frankfurt': [398.0478469638, 432.4361062425, 379.8039282662, 868.3617642835, 548.7707546221, 828.6652426012, 449.2907519075, 699.1637663734, 915.8667802518, 414.8876464034],
    'Norway': [820.035835936, 854.8340468618, 42.550744351, 647.5482327851, 884.0738733306, 509.0624485516, 595.6079648147, 291.6424496984, 2.1534925491, 760.7401765038],
    'Norwich': [415.4625642653, 262.6061464526, 418.4763531902, 552.9595393098, 218.159858091, 791.9762655836, 531.8706808219, 23.5134667186, 970.0590684572, 0.9248336907],
    'Bremen': [640.0863775411, 703.554333706, 440.8361303183, 612.5763056818, 803.4367808051, 605.4006873582, 641.0905902397, 408.0085411725, 912.2477761646, 898.0530916423],
    'Manchester': [857.5514402011, 750.5996237166, 156.5648760141, 527.8708221189, 83.8977589634, 676.6233193474, 731.1371004827, 553.3448891847, 298.338082262, 768.2905859888],
}  # fmt: skip


def build():
    """The example network, stated as the calls that build it.

    A rung states its data inline, so that the PyPSA model under review is the
    script — ``reference.py`` says so and ``test_pypsa_references.py`` checks
    it. The numbers here are PyPSA's own ``ac_dc_meshed``, which is where this
    rung's published objective comes from; ``reference.py`` pins the version
    they were read at.
    """
    import pypsa

    n = pypsa.Network()
    n.set_snapshots(SNAPSHOTS)
    # Bus
    n.add('Bus', 'London', v_nom=380.0, x=-0.13, y=51.5)
    n.add('Bus', 'Norwich', v_nom=380.0, x=1.3, y=52.6)
    n.add('Bus', 'Norwich DC', v_nom=200.0, x=1.3, y=52.5, carrier='DC')
    n.add('Bus', 'Manchester', v_nom=380.0, x=-2.2, y=53.47)
    n.add('Bus', 'Bremen', v_nom=380.0, x=8.8, y=53.08)
    n.add('Bus', 'Bremen DC', v_nom=200.0, x=8.8, y=52.98, carrier='DC')
    n.add('Bus', 'Frankfurt', v_nom=380.0, x=8.7, y=50.12)
    n.add('Bus', 'Norway', v_nom=380.0, x=10.75, y=60.0)
    n.add('Bus', 'Norway DC', v_nom=200.0, x=10.75, y=60.0, carrier='DC')
    # Carrier
    n.add('Carrier', 'gas', co2_emissions=0.24, color='red')
    n.add('Carrier', 'wind', color='blue')
    n.add('Carrier', 'battery', color='green')
    n.add('Carrier', 'load', color='black')
    n.add('Carrier', 'AC', color='orange')
    n.add('Carrier', 'DC', color='purple')
    # Generator
    n.add(
        'Generator',
        'Manchester Wind',
        bus='Manchester',
        p_nom=80.0,
        p_nom_extendable=True,
        p_nom_min=100.0,
        p_max_pu=P_MAX_PU['Manchester Wind'],
        carrier='wind',
        marginal_cost=0.11,
        capital_cost=2793.6516029328,
    )
    n.add(
        'Generator',
        'Manchester Gas',
        bus='Manchester',
        p_nom=50000.0,
        p_nom_extendable=True,
        carrier='gas',
        marginal_cost=4.5323676307,
        capital_cost=196.6151679691,
        efficiency=0.3500264336,
    )
    n.add(
        'Generator',
        'Norway Wind',
        bus='Norway',
        p_nom=100.0,
        p_nom_extendable=True,
        p_nom_min=100.0,
        p_max_pu=P_MAX_PU['Norway Wind'],
        carrier='wind',
        marginal_cost=0.09,
        capital_cost=2184.3747960912,
    )
    n.add(
        'Generator',
        'Norway Gas',
        bus='Norway',
        p_nom=20000.0,
        p_nom_extendable=True,
        carrier='gas',
        marginal_cost=5.8928445406,
        capital_cost=158.2512497168,
        efficiency=0.3568363832,
    )
    n.add(
        'Generator',
        'Frankfurt Wind',
        bus='Frankfurt',
        p_nom=110.0,
        p_nom_extendable=True,
        p_nom_min=100.0,
        p_max_pu=P_MAX_PU['Frankfurt Wind'],
        carrier='wind',
        marginal_cost=0.1,
        capital_cost=2129.4561224763,
    )
    n.add(
        'Generator',
        'Frankfurt Gas',
        bus='Frankfurt',
        p_nom=80000.0,
        p_nom_extendable=True,
        carrier='gas',
        marginal_cost=4.0863219899,
        capital_cost=102.6769530076,
        efficiency=0.3516658529,
    )
    # Line
    n.add(
        'Line',
        '0',
        bus0='London',
        bus1='Manchester',
        x=0.7968782824,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.1367157553,
        carrier='AC',
    )
    n.add(
        'Line',
        '1',
        bus0='Manchester',
        bus1='Norwich',
        x=0.3915599178,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.1334916779,
        carrier='AC',
    )
    n.add(
        'Line',
        '2',
        bus0='Bremen DC',
        bus1='Norwich DC',
        r=0.2126041927,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.0086734246,
        carrier='AC',
    )
    n.add(
        'Line',
        '3',
        bus0='Norwich DC',
        bus1='Norway DC',
        r=0.4861637504,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.1291260515,
        carrier='AC',
    )
    n.add(
        'Line',
        '4',
        bus0='Norway DC',
        bus1='Bremen DC',
        r=0.4287266497,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.0624298729,
        carrier='AC',
    )
    n.add(
        'Line',
        '5',
        bus0='Norwich',
        bus1='London',
        x=0.2388003463,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.0218524519,
        carrier='AC',
    )
    n.add(
        'Line',
        '6',
        bus0='Bremen',
        bus1='Frankfurt',
        x=0.4,
        s_nom=40000.0,
        s_nom_extendable=True,
        capital_cost=0.2,
        carrier='AC',
    )
    # Link
    n.add(
        'Link',
        'Norwich Converter',
        bus0='Norwich',
        bus1='Norwich DC',
        carrier='DC',
        p_nom=1000.0,
        p_nom_extendable=True,
        p_min_pu=-0.9,
        p_max_pu=0.9,
        capital_cost=0.21,
    )
    n.add(
        'Link',
        'Norway Converter',
        bus0='Norway',
        bus1='Norway DC',
        carrier='DC',
        p_nom=1000.0,
        p_nom_extendable=True,
        p_min_pu=-0.9,
        p_max_pu=0.9,
        capital_cost=0.2,
    )
    n.add(
        'Link',
        'Bremen Converter',
        bus0='Bremen',
        bus1='Bremen DC',
        carrier='DC',
        p_nom=1000.0,
        p_nom_extendable=True,
        p_min_pu=-0.9,
        p_max_pu=0.9,
        capital_cost=0.19,
    )
    n.add(
        'Link',
        'DC link',
        bus0='London',
        bus1='Bremen',
        carrier='DC',
        p_nom=1000.0,
        p_nom_extendable=True,
        p_min_pu=-0.9,
        p_max_pu=0.9,
        capital_cost=0.8765342,
    )
    # Load
    n.add('Load', 'London', bus='London', carrier='load', p_set=P_SET['London'])
    n.add('Load', 'Frankfurt', bus='Frankfurt', carrier='load', p_set=P_SET['Frankfurt'])
    n.add('Load', 'Norway', bus='Norway', carrier='load', p_set=P_SET['Norway'])
    n.add('Load', 'Norwich', bus='Norwich', carrier='load', p_set=P_SET['Norwich'])
    n.add('Load', 'Bremen', bus='Bremen', carrier='load', p_set=P_SET['Bremen'])
    n.add('Load', 'Manchester', bus='Manchester', carrier='load', p_set=P_SET['Manchester'])
    # GlobalConstraint
    n.add('GlobalConstraint', 'co2_limit', sense='<=', constant=1000.0)
    return n

n = build()
n.optimize(solver_name='highs')
n.objective  # 18441021.477729